action research examples in math

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Action research projects.

Using Cooperative Learning In A Sixth Grade Math Classroom , Teena Andersen

Algebra in the Fifth Grade Mathematics Program , Kathy Bohac

Real Life Problem Solving in Eighth Grade Mathematics , Michael Bomar

Holding Students Accountable , Jeremy Fries

Writing In Math Class? Written Communication in the Mathematics Classroom , Stephanie Fuehrer

The Role of Manipulatives in the Eighth Grade Mathematics Classroom , Michaela Ann Goracke

Reasonable or Not? A Study of the Use of Teacher Questioning to Promote Reasonable Mathematical Answers from Sixth Grade Students , Marlene Grayer

Improving Achievement and Attitude Through Cooperative Learning in Math Class , Scott Johnsen

Oral Communication and Presentations in Mathematics , Brian Johnson

Meaningful Independent Practice in Mathematics , Michelle Looky

Making Better Problem Solvers through Oral and Written Communication , Sheila McCartney

Student Understanding and Achievement When Focusing on Peer-led Reviews , Ryon Nilson

Students Writing Original Word Problems , Marcia Ostmeyer

Cooperative Grouping Working on Mathematics Homework , Maggie Pickering

Making Sense of Word Problems , Edie Ronhovde

Oral and Written Communication in Classroom Mathematics , Lindsey Sample

Written Communication in a Sixth-Grade Mathematics Classroom , Mary Schneider

The Use of Vocabulary in an Eighth Grade Mathematics Classroom: Improving Usage of Mathematics Vocabulary in Oral and Written Communication , Amy Solomon

Enhancing Problem Solving Through Math Clubs , Jessica Haley Thompson

Communication: A Vital Skill of Mathematics , Lexi Wichelt

Mathematical Communication through Written and Oral Expression , Brandee Wilson

Oral Presentation: Exploring Oral Presentations of Homework Problems as a Means of Assessing Homework

Building Confidence in Low Achievers through Building Mathematics Vocabulary , Val Adams

An Uphill Battle: Incorporating cooperative learning using a largely individualized curriculum , Anna Anderson

Using Descriptive Feedback In a Sixth Grade Mathematics Classroom , Vicki J. Barry

Does Decoding Increase Word Problem Solving Skills? , JaLena J. Clement

Using Non-Traditional Activities to Enhance Mathematical Connections , Sandy Dean

Producing More Problem Solving by Emphasizing Vocabulary , Jill Edgren

Reading as a Learning Strategy for Mathematics , Monte Else

Perceptions of Math Homework: Exploring the Connections between Written Explanations and Oral Presentations and the Influence on Students’ Understanding of Math Homework , Kyla Hall

Homework Presentations: Are They Worth the Time? , Kacy Heiser

Reduce Late Assignments through Classroom Presentations , Cole Hilker

Mathematical Communication, Conceptual Understanding, and Students' Attitudes Toward Mathematics , Kimberly Hirschfeld-Cotton

Enhancing Thinking Skills: Will Daily Problem Solving Activities Help? , Julie Hoaglund

Can homework become more meaningful with the inclusion of oral presentations? , Emy Jones

Confidence in Communication: Can My Whole Class Achieve This? , Emily Lashley

Exploring the Influence of Vocabulary Instruction on Students’ Understanding of Mathematical Concepts , Micki McConnell

Using Relearning Groups to Help All Students Understand Learning Objectives Before Tests , Katie Pease

Cooperative Learning in Relation to Problem Solving in the Mathematics Classroom , Shelley Poore

How Student Self-Assessment Influences Mastery Of Objectives , Jeremy John Renfro

RAP (Reasoning and Proof) Journals: I Am Here , Bryce Schwanke

Homework: Is There More To It Than Answers? , Shelly Sehnert

Written Solutions of Mathematical Word Problems , Marcia J. Smith

Rubric Assessment of Mathematical Processes in Homework , Aubrey Weitzenkamp

Calculators in a Middle School Mathematics Classroom: Helpful or Harmful? , Leah Wilcox

Pre-Reading Mathematics Empowers Students , Stacey Aldag

The Importance of Teaching Students How to Read to Comprehend Mathematical Language , Tricia Buchanan

Cooperative Learning as an Effective Way to Interact , Gary Eisenhauer

Generating Interest in Mathematics Using Discussion in the Middle School Classroom , Jessica Fricke

“Let’s Review.” A Look at the Effects of Re-teaching Basic Mathematic Skills , Thomas J. Harrington

The Importance of Vocabulary Instruction in Everyday Mathematics , Chad Larson

Understanding the Mathematical Language , Carmen Melliger

Writing for Understanding in Math Class , Linda Moore

Improving Student Engagement and Verbal Behavior Through Cooperative Learning , Daniel Schaben

Improving Students’ Story Problem Solving Abilities , Josh Severin

Calculators in the Classroom: Help or Hindrance? , Christina L. Sheets

Do Students Progress if They Self-Assess? A Study in Small-Group Work , Cindy Steinkruger

Why Are We Writing? This is Math Class! , Shana Streeks

Effects of Self-Assessment on Math Homework , Diane Swartzlander

The Effects Improving Student Discourse Has on Learning Mathematics , Lindsey Thompson

Increasing Teacher Involvement with Other Teachers Through Reflective Interaction , Tina Thompson

Increasing Conceptual Learning through Student Participation , Janet Timoney

Improving the Effectiveness of Independent Practice with Corrective Feedback , Greg Vanderbeek

Using Math Vocabulary Building to Increase Problem Solving Abilities in a 5th Grade Classroom , Julane Amen

Departmentalization in the 5th Grade Classroom: Re-thinking the Elementary School Model , Delise Andrews

Cooperative Learning Groups in the Eighth Grade Math Classroom , Dean J. Davis

Daily Problem-Solving Warm-Ups: Harboring Mathematical Thinking In The Middle School Classroom , Diana French

Student Transition to College , Doug Glasshoff

The Effects of Teaching Problem Solving Strategies to Low Achieving Students , Kristin Johnson and Anne Schmidt

The Effects of Self-Assessment on Student Learning , Darla Rae Kelberlau-Berks

Writing in a Mathematics Classroom: A Form of Communication and Reflection , Stacie Lefler

Math in the George Middle School , Tiffany D. Lothrop

Bad Medicine: Homework or Headache? Responsibility and Accountability for Middle Level Mathematics Students , Shawn Mousel

Self-Directed Learning in the Middle School Classroom , Jim Pfeiffer

How to Better Prepare for Assessment and Create a More Technologically Advanced Classroom , Kyle Lannin Poore

Cooperative Learning Groups in the Middle School Mathematics Classroom , Sandra S. Snyder

Motivating Middle School Mathematics Students , Vicki Sorensen

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21 Action Research Examples (In Education)

Dave Cornell (PhD)

Dr. Cornell has worked in education for more than 20 years. His work has involved designing teacher certification for Trinity College in London and in-service training for state governments in the United States. He has trained kindergarten teachers in 8 countries and helped businessmen and women open baby centers and kindergartens in 3 countries.

Learn about our Editorial Process

Chris Drew (PhD)

This article was peer-reviewed and edited by Chris Drew (PhD). The review process on Helpful Professor involves having a PhD level expert fact check, edit, and contribute to articles. Reviewers ensure all content reflects expert academic consensus and is backed up with reference to academic studies. Dr. Drew has published over 20 academic articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education and holds a PhD in Education from ACU.

Action research is an example of qualitative research . It refers to a wide range of evaluative or investigative methods designed to analyze professional practices and take action for improvement.

Commonly used in education, those practices could be related to instructional methods, classroom practices, or school organizational matters.

The creation of action research is attributed to Kurt Lewin , a German-American psychologist also considered to be the father of social psychology.

Gillis and Jackson (2002) offer a very concise definition of action research: “systematic collection and analysis of data for the purpose of taking action and making change” (p.264).

The methods of action research in education include:

• conducting in-class observations
• taking field notes
• surveying or interviewing teachers, administrators, or parents
• using audio and video recordings.

The goal is to identify problematic issues, test possible solutions, or simply carry-out continuous improvement.

There are several steps in action research : identify a problem, design a plan to resolve, implement the plan, evaluate effectiveness, reflect on results, make necessary adjustment and repeat the process.

Action Research Examples

• Digital literacy assessment and training: The school’s IT department conducts a survey on students’ digital literacy skills. Based on the results, a tailored training program is designed for different age groups.
• Library resources utilization study: The school librarian tracks the frequency and type of books checked out by students. The data is then used to curate a more relevant collection and organize reading programs.
• Extracurricular activities and student well-being: A team of teachers and counselors assess the impact of extracurricular activities on student mental health through surveys and interviews. Adjustments are made based on findings.
• Parent-teacher communication channels: The school evaluates the effectiveness of current communication tools (e.g., newsletters, apps) between teachers and parents. Feedback is used to implement a more streamlined system.
• Homework load evaluation: Teachers across grade levels assess the amount and effectiveness of homework given. Adjustments are made to ensure a balance between academic rigor and student well-being.
• Classroom environment and learning: A group of teachers collaborates to study the impact of classroom layouts and decorations on student engagement and comprehension. Changes are made based on the findings.
• Student feedback on curriculum content: High school students are surveyed about the relevance and applicability of their current curriculum. The feedback is then used to make necessary curriculum adjustments.
• Teacher mentoring and support: New teachers are paired with experienced mentors. Both parties provide feedback on the effectiveness of the mentoring program, leading to continuous improvements.
• Assessment of school transportation: The school board evaluates the efficiency and safety of school buses through surveys with students and parents. Necessary changes are implemented based on the results.
• Cultural sensitivity training: After conducting a survey on students’ cultural backgrounds and experiences, the school organizes workshops for teachers to promote a more inclusive classroom environment.
• Environmental initiatives and student involvement: The school’s eco-club assesses the school’s carbon footprint and waste management. They then collaborate with the administration to implement greener practices and raise environmental awareness.
• Working with parents through research: A school’s admin staff conduct focus group sessions with parents to identify top concerns.Those concerns will then be addressed and another session conducted at the end of the school year.
• Peer teaching observations and improvements: Kindergarten teachers observe other teachers handling class transition techniques to share best practices.
• PTA surveys and resultant action: The PTA of a district conducts a survey of members regarding their satisfaction with remote learning classes.The results will be presented to the school board for further action.
• Recording and reflecting: A school administrator takes video recordings of playground behavior and then plays them for the teachers. The teachers work together to formulate a list of 10 playground safety guidelines.
• Pre/post testing of interventions: A school board conducts a district wide evaluation of a STEM program by conducting a pre/post-test of students’ skills in computer programming.
• Focus groups of practitioners : The professional development needs of teachers are determined from structured focus group sessions with teachers and admin.
• School lunch research and intervention: A nutrition expert is hired to evaluate and improve the quality of school lunches.
• School nurse systematic checklist and improvements: The school nurse implements a bathroom cleaning checklist to monitor cleanliness after the results of a recent teacher survey revealed several issues.
• Wearable technologies for pedagogical improvements; Students wear accelerometers attached to their hips to gain a baseline measure of physical activity.The results will identify if any issues exist.
• School counselor reflective practice : The school counselor conducts a student survey on antisocial behavior and then plans a series of workshops for both teachers and parents.

Detailed Examples

1. cooperation and leadership.

A science teacher has noticed that her 9 th grade students do not cooperate with each other when doing group projects. There is a lot of arguing and battles over whose ideas will be followed.

So, she decides to implement a simple action research project on the matter. First, she conducts a structured observation of the students’ behavior during meetings. She also has the students respond to a short questionnaire regarding their notions of leadership.

She then designs a two-week course on group dynamics and leadership styles. The course involves learning about leadership concepts and practices . In another element of the short course, students randomly select a leadership style and then engage in a role-play with other students.

At the end of the two weeks, she has the students work on a group project and conducts the same structured observation as before. She also gives the students a slightly different questionnaire on leadership as it relates to the group.

She plans to analyze the results and present the findings at a teachers’ meeting at the end of the term.

2. Professional Development Needs

Two high-school teachers have been selected to participate in a 1-year project in a third-world country. The project goal is to improve the classroom effectiveness of local teachers. 

The two teachers arrive in the country and begin to plan their action research. First, they decide to conduct a survey of teachers in the nearby communities of the school they are assigned to.

The survey will assess their professional development needs by directly asking the teachers and administrators. After collecting the surveys, they analyze the results by grouping the teachers based on subject matter.

They discover that history and social science teachers would like professional development on integrating smartboards into classroom instruction. Math teachers would like to attend workshops on project-based learning, while chemistry teachers feel that they need equipment more than training.

The two teachers then get started on finding the necessary training experts for the workshops and applying for equipment grants for the science teachers.

3. Playground Accidents

The school nurse has noticed a lot of students coming in after having mild accidents on the playground. She’s not sure if this is just her perception or if there really is an unusual increase this year.  So, she starts pulling data from the records over the last two years. She chooses the months carefully and only selects data from the first three months of each school year.

She creates a chart to make the data more easily understood. Sure enough, there seems to have been a dramatic increase in accidents this year compared to the same period of time from the previous two years.

She shows the data to the principal and teachers at the next meeting. They all agree that a field observation of the playground is needed.

Those observations reveal that the kids are not having accidents on the playground equipment as originally suspected. It turns out that the kids are tripping on the new sod that was installed over the summer.

They examine the sod and observe small gaps between the slabs. Each gap is approximately 1.5 inches wide and nearly two inches deep. The kids are tripping on this gap as they run.

They then discuss possible solutions.

4. Differentiated Learning

Trying to use the same content, methods, and processes for all students is a recipe for failure. This is why modifying each lesson to be flexible is highly recommended. Differentiated learning allows the teacher to adjust their teaching strategy based on all the different personalities and learning styles they see in their classroom.

Of course, differentiated learning should undergo the same rigorous assessment that all teaching techniques go through. So, a third-grade social science teacher asks his students to take a simple quiz on the industrial revolution. Then, he applies differentiated learning to the lesson.

By creating several different learning stations in his classroom, he gives his students a chance to learn about the industrial revolution in a way that captures their interests. The different stations contain: short videos, fact cards, PowerPoints, mini-chapters, and role-plays.

At the end of the lesson, students get to choose how they demonstrate their knowledge. They can take a test, construct a PPT, give an oral presentation, or conduct a simulated TV interview with different characters.

During this last phase of the lesson, the teacher is able to assess if they demonstrate the necessary knowledge and have achieved the defined learning outcomes. This analysis will allow him to make further adjustments to future lessons.

5. Healthy Habits Program

While looking at obesity rates of students, the school board of a large city is shocked by the dramatic increase in the weight of their students over the last five years. After consulting with three companies that specialize in student physical health, they offer the companies an opportunity to prove their value.

So, the board randomly assigns each company to a group of schools. Starting in the next academic year, each company will implement their healthy habits program in 5 middle schools.

Preliminary data is collected at each school at the beginning of the school year. Each and every student is weighed, their resting heart rate, blood pressure and cholesterol are also measured.

After analyzing the data, it is found that the schools assigned to each of the three companies are relatively similar on all of these measures.

At the end of the year, data for students at each school will be collected again. A simple comparison of pre- and post-program measurements will be conducted. The company with the best outcomes will be selected to implement their program city-wide.

Action research is a great way to collect data on a specific issue, implement a change, and then evaluate the effects of that change. It is perhaps the most practical of all types of primary research .

Most likely, the results will be mixed. Some aspects of the change were effective, while other elements were not. That’s okay. This just means that additional modifications to the change plan need to be made, which is usually quite easy to do.

There are many methods that can be utilized, such as surveys, field observations , and program evaluations.

The beauty of action research is based in its utility and flexibility. Just about anyone in a school setting is capable of conducting action research and the information can be incredibly useful.

Aronson, E., & Patnoe, S. (1997). The jigsaw classroom: Building cooperation in the classroom (2nd ed.). New York: Addison Wesley Longman.

Gillis, A., & Jackson, W. (2002). Research Methods for Nurses: Methods and Interpretation . Philadelphia: F.A. Davis Company.

Lewin, K. (1946). Action research and minority problems. Journal of SocialIssues, 2 (4), 34-46.

Macdonald, C. (2012). Understanding participatory action research: A qualitative research methodology option. Canadian Journal of Action Research, 13 , 34-50. https://doi.org/10.33524/cjar.v13i2.37 Mertler, C. A. (2008). Action Research: Teachers as Researchers in the Classroom . London: Sage.

• Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ 23 Achieved Status Examples
• Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ 25 Defense Mechanisms Examples
• Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ 15 Theory of Planned Behavior Examples
• Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ 18 Adaptive Behavior Examples

• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 23 Achieved Status Examples
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 15 Ableism Examples
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 25 Defense Mechanisms Examples
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 15 Theory of Planned Behavior Examples

2 thoughts on “21 Action Research Examples (In Education)”

Where can I capture this article in a better user-friendly format, since I would like to provide it to my students in a Qualitative Methods course at the University of Prince Edward Island? It is a good article, however, it is visually disjointed in its current format. Thanks, Dr. Frank T. Lavandier

Hi Dr. Lavandier,

I’ve emailed you a word doc copy that you can use and edit with your class.

Best, Chris.

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1 What is Action Research for Classroom Teachers?

ESSENTIAL QUESTIONS

• What is the nature of action research?
• How does action research develop in the classroom?
• What models of action research work best for your classroom?
• What are the epistemological, ontological, theoretical underpinnings of action research?

Educational research provides a vast landscape of knowledge on topics related to teaching and learning, curriculum and assessment, students’ cognitive and affective needs, cultural and socio-economic factors of schools, and many other factors considered viable to improving schools. Educational stakeholders rely on research to make informed decisions that ultimately affect the quality of schooling for their students. Accordingly, the purpose of educational research is to engage in disciplined inquiry to generate knowledge on topics significant to the students, teachers, administrators, schools, and other educational stakeholders. Just as the topics of educational research vary, so do the approaches to conducting educational research in the classroom. Your approach to research will be shaped by your context, your professional identity, and paradigm (set of beliefs and assumptions that guide your inquiry). These will all be key factors in how you generate knowledge related to your work as an educator.

Action research is an approach to educational research that is commonly used by educational practitioners and professionals to examine, and ultimately improve, their pedagogy and practice. In this way, action research represents an extension of the reflection and critical self-reflection that an educator employs on a daily basis in their classroom. When students are actively engaged in learning, the classroom can be dynamic and uncertain, demanding the constant attention of the educator. Considering these demands, educators are often only able to engage in reflection that is fleeting, and for the purpose of accommodation, modification, or formative assessment. Action research offers one path to more deliberate, substantial, and critical reflection that can be documented and analyzed to improve an educator’s practice.

Purpose of Action Research

As one of many approaches to educational research, it is important to distinguish the potential purposes of action research in the classroom. This book focuses on action research as a method to enable and support educators in pursuing effective pedagogical practices by transforming the quality of teaching decisions and actions, to subsequently enhance student engagement and learning. Being mindful of this purpose, the following aspects of action research are important to consider as you contemplate and engage with action research methodology in your classroom:

• Action research is a process for improving educational practice. Its methods involve action, evaluation, and reflection. It is a process to gather evidence to implement change in practices.
• Action research is participative and collaborative. It is undertaken by individuals with a common purpose.
• Action research is situation and context-based.
• Action research develops reflection practices based on the interpretations made by participants.
• Knowledge is created through action and application.
• Action research can be based in problem-solving, if the solution to the problem results in the improvement of practice.
• Action research is iterative; plans are created, implemented, revised, then implemented, lending itself to an ongoing process of reflection and revision.
• In action research, findings emerge as action develops and takes place; however, they are not conclusive or absolute, but ongoing (Koshy, 2010, pgs. 1-2).

In thinking about the purpose of action research, it is helpful to situate action research as a distinct paradigm of educational research. I like to think about action research as part of the larger concept of living knowledge. Living knowledge has been characterized as “a quest for life, to understand life and to create… knowledge which is valid for the people with whom I work and for myself” (Swantz, in Reason & Bradbury, 2001, pg. 1). Why should educators care about living knowledge as part of educational research? As mentioned above, action research is meant “to produce practical knowledge that is useful to people in the everyday conduct of their lives and to see that action research is about working towards practical outcomes” (Koshy, 2010, pg. 2). However, it is also about:

creating new forms of understanding, since action without reflection and understanding is blind, just as theory without action is meaningless. The participatory nature of action research makes it only possible with, for and by persons and communities, ideally involving all stakeholders both in the questioning and sense making that informs the research, and in the action, which is its focus. (Reason & Bradbury, 2001, pg. 2)

In an effort to further situate action research as living knowledge, Jean McNiff reminds us that “there is no such ‘thing’ as ‘action research’” (2013, pg. 24). In other words, action research is not static or finished, it defines itself as it proceeds. McNiff’s reminder characterizes action research as action-oriented, and a process that individuals go through to make their learning public to explain how it informs their practice. Action research does not derive its meaning from an abstract idea, or a self-contained discovery – action research’s meaning stems from the way educators negotiate the problems and successes of living and working in the classroom, school, and community.

While we can debate the idea of action research, there are people who are action researchers, and they use the idea of action research to develop principles and theories to guide their practice. Action research, then, refers to an organization of principles that guide action researchers as they act on shared beliefs, commitments, and expectations in their inquiry.

Reflection and the Process of Action Research

When an individual engages in reflection on their actions or experiences, it is typically for the purpose of better understanding those experiences, or the consequences of those actions to improve related action and experiences in the future. Reflection in this way develops knowledge around these actions and experiences to help us better regulate those actions in the future. The reflective process generates new knowledge regularly for classroom teachers and informs their classroom actions.

Unfortunately, the knowledge generated by educators through the reflective process is not always prioritized among the other sources of knowledge educators are expected to utilize in the classroom. Educators are expected to draw upon formal types of knowledge, such as textbooks, content standards, teaching standards, district curriculum and behavioral programs, etc., to gain new knowledge and make decisions in the classroom. While these forms of knowledge are important, the reflective knowledge that educators generate through their pedagogy is the amalgamation of these types of knowledge enacted in the classroom. Therefore, reflective knowledge is uniquely developed based on the action and implementation of an educator’s pedagogy in the classroom. Action research offers a way to formalize the knowledge generated by educators so that it can be utilized and disseminated throughout the teaching profession.

Research is concerned with the generation of knowledge, and typically creating knowledge related to a concept, idea, phenomenon, or topic. Action research generates knowledge around inquiry in practical educational contexts. Action research allows educators to learn through their actions with the purpose of developing personally or professionally. Due to its participatory nature, the process of action research is also distinct in educational research. There are many models for how the action research process takes shape. I will share a few of those here. Each model utilizes the following processes to some extent:

• Plan a change;
• Take action to enact the change;
• Observe the process and consequences of the change;
• Reflect on the process and consequences;
• Act, observe, & reflect again and so on.

Figure 1.1 Basic action research cycle

There are many other models that supplement the basic process of action research with other aspects of the research process to consider. For example, figure 1.2 illustrates a spiral model of action research proposed by Kemmis and McTaggart (2004). The spiral model emphasizes the cyclical process that moves beyond the initial plan for change. The spiral model also emphasizes revisiting the initial plan and revising based on the initial cycle of research:

Figure 1.2 Interpretation of action research spiral, Kemmis and McTaggart (2004, p. 595)

Other models of action research reorganize the process to emphasize the distinct ways knowledge takes shape in the reflection process. O’Leary’s (2004, p. 141) model, for example, recognizes that the research may take shape in the classroom as knowledge emerges from the teacher’s observations. O’Leary highlights the need for action research to be focused on situational understanding and implementation of action, initiated organically from real-time issues:

Figure 1.3 Interpretation of O’Leary’s cycles of research, O’Leary (2000, p. 141)

Lastly, Macintyre’s (2000, p. 1) model, offers a different characterization of the action research process. Macintyre emphasizes a messier process of research with the initial reflections and conclusions as the benchmarks for guiding the research process. Macintyre emphasizes the flexibility in planning, acting, and observing stages to allow the process to be naturalistic. Our interpretation of Macintyre process is below:

Figure 1.4 Interpretation of the action research cycle, Macintyre (2000, p. 1)

We believe it is important to prioritize the flexibility of the process, and encourage you to only use these models as basic guides for your process. Your process may look similar, or you may diverge from these models as you better understand your students, context, and data.

Definitions of Action Research and Examples

At this point, it may be helpful for readers to have a working definition of action research and some examples to illustrate the methodology in the classroom. Bassey (1998, p. 93) offers a very practical definition and describes “action research as an inquiry which is carried out in order to understand, to evaluate and then to change, in order to improve educational practice.” Cohen and Manion (1994, p. 192) situate action research differently, and describe action research as emergent, writing:

essentially an on-the-spot procedure designed to deal with a concrete problem located in an immediate situation. This means that ideally, the step-by-step process is constantly monitored over varying periods of time and by a variety of mechanisms (questionnaires, diaries, interviews and case studies, for example) so that the ensuing feedback may be translated into modifications, adjustment, directional changes, redefinitions, as necessary, so as to bring about lasting benefit to the ongoing process itself rather than to some future occasion.

Lastly, Koshy (2010, p. 9) describes action research as:

a constructive inquiry, during which the researcher constructs his or her knowledge of specific issues through planning, acting, evaluating, refining and learning from the experience. It is a continuous learning process in which the researcher learns and also shares the newly generated knowledge with those who may benefit from it.

These definitions highlight the distinct features of action research and emphasize the purposeful intent of action researchers to improve, refine, reform, and problem-solve issues in their educational context. To better understand the distinctness of action research, these are some examples of action research topics:

Examples of Action Research Topics

• Flexible seating in 4th grade classroom to increase effective collaborative learning.
• Structured homework protocols for increasing student achievement.
• Developing a system of formative feedback for 8th grade writing.
• Using music to stimulate creative writing.
• Weekly brown bag lunch sessions to improve responses to PD from staff.
• Using exercise balls as chairs for better classroom management.

Action Research in Theory

Action research-based inquiry in educational contexts and classrooms involves distinct participants – students, teachers, and other educational stakeholders within the system. All of these participants are engaged in activities to benefit the students, and subsequently society as a whole. Action research contributes to these activities and potentially enhances the participants’ roles in the education system. Participants’ roles are enhanced based on two underlying principles:

• communities, schools, and classrooms are sites of socially mediated actions, and action research provides a greater understanding of self and new knowledge of how to negotiate these socially mediated environments;
• communities, schools, and classrooms are part of social systems in which humans interact with many cultural tools, and action research provides a basis to construct and analyze these interactions.

In our quest for knowledge and understanding, we have consistently analyzed human experience over time and have distinguished between types of reality. Humans have constantly sought “facts” and “truth” about reality that can be empirically demonstrated or observed.

Social systems are based on beliefs, and generally, beliefs about what will benefit the greatest amount of people in that society. Beliefs, and more specifically the rationale or support for beliefs, are not always easy to demonstrate or observe as part of our reality. Take the example of an English Language Arts teacher who prioritizes argumentative writing in her class. She believes that argumentative writing demonstrates the mechanics of writing best among types of writing, while also providing students a skill they will need as citizens and professionals. While we can observe the students writing, and we can assess their ability to develop a written argument, it is difficult to observe the students’ understanding of argumentative writing and its purpose in their future. This relates to the teacher’s beliefs about argumentative writing; we cannot observe the real value of the teaching of argumentative writing. The teacher’s rationale and beliefs about teaching argumentative writing are bound to the social system and the skills their students will need to be active parts of that system. Therefore, our goal through action research is to demonstrate the best ways to teach argumentative writing to help all participants understand its value as part of a social system.

The knowledge that is conveyed in a classroom is bound to, and justified by, a social system. A postmodernist approach to understanding our world seeks knowledge within a social system, which is directly opposed to the empirical or positivist approach which demands evidence based on logic or science as rationale for beliefs. Action research does not rely on a positivist viewpoint to develop evidence and conclusions as part of the research process. Action research offers a postmodernist stance to epistemology (theory of knowledge) and supports developing questions and new inquiries during the research process. In this way action research is an emergent process that allows beliefs and decisions to be negotiated as reality and meaning are being constructed in the socially mediated space of the classroom.

Theorizing Action Research for the Classroom

All research, at its core, is for the purpose of generating new knowledge and contributing to the knowledge base of educational research. Action researchers in the classroom want to explore methods of improving their pedagogy and practice. The starting place of their inquiry stems from their pedagogy and practice, so by nature the knowledge created from their inquiry is often contextually specific to their classroom, school, or community. Therefore, we should examine the theoretical underpinnings of action research for the classroom. It is important to connect action research conceptually to experience; for example, Levin and Greenwood (2001, p. 105) make these connections:

• Action research is context bound and addresses real life problems.
• Action research is inquiry where participants and researchers cogenerate knowledge through collaborative communicative processes in which all participants’ contributions are taken seriously.
• The meanings constructed in the inquiry process lead to social action or these reflections and action lead to the construction of new meanings.
• The credibility/validity of action research knowledge is measured according to whether the actions that arise from it solve problems (workability) and increase participants’ control over their own situation.

Educators who engage in action research will generate new knowledge and beliefs based on their experiences in the classroom. Let us emphasize that these are all important to you and your work, as both an educator and researcher. It is these experiences, beliefs, and theories that are often discounted when more official forms of knowledge (e.g., textbooks, curriculum standards, districts standards) are prioritized. These beliefs and theories based on experiences should be valued and explored further, and this is one of the primary purposes of action research in the classroom. These beliefs and theories should be valued because they were meaningful aspects of knowledge constructed from teachers’ experiences. Developing meaning and knowledge in this way forms the basis of constructivist ideology, just as teachers often try to get their students to construct their own meanings and understandings when experiencing new ideas.  

Classroom Teachers Constructing their Own Knowledge

Most of you are probably at least minimally familiar with constructivism, or the process of constructing knowledge. However, what is constructivism precisely, for the purposes of action research? Many scholars have theorized constructivism and have identified two key attributes (Koshy, 2010; von Glasersfeld, 1987):

• Knowledge is not passively received, but actively developed through an individual’s cognition;
• Human cognition is adaptive and finds purpose in organizing the new experiences of the world, instead of settling for absolute or objective truth.

Considering these two attributes, constructivism is distinct from conventional knowledge formation because people can develop a theory of knowledge that orders and organizes the world based on their experiences, instead of an objective or neutral reality. When individuals construct knowledge, there are interactions between an individual and their environment where communication, negotiation and meaning-making are collectively developing knowledge. For most educators, constructivism may be a natural inclination of their pedagogy. Action researchers have a similar relationship to constructivism because they are actively engaged in a process of constructing knowledge. However, their constructions may be more formal and based on the data they collect in the research process. Action researchers also are engaged in the meaning making process, making interpretations from their data. These aspects of the action research process situate them in the constructivist ideology. Just like constructivist educators, action researchers’ constructions of knowledge will be affected by their individual and professional ideas and values, as well as the ecological context in which they work (Biesta & Tedder, 2006). The relations between constructivist inquiry and action research is important, as Lincoln (2001, p. 130) states:

much of the epistemological, ontological, and axiological belief systems are the same or similar, and methodologically, constructivists and action researchers work in similar ways, relying on qualitative methods in face-to-face work, while buttressing information, data and background with quantitative method work when necessary or useful.

While there are many links between action research and educators in the classroom, constructivism offers the most familiar and practical threads to bind the beliefs of educators and action researchers.  

Epistemology, Ontology, and Action Research

It is also important for educators to consider the philosophical stances related to action research to better situate it with their beliefs and reality. When researchers make decisions about the methodology they intend to use, they will consider their ontological and epistemological stances. It is vital that researchers clearly distinguish their philosophical stances and understand the implications of their stance in the research process, especially when collecting and analyzing their data. In what follows, we will discuss ontological and epistemological stances in relation to action research methodology.

Ontology, or the theory of being, is concerned with the claims or assumptions we make about ourselves within our social reality – what do we think exists, what does it look like, what entities are involved and how do these entities interact with each other (Blaikie, 2007). In relation to the discussion of constructivism, generally action researchers would consider their educational reality as socially constructed. Social construction of reality happens when individuals interact in a social system. Meaningful construction of concepts and representations of reality develop through an individual’s interpretations of others’ actions. These interpretations become agreed upon by members of a social system and become part of social fabric, reproduced as knowledge and beliefs to develop assumptions about reality. Researchers develop meaningful constructions based on their experiences and through communication. Educators as action researchers will be examining the socially constructed reality of schools. In the United States, many of our concepts, knowledge, and beliefs about schooling have been socially constructed over the last hundred years. For example, a group of teachers may look at why fewer female students enroll in upper-level science courses at their school. This question deals directly with the social construction of gender and specifically what careers females have been conditioned to pursue. We know this is a social construction in some school social systems because in other parts of the world, or even the United States, there are schools that have more females enrolled in upper level science courses than male students. Therefore, the educators conducting the research have to recognize the socially constructed reality of their school and consider this reality throughout the research process. Action researchers will use methods of data collection that support their ontological stance and clarify their theoretical stance throughout the research process.

Koshy (2010, p. 23-24) offers another example of addressing the ontological challenges in the classroom:

A teacher who was concerned with increasing her pupils’ motivation and enthusiasm for learning decided to introduce learning diaries which the children could take home. They were invited to record their reactions to the day’s lessons and what they had learnt. The teacher reported in her field diary that the learning diaries stimulated the children’s interest in her lessons, increased their capacity to learn, and generally improved their level of participation in lessons. The challenge for the teacher here is in the analysis and interpretation of the multiplicity of factors accompanying the use of diaries. The diaries were taken home so the entries may have been influenced by discussions with parents. Another possibility is that children felt the need to please their teacher. Another possible influence was that their increased motivation was as a result of the difference in style of teaching which included more discussions in the classroom based on the entries in the dairies.

Here you can see the challenge for the action researcher is working in a social context with multiple factors, values, and experiences that were outside of the teacher’s control. The teacher was only responsible for introducing the diaries as a new style of learning. The students’ engagement and interactions with this new style of learning were all based upon their socially constructed notions of learning inside and outside of the classroom. A researcher with a positivist ontological stance would not consider these factors, and instead might simply conclude that the dairies increased motivation and interest in the topic, as a result of introducing the diaries as a learning strategy.

Epistemology, or the theory of knowledge, signifies a philosophical view of what counts as knowledge – it justifies what is possible to be known and what criteria distinguishes knowledge from beliefs (Blaikie, 1993). Positivist researchers, for example, consider knowledge to be certain and discovered through scientific processes. Action researchers collect data that is more subjective and examine personal experience, insights, and beliefs.

Action researchers utilize interpretation as a means for knowledge creation. Action researchers have many epistemologies to choose from as means of situating the types of knowledge they will generate by interpreting the data from their research. For example, Koro-Ljungberg et al., (2009) identified several common epistemologies in their article that examined epistemological awareness in qualitative educational research, such as: objectivism, subjectivism, constructionism, contextualism, social epistemology, feminist epistemology, idealism, naturalized epistemology, externalism, relativism, skepticism, and pluralism. All of these epistemological stances have implications for the research process, especially data collection and analysis. Please see the table on pages 689-90, linked below for a sketch of these potential implications:

Again, Koshy (2010, p. 24) provides an excellent example to illustrate the epistemological challenges within action research:

A teacher of 11-year-old children decided to carry out an action research project which involved a change in style in teaching mathematics. Instead of giving children mathematical tasks displaying the subject as abstract principles, she made links with other subjects which she believed would encourage children to see mathematics as a discipline that could improve their understanding of the environment and historic events. At the conclusion of the project, the teacher reported that applicable mathematics generated greater enthusiasm and understanding of the subject.

The educator/researcher engaged in action research-based inquiry to improve an aspect of her pedagogy. She generated knowledge that indicated she had improved her students’ understanding of mathematics by integrating it with other subjects – specifically in the social and ecological context of her classroom, school, and community. She valued constructivism and students generating their own understanding of mathematics based on related topics in other subjects. Action researchers working in a social context do not generate certain knowledge, but knowledge that emerges and can be observed and researched again, building upon their knowledge each time.

Researcher Positionality in Action Research

In this first chapter, we have discussed a lot about the role of experiences in sparking the research process in the classroom. Your experiences as an educator will shape how you approach action research in your classroom. Your experiences as a person in general will also shape how you create knowledge from your research process. In particular, your experiences will shape how you make meaning from your findings. It is important to be clear about your experiences when developing your methodology too. This is referred to as researcher positionality. Maher and Tetreault (1993, p. 118) define positionality as:

Gender, race, class, and other aspects of our identities are markers of relational positions rather than essential qualities. Knowledge is valid when it includes an acknowledgment of the knower’s specific position in any context, because changing contextual and relational factors are crucial for defining identities and our knowledge in any given situation.

By presenting your positionality in the research process, you are signifying the type of socially constructed, and other types of, knowledge you will be using to make sense of the data. As Maher and Tetreault explain, this increases the trustworthiness of your conclusions about the data. This would not be possible with a positivist ontology. We will discuss positionality more in chapter 6, but we wanted to connect it to the overall theoretical underpinnings of action research.

Advantages of Engaging in Action Research in the Classroom

In the following chapters, we will discuss how action research takes shape in your classroom, and we wanted to briefly summarize the key advantages to action research methodology over other types of research methodology. As Koshy (2010, p. 25) notes, action research provides useful methodology for school and classroom research because:

Advantages of Action Research for the Classroom

• research can be set within a specific context or situation;
• researchers can be participants – they don’t have to be distant and detached from the situation;
• it involves continuous evaluation and modifications can be made easily as the project progresses;
• there are opportunities for theory to emerge from the research rather than always follow a previously formulated theory;
• the study can lead to open-ended outcomes;
• through action research, a researcher can bring a story to life.

Action Research Copyright © by J. Spencer Clark; Suzanne Porath; Julie Thiele; and Morgan Jobe is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License , except where otherwise noted.

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Using Focus Groups to Guide Action Research in Mathematics Education

Mr Marc Jacobs, Reading University

Abstract The aim of this doctoral research is to determine how students learn mathematics successfully and what strategies work best in secondary classrooms. Mathematics classrooms and teachers’ practice were investigated through several research methods. One method was student focus group interviews to reveal students’ views of teacher practice. It is widely appreciated (Dowker, 2009; Wilson & Räsänen, 2008) that there is limited research available on effective strategies for supporting students with their learning in mathematics compared to that available for literacy. Wilson and Räsänen (2008) suggest that there are several reasons for this limited research including the cost in terms of monetary considerations and implementation, particularly with large numbers. Therefore, implementing any form of successful mathematical investigation and intervention is challenging when attempting to use a strategy that works across a modern secondary school with a diverse population of teachers and students. This paper reports on the use of focus group interviews for the purpose of obtaining data from students about their learning experiences in mathematics lessons and their views of their teachers’ practice. Teachers’ practice is fundamental to successful learning experiences and Ball (1988) acknowledges that their practice is influenced by their beliefs about teaching and learning, about their students, and about their context thereby shaping how they teach.

Keywords: mathematics, focus groups, research methods

Introduction In the past few years, focus group interviews have been used increasingly in fields other than market research, where the technique was first developed (Berg, 1995). Berg (1995:65) also notes, focus group interviews have traditionally been dismissed as part of the “vulgar world of marketing research”. However, it is a method that is increasingly being appreciated for the advantages it offers to researchers in other data collection situations (Morgan, 1993; Gibbs, 1997; Barbour & Kitzinger, 1998). During the 1990s, one begins to see what a reversal in the elitist attitude that may be that focus group interviewing belongs to the somehow vulgar realm of marketing research. Instead, social scientists have begun regarding the approach with greater respect. Sussman, Burton, Dent, Stacy and Flay (1991: 773) state that “focus group methodology is one of the most widely used qualitative research tools in the applied social sciences.” Similar arguments have been offered by Basch (1987, 1989) and by Stewart and Shamdasani (1990). Clearly, there are some advantages to the use of this data-collecting orientation in certain situations. This research aims to explore how students believe they learn mathematics successfully and what classroom strategies work best by initially drawing upon reviews of this method and then subsequently using it with a group of secondary student participants. This paper is part of a wider doctoral project entitled Intervention in Mathematics: Creating successful strategies to ensure success in Secondary Schools where focus groups were used as one of the methods of data collection.

Definition of focus groups There are many definitions of a focus group interview and Kitzinger (2005) suggests the focus group method is an ‘ideal’ approach for examining the stories, experiences, points of view, beliefs, needs and concerns of individuals. The method is especially valuable for permitting the participants to develop their own questions and frameworks as well as to seek their own needs and concerns in their own words and on their own terms. Powell, Single and Lloyd (1996) define a focus group interview as a group of individuals selected and assembled by researchers to discuss and comment on, from personal experience, the topic that is the subject of the research. Morgan (1997) notes that a focus group (also called a focus group interview or a focus group discussion) is a form of group interviewing but it is important to distinguish between the two. Group interviewing involves interviewing a number of people at the same time and the emphasis is on questions and responses between the researcher and participants. Focus groups, however, rely on interaction within the group based on topics that are supplied by the researcher. The key characteristic, which distinguishes group interviewing from focus groups, is the insight and data produced by the interaction between participants (Morgan, 1997). A focus group is a form of qualitative research in which a group of people is asked about their perceptions, opinions, beliefs, and attitudes towards a phenomenon. Furthermore, focus groups are a form of group interview that capitalises on communication between research participants in order to generate data. Focus groups explicitly use group interaction as part of the method (Kitzinger, 1994). This means that instead of the researcher asking each person to respond to a question in turn, people are encouraged to talk to one another by asking questions, exchanging anecdotes and commenting on each other’s experiences and points of view (Kitzinger, 1994). During the 1980s focus groups reappeared in social sciences after being absent for some time and are now commonly used in cross-cultural research in a variety of fields, such as academic, policy-related or marketing research. Malhotra (1996:171-172) remarked that “focus groups are the most important qualitative research procedure. They are so popular that many marketing research practitioners consider this technique synonymous with qualitative research.” Even though this statement refers to the mid-1980s in the USA, it still has relevance today, although the arrival of new techniques, among them online focus groups, has certainly redesigned the overall picture.

The origins and history of focus group research The first use of group interviews was in the 1920s by social scientists Emory Bogardus and Walter Thurstone who used it to develop survey instruments. The methodology is mainly attributed to Bogardus who in 1926 described focus groups in his social psychological research to develop the social distance scale (see Wilkinson 1998). During World War II Robert Merton and Paul Lazarsfeld used group interviews to assist the allied forces in the development of propaganda materials, training manuals and to understand social issues. In the 1950s, focus groups became commonplace among marketers to understand customers while social scientists continued to prefer formal survey research. Sociologist Robert Merton worked with colleagues on the effectiveness of focus group in the years following World War II and the group (Merton, Fiske & Kendall) later wrote a seminal text entitled The Focused Interview: A manual of problems and procedures which was published in 1956. Of particular interest in the post-World War II era was the study of mass-mediated ‘propaganda’. The term focus group replaced group interview as the name of this technique. Over the last twenty years, there has been a steadily increasing interest in establishing qualitative research’s place in the academy which has resulted in the growing use of focus groups, especially in social sciences. In the 1980s focus groups re-emerged as a distinct research method in the social sciences (Conradson, 2005). Kamberelis and Dimitriadis (2005) state that focus groups have been popular and used extensively in several disciplines. Many social scientists and other professionals have found this qualitative approach very useful. Political scientists, for example, employed focus groups to examine the public perceptions of political candidates and their opinions on particular political issues (Madriz, 2003; Gaiser, 2008). During President Ronald Reagan’s administration in the 1980s, focus groups were adopted to learn about the perceptions of relations between the United States and the Soviet Union and their citizens (Stewart, Shamdasani & Rook, 2007). Focus groups were also used by the New Labour government from the early 1990s to early 2000s in the UK to examine British opinions about health spending, education policy and military action. The aim was to explore ‘a better understanding of the multiple and sometimes conflicting perspectives held by the public on particular issues’ (Conradson, 2005:130). The use of focus groups has been established over a period of time so their value to researchers for uncovering significant information is of interest.

Advantages of focus groups Focus groups are valuable when you want to consider not only people’s personal accounts of reality but also the way they negotiate these accounts with others, therefore showing divergence or convergence between their views. Cambridge and McCarthy (2001) describe a focus group interview as a group dynamic that can help build confidence, safe environments that are not threatening or intimidating and peer support and validation, enabling all people, regardless of perceived competence, to contribute to research discussions. Focus groups appear to be of value for all members of society and this success was evidenced by Fraser and Fraser (2001) whose research engaged participants with communication difficulties. Focus groups require both individual contributions and group dynamics and they found that with participants with communication difficulties groups smaller than the six-ten usually recommended were better and that the addition of an interpreter familiar with the participants’ communication was also important. Moreover, Fraser and Fraser (2001) found that participants’ ability to interact with others in a group was more important to success than their various types of communication challenges such as the ability to produce more than a few words, reliance on Makaton sign language, or even repetitive language. They concluded that ‘focus groups are a very good method for some people with learning disabilities in some situations but not in others; it is important to be able to distinguish this before setting up the group’ (Fraser & Fraser, 2001:225). So, there are clearly some limitations that need to be considered before the method is developed as a data collection instrument.

Limitations of focus groups Like any other research method focus groups do not suit all research aims and there have been times when they were found to be inappropriate or problematic. For example, compared to individual interviews, focus groups may not be as efficient in providing maximum depth on a particular issue. A particular disadvantage of a focus group is the possibility that the members may not express their honest and personal opinions about the topic at hand (Smithson, 2008). They may be hesitant to express their thoughts, especially when their thoughts oppose the views of another participant. Smithson (2008), a researcher who uses focus groups extensively, contends that some research topics are unsuitable for focus group environments. For example, topics which are seen as too personal (such as living with HIV/AIDS, sexuality, infertility, financial status, divorce, domestic violence and abortion) may be better carried out by other methods such as individual interviews. In institutional contexts (such as the workplace or schools), people may be reluctant to express their opinions or discuss their personal experiences in front of colleagues. Hopkins (2007) and Krueger and Casey (2009) found that often focus groups are criticised for only offering a shallower understanding of an issue than those obtained from individual interviews. In a focus group discussion, personal information and experiences may not be discussed thereby reducing the natural narrative that emerges from rich discourse. An example of this is Hopkins’ (2007) qualitative research project about the life and times of young Muslim men living in Scotland which showed that they revealed personal experiences of racism during individual interviews far more than they did in focus group discussions. The fact that focus groups are driven by the researcher’s interests can also be a source of weakness. What may be of intense interest to the researcher may be a non-issue to the participants. However, the fact that the researcher creates and directs the groups makes them distinctly less naturalistic than participant observation so there is always some residual uncertainty (Morgan 1996) about the accuracy of what the participants say. In particular, there is a very real concern that the researcher, in the name of maintaining the interview’s focus, will influence the group’s interactions. This problem is hardly unique to focus groups because the researcher influences all but the most unobtrusive social science methods. In reality, there is no hard evidence that the focus group researcher’s impact on the data is any greater than the researcher’s impact in participant observation or individual interviewing. Indeed, the dyadic nature of individual interviewing would seem to create at least as many opportunities for researcher influence. The concerns for focus groups include both a tendency toward conformity, in which some participants withhold things that they might say in private, and a tendency toward ‘polarization’ in which some participants express more extreme views in a group than in private (Sussman, Burton, Dent, et al., 1991). It is clear, however, that for some types of participants discussing some types of topics the presence of a group will affect what they say and how they say it. This is an inevitable aspect of focus groups that should be considered as a potential source of weakness for any given research project. Morgan (1988) states that the researcher, or moderator as they are often termed, has less control over the data produced than in either quantitative studies or one-to-one interviewing. The researcher has to allow participants to talk to each other, ask questions and express doubts and opinions while having very little control over the interaction other than generally keeping participants focused on the topic. By its nature focus group research is open-ended and cannot be entirely predetermined. On a practical note, focus groups can be also difficult to assemble. It may not be easy to get a representative sample and focus groups may discourage certain people from participating, for example, those who are not very articulate or confident, and those who have communication problems or special needs. The method of focus group discussion may also discourage some people from trusting others with sensitive or personal information. In such cases, personal interviews or the use of workbooks alongside focus groups may be a more suitable approach. Finally, focus groups are not fully confidential or anonymous, because the material is shared with the others in the group (Morgan 1997) and this has ethical implications that need to be considered when developing a methodological approach.

Types of focus groups There are different formations of focus groups and this section explores those types. Traditional Focus Groups are more straightforward, question-oriented groups. Usually, there is a ‘warm-up’ then the concept, idea, situation or product is presented to the group for their reaction. A neutral moderator who probes for issues of interest and follows up on interesting or relevant comments made by the participants’ guides this process. The key factors to successful traditional groups include clearly defined research issues, an experienced moderator who understands the issues at hand and decisions to be made; and diligent recruiting (Morgan, 1984). Projective Focus Groups bear a resemblance to traditional focus group discussions in that they are an informal, subtly structured conversation on a specific subject lead by a neutral moderator. They differ in the methods used to explore thoughts and feelings about the subject, and in the emotional depth that can be reached using these methods. Projective Groups rely more on indirect questioning and strongly emphasize the interpretation of group input. Some of the techniques that may be used in Projective Focus Groups include collage-building, brand personification, guided journey and pictorial symbols (Morgan, 1984). Projective Focus Groups are used extensively in exploring brand image and the development of creative concepts for products, services and advertising. A few of the questions addressed in Projective Focus Groups have included: Is this the right name for the product? What feelings are evoked by our brand? What mood should our advertising and collateral material invoke? I have used the traditional focus group interview as I wanted to hear what students think – literally. There is nothing more powerful than hearing first-hand what students have to say about how they learn mathematics.

Uses of focus groups Morgan and Kreuger (1993) state that the main purpose of focus group research is to draw upon respondents’ attitudes, feelings, beliefs, experiences and reactions in a way in which would not be feasible using other methods such as observation, one-to-one interviewing, or questionnaire surveys. These attitudes, feelings and beliefs may be partially independent of a group or its social setting but are more likely to be revealed via the social gathering and the interaction which being in a focus group entails. Compared to individual interviews, which aim to obtain individual attitudes, beliefs and feelings, focus groups elicit a multiplicity of views and emotional processes within a group context. The individual interview is easier for the researcher to control than a focus group in which participants may take the initiative. Compared to observation, a focus group enables the researcher to gain a larger amount of information in a shorter period of time (Morgan & Kreuger, 1993). Observational methods tend to depend on waiting for things to happen, whereas the researcher follows an interview guide in a focus group. In this sense, focus groups are not natural but organised events. Morgan and Kreuger (1993) suggest that the method is particularly useful when there are power differences between the participants and decision-makers or professionals, when the everyday use of language and culture of particular groups is of interest, and when one wants to explore the degree of consensus on a given topic.

Ethical issues According to Homan (1991), ethical considerations for focus groups are the same as for most other methods of social research. For example, when selecting and involving participants, researchers must ensure that full information about the purpose and uses of participants’ contributions is given. Being honest and keeping participants informed about the expectations of the group and topic, and not pressuring participants to speak is ethical practice. At the outset, moderators will need to clarify that each participant’s contributions will be shared with the others in the group as well as with the moderator. Participants need to be encouraged to keep confidential what they hear during the meeting and researchers have the responsibility to anonymise data from the group.

The Research Study

a) Selecting participants Miles and Huberman (1994) explain that most focus groups rely on purposive sampling with researchers selecting participants on the project and on the potential contributions of participants. Alternatively, participants can be randomly selected from a larger group that should be able to give insight into the topic. For example, if someone wanted to know more about a particular religious congregation purposive sampling, such as obtaining a church membership listing and randomly selecting parishioners to participate, would be an efficacious approach (Patton, 1990). This action research project has a wider population of 240 students in Year Seven (2013-2014) but the focus group interviews included 10 participants selected anonymously; one child from each of ten mathematics sets was selected to form two focus groups of five. The members of a focus group were invited because they are known to have experience from a particular context which in this case was secondary mathematics classrooms.

b) Structure Researchers such as Kitzinger and Barbour (1990), Lindlof (1995), Kreuger (1998), Green and Hart (1999) and Brown (1999) disagree about the practicable number of participants for a successful focus group. Many experienced moderators prefer a group ranging from eight to twelve suggesting further that the group should consist of four to twelve if the group is homogeneous and six to twelve if heterogeneous. A balance between the need to have sufficient participants for a lively discussion and the unwieldy milieu of a large group is the goal of the researcher.

c) The role of the moderator The moderator’s management of the focus group can determine the success or otherwise of the method regardless of the context. Morgan (1998) describes the moderator as the person who has the task of leading the focus group. This leadership or management involves: a) setting the scene; b) explaining the purpose of the focus group; c) introducing participants to the topics for discussion; d) keeping the group on time; e) focused on the topics; f) encouraging participation from all the group members; and, g) ensuring that all the key issues are addressed (Morgan, 1998). It is useful to have a note-taker recording all discussions so the moderator can give all their attention to the group. The notion of conducting a focus group interview effectively includes an assumption that the interview will be facilitated. The moderator had assumed most of the practical roles concerned with the planning of the physical environment of the interview room and the organisation of equipment and refreshments. The moderator also took responsibility for the welcoming of participants on the day and therefore began the process of setting participants at their ease and opening up channels of communication. According to Kitzinger (1995:299) the moderator ‘leads’ the focus group, their role is only to keep the discussion on track and should not influence the opinions of the group, this has been referred to as “structured eavesdropping”. During the start of proceedings of the focus group, the moderator’s first question is critical in breaking the ice. After each participant has said something it becomes easier to make further contributions and feel that their opinion is valued. With the use of focus groups in this research, it was particularly important to avoid domination by any particular participant, making sure that everybody had their say and enabling some level of consistent data collection between focus groups. This study worked with young teenagers and it became apparent that the moderator’s role was to ensure that all children felt their ideas were valued and that no one child dominated the discussion. d) Running the Focus Groups Two focus groups were held as part of the initial data collection period of this study. I undertook the role of the moderator and my supervisor took the role of the assistant who was responsible for the audio recording of the event and note-taking during the discussions to capture non-verbal signals and nuances. There were five participants in each of the two focus groups which were conducted during the students’ regular mathematics lesson time in a quiet library space on their campus.

e) Conducting and Observing the Focus Group The moderator and assistant sought to provide a friendly introductory environment which was established as the students arrived at the library. The moderator introduced himself and his assistant. Thanks, were extended to the students for attending and the purpose of the meeting was explained. The conventions of the group discussions were outlined together with reassurances about guarantees of confidentiality. Any initial anxieties or questions about the proceedings were invited. Each participant was asked to introduce themselves before the questions were addressed. The focus groups went smoothly and generated a great deal of data within the allocated timeframes. Moderator intervention was mainly restricted to prompts, probes and moving the discussion on when a particular issue had been exhausted. An example of moving them on to the next topic was when one of the participants could not think of a time he had a ‘good learning experience’; I told him that I would give him time to think and that I would come back to him. He then told us about a ‘good learning experience’. There was no domination in the group. The assistant moderator contributed or intervened in the discussion and sat at the main table to support the clarity of the Student contributions and to witness the discussion. Once the formal proceedings were brought to a close, participants were once again thanked for their contributions to the focus group.

Ethics Focus group research raises a number of ethical issues. We were particularly concerned to ensure confidentiality in and after the discussions. To this end no questions probed for any personal or sensitive information. Anonymity remains paramount and pseudonym use ensures that participants cannot be identified in any publications. Data from tapes and transcripts of the interviews are retained by the researcher and all data stored on university computers.

Analysis of the data There are a variety of methods of analysing data for focus groups (see Johnson & Christensen, 2004). The audio recordings were transcribed and the data together with the notes were discussed with the researcher’s supervisor. The discussions on a number of topics revealed the high level of detail which focus groups can engender as a result of the group interaction. For example, in the first focus group discussion on the topic of ‘how maths should be taught at secondary school,’ this led to a lively debate in which the students were very open about their own views and experiences. An example of this was, all the participants in the focus group wanted to express their views that maths should be interactive, fun and hands-on. Any reservations that we had that students would be reluctant to open up in front of their peers on such a sensitive issue were not borne out. Although it might be expected that participants would be guarded concerning their knowledge around maths teaching, they revealed that they felt trapped and teachers are unable to relinquish textbook teaching. The participants were therefore particularly interested in hearing the experiences of their peers as they were all taught by different teachers. The students reflected upon the use of textbooks as the primary resource, in most lessons and they reflected on how they felt in using textbooks on a daily basis, four times a week. It is commonly assumed that textbooks (with accompanying teacher guides) are one of the main sources for the content covered and the pedagogical styles used in classrooms. It is not surprising, then, that considerable attention has focussed on textbooks, including the economic and political circumstances of their production (Apple, 1986 and 1992), their linguistic features (Castell et al, 1989) and their sociological features (Dowling, 1996). Students in this study were put in sets for mathematics during their first year in secondary school according to their results in national curriculum tests. Once in those sets, they followed the same national curriculum but from different starting points and with different endpoints in mind. Textbooks reflected this way of organising students so that in any year group, a particular textbook scheme might have different textbooks aimed at different sets of students. Teachers used textbooks regularly, and almost all that use in lesson times was for students to practice exercises selected by the teacher following from teacher explanation of a particular skill or technique. Listening to the students and their concerns regarding the use of textbooks and their need for more ‘hands-on’ activities, gave me sufficient information to enact change in the mathematics classrooms as part of the Action Research for this project.

Discussion The main purpose of focus group research is to draw upon respondents’ attitudes, feelings, beliefs, experiences and reactions in a way in which would not be feasible using other methods, for example, observation, one-to-one interviewing, or questionnaire surveys. Focus groups rely on interaction within the group based on topics that are supplied by the researcher (Morgan 1997: 12). Hence the key characteristic which distinguishes focus groups is the insight and data produced by the interaction between participants. This is to ensure that participants have a specific experience of or opinion about the topic under investigation; that an explicit interview guide is used; and that the subjective experiences of participants are explored in relation to predetermined research questions. An example is when the participants were asked ‘Which class or which teacher helped you?’ and one of the participants responded: Well, there’s, like, most of them, they’re really nice and supportive, but some lessons are, like, a bit, like, they help a few people that are, like, really struggling, but they never really help the rest of the people. Like, they focus on a few people and that’s about it. But that’s only a few. That’s, like, three classes or two. And another participant replied: Yes, most of my teachers are quite supportive in that way, but like A, some of them can be a bit focusing on some people and, like, thinking other people can do well, so it doesn’t mean they’re… It means they’re not struggling. So they, sort of, put you aside and, like, …, you’re fine, you can do it yourself, even when you’re struggling on the topic.’ Therefore, focus groups are particularly useful when there are power differences between the participants when the everyday use of language and culture of particular groups is of interest, and when one wants to explore the degree of consensus on a given topic (Morgan & Kreuger, 1993). An advantage of focus groups to clients, users, participants or consumers is that they can become a forum for change, both during the focus group meeting itself and afterwards. For example, in this research the participants were asked: ‘… to design how maths should be taught at Secondary School, how students can really learn well…’ and they replied: Like, maybe a bit more interactive lessons because, like, it’s really, like, when they’re, like, with their friends and they can learn with their friends, but then still be with someone that they hang around with and, like, and then, but still have, like… Sort of, sometimes it’s really like they could be really interactive because people… Like, textbooks, example, are a little bit boring and, like, put you off, like, you just, sort of, read that. Like, say the teachers maybe help a bit more because, like, they say I can’t really explain this to you. It’s a bit, like, it’s, kind of, annoying when they can’t really do that. Not in my test, but, like, just in general classwork. So yes. I think they should make lessons more interactive because we usually always do textbook work and when, like, you’re stuck in your seat and you’re stuck in a textbook it gets, like, really boring, so I’d like to every once in a while, like, have an interactive lesson. A focus group is a small-group discussion guided by a trained leader. It is used to learn more about opinions on a designated topic, and then to guide future action that can bring change to an organisation (Morgan & Kreuger 1993). A main advantage of this method derives from group relations evident in the sessions. Students were encouraged to explain, challenge and share their honest views on questions asked. Listening to the ideas, opinions and experiences of others demands that we interrogate our own beliefs, and this was evident in these interviews. The reason for a significant level of candidness may derive from a move in the influence of the relationship between the researcher and participants. In focus groups, the researcher is in a marginal position and participants are amongst their peer group. This seems to make participants more willing to discuss topics openly in their own language than they would in one-to-one research environments. Here the manner was particularly useful as a means of allowing students to express their views and experiences without hindrance by the constraints inherent in one-to-one discussions with a researcher. Thus, focus groups are an effective way of ascertaining detailed views and experiences on relevant mathematical questions asked. Although the groups were guided by an agenda, they were able to ‘snowball’ their views on issues, presenting a wider context for their own position. For example, views on motivations and learning often generated a wider discussion. The advantage of this method over face-to-face interviews is that each speaker provides a platform for another to contribute, rather than responding only to a predetermined list of questions. Here participants were prepared to add to or qualify what had been said previously, providing a much more complete picture of their mathematical world. Participants provided long, detailed narratives about their experiences in mathematics, which often revealed their views and motivations. However, the analysis of the data emerging from group interaction can also provide a rich understanding of how students learn mathematically and, on balance, I would argue that focus groups should be used more widely. From the experience so far, the method generated data of range, depth, specificity and personal context which can stand alone or complement other research methods. Ultimately, using focus groups with students in education can help close the ‘culture gap’ between researchers and the subject they seek to understand.

Conclusion This paper has examined the use of focus groups as a method of understanding teachers’ practice in secondary mathematics through the interrogation of students’ ideas, beliefs and experiences. The results illustrate that a series of ongoing focus groups should provide a valuable longitudinal viewpoint. Although focus groups seem to have been used seldom in educational research, the results of the groups reported here illustrate the contribution that this method can make as a method to provide a picture of the views and experiences of students in a secondary school.

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Action Research in Mathematics: Providing Metacognitive Support (as a Heutagogical Technique) to Grade 3 Students

By Zoriana Myburgh

Self-determination, as one of the 21st-century skills, prepares students for our constantly changing world. Can metacognition help students become self-determined and is it worth starting to introduce metacognitive elements at an elementary school? Based on the current literature from teachers’ and administrators’ points of view, metacognition positively influences students’ performance and wellbeing. Therefore, there is a need to continue researching the effects of metacognition at a young age but from students’ perspectives.

The purpose of this research is to enhance grade 3 students’ metacognitive abilities to help them manage their learning. The data was collected using the students’ personal thoughts and emotions during semi-structured interviews and the researcher’s observation notes in order to summarise whether or not metacognitive interventions were helping students become self-determined. A lack of qualitative action research in existing literature highlighted the need for this research design.

It has been found that metacognition as a heutagogical technique can be used to improve students’ self-determination in an elementary school. Students mostly showed improvement in the Commitment category: goal-setting, self-questioning and self-monitoring. Less than half of the students showed the development of metacognitive skills in the Capacity category. Most of them already had some skills before the experiment started (e.g., strategies for solving problems, improvement strategies, and asking for help when needed). The Value category represented how students developed their metacognitive experience and supported the finding of the previous categories. Considering the significance of metacognitive development, teachers should constantly strengthen the metacognitive abilities of their students.

University of Southampton, 2021

FACULTY OF SOCIAL SCIENCES

ACTION RESEARCH IN MATHEMATICS: PROVIDING METACOGNITIVE SUPPORT (AS A HEUTAGOGICAL TECHNIQUE) TO GRADE 3 STUDENTS

by Zoriana Myburgh

A dissertation submitted in partial fulfilment of the degree of

<MSc Education (online) PT>

by taught course.

You can view this dissertation in its entirety in PDF form here.

1. INTRODUCTION

Background of the study.

Due to constant and rapid changes in our society, the importance of lifelong learning is also increasing. People need to constantly evaluate their ideas and experience. This ceaseless “transformation of information, the creation, construction and renewal of knowledge, is at the heart of reflexivity” (Dyke, 2009, p. 295). Traditional learning models might not be satisfactory for current learners nowadays who look for greater independence and integration (McLoughlin and Lee, 2008). Taking into account COVID-19 pandemic restrictions all over the world and the availability of online learning resources, it’s essential for students to learn how to manage their learning. Furthermore, some of the jobs that we have now might be replaced by the time our primary students will finish school. In that case, it is necessary to teach 21st-century skills, namely critical thinking, self-determination, and socialization, that will help students adapt to these new requirements (Irgatoglu and Pakkan, 2020).

Being an elementary school teacher, I often noticed that when students are given a word problem to solve, they will say, “I do not know, teacher” or “Teacher, what to do here?”, or will patiently wait until the teacher scaffolds it, or someone else finds the answer. Can coaching students on metacognition as one of the heutagogical techniques solve this issue? The main goal of developing students’ metacognition is to make them autonomous and self-determined learners (Thomas, 2003). Self-determined learners set their own goals and learning paths, monitor timing, and reflect on their final outcomes.

Based on Self-determination Theory, students have three primary needs : autonomy, competence, and relatedness (Deci and Ryan, 2000). Autonomy means the freedom of choice and the wish to control the learning process. Competence refers to having the confidence and capabilities to complete a task. Relatedness is about working with others and feeling connected (Marshik, Ashton and Algina, 2017).

Definition of Terms

This paper will be based on three main terms: heutagogy, self-determination, and metacognition.

First, it is important to differentiate between self-determination, self-regulation, and self-efficacy as these three terms will appear in this paper.

• Self-determination refers to individual motivation that is influenced by internal impetuses (Ryan and Deci, 2000).
• Self-regulation is defined as self-management, the ability to control the thoughts and emotions that direct human’s behaviour (Panadero, 2017).
• Self-efficacy is one of the tools of self-regulation and means the beliefs people have in achieving a task successfully (Bandura, 1977).

Self-determined learning is also known as heutagogy , a concept introduced by Hase and Kenyon (2000) and refers to student-centred learning “where the individual student’s interests and motivations create a focus area for new learning” (Jones et al ., 2019, p. 1172) and the teacher acts more like a mentor in a classroom. One of the main heutagogical principles is self-reflection (Blaschke, 2012) which is known as metacognition. Metacognition is “thinking about thinking”, “cognition about cognition” (Pritchard, 2013, p. 27) or “our ability to know what we know and what we don’t know” (Costa and Kallick, 2008, p. 24).

Metacognition is not only about planning and knowledge activation but also the intentional monitoring of students’ cognitive processes, reflection, time management, and self-evaluation (Bol et al ., 2016) and determining new ways to proceed and learning from the experience (Edwards and Costa, 2012).

Metacognition is one of the 16 Habits of Mind (HoMs) developed by Costa and Kallick (2000) that are a collection of behaviours that can help students tackle different problems they encounter at school or in other settings. Students need more than just academic knowledge and skills in order to succeed. HoMs focus not only on how much students know but also on what they do when they do not know an answer (Costa and Kallick, 2008). Teachers can help them practice these behaviours by modelling them, immersing these habits in the school curriculum and culture, and constantly checking their growth (Edwards and Costa, 2012).

Problem Statement

Considering that learning is a lifelong process, it is logical to start teaching self-determination skills as soon as possible (Palmer & Wehmeyer, 2003). Moreover, it is recommended by some researchers to start teaching self-determination at a young age as it will become more difficult at later stages (Danneker & Bottge, 2009). Stein (2018, p. 4) underlines that “effective teaching and learning [should] take place early on so that students can be successful in secondary school and beyond”. For instance, elementary school students can be taught how to set goals, make decisions, assess, and reflect on one’s own work. Knox (2017) emphasises that students who developed metacognitive skills can organise, examine, and assess their thoughts. However, there is not much qualitative research that investigates the impact of metacognitive support on elementary students, particularly in the context of mathematics. Most of the studies focus on quantitative data based on students’ performance. Previous literature was more focused on the teachers’ perspectives disregarding the views of students.

Self-reflection tasks are often treated as some extra time-consuming work for students, especially during mathematics classes because students do not see any value in them (Kiles, Vishenchuk and Hohmeier, 2020). Metacognitive skills that lead to self-determination are not instinctive and might be challenging (Bouldin, 2017). Considering that self-determination plays an important role in students’ well-being (Martinek and Kipman, 2016), it is important to dedicate this study to research the effects of metacognition on learners’ self-determination at a young age from students’ vision.

Fifteen grade 3 students (9-10 years old, 8 girls and 7 boys) took part in this experiment at an elementary school in Cambodia. Data from the participants were collected as semi-structured interviews with students recorded via Google Meets and the researcher’s observation notes taken during math classes. During the research period, all schools in Cambodia were operating online because of COVID-19 pandemic restrictions. The experiment lasted 9 weeks from April 29 to June 30, 2021.

Purpose of the Study and Research Questions

The purpose of this study is (a) to understand the necessity of a heutagogical framework from the perspectives of students during maths classes in an elementary school in Cambodia, and (b) to find out whether metacognition can help students become self-determined at a young age. Action research cycles will be used to examine self-determined learning in the context of mathematics at an elementary school. Action research can be conducted by teachers in their classrooms with the aim of refining pedagogy and student learning (Nasrollahi, 2015). Coding student perspectives and researcher’s notes will help understand the phenomenon of self-determination and the use of metacognitive elements, namely goal-setting, self-assessment, self-questioning, self-monitoring, responding to and reflecting on feedback, note-taking, problem-solving strategies, and improvement strategies, etc.

The aim of the study was supported by the following research questions:

Central Question: How can students’ needs be met using the heutagogical framework while teaching maths in an elementary school in Cambodia? Subquestion 1: What tools and strategies should teachers use to implement the heutagogical framework? Subquestion 2: How can metacognition as a heutagogical technique be used to improve students’ self-determination

By answering these research questions and gaining insight from students, we can better understand the conceptions and misconceptions about the heutagogical framework in an elementary school. We will see whether metacognitive elements in a lesson plan encourage self-determination based on students’ responses and the researcher’s observation notes. With this undertaking, elementary teachers might be inspired to design better lesson plans.

Organization of the Study

The structure of the study is as follows. The literature review provides the context for current research, explains the importance of metacognition as a heutagogical technique in the learning process from teachers’ perspectives. It was considered whether metacognition can be taught and what techniques work best based on the current empirical data. The methodology chapter explains the rationale for research design and the methods chosen as the most appropriate for this study. Plus, it gives an insight into how data was collected and analysed. The findings chapter presents the themes developed during the analysis of the collected data. The research outcomes are compared with the existing literature in the discussion chapter. Based on the research findings, implications for further research are suggested and conclusions are made.

2. LITERATURE REVIEW

Metacognition will be studied through constructivism and individualism leading to postmodernism. Literature was reviewed to examine the importance of metacognition as one of the heutagogical techniques and a Habit of Mind in the learning process. It was taken into account whether metacognition can be taught and what approaches on the current empirical evidence work best to enhance self-determination. Finally, some quantitative and qualitative tools to measure metacognition were analysed. The search was not limited to specific dates although preference was given to the last two decades.

2.1 Metacognition through the lens of constructivism, individualism, and postmodernism

From a constructivist viewpoint, metacognition is “the result of mental construction” (Pritchard, 2013, p. 18). According to constructivist theory, learning is a metacognitive process (Wray and Lewis, 1997). Reuer states that constructivism happens when students connect their experiences and ideas (Reuer, 2017). Constructivists claim that we learn better if we constantly build our understanding (Pritchard, 2013). Since metacognition is also about self-assessing and self-monitoring, it complements constructivism perfectly. Different people learn things differently. We, as teachers, might not know which approach will be the best for a specific topic for different students but we can encourage them to experiment with various methods and decide metacognitively how to approach and solve a mathematical problem. Pritchard (2013) also claims that if students are asked to share their approaches or evaluate their classmates’ ideas in a constructive way in a safe and supportive environment, it will eventually lead them to develop their processes of thinking and help them solve problems.

It’s important to understand the teacher’s role in this domain. Constructivism is often criticised because students are left “to teach themselves” (Hubbard, 2012, p. 160). According to heutagogy, teachers act more like coaches (Mohammad et al ., 2019) and facilitators (Akyildiz, 2019). Akyildiz interviewed 40 educators from Turkey who implemented heutagogical frameworks within their classes and summarised that 30% of teachers reported that they had to reflect more if they wanted to progress with heutagogical education and 40% of them claimed that they lost power in the classroom. However, Horrigan (2018, p. 57) argues that “empowering students is not the same as a teacher losing power”. Can metacognition help students and teachers because both need to adapt to the 21st-century requirements?

Furthermore, metacognition is connected to the values of individualism, encouraging self-directedness and heutagogical principles in general. Working at one’s own pace and reflecting on one’s learning are paramount skills for students in order to transform into independent learners (Sart, 2014).

Seeing each child as an individual with their own personality, mental and physical capabilities is an example of individualism (Fevre, Guimarães and Zhao, 2020). According to constructivists, knowledge is built by an individual through the explanation and combination of different ideas (Hubbard, 2012). Thus, both the constructivist methods and the individualism of heutagogy lead to postmodernism because postmodernists believe that the goal of education is “teaching critical thinking, production of knowledge, development of individual and social identity, self-creation” (Hossieni and Khalili, 2011, p. 1307). This aligns with 21st-century skills discussed in the previous chapter. Following this philosophical approach, teachers as mentors guide students to come across new things and reflect on them on their own (Hossieni and Khalili, 2011), therefore, students alter from passive recipients of knowledge to active constructivists (Reuer, 2017).

2.2 Metacognition through self-determination, self-regulation, and self-efficacy

Self-determination and even heutagogy are not new terms in education but their importance in elementary school has emerged within recent years. Some findings suggest that nurturing metacognitive beliefs in kindergarten children will increase their behavioural self-regulation (Compagnoni, Sieber and Job, 2020). Therefore, teachers must “maximize the learning classroom climate for self-regulated learning” (Panadero, 2017, p. 23). Using action research cycles (Plan – Act – Observe – Reflect – Revise – Plan), the behaviour of students engaging in self-directed learning was investigated in Ireland (Newman and Farren, 2018). They claimed that reflections and critical self-analysis motivated students to become more self-directed. However, the authors believed that the terms “self-directed” and “self-determined” are interchangeable. This definitional vulnerability questions the validity of this study. Self-directedness is based on single-loop learning (correcting the mistakes without reflections) and self-determination is founded on double-loop learning (questioning beliefs and assumptions) (Peeters and Robinson, 2015).

Self-determination techniques are often analysed alongside metacognitive strategies because according to heutagogy, metacognition is a major characteristic of how people naturally learn (Blaschke, 2012). Moreover, “the autonomy and flexibility of heutagogical models are managed well when incorporated into a reflective practice” (Newman and Farren, 2018, p. 6). If learners reflect on their results through the problem-solving process and take their actions and beliefs into account, new learning situations can be adapted to various learning styles (Blaschke, 2012). Blaschke is talking about the double-loop learning model, the key principle in the heutagogical framework. It was examined in Indonesia among 48 middle-school participants who were split into two groups (Nur et al ., 2019). Using questionnaires, pre-tests and post-tests students’ progress was measured. It was summarised that this constant reflection using a double-loop learning model positively affected students’ results. However, the analysis is lacking in rigour. First, it is not mentioned whether multiple observers were invited to this study and the duration of the experiment is not clear. Secondly, it is difficult to judge the validity of the data without the examples of pre-tests and post-tests.

Some researchers even consider metacognition as a general term combining other definitions, such as self-regulated learning, thinking skills, etc. (Perry, Lundie and Golder, 2019). Winne and Hadwin (2008) explored self-regulated learning and its effects on motivation from a metacognitive perspective and described it as a cycle: define a task, set goals, perform the task and metacognitively modify if needed. According to their study, self-regulated learners can use metacognitive strategies to monitor their goals and progress in completing them. Analysing this model, Greene and Azevedo (2007) noticed that metacognitive monitoring is a significant part of self-regulated learning. However, these authors together with Panadero (2017) in his meta-analysis, argued that it was unclear how the last phase worked in Winne and Hadwin’s cycled model, specifically they believed that metacognition should occur throughout each phase and not as an end product.

Students who are confident in their abilities, try to achieve their goals, look for academic help and self-reflect will show better performance at school (Martinek and Kipman, 2016). Martinek and Kipman (2016) argue that if supporting students’ autonomy increases students’ motivation, then self-determined learning will also improve students’ self-efficacy (self-confidence in succeeding in the task). Self-efficacy is one of the variables that influences self-regulated learning (Panadero, 2017). According to the Self-determination Theory, there are three basic needs: autonomy, competence, and relatedness. Therefore, if students have a choice and understand the purpose and relevance of the tasks, students’ intrinsic motivation will be increased (Ryan and Deci, 2000). Martinek and Kipman (2016) predicted that self-determination, academic self-regulation and self-efficacy (𝑆𝐸³) will have positive consequences on students’ subjective well-being ( W ). 131 students from an Austrian primary school completed questionnaires regarding this study called 𝑆𝐸³𝑊. It was concluded that 𝑆𝐸³ decreased noticeably from grade 1 to grade 2, but the general W did not change. Martinek and Kipman (2016, p. 130) assumed that the teachers did not provide enough autonomy to their students because they did not “trust in the learning abilities” of their students or felt “a loss of control” in actual students’ work. However, some researchers believe that using questionnaires in elementary school is not appropriate because of the students’ age and observer’s reports are essential in future studies (Morison et al ., 2000). Others think that teachers do not have enough training on self-determined learning (Panadero, 2017).

Teachers’ behaviour as an example of self-determination is truly crucial. If students do not feel these supportive interactions, their self-determination might not be ignited. 2,587 students in the USA took part in a survey that examines how the social aspects of schools foster students’ self-determination (Adams and Khojasteh, 2018). Having applied quantitative methods, the authors concluded that the school climate does have consequences. At the same time, a similar experiment in the USA was conducted with 106 university students (Hayward et al ., 2018). The authors used a mixed-methods research approach to examine how inner directedness (in particular, metacognition) will affect students’ motivation. For each experimental section instructors recruited three to five volunteers called Student Pedagogical Teams. Their role was to collect feedback from other students and to present it to their instructors. The instructors followed this repeating cycle: teach a class, receive feedback, modify the classroom activities, receive students’ feedback again, reflect on the results and plan the next task. Metacognition through self-assessment, reflections, and self-regulated learning promoted teachers’ self-directed professional development (Hayward et al ., 2018).

2.3 Metacognition as a Habit of Mind

Metacognition is one of the Habits of Mind (HoM), “the characteristics of what intelligent people do when they are confronted with problems” (Costa and Kallick, 2008, p. 15). The authors of 16 HoMs, Costa and Kallick, believe that the main purpose of all HoMs is to create self-determined, lifelong learners. Therefore, students need to self-monitor and self-regulate to achieve this goal. This HoM is subjectively the heart of all Habits of Mind and a core of heutagogy. If an individual can self-regulate their thinking processes, they can choose other appropriate habits to succeed in the task. Based on the empirical evidence presented by Muscott, students who were trained in and demonstrated how to think about their thinking did better in assessments (Muscott, 2018).

There are two main components of metacognition: metacognitive knowledge (MK) and metacognitive experience (ME) (Flavell, 1979). MK is the strategy students use to solve problems and ME is about contact with the environment. ME could inspire both cognitive and metacognitive strategies necessary to solve mathematics word problems. “Cognitive strategies are invoked to make cognitive progress, metacognitive strategies to monitor it” (Flavell, 1979, p. 909). Efklides separated metacognitive skills (MS) from MK and ME. She defines MS as “procedural knowledge” (Efklides, 2006, p. 5). Students must get used to “linking and constructing meaning from their experiences” (Costa and Kallick, 2008). Costa and Kallick add two more components: inner awareness and the strategy of recovery. They explain it with an example of reading an unfamiliar story. When a person reads a text and suddenly loses the meaning, he/she will reread it and get back the connection to understand what is happening.

Costa and Kallick (2008, p. 63, fig. 4.1) developed five dimensions within which students can grow regarding Habits of Mind: meaning, capacity, alertness, commitment, and value.

By exploring meaning the authors mean that students understand the meaning of HoMs. Increasing alertness is about applying HoMs without being asked. Extending values is understanding why some HoMs are more applicable in specific situations so if the students extend the value of metacognition in mathematics, it might turn into a pattern of behaviour eventually. Expanding capacities is about developing various techniques when solving problems or making decisions. If students develop metacognitive strategies, they might be able to apply other HoMs more effectively. Building commitment is constant development in the use of HoMs when students progressively become self-determined. This dimension is closely related to heutagogy as students learn to self-manage, self-monitor, self-reflect, and set higher expectations for themselves (Costa and Kallick, 2008).

Wagaba, Treagust and Chandrasegaran (2016) were also trying to conceptualise the dimensions that characterise metacognitively-oriented learning environments: (1) metacognitive demands, (2) student-student discourse, (3) student-teacher discourse, (4) student voice, and (5) teacher encouragement and support. If we are talking about metacognitive demands, it is recommended to model metacognition and not assume that the students already know organisational techniques or how to set goals, collaborate, etc. but explicitly teach these metacognitive strategies. The student-student dimension refers to whether students think interdependently and discuss how they learn with their peers. Student-teacher interaction means whether students discuss how they learn with their teacher. By “student voice” the author means students’ contribution to lesson planning. That is especially important in heutagogy. Thomas (2003) argues if students have control over their learning tasks, it will be easier for them to meet their learning goals. Lastly, teacher encouragement and support might not influence students’ metacognitive abilities directly, but it might be the first step in developing those skills. As Gallucci (2006, p. 19) mentioned, “the heart of teaching is providing students with the tools to make them more effective learners” and not just teaching the content.

2.4 Can metacognition be taught?

Some researchers argue that metacognition can be taught, and it might improve academic achievement (Muscott, 2018). The effects of metacognitive training on students’ achievement in maths were tested recently in the USA (Bol et al ., 2016). 116 randomly selected participants who were split into two groups (control and experiment) took part in this three-week research. The authors concluded that this training in self-regulated learning (specifically, such skills as goal-setting, self-monitoring and self-reflection) improved not only students’ maths results but also their time management skills. However, the validity is questionable since this questionnaire is a self-reported measure and some students might have overestimated their use of self-regulatory strategies (Young and Ley, 2005). Their paper states that questions about self-regulation could be difficult for poorly self-regulated students.

A year earlier a similar experimental design was employed in Italy among 135 elementary school students (Cornoldi et al ., 2015). By using regression analysis, the authors concluded that training in metacognition transferred positively onto students’ abilities to solve maths problems. Mathematical word problems are “complex cognitive tasks” (Cornoldi et al ., 2015, p. 434) and apart from mathematical abilities, children also need reading comprehension, metacognitive abilities, and motivation. In this experiment, not only were activities focused on metacognition, but the students reflected on their beliefs about mathematics. Referring to this study, Davey (2016) also emphasised the importance of metacognitive training programmes. Having conducted a case study, she claimed that the teachers’ actions and words are crucial in developing students’ metacognitive abilities.

Mutambuki et al . (2020) combined metacognition and active learning and by applying a quasiexperimental design investigated the influence of both on the first-year undergraduate students in chemistry courses. By active learning, the authors mean frequent questions, discussions, problemsolving tasks, etc. Such metacognitive prompts as planning, reflecting, developing self-awareness, and making adjustments were mentioned in this paper. The authors concluded that active learning implemented with metacognitive instruction impacted students’ results in General Chemistry, “particularly on cognitively demanding chemistry concepts” (Mutambuki et al ., 2020, p. 1832). Having 240 students in the control group and 270 students in the treatment group increased the validity of the findings. However, the two groups had different instructors with different teaching styles which could have influenced students’ learning in a course.

Belenky and Nokes (2009) took into account not only students’ performance but also engagement while using metacognitive prompts. Based on the questionnaires, low-achievers “showed better learning and transfer when getting metacognitive prompts” (e.g., How does the solution relate to what you did?) and high-achievers “showed better learning and transfer when getting the problemfocused prompts” (e.g., What is your goal now?) (Belenky and Nokes, 2009, p. 102). The study proves that manipulatives alone do not necessarily make students think and reason deeply, it is also the way they are engaged with them. Plus, students’ engagement does not depend on whether concrete or abstract materials are used.

As it was mentioned in the previous chapter, writing reflections can be met with resistance among learners. Though reflective journals are commonly used among researchers (O’Loughlin and Griffith, 2020; Ramadhanti et al ., 2020), there are other audio or video tools to record self-reflections and at the same time engage students, for example, Flipgrid (Flipgrid, Inc., 2021), an online video forum platform. Flipgrid was recently implemented as a pilot study in the USA (Kiles, Vishenchuk and Hohmeier, 2020). In 2019 about 30-35.7% of students wrote reflections in journals and in 2020 87-93.4% participated in Flipgrid forums. 96% of students preferred to record short videos instead of writing journals. The authors believed that the casual nature of Flipgrid might have motivated students to share deeper reflections. It was concluded that this online platform has the potential as “a self-reflection tool used in combination with other pedagogical techniques to facilitate learning” but the depth of reflections should be explored further (Kiles, Vishenchuk and Hohmeier, 2020, p. 4).

As for students, changes for teachers might be difficult too. To promote metacognition during math classes, a teacher should model it first (Knox, 2017). That is why it is important to have professional development about this topic. Many teachers do not see the connection between mathematics, reading, and metacognition (Tok, 2013). Tok believes that it’s essential to grasp reading and mathematical skills in order to succeed. Both Tok (2013) and Knox (2017) argue that classroom instructions usually pay more attention to content rather than analysing the problem-solving process.

Noteworthy research was conducted in the USA for a similar duration (4 weeks) (Siegle and McCoach, 2007). However, the sample in this experiment was even larger (872 grade 5 students) and the aim was to investigate whether teachers who are trained in self-efficacy will have a better effect on students’ performance. It was also organised with a control group and a treatment group, but the teachers had professional development regarding metacognitive support in the latter. As a result, the students from this group were more confident and it had a positive effect on their self-efficacy.

Therefore, factors that support metacognitive development are (1) attention to learning goals (Buzza and Dol, 2015), (2) constant self-assessment, (3) reflection using different tools, (4) applying one strategy at a time (Davey, 2016). Meanwhile, (a) predetermined curricula, (b) predefined answers to open-ended questions, and (c) ineffective classroom management (Greene, Costa & Dellinger, 2011) can decrease metacognitive development and educators should be aware of that.

2.5 How to measure metacognition?

There are different quantitative tools to measure metacognition: the Metacognitive Awareness Questionnaire (Schraw and Dennison, 1994), the Metacognitive Awareness Inventory for Children (Jr. MAI) B Form (Sperling et al ., 2002), the Motivated Strategies for Learning Questionnaire, (Valencia-Vallejo, López-Vargas and Sanabria-Rodríguez, 2019).

Wagaba, Treagust and Chandrasegaran (2016, p. 5379) argue that sometimes it’s hard to check how students are progressing metacognitively because most tests assess only cognitive abilities. Similar to the current study, action research was conducted but quantitative data analysis methods (Metacognitive Support Pre- and Post-questionnaires) were applied. Seventy-nine students took part in this study, but the number varied throughout the research cycles. Frequently, students reported that they didn’t discuss with their peers how they learned science because they either did not have an opportunity to do so or, as the authors stated, most of them were low achievers. The researchers concluded that some results could have been “misleading because many of the scales had generally high pre- and post- mean scores in the three cycles, therefore there was not much room to move up on the Likert scale” (Wagaba, Treagust and Chandrasegaran, 2016, p. 5392). They also believed that the 20-weeks cycle is too long to enhance the necessary changes and it is better to have the same topic and the same students in all three cycles. It is also recommended to find a better instrument to test metacognition in the classroom.

One of the tools to measure metacognition is called the Metacognitive Awareness Inventory for Children (Jr. MAI) B Form (Sperling et al ., 2002). This questionnaire consists of 18 items (5-point Likert-type scale). It was adopted while studying metacognitive abilities among 150 gifted and 150 non-gifted students (Ogurlu and Saricam, 2016). Researchers claimed that gifted students possessed greater metacognition which should be considered while creating lesson plans. However, they mentioned social-desirability bias as a common vulnerability in questionnaires. Valencia-Vallejo et al . (2019, p. 15) also underlined that “the subjectivity of students’ answers is a limiting factor of self-reporting questionnaires”. Thus, further qualitative research is needed to observe metacognitive awareness among young gifted and non-gifted students, and it proves the importance of the current qualitative study.

Another fascinating research was conducted in Malaysia among 378 students to show the correlation between metacognitive abilities and achievement in mathematical problem solving (Zakaria, Yazid and Ahmad, 2009). A Metacognitive Awareness Questionnaire, modified from the one created by Schraw and Dennison (1994), was used in this research to prove that the higher students’ metacognitive abilities, the higher their results in a Mathematical Problem-Solving test. However, Muscott (2018) questions the authenticity of the problems used in this test. Employing quantitative methods, he concluded that HoMs, particularly HoM 5 Metacognition, have positive effects on students’ performance outcomes but an assessment tool to measure HoM competencies is still required.

Qualitative measuring tools use the coding of responses. The codes will depend on student answers or the researcher’s interpretation of metacognition. Responses might be scored as high, medium, or low levels (Strauss and Corbin, 1998). Stanton et al . (2015) used students’ answers to make deductions about their levels of metacognition and developed a coding system as Sufficient/Provides Evidence or Insufficient/Provides No Evidence. 245 undergraduate students in the USA took part in this experiment. Researchers coded all answers individually. Then, they discussed all findings together and came to a consensus for the final coding. Following this model allowed the researchers to get some valid data. It was summarised that metacognitive skills had an effect on learners’ performance and what is more important would assist them to become more self-regulated students in the future.

These findings support the significance of metacognitive training as a heutagogical technique among teachers and students to enhance cognitive abilities and mathematical reasoning. There is some strong empirical evidence that metacognition has positive effects on students’ performance, specifically in mathematics. However, there is still not enough evidence to prove its importance in elementary school, especially from the students’ point of view, which validates the purpose of this qualitative action research. In the next chapter, the research design and methods to solve this problem will be discussed.

3. RESEARCH METHODOLOGY

This study aims to explore the perceptions of students on the heutagogical framework while teaching maths at an elementary school in Cambodia. The study focuses on some metacognitive elements that can assist students to become more self-determined.

Central Question: How can students’ needs be met using the heutagogical framework while teaching maths in an elementary school in Cambodia? Subquestion 1: What tools and strategies should teachers use to implement the heutagogical framework? Subquestion 2: How can metacognition as a heutagogical technique be used to improve students’ self-determination?

This chapter aims to explain the research design and methods that were selected as appropriate to research the issue related to the research questions.

3.1 Research design

A lack of qualitative action research in existing literature highlighted the need for this investigation into self-determination through metacognition at a young age. Compared to traditional experimental studies, action research is an amalgam of theory and practice (research and action) that “focuses on specific situations and localized solutions” (Stringer, 2007, p. 1). It is a compass leading teacher in the right direction and helping them see changes in their practice (Simon and Wilder, 2018). Action research is “grounded in a qualitative research paradigm whose purpose is to gain greater clarity and understanding of a question” (Stringer, 2007, p. 19).

Action research was promoted in the mid-1940s with the purpose to solve some practical problems in everyday life. The goal was to distinguish the problem, try to change the situation, and check the results (Coolican, 2014). Since the main purpose of action research is to improve the practice of education by studying issues or problems (Creswell, 2012), it was decided to choose this research design to align with the purpose of the study. Self-determination is like “mini action research”. It also has a cyclical model: setting goals, attempting to achieve them, self-assessing and making adjustments (Zimmerman, 2002). Metacognition itself has a cyclical model too: planning, thinking about it and making changes if needed, reflecting, and making new plans based on the results (Costa and Kallick, 2008). Thus, it was the other reason for choosing action research as a research design for this investigation.

The main attribute of almost all action research models is the cycles, specifically that each cycle is based on the conclusions of the previous cycle (Edwards and Willis, 2014) which “guides teacher preparation and instruction” (Stringer, Christensen and Baldwin, 2010, p. 1). Sometimes they are named spirals or helices (Punch and Oancea, 2014). Edwards and Willis’ (2014) model starts with reflection: Reflect – Plan – Act – Observe, while Stringer’s (2010) model commences with the observation cycle: Look – Think – Act. Even though it seems straightforward, it is not as simple as it looks. There are no arrows between them so it is not a linear process and the researchers can go back to any cycle when changes or adjustments are needed. The “Act” stage also includes reflection and evaluation. Reflection is the key characteristic of each cycle, and the results indicate whether changes should happen or an additional cycle or “mini-experiment in practice” is needed (Wagaba, Treagust and Chandrasegaran, 2016, p. 5378). Since its purpose is not just understanding the problem but finding the solution, it is a suitable form of research for this investigation. Moreover, Nasrollahi (2015, p. 18667) noticed that Stringer’s model does not only involve teachers but also students “as action researchers collaborating in the action research process”. It is a standard model that has been similar to hundreds of other models created in the last eighty years.

The present action research will include these research tools : interviews with students and observations using the researcher journal. The research questions that require qualitative data to investigate students’ views justified the qualitative approach of this study. Interviews (qualitative methods) show the complexity of the data provided by participants (Creswell, 2012). At the same time, some quantitative methods, such as questionnaires, can be “inappropriate because of the child’s age” (Morison et al ., 2000, p. 113). Qualitative methods and students’ involvement can provide more light on heutagogy in elementary schools and explore any misconceptions.

3.2 Setting and participants

Metacognition is one of the sixteen Habits of Mind (Costa and Kallick, 2008) adopted by the participating school in Cambodia. Thus, it provided an ideal setting to apply action research on metacognitive support in mathematics. Secondly, being a subject coordinator allowed the researcher to take action and adapt the math curriculum using metacognition as a heutagogical tool. Stringer (2007) underlines that conducting action research helps in curriculum construction and evaluation. Finally, as a participant-researcher, the researcher had a chance to work closely with the participants and gather data during math classes.

Previous research in self-determination in elementary school is mostly from the teachers’ (Stein, 2018) or school administrators’ points of view (Akyildiz, 2019) which indicates the need for the present study. Earlier, children were treated as “dependent” on others to guide them on what to do (Elden, 2013, p. 78). Later, Arnold and Triki (2017) argued that children might be participants in experimental research, however, the chance exists that students would only say what they think researchers want to hear instead of their honest statements. It is understandable that writing a high-quality study with children may be a noteworthy challenge (Ponizovsky-Bergelson et al ., 2019), yet open-ended questions and encouragement can elicit some valuable data. Hoover (2018) recommends using short semi-structured individual interviews while working with young children. Semi-structured interviews “have in-built flexibility to adapt to particular respondents” (Punch and Oancea, 2014, p. 184) which is also preferable for interviews with children. Punch also suggests having natural settings and making sure that the language is age appropriate. All these recommendations were taken into account during this study. Interview questions can be found in Appendix III. Each interview with each student was not longer than 15 minutes, with three interviews during the experiment (the beginning, middle and end of the unit). Interviews were conducted via Google Meet, the platform used at school during online learning.

23 grade three students (9-10 years old) and their parents were informed about this research. 15 of them returned the signed consent forms, 8 parents did not reply to the email sent, so their children were not involved in research. In the end, 7 boys and 8 girls took part in the study.

All the students were Cambodian. Their native language is Khmer (the official language of Cambodia). The interviews were conducted in English as this is the language they use to study at this International School. This language barrier is why math in English might be particularly challenging and metacognitive strategies might be beneficial to them. All interviews were transcribed verbatim by the researcher.

Consent forms were sent on April 28, 2021, as soon as permission was granted by ERGO. Parents were called by the academic assistant from the school who informed them about an email sent. As soon as some consent forms signed by parents were returned, consent forms were sent to their children. Observations began as soon as both parents and students signed the consent forms. The first interviews were held on the same or following days as soon as the consent forms were returned:

29/04 : S2, S3, S13, S14 03/05 : S17, S21, S22 04/05 : S16, S23 05/05 : S5, S7, S8, S12, S19 07/05 : S20

The second round of interviews was held on June 17-21. The third round was recorded on June 14- 15, 2021.

3.3 Data collection

The experiment lasted 9 weeks starting on April 29 until June 30, 2021. Three cycles of Stringer’s model were incorporated into three phases of instruction (Stringer, 2007, p. 9, fig. 1.1).

PHASE 1: PLANNING

1. LOOK (3 days)

Consent forms are sent to parents and students ( Appendices I and II ). The first semi-structured interviews with some students are recorded. Field notes are taken every day.

This first stage allows the researcher to collect data about participants’ perspectives and to define the problem.

2. THINK (1 week)

Data are organised, the answers are coded and analysed, and observations continue during this time. Metacognition Diaries (MD) and the final assignment that incorporated metacognition elements are created based on the results of the interviews and on the theory of the process of metacognition which consists of three dimensions – commitment, value, and capacity (Costa and Kallick, 2008). Even though the authors presented five dimensions in their book, and they are discussed in the previous chapter, the core of this study constituted only three dimensions. First, HoMs are included in the school curriculum since kindergarten, it is assumed that by grade 3 most of the students should know the meaning of 16 HoMs, thus, Expanding Meaning as a dimension was not covered by this research. Secondly, considering the age of students and the time constraints it would have been overwhelming for students to reflect properly on all five dimensions at the same time. Since the focus of this paper was self-directedness through metacognition, Increasing Alertness as a dimension was not included in this study.

3. ACT (1 week)

MDs are shared with the students in Google Classroom (Appendices VI, VII, VIII). The final assignment is explained to students (Appendix IV). Before being given to participants, MD and the final assessment were examined by our school curriculum coordinators who supported that both assignments can be used to monitor students’ metacognitive growth.

The Flipgrid platform is introduced to students. Students have a choice to either complete MD in Google Classroom or answer these questions by recording videos in Flipgrid (video diaries). To set the tone of reflection, at the end of each math lesson students have five to ten minutes of “silent thinking time” where they have a chance to reflect and answer the questions in the diaries or record the videos. Observations continue during this time. Organisational skills are taught by using checklists.

This part of implementing practical solutions distinguishes action research from other types of research. Stringer (2007, p. 142) calls it “the sharp end of the stick”. This is the part where the action happens.

PHASE 2: INSTRUCTION

1. LOOK (1 week)

The second semi-structured interviews are recorded to check what modifications should be made. Observations continue during this time. MDs and Flipgrid Videos are checked by the researcher. Most of the student answers in the diaries are short and not specific. Multiple students do not stay online until the end of the class and do not complete the MDs or do not record the videos.

Answers are coded and categories are added or modified. Observations continue during this time. Reasons for students leaving online classes early could be family circumstances, bad Internet connection, no interest in the topic, other distractions. Student answers might be improved by providing more scaffolding and teaching how to set goals, how to monitor learning by using checklists and rubrics, how to take notes, etc. The benefits of reflections should be discussed with the students.

3. ACT (2 weeks)

This cycle takes longer because it is necessary to spend more time on interventions. All math lesson plans are modified and include metacognitive elements (Appendix V), namely goal-setting, selfassessment, peer feedback, HoM Discussion, assessing using a rubric, exit tickets, note-taking, post-assessment. Not all lessons include all these elements at once because of time constraints. It is decided to add metacognitive elements in the beginning and middle of the lessons so that all students have a chance to reflect before they leave the class. Observations continue during this time.

PHASE 3: EVALUATION

The third semi-structured interviews are recorded on June 14-15 and observations continue during this week. All lesson plans continue to have metacognitive elements and students continue to write MDs or record video diaries on Flipgrid.

Final interviews are analysed. Student MDs, videos and observation notes are reviewed, final codes and categories are added, the strengths and weaknesses of the experiment are identified. All core categories, abstract concepts and specific indicators were organised in a spreadsheet.

3. ACT (3 days)

General and brief results were discussed with colleagues during the subject meeting at the end of the school year. These continuous cycles of looking, thinking, and acting allowed the researcher to identify the necessity of metacognition as a heutagogical technique in fostering self-determination in young students.

3.4 Data analysis

Metacognition is not only about planning and knowledge activation but also the intentional monitoring of students’ cognitive processes, reflection, time management, and self-evaluation. That is why the participants frequently had chances to set goals in using HoM 5 Metacognition, self-reflect on whether they achieved those goals, monitor their progress in solving math problems, reflect on their progress using the rubric, apply different strategies in solving word problems and reflect on them. These topics were observed by the researcher and discussed during each of the three interviews. The analysis began after the data was collected from the initial interviews, starting from April 29, 2021, as soon as some parents and students returned the signed consent forms. From that point onwards, data collection (from the following interviews and field notes) and analysis occurred simultaneously. This approach has become a regular practice in qualitative research (Charmaz and Belgrave, 2015).

In order to understand the context, Stringer (2007, p. 100) suggests researchers should start with interviews and then move to other sources of information in the next cycles of action research. Observations written in the research journal were held during all three cycles of action research. The focus was on behaviours related to self-determination, particularly the metacognitive skills related to goal-setting, self-reflection, reflecting and monitoring the progress in solving math word problems, and the emotional aspect after solving problems (feeling of difficulty, feeling of confidence, etc.). As soon as the student showed some evidence of applying metacognition, it was recorded as a memo or a sentence. Thus, the protocols were kept for each student who signed the consent form. Observations were overt since both students and parents were asked to give their consent before the beginning of the study. The primary data were derived from interviews but observations further clarified or extended understanding of the issue being investigated. Punch (2014) underlines that combining interviews and observations is a good method that can lead to high-quality data.

Students’ interview data, as well as observation notes, were coded and analysed using a grounded theory approach. Creswell (2012) believes that it helps the analysts remain close to the data during the whole process. Codes and themes were developed, and connections were identified between different themes in order to generate conclusions. Based on the systematic design of the grounded theory, there are three types of codes represented diagrammatically by Punch and Oancea (2014, p. 238, fig. 10.4):

a) substantive (or open coding) is done at the beginning of the analysis to generate more abstract concepts, b) theoretical (or axial coding) to see how data is interconnected, and c) core (or selective coding) concentrates on core categories around which the theory is designed.

Charmaz (2006) emphasizes that it’s not a linear process and a researcher can go back to the initial data and make new codes at any moment of action research. Moreover, the grounded theory implies that the experiment doesn’t commence with an already formulated theory but rather “allows the theory to emerge from the data” (Strauss and Corbin, 1998, p. 12). Analysts are encouraged to (a) remain open to various opportunities, (b) produce a few options, (c) investigate different opportunities before selecting one, (d) use cycles to go back to the experiment and get a new vision, (e) believe in the study, (f) circumvent shortcuts, (g) enjoy the research (Ezell, 2017, p. 72).

Information was collected, analysed, and compared until data saturation was achieved.

3.5 Ethics and risk assessment procedures

The approval to conduct this research was confirmed through the Ethics and Research Governance Online system of the University of Southampton. In order to start the study, it was obligatory to obtain confirmation. After that, the potential participants and their guardians were invited to take part in the study via email.

First, the Board of Directors of the participating school were informed about the study. Since the children are 9-10 years old, the consent forms were first signed by students’ guardians and after that, if the parents approved, they were sent to students. Both the guardians and the participants agreed that the interviews will be recorded. Confidentiality was guaranteed to all participants. The participants had the right to withdraw from the interviews at any moment before June 30. Personal information was anonymised during the transcription process and coded as Student 2, Student 3 etc. Since February 20, all schools in Cambodia moved to online learning, thus, both interviews and observations took place via Google Meet. Only the researcher had access to the audio-recorded data which were held on a University of Southampton file storage space and were destroyed after the transcriptions were complete. The transcribed interviews and the observation notes were stored on a password-protected University of Southampton file storage space too.

3.6 Validating findings

To avoid an incorrect interpretation of data, multiple methods of qualitative data collection should be used (Oliver-Hoyo and Allen, 2006). The accuracy of the findings was validated through the triangulation analysis:

– interview with students, – observation notes, – literature review.

Triangulation of data ensured the chosen key themes, providing an insight into self-determination from the students’ views. Punch (2014) also suggests getting feedback from responders. After the interviews were transcribed verbatim, the participants were asked to check them. Triangulation and member checking are the most common validation techniques (Creswell, 2012).

In the next chapter, the results of qualitative action research will be presented.

4. FINDINGS

4.1 overview of the chapter.

Using an action research framework, it was investigated how engaging in reflection can change grade 3 students’ behaviour, making them more confident in their abilities to solve mathematical tasks and motivating them to be more active and consistently remain self-determined. Data was collected over a period of 9 weeks from April 29th to June 30th, 2021 during a lockdown (all classes were online). The data analysis stage was conducted concurrently with data collection during the three cycles of action research.

This chapter presents the data collected during the interviews with the participants and the observation notes collected by the researcher while teaching mathematics. The participants were 15 grade 3 students (9-10 years old) in one of the private schools in Cambodia. The responses and the field notes were grouped into categories and analysed to answer the research questions.

Core categories, abstract concepts, and specific indicators (Punch and Oancea, 2014) were selected. Having analysed all interviews, it was clear that open coding and deductive analysis did not answer the research questions because they focused more on the categories selected rather than how students developed their metacognitive knowledge and skills throughout the unit. Therefore, during the axial and selective coding, inductive analysis was conducted, new codes were created based on the previous analysis.

The following core categories were decided on during the analysis and were based on the Habit of Mind Dimensions of Growth by Costa and Kallick (2008):

A. Commitment (ability to self-assess, self-direct and self-monitor in their development of HoM 5 Metacognition within the unit) B. Value (ability to recognise the benefits and advantages of engaging in the HoM 5 Metacognition) C. Capacity (ability to develop skills, strategies, and techniques through which they engage in the HoM 5 Metacognition within the unit)

Each core category covered three to five abstract concepts. The specific indicators are the same for each abstract concept in each category and coloured accordingly:

• Indicator 1: not attempting to do (red).
• Indicator 2: attempting to do (yellow).
• Indicator 3: able to do successfully (green).

After reading each student’s response, it was categorised to a core category and then assigned to an abstract concept. After that, it was colour-coded based on the indicators above (Appendix IX).

4.2 Core category: Commitment

In general, most of the students showed the development of metacognitive knowledge. Four abstract concepts were defined during the analysis based on students’ responses:

1) Setting goals 2) Self-questioning 3) Self-monitoring 4) Responding to feedback

Table 1: Core Category Commitment – Overall Picture during 3 Phases

* Major improvement – moved from red to green indicator. * Minor improvement – moved from red to yellow indicator or from yellow to green indicator. * Stay in red – did not show any progress. * Stay in yellow/green – already had good self-determined skills at the beginning of the research.

More examples and notes can be found in Appendices X – XIII that complement Table 1.

4.2.1 Setting goals

It is interesting to find out how all students understood and could define the importance of setting goals during the first interviews but most of them did not set goals in mathematics or did it only when teachers asked them.

After completing the tasks with the metacognitive elements, some students shared their views on how goals helped them:

“don’t give up and try to solve a problem” (S17-P3), “know what to do and you will not lounge, so you’ll be better” (S5-P3), “learn and stay happy and, like, don’t get bored of learning” (S13-P3).

However, according to the field notes Students 5 and 17 were not persistent in achieving their goals during the unit. Other students believed that it was not necessary to set goals because they did not have time to do them (S20), or they were not important in maths because “you don’t have to calculate” when you write goals (S23-P3). Student 7 did not set any goals because she forgot about them. Based on the observation notes, she also missed some classes or did not complete most of the metacognitive activities before the third interview was held.

4.2.2 Self-questioning

The analysis of the interviews highlighted the importance of self-questioning. Some students were consistent throughout the unit and shared some questions they asked themselves: “is this answer correct” or “have I filled the checklist” or “do I have to start over again?” (S8-P1).

Others claimed that they did not ask themselves questions (S5-P1). However, during the last interview, they mentioned the importance of self-questioning “because if you don’t ask yourself, you might don’t know what to do” (S5-P3) or referred to past knowledge “because you can ask yourself…or just get some ideas from the past” (S20-P3). While during the first interview Student 3 said she would rather wait for the teacher to ask questions, later she noticed “my PT [Performance Task] is not that good so I change my PT, and so I ask question, ‘how good is my PT?’ “ .

Another theme that emerged from the interviews is the lack of persistence: “I ask, ‘what do this task do?’ and sometime even I don’t understand… but sometime I guess” (S22-P3), or “I ask myself ‘Really?’ and go back and sit one more” (S7-P3) or the students simply replied they did not ask any questions (S2). Some participants claimed that they preferred to ask other people because “I don’t know about myself” (S12-P3).

4.2.3 Self-monitoring

Out of all the concepts, this was the only one where all students showed improvement by the end of the unit which is an important sign of self-directed learning. Starting from not using the diary “because I forgot about it” (S14-P1) to using it to find the unfinished assignments “When I go to checklist they will have a link to go in the work for math… it help us know what work that we still haven’t finish” (S14-P2). Field notes show that Student 14 participated more in the middle of the unit. According to the data collected from the interviews, Students 2, 3 and 16 already had good self-monitoring knowledge since Phase 2.

It was thought-provoking to listen to what students think about using rubrics ( Appendices IV and V ) and self-assessment in maths. Most of the participants highlighted that it was useful to have rubrics in the Metacognition Diaries:

“so Teacher can know which task they don’t really understand” (S22-P3), “students write goals and look at rubrics to see what their grades and grade theirself and do important stuff on it” (S3-P3),

On the other hand, some students pointed out such issues as dishonesty, inability to use the rubric without knowing the correct answer, and overconfidence. Student 21 (P2) mentioned that some students might not be honest when they grade their own work: “they want a perfect score and then when they’re bad they just put four and they’re saying that, ‘I’m good, I’m good’ “ . Student 19 (P3) pointed out that it is difficult to use the rubric when you do not know whether the answer is correct or not: “So, when kids do it, no one, he or she in the PT cannot predict if they’re correct or not” . And during Phase 2, he mentioned that he used the rubric when the teacher projected it but not on his own initiative “when you just post the assignment with the rubric under it, it’s very hard for you to make me watch rubric” . Student 20 (P2) also underlined that “it’s kinda helpful if you’re not good, but if you’re good already, you always grade yourself four, I think it’s not really that useful” .

4.2.4 Responding to feedback

This abstract concept was mostly based on the observation notes because students were not asked about feedback during Phases 1 and 3. The planning for the interviews was not done properly. The list of selected questions differed during three Phases. Students were asked specifically about feedback during Phase 2. After the analysis was done, it became evident that they should have been the same questions in all three Phases.

What some students said in the interviews did not match their behaviour during the observations. I believe it happened because they probably wanted to say what they thought the teacher would want to hear or they wanted to present themselves in a positive light (social desirability bias). For example, Students 17, 21 and 22 said that they often checked the feedback in Google Classroom but based on the observation notes, they did not reply to them. Having read the questions that the researcher asked about feedback, some of them could have been reworded or asked indirectly (how a third party would behave) so that students do not feel embarrassed. It proved to be effective while interviewing Student 23:

“Researcher: What advice would you give to students who just finished grade two and are moving to grade three? … Student 23: … I recommend them to use, study more math, use more link and make sure that do more work than me, ‘cause I never do my work. Researcher: Why not? Student 23: You don’t remember at the last interview I said. I’m lazy, but now I do. Researcher: I remember you said so. Student 23: But now I do it.” (P3)

Most students understood that they had to check teacher’s comments and correct their mistakes “If I get feedback I try to make it better, for example, the math what is perimeter, I always do it then you always feedback me, that time I had [a perimeter of] more than 24 and then now I have [a perimeter] over 40” (S20-P2). Some of them checked and replied to comments frequently: “I check on the private comments and I finish some of your private comment and then after, later I will do the next comment and then after that I turn in the work” (S8-P2). Observation notes confirm this data too.

Other students explained why they did not respond to feedback. They either missed the notification “sometime I didn’t see my email to me” (S12-P2) or they were overwhelmed “I have a lot of email and then it comes a lot of email now” (S16-P2), or they still do not understand the feedback “sometime I just don’t understand the question” (S13-P2), or they forgot about it “sometime I forgot” (S14-P2). All these reasons are understandable for grade 3 students who moved to online learning a few months ago. When the students were studying onsite, real-time feedback was provided every day during classes. For example, when students completed a task, the teacher would return their notebooks and they had a chance to ask questions for clarification in person.

Even though some students understood that they could have asked for feedback “Maybe I can ask for feedbacks or I just, when I’m offline or I don’t have anything to do, I’ll just try a little more” (S7-P1), they could not identify why they had not responded to it: “sometimes I just miss it” (S7-P2).

4.3 Core category: Value

In general, most of the students showed the development of metacognitive experience. Three abstract concepts were defined:

1) Making connections to real life and the future 2) Giving advice to other students 3) Emotional aspect after solving problems

Due to the subjective nature of this core category, it was not quantified as the other two.

4.3.1 Making connections to real life and the future

Almost all students could have connected the unit to real-life or to the future starting from the first interview, so these questions were not asked in further interviews:

“I know how to measure, like, when I don’t have a standard unit, I can use the non-standard unit” (S2-P1); “we learn about litres… so, as a scientist, we have to put portion… to invent something” (S8-P1); “because my parents own a business… they just [bought something] from China and we measure the stuff” (S13-P1).

Students who did not make clear connections between reality and the unit did not participate actively in class. They mentioned some general math connections, e.g., counting money (S5), multiplying something (S7) or calculating the cost of the units (S22) which were not relevant to the current unit.

4.3.2 Giving advice to other students

The purpose of this concept was to see if students can apply self-directedness to external situations.

When students were asked to recommend something to children who are moving to grade 3, these themes emerged:

• Use HoMs when solving difficult problems “Persisting and Apply Past Knowledge to New Situations and Listening and Communicating with Clarity and Precision” (S8-P3);
• Watch the recorded lessons and Youtube videos “I will tell them what to watch in the YouTube to help them a success in grade three” (S16-P3);
• Read more books (S14);
• Do extra research “search more about shapes and math because when you go to grade three, now you will learn about the fractions and rhombus, new shapes” (S20-P3);
• Ask questions and no copying (S21);
• Review difficult topics before studying in grade 3 (S22).

4.3.3 Emotional aspect after solving problems

This was the only abstract concept that was not colour-coded based on the specific indicators as they were not applicable here. The purpose of this concept was to observe whether emotions can have some effect on metacognition and self-directedness in general. Students were asked about their feelings directly during the interviews and some of them were also inferred from their answers or observations.

This category explained the answers to other categories. For example, a lot of Student’s 2 answers were simply “No” or “I don’t know”. Thus, in some cases, this lack of persistence could have contributed to less self-questioning and less note-taking.

Students 5, 8 and 20 did not get sad when they made mistakes (P1). They said it was a chance for them to improve more. However, as observation notes show, Student 5 lost his motivation during the unit and did not complete most of the graded tasks. Reasons might be different: family circumstances, no ability to become independent and control his learning or even that it was the last unit of the year, and he was simply tired. Meanwhile, Students 8 and 20 were developing their metacognitive knowledge and skills. Thus, while these reasons helped some students, they hindered others.

During Phase 3, Student 7 was worried that she did not complete most of the tasks, but she also did not ask for help during the unit and missed a lot of online classes. Same as Student 14 who could not identify the difficult topics and thus, could not make an improvement plan. It is possible that lockdown impeded teachers’ ability to reach out more to students in need. In order to help students who struggle, the teacher could have initiated some interventions to learn more about the students’ circumstances.

Student 12 could identify the difficult parts of the unit and was very persistent to learn these topics. Her answers for goal-setting, strategies and self-monitoring concepts, and the observation notes combined into a complete picture to show improvement in self-directedness, similar to Student 13 who also showed enthusiasm to study more on her own. These are the students who were doing well before lockdown and continued doing well during online learning.

4.4 Core category: Capacity

In general, some students showed the development of metacognitive skills. Five abstract concepts were defined:

1) Connecting metacognition to math 2) Applying different strategies when solving problems 3) Asking for help when needed 4) Taking notes 5) Improvement strategies

Table 2: Core Category Capacity – Overall Picture during 3 Phases

* Major improvement – moved from red to green indicator; * Minor improvement – moved from red to yellow indicator or from yellow to green indicator; * Stay in red – did not show any progress; * Stay in yellow/green – already had good self-determined skills at the beginning of the research.

More examples and notes can be found in Appendices XIV – XVIII that complement Table 2.

4.4.1 Connecting metacognition to math

About half of the students were able to connect metacognition to math at the end of the unit. Students could recognise the purpose of using Metacognition Diaries in class:

• to understand the meaning of the HoM (S21-P3),
• to help set goals and self-assess (S17-P2),
• to talk about feelings, improvements, and plans (S16-P2),
• to make it more challenging (S13-P3).

Student 12 connected it to the lesson when she solved word problems about time “because I really struggling about time so I need to think if I go backwards” (P3). Student 8 made a connection to the lesson about perimeter “so that we can express our opinion of our commitment over doing those tasks.” (P2). Student 23 recognised her internal doubts and uncertainty and understood that they need to be eliminated:

“I think about my thinking because if we don’t think about our thinking, for example, I think to do my work, but my mind, my half-mind say don’t know. So, it’s still no. Researcher: So, what do you do then? Student 23: I make that mind go together to get along.” (P3)

Some students still did not see a clear connection to math and said they only used it when completing Metacognition Diaries (S2-P3), when the teacher asked to do the tasks (S19-P2), or when recording videos in Flipgrid “I need to think what I need to say” (S20-P2), “it really help not to always write, we need to talk to people, to not be shy, to show your feeling and your answer, so, I think it’s good” (S13-P2). The students who completed only 1 Metacognition Diary or did not write at all (based on the observation notes) did not see the importance of thinking about their thinking:

“I didn’t think of that” (S14-P3), “I don’t know how to answer this question” (S5-P3), “I do not understand the HoM yet. It’s kind of difficult.” (S3-P3).

4.4.2 Applying different strategies when solving problems

The following strategies were mentioned during the interviews:

• asking the teacher or listening how it was explained to other students (S3);
• asking other family members (S21)
• Striving for Accuracy (S5);
• Persisting (S16);
• Thinking Flexibly (S17, 22);
• Applying Past Knowledge to New Situations (S20).
• completing the shortest tasks first: “Because I was like, ‘What, I still have more task?’, so I have to go do the small task so when I did the small task I will do the long task later” (S8-P2);
• finding clues and drawing a model: “First, I need to find clues. And the second, I try to do a model but drawing a model is very easier” (S12-P1);
• using a calculator (S13).

Five students showed some improvement during the unit. The rest of the students stayed on the same level as they were in the beginning and could not identify any strategies (S2, 7, 14) or said they would just guess the answers “sometimes following your gut you get it right” (S20-P).

I think this concept was not developed well during the unit. The prepared lesson plans did not include any specific strategies to help the students because of time constraints.

4.4.3 Asking for help when needed

Most of the students stated that if they did not understand the problem, they would ask their teacher (S3), family members (S21) or friends (S5).

Even though some students said during Phase 1 that they did not ask anyone “I do not need someone to help when it’s math” (S2), later they mentioned they would ask their relatives if they did not understand. Student 14 remarked that he was scared to ask the teacher “because I ask too much” (P1) and observation notes indicate that he rarely asked for clarification during the unit. This lack of confidence could have hindered his metacognitive skills.

Some students noticed that before solving some problems on their own, they would ask someone to help (S7, 8). Maybe studying at home during the pandemic is the reason for it. Meanwhile, Student 13 mentioned that she would try to solve the problem by herself first and then she would ask someone if needed “or when they’re not home, I would try to research a bit” (P2). Student 20 (P3) also mentioned that he would research by himself before asking anyone. During Phase 1 and 2, Student 22 understood that she needed to ask the teacher more often “but sometime I didn’t ask about, I just do it” . During Phase 3, she stated that she asked the teacher when she needed help which is also mentioned once in the observation notes.

4.4.4 Taking notes

Most students understood the purpose of taking notes: “we take a note and then when we go back to try finishing [a problem], we can copy instead of wasting our time on thinking too long” (S7-P1). However, based on the observation notes, this student did not follow her own advice. During Phase 3, she stated that she only noted on her whiteboard which tasks she had not finished yet. When students were asked to give a piece of advice to their younger peers, Student 13 (P3) suggested watching some videos on YouTube because “mostly people just watch it for fun, not education … so when they have free time they can watch it and take a lot of notes from the video and what do they understand from the video” . She also mentioned that she did not take any notes during Phase 1 and used to forget many things but during Phase 2 she took some notes in order to prepare for the quiz. It was interesting to see how one student understood that he needed to work on controlling his emotions during classes and mentioned that he took notes to remember it (S19).

Students shared how and when they took notes during this unit:

• Whiteboards “Because if you do it like that, the answer is correct” (S2-P1). However, later he said, “I don’t know why I need to take notes” (P3). Similar answers were provided by Student 3.
• Sticky notes “when you show example of one of the EQ [Essential Question], I have to go on the notes and write what you said, so when I go back to my EQ, I know what I, I can learn off that example” (S8-P3).
• Notebook “get notebooks that I write lessons inside” (S12-P1).
• Google Docs or Slides “when we did the clock hand I get a paper and then I write about the short hand and long hand and for this end this unit, for the polygon, I also write it in a Docs” (S16-P3). Meanwhile, during Phase 1 she remarked that she usually forgot to take notes.

Other students mentioned that they took notes when the teacher told them to do it but did not show the initiative themselves “maybe I’m not sure about this, maybe it’s wrong and why did I take note about it if it wrong” (S12-P3). Based on the interview and observation data, some students (14 and 17) did not show any improvement in this concept.

4.4.5 Improvement strategies

Generally, students could identify some specific improvement strategies, such as:

• watching videos on Youtube or the recorded lessons (S12),
• playing online games connected to the topic (S14),
• applying HoM’s Listening with Understanding and Empathy (S17), Creating, Imagining and Innovating (S19) and Applying Past Knowledge to New Situations (S20),
• asking more questions and participating during classes (S19).

Some students shared the view that they would like to have Metacognition Diaries when they study in grade 4 so they could set goals for improvement (S12). This student also said she would do the same extra activities as she was doing in grade 3. Even though she felt they did not help much, she could not identify how to change the situation. A quiet environment when studying online was also mentioned in one of the interviews (S13). In the previous interviews, this student also said she could have asked her family to prepare some extra tasks for her to practice or set a goal to improve. Student 20 emphasised that it was important to know what topics and PT we would study in advance so that he could prepare better.

Changing Behaviour

Another theme that emerged from the interviews was changing behaviour. One of the problems was joining online classes on time. Student 23 started to ask her grandmother to wake her up so she would know how to do the assignments. Student 3 wanted to stop doing the tasks without thinking. To change the situation, she would “[ask] in Hangouts and then just try to do it, one by one and be careful” (P3). Meanwhile, Student 2 could not provide explanations for how to change his behaviour.

Other students either could not define whether they needed to change anything (S5 and 7) or did not specify any improvement strategies apart from “practice about the lesson that I don’t understand” (S22-P3). Student 22 also did not feel she was getting better because she said she did not understand maths. Observation notes show that she missed a lot of classes or did not do the prepared tasks. Finally, some students underlined that they wanted to study at school because they did not have enough materials at home (S20).

These findings are thought-provoking and will be discussed further in relation to academic literature in Chapter 5.

5. DISCUSSION AND CONCLUSION

5.1 overview of key findings.

The research question of this study: How can students’ needs be met using the heutagogical framework while teaching maths in an elementary school in Cambodia? By students’ needs we mean self-determined learning needs. Following the Self-determination Theory (Ryan and Deci, 2000) and the findings from the current research, it is possible that students’ basic needs – autonomy , competence , and relatedness – can be met using the heutagogical framework while teaching maths in an elementary school. Having a choice in choosing their goals, self-monitoring, taking notes and connecting metacognition to maths, eight students were able to control their learning process. Competence was practised by applying different strategies when solving problems and reflecting on improvement strategies. Relatedness was achieved by responding to feedback, self-questioning and asking for help when needed. The data were obtained from 45 interviews (3 phases – 15 interviews each) with students and constant researcher’s observations during online classes for 9 weeks. The data presented in this action research have shown that some metacognitive strategies are necessary at elementary school from students’ perspectives.

Students’ answers were grouped into three categories: Commitment, Capacity and Value – three dimensions of Habits of Mind developed by Costa and Kallick (2008). The majority of students showed improvement in the Commitment category: they often set goals for improvement, questioned themselves and monitored their learning. The results showed that most of the students found them useful, especially when studying at home. Less than half of the students showed the development of metacognitive skills in the Capacity category. Most of them already had some skills before the experiment started (e.g., some strategies for solving problems, improvement strategies, and asking for help when needed). The Value category represented how students developed their metacognitive experience and supported the finding of the previous categories.

5.2 Research outcomes in the framework of existing literature

The findings of this research have several themes that have been discussed previously in the literature review.

Research subquestion 1: What tools and strategies should teachers use to implement the heutagogical framework?

It was found that the following tools and strategies were used to implement the heutagogical framework:

• goal-setting in Google Classroom (at least once a week),
• using checklists, rubrics and self-assessments to self-monitor,
• note-taking,
• discussions at the end of the class,
• recording video diaries on Flipgrid to share strategies implemented during the day and/or completing Metacognition Diaries.

Goal-setting

According to the findings, most students started setting goals regularly during the unit and found them helpful in mathematics. The data reported in this study support the results of Erwin et al . (2016) who claimed that self-determination in adults and children is different, but that some elements can be practised in elementary schools, namely goal-setting. They developed a model with four steps: assess, select, try it, and reflect. The focus was on goals and reflection strategies which promoted good results and consistent communication between parents and teachers. Goal-setting can eventually help students become independent. The learning goal orientation might be a starting point in training self-determination (Compagnoni, Sieber and Job, 2020).

Students who showed high metacognitive knowledge and skills since the first interview noticed that rubrics were not as useful for them as they used to score high and did not feel any improvement. Other students also highlighted that some students might not be honest when they self-assessed and in that case, it was not beneficial. These disadvantages were previously discussed by Jamrus and Razali (2019) who believed that these constraints could be overcome if proper instructions and observations were conducted by a teacher. Moreover, rubrics should challenge students’ abilities, but rubrics’ language should be age-appropriate (Costa and Kallick, 2000).

Another self-monitoring tool that the students used was the checklist. Organising the thought processes and refining the thinking skills is essential for lifelong learners (Knox, 2017). Students found the checklist convenient while studying at home because they could quickly find the tasks and self-monitor. Nidus and Sadder (2016) emphasise the importance of teaching this art of noticing at school. They believe that when students learn how to use the checklist, they can focus on specific tasks, set goals for improvement, thus ask for more detailed feedback and evaluate their progress. The findings of this study about feedback support the results of a quantitative study of Molin et al . (2020) who found that there are positive effects of feedback from teachers or peers on both students’ metacognitive skills and motivation. According to them, responding to feedback is a key element of self-determination. Even though the findings for this specific abstract concept are not complete as the students were not asked about feedback during all three phases, it is still important to take their responses into account, specifically the ones connected to the lockdown.

Metacognitive Diaries (MD)

MD – reflective journals – as a tool of students’ self-assessment positively influenced students’ metacognitive experiences. Knox (2017) recommends journal writing and writing through the problem-solving process during math classes to define students’ mental processes while gaining knowledge. Following the action research framework in this study, students’ reflections were reviewed, and notes were made about their progress. It was also interesting to observe how some reflections reported in the Findings chapter moved from superficial to in-depth in Phase 3. By in-depth reflections, Costa and Kallick (2008, p. 235) mean “making specific reference to the learning event, providing examples and elaboration, making connections to other learning, and discussing modifications based on insights from this experience” . While most of the students from our study reported that they would like to have MD in further grades because “we can tell about the goals that we want to achieve and we can tell how we feel to the teacher and the score that we give to ourself if we give ourself a low score, the teacher will know that we don’t really understand it” (S16-P3), three students did not want to have MDs when they move to grade 4 stating that – “I can think of by my own and then study” (S2-P3). Recent research with elementary students supports the previous findings with university students (O’Loughlin and Griffith, 2020) and illustrate that not only students’ metacognitive skills were affected but also teachers had evidence of how students progressed during the unit. A similar experiment with reflective journals was recently designed in Indonesia (Ramadhanti et al ., 2020). However, the questions in that study were grouped around such aspects of metacognition as awareness, evaluation, and regulation. Fifty students who were involved in Ramadhanti et al. (2020) study went through these processes and were able to become independent learners.

Video Diaries (Flipgrid)

Flipgrid (Flipgrid, Inc., 2021) was used as an alternative online video-response tool to self-reflect and facilitate discussions. Students were already familiar with the concept of journaling. This app was used as an alternative to MDs to increase students’ engagement. Students had a choice of how to answer metacognition questions: writing MD, recording a video on Flipgrid or both. Most of the students reported that they enjoyed using the app because it was something new and they could show their feelings, but student engagement has not dramatically increased. The findings of this study differ from those reported by Stoszkowski, Hodgkinson and Collins (2021) which indicate that participants provided more frequent and more critical answers when using Flipgrid. Although, it might happen because older students took part in that experiment, or the differing amount of scaffolding provided by teachers in various studies. Educators should understand that this platform is not a “magic bullet” to increase participation (Kiles, Vishenchuk and Hohmeier, 2020, p.1).

Research subquestion 2: How can metacognition as a heutagogical technique be used to improve students’ self-determination?

It was found that metacognition as a heutagogical technique might be used to improve students’ self-determination.

The findings of this study are in line with previous literature (Gourgey, 1998; Costa and Kallick, 2008). It proved that students who did not have a habit of thinking metacognitively might not show a lot of enthusiasm in the beginning, especially if they had been passive learners for some time. Panadero (2017) believes that interventions have different effects on students because of their educational level. Moreover, the learning environment played a significant role in developing metacognitive capabilities in mathematics, especially in the current lockdown situation. On the other hand, some students were able to recognise other HoMs during the interviews or even spontaneously during classes, according to the observation notes. The creators of HoMs believe that it is one of the strategies that students can use to build deep reflections in order to become lifelong learners (Costa and Kallick, 2008).

During our maths lessons, some students were able to choose what strategies worked well in achieving their goals or they could change their learning approach if needed. This ability to monitor and regulate is the nature of metacognition (Wagaba, Treagust and Chandrasegaran, 2016). Students reported such strategies as applying other HoMs, finding clues and drawing a model, completing the shortest tasks first, using a calculator, asking the teacher or family members. Nevertheless, when looking at the strategies reported by the students during the interviews, five students stayed in the same yellow or green indicator during three phases and same number of students showed major or minor improvements. Therefore, it is difficult to say whether they were the results of applying past knowledge or strategies offered by previous teachers, peers, family members or they were the strategies taught in this unit. Corresponding findings have also been reported by the studies of Davey (2016). Investigating metacognitive development in early years children, she underlined that even younger students can talk about strategies they implemented when facing a problem to solve. The only thing that is clear is that three students still stayed in a red indicator by the end of Phase 3. Perhaps, more focus should be provided on this area when creating lesson plans.

Different studies argue that if students are taught metacognitive strategies at school, they will perform better and even their general wellbeing will improve (Perry, Lundie and Golder, 2019). This study was not focused on students’ performance, but their emotions were taken into account in the Value Category. The findings support the studies of Gabriel, Buckley and Barthakur (2020) who concluded that motivational and emotional factors affect students’ abilities to self-regulate their learning. Mathematics anxiety is an obstacle to learn maths and might impede students’ engagement and the metacognitive processes in general. It was particularly observed during online classes when students could simply leave the meeting when they wanted or do not join at all. The reports in the findings chapter prove that the students who did that felt worried or stressed by the end of the unit because they did not know how to solve the tasks and since they did not have developed metacognitive skills, they could not self-regulate their learning.

5.3 Limitations of research

The researcher acknowledges several constraints of the study. First, it was difficult to set the tone of reflection while teaching online. Most of the metacognitive tasks were done at the end of the lesson and by that time half of the students left the meeting (bad Internet connection, family circumstances, distractions etc.). The results could have been different if teaching on campus. On the other hand, online settings can test self-directedness even better (Cano-Hila and Argemí-Baldich, 2021) so it probably shows that some students were not ready yet to monitor their learning.

Secondly, it would have been better to have this pilot in the middle of the year. At the end of the year, a lot of graded tasks had to be done and there was not enough time to do as many reflections as was planned. Costa and Kallick (2000) recommend that students should reread their journals from time to time to compare their thoughts and make an action plan. During this study, the students were asked to review their Metacognition Diaries but a lot of them did not do it because of the time limits. Adding to this, the scope of this research project was too broad for the timeframe in which it was conducted.

Finally, the concept of semi-structured interviews was partly misunderstood by the researcher. Some of the questions differed during the three phases, thus the progression might not be completely visible. Moreover, some of the questions could have been reworded to avoid different biases.

Overall, while the results of this study appear promising, they should be treated with caution due to the above limitations.

5.4 Implications for further research

The recommendations for other researchers have been made to provide an impetus to continue research on metacognition from students’ perspectives. The data collected could greatly support teachers and curriculum coordinators in finding solutions to overcome the issue of low self-determination in elementary schools. Stringer recommends being careful while creating the questions so that the interviewers do not integrate their ideas into the interviewees’ answers (Stringer, 2007, p. 65). Having analysed the data, it was noticed that some students’ responses contradicted what was observed in the class. Meanwhile, when they were asked indirectly (e.g., “What advice would you give to students who are moving to grade 3?”) they could make connections to themselves and their learning styles. Kaminska and Foulsham (2013) believe that this social desirability bias is caused because of students’ embarrassment and uneasiness if their answers do not match with teachers’ expectations. It is recommended to reword some questions if this research is about to be repeated. For example, instead of asking “Do you think the rubric that we used in class was helpful or just a waste of time?” it is better to ask “Would you recommend having rubrics like this in grade 3? Why or why not?”.

For teachers, it is crucial to inspire students, at every age, to find how they learn and what benefits them individually (Pritchard, 2013). That is why it is important to have professional development in teaching metacognition at this early age. Plus, further research can be carried out to demonstrate whether different teaching styles have an effect on how students develop metacognitive knowledge and skills.

Regarding future research, there is one more perspective worth investigating, that of the parents. First, parents have a big influence on their children’s achievements (Jezierski and Wall, 2019). Secondly, it is paramount to know whether the students apply these metacognitive strategies or other heutagogical techniques at home and whether their behaviour has changed because of it, especially during the lockdown.

5.5 Practical recommendations

Even though some educators believe that developing metacognitive skills is often difficult and time-consuming (Thomas, 2003), it is an important goal of education. There are a lot of techniques and strategies that teachers might implement to train students’ metacognitive abilities. Students should be given opportunities to learn how to set goals, assess their progress and take ownership of their learning.

However, teachers should not expect that students already know how to monitor their progress, plan and self-evaluate as all these skills should be explicitly taught and modelled (Perry, Lundie and Golder, 2019). We cannot expect elementary students to already have metacognitive knowledge and skills (Wagaba, Treagust and Chandrasegaran, 2016). One of the goal-setting strategies that worked during this study was to have students self-assess first and based on their results ask them to write what they can improve and how. It was important to model that our goals should be specific, achievable, and timely. Furthermore, it was repeated every time before the activity started that these goals are for them and not for the teacher so that students synthesize the importance of goal-setting.

Conducting discussions turned out to be one of the tools that promoted metacognition in the classroom. Following Costa and Kallick’s (2008) advice, some thought-provoking questions were designed for the MDs (Appendices VI-VIII). During these moments, students learned how their peers applied some strategies and grew in this Habit of Mind. If the students are studying onsite, it might be better to conduct discussions at the end of mathematics classes but if lessons are online, it is recommended to either ask the students to complete the journal in their free time or choose a moment when most of the students are present.

It is crucial to demonstrate that solving problems is not only about finding the correct answer but about the process. Moreover, reflective writing might support students in determining their strengths and weaknesses in the topic. Costa and Kallick (2008) also suggest students should reread these journals from time to time, comparing what they have learned in the past and now. Based on the observation notes, teachers should encourage students to complete the diaries regularly to habitualize them. Perhaps teachers may complete the diaries as well as an example.

It is also important not to expect immediate results. Even though this study lasted 9 weeks, it was not enough to coach on metacognition. Students should have enough time to understand their learning processes and to develop a habit of reflecting on their learning and experiences.

5.6 Conclusion

This section is an overall conclusion of the current research. Previous studies from teachers’ and administrators’ perspectives summarised that implementing metacognitive techniques will positively influence students’ performance (Stein, 2018). Nevertheless, the lack of empirical studies from students’ points of view is still a concern in education.

The purpose of this study was to enable grade 3 students to reflect on their learning practices and habits by using metacognitive methods and to see whether it can help them become self-determined learners. Self-determined learners are students who can self-assess, self-direct and self-monitor their learning (Commitment Category), can recognise the benefits and advantages of engaging in metacognitive processes (Value Category) and develop skills, strategies, and techniques through which they engage with their peers (Capacity Category).

Metacognition is the foundation of lifelong learning. Action research cycles with constant reflections helped the researcher as an educator to learn what is best for her students and how to adapt to meet the 21-st century requirements. Based on the observation notes and interview data, most grade 3 students were able to find more motivation for learning mathematics, therefore became more engaged in the learning process. Hence, it might be useful to stimulate deep reflections at an early age. By increasing metacognition, students could find different strategies, apply them, and choose the most effective ones based on the situation. That’s why it is a heutagogical technique. However, some students still could not regulate their learning even after the metacognitive interventions were implemented.

Less than half of the students could connect metacognition to mathematics by the end of phase 3 and three students were able to do it before the experiment started. Four students either stayed in the red indicator or dropped from yellow or green. However, it is important to note that these students missed more than a third of online mathematics classes or did not do most of the metacognitive activities assigned during the unit.

The pandemic lockdown affected children’s learning. Even though there are a lot of physical and emotional limitations connected to the pandemic (Cano-Hila and Argemí-Baldich, 2021), it might be considered a perfect setting to practice metacognitive skills when students can set goals, monitor their learning using different checklists and rubrics, reflect on the feedback provided in Google Classroom and think about improving strategies while writing diaries. Hopefully, these positive aspects of online learning concerning metacognition should remain even after lockdown.

However, recent research in education showed that in fact, the lockdown increased the gap between high and low achievers: stronger students had more ability to concentrate on the tasks while weaker students were less able to focus (Spitzer, 2021). This study supports this statement because when we look at the findings, it is noticeable that the students with yellow or green specific indicators in Phase 1, continued to show progress in other Phases. But if they started in a red indicator and did not join classes or did not do the metacognitive tasks, they stayed in the same colour code. If students are studying at school, they are approximately equal in terms of metacognitive support provided by a teacher. Meanwhile, when studying at home, there are different family circumstances that can increase or decrease their metacognitive skills (e.g., eliminating distractions, helping with monitoring their progress, doing work with parents, etc.) (Cano-Hila and Argemí-Baldich, 2021). Another term used recently in research is “Zoom fatigue” when students are getting tired from overusing virtual platforms (Wiederhold, 2020). A few children reported during the interviews that they were overwhelmed with the number of emails and feedback on different platforms that sometimes they missed and did not reply to the teacher.

The study has revealed that such tools as Metacognition Diaries and video diaries on Flipgrid were effective from students’ perspectives to regulate their learning. This indicates that these tools might be useful in implementing the heutagogical framework. Based on students’ responses, rubrics were useful during mathematics classes by helping students improve their work or informing the teacher about their progress. However, such issues as dishonesty, overconfidence, and the inability to use the rubric without knowing the correct answer were also highlighted and should be taken into account by educators. Checklists, on the other hand, turned out to be very helpful self-monitoring tools during online classes.

Another summary related to the results of the study shows that although some students stated that they wrote goals, responded to the teacher’s feedback, took notes, it disagreed with the researcher’s observation notes. Even though MDs were not graded, the final assessment about HoM 5 Metacognition was included in students’ grade books. It could have influenced some students’ answers. Some students could have hidden what they did not know, and it is not the purpose of reflections (Ramadhanti et al ., 2020). That is why it is better to have it not graded in further studies.

I would like to conclude this paper with the quote of Mark Van Doren, “The art of teaching is the art of assisting discovery” (BrainyMedia Inc, no date). As researchers and as practitioners this should be our aim and metacognition as a heutagogical technique might assist in it. What if teachers were more concerned about students’ abilities after graduation (e.g., problem-solving, decision-making, being a lifelong learner) rather than focusing only on the acquisition and end-of-year exams? Finally, the ultimate goal of education is to develop lifelong learners and, I would add, metacognitive and self-determined lifelong learners.

For references and appendices please refer to the full dissertation in PDF form.

Appendix I: Consent Form (Parents) Appendix II: Consent Form (Students) Appendix III: Interview Questions Appendix IV: Final Assessment Appendix V: Lesson Plan with Metacognitive Elements Appendix VI: Metacognition Diary (MD) – Value Appendix VII: Metacognition Diary (MD) – Capacity Appendix VIII: Metacognition Diary (MD) – Commitment Appendix IX: Coding Legend Appendix X: Qualitative Analysis of Abstract Concepts – Setting goals Appendix XI: Qualitative Analysis of Abstract Concepts – Self-questioning Appendix XII: Qualitative Analysis of Abstract Concepts – Self-monitoring Appendix XIII: Qualitative Analysis of Abstract Concepts – Responding to feedback Appendix XIV: Qualitative Analysis of Abstract Concepts – Connecting metacognition to math Appendix XV: Qualitative Analysis of Abstract Concepts – Applying different strategies when solving problems Appendix XVI: Qualitative Analysis of Abstract Concepts – Asking for help when needed Appendix XVII: Qualitative Analysis of Abstract Concepts – Taking notes Appendix XVIII: Qualitative Analysis of Abstract Concepts – Improvement strategies

LIST OF TABLES Table 1: Core Category Commitment – Overall Picture during 3 Phases Table 2: Core Category Capacity – Overall Picture during 3 Phases

LIST OF ABBREVIATIONS AND ACRONYMS EQ = Essential Question GC = Google Classroom HoM = Habit of Mind MD = Metacognition Diary MK = Metacognitive Knowledge ME = Metacognitive Experience MS = Metacognitive Skills PT = Performance Task P = Phase S = Student S2-P1 = Student 2 – Phase 1 SLO = Schoolwide Learner Outcomes

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• Open access
• Published: 11 March 2019

Enhancing achievement and interest in mathematics learning through Math-Island

• Charles Y. C. Yeh   ORCID: orcid.org/0000-0003-4581-6575 1 ,
• Hercy N. H. Cheng 2 ,
• Zhi-Hong Chen 3 ,
• Calvin C. Y. Liao 4 &
• Tak-Wai Chan 5  

Research and Practice in Technology Enhanced Learning volume  14 , Article number:  5 ( 2019 ) Cite this article

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Conventional teacher-led instruction remains dominant in most elementary mathematics classrooms in Taiwan. Under such instruction, the teacher can rarely take care of all students. Many students may then continue to fall behind the standard of mathematics achievement and lose their interest in mathematics; they eventually give up on learning mathematics. In fact, students in Taiwan generally have lower interest in learning mathematics compared to many other regions/countries. Thus, how to enhance students’ mathematics achievement and interest are two major problems, especially for those low-achieving students. This paper describes how we designed a game-based learning environment, called Math-Island , by incorporating the mechanisms of a construction management game into the knowledge map of the elementary mathematics curriculum. We also report an experiment conducted with 215 elementary students for 2 years, from grade 2 to grade 3. In this experiment, in addition to teacher-led instruction in the classroom, students were directed to learn with Math-Island by using their own tablets at school and at home. As a result of this experiment, we found that there is an increase in students’ mathematics achievement, especially in the calculation and word problems. Moreover, the achievements of low-achieving students in the experimental school outperformed the low-achieving students in the control school (a control group in another school) in word problems. Moreover, both the low-achieving students and the high-achieving students in the experimental school maintained a rather high level of interest in mathematics and in the system.

Introduction

Mathematics has been regarded as a fundamental subject because arithmetic and logical reasoning are the basis of science and technology. For this reason, educational authorities emphasize students’ proficiency in computational skills and problem-solving. Recently, the results of the Program for International Student Assessment (PISA) and the Trends in Mathematics and Science Study (TIMSS) in 2015 (OECD 2016 ; Mullis et al. 2016 ) revealed a challenge for Taiwan. Although Taiwanese students had higher average performance in mathematics literacy compared to students in other countries, there was still a significant percentage of low-achieving students in Taiwan. Additionally, most Taiwanese students show low levels of interest and confidence in learning mathematics (Lee 2012 ).

The existence of a significant percentage of low-achieving students is probably due to teacher-led instruction, which still dominates mathematics classrooms in most Asian countries. It should be noted that students in every classroom possess different abilities and hence demonstrate different achievements. Unfortunately, in teacher-led instruction, all the students are required to learn from the teacher in the same way at the same pace (Hwang et al. 2012 ). Low-achieving students, without sufficient time, are forced to receive knowledge passively. Barr and Tagg ( 1995 ) pointed out that it is urgent for low-achieving students to have more opportunities to learn mathematics at their own pace. Researchers suggested one-to-one technology (Chan et al. 2006 ) through which every student is equipped with a device to learn in school or at home seamlessly. Furthermore, they can receive immediate feedback from Math-Island, which supports their individualized learning actively and productively. Thus, this may provide more opportunities for helping low-achieving students improve their achievement.

The low-interest problem for almost all students in Taiwan is usually accompanied by low motivation (Krapp 1999 ). Furthermore, students with continuously low performance in mathematics may eventually lose their interest and refuse to learn further (Schraw et al. 2001 ). This is a severe problem. To motivate students to learn, researchers design educational games to provide enjoyable and engaging learning experiences (Kiili and Ketamo 2007 ). Some of these researchers found that game-based learning may facilitate students’ learning in terms of motivation and learning effects (Liu and Chu 2010 ), spatial abilities and attention (Barlett et al. 2009 ), situated learning, and problem-solving (Li and Tsai 2013 ). Given these positive results, we hope that our educational game can enhance and sustain the student’s interest in learning mathematics.

In fact, many researchers who endeavored to develop educational games for learning mathematics have shown that their games could facilitate mathematics performance, enjoyment, and self-efficacy (Ku et al. 2014 ; McLaren et al. 2017 ). Although some of the studies were conducted for as many as 4 months (e.g., Hanus and Fox 2015 ), one may still criticize them for the possibility that the students’ interest could be a novelty effect—meaning their interest will decrease as the feeling of novelty diminishes over time (Koivisto and Hamari 2014 ). Due to the limitations of either experimental time or sample sizes, most studies could not effectively exclude the novelty effect of games, unless they were conducted in a natural setting for a long time.

In this study, we collaborated with an experimental elementary school for more than 2 years. The mathematics teachers in the school adopted our online educational game, Math-Island . The students used their own tablet PCs to learn mathematics from the game in class or at home at their own pace. In particular, low-achieving students might have a chance to catch up with the other students and start to feel interested in learning mathematics. Most importantly, because the online educational game was a part of the mathematics curriculum, the students could treat the game as their ordinary learning materials like textbooks. In this paper, we reported a 2-year study, in which 215 second graders in the school adopted the Math-Island game in their daily routine. More specifically, the purpose of this paper was to investigate the effect of the game on students’ mathematics achievement. Additionally, we were also concerned about how well the low-achieving students learned, whether they were interested in mathematics and the game, and how their interest in mathematics compared with that of high-achieving students. In such a long-term study with a large sample size, it was expected that the novelty effect would be considerably reduced, allowing us to evaluate the effect of the educational game on students’ achievement and interest.

The paper is organized as follows. In the “ Related works ” section, we review related studies on computer-supported mathematics learning and educational games. In the “ Design ” section, the game mechanism and the system design are presented. In the “ Method ” section, we describe the research method and the procedures of this study. In the “ Results ” section, the research results about students’ achievement and interest are presented. In the “ Discussion on some features of this study ” section, we discuss the long-term study, knowledge map design, and the two game mechanisms. Finally, the summary of the current situation and potential future work is described in the “ Conclusion and future work ” section.

Related works

Computer-supported mathematics learning.

The mathematics curriculum in elementary schools basically includes conceptual understanding, procedural fluency, and strategic competence in terms of mathematical proficiency (see Kilpatrick et al. 2001 ). First, conceptual understanding refers to students’ comprehension of mathematical concepts and the relationships between concepts. Researchers have designed various computer-based scaffolds and feedback to build students’ concepts and clarify potential misconceptions. For example, for guiding students’ discovery of the patterns of concepts, Yang et al. ( 2012 ) adopted an inductive discovery learning approach to design online learning materials in which students were provided with similar examples with a critical attribute of the concept varied. McLaren et al. ( 2017 ) provided students with prompts to correct their common misconceptions about decimals. They conducted a study with the game adopted as a replacement for seven lessons of regular mathematics classes. Their results showed that the educational game could facilitate better learning performance and enjoyment than a conventional instructional approach.

Second, procedural fluency refers to the skill in carrying out calculations correctly and efficiently. For improving procedural fluency, students need to have knowledge of calculation rules (e.g., place values) and practice the procedure without mistakes. Researchers developed various digital games to overcome the boredom of practice. For example, Chen et al. ( 2012a , 2012b ) designed a Cross Number Puzzle game for practicing arithmetic expressions. In the game, students could individually or collaboratively solve a puzzle, which involved extensive calculation. Their study showed that the low-ability students in the collaborative condition made the most improvement in calculation skills. Ku et al. ( 2014 ) developed mini-games to train students’ mental calculation ability. They showed that the mini-games could not only improve students’ calculation performance but also increase their confidence in mathematics.

Third, strategic competence refers to mathematical problem-solving ability, in particular, word problem-solving in elementary education. Some researchers developed multilevel computer-based scaffolds to help students translate word problems to equations step by step (e.g., González-Calero et al. 2014 ), while other researchers noticed the problem of over-scaffolding. Specifically, students could be too scaffolded and have little space to develop their abilities. To avoid this situation, many researchers proposed allowing students to seek help during word problem-solving (Chase and Abrahamson 2015 ; Roll et al. 2014 ). For example, Cheng et al. ( 2015 ) designed a Scaffolding Seeking system to encourage elementary students to solve word problems by themselves by expressing their thinking first, instead of receiving and potentially abusing scaffolds.

Digital educational games for mathematics learning

Because mathematics is an abstract subject, elementary students easily lose interest in it, especially low-achieving students. Some researchers tailored educational games for learning a specific set of mathematical knowledge (e.g., the Decimal Points game; McLaren et al. 2017 ), so that students could be motivated to learn mathematics. However, if our purpose was to support a complete mathematics curriculum for elementary schools, it seemed impractical to design various educational games for all kinds of knowledge. A feasible approach is to adopt a gamified content structure to reorganize all learning materials. For example, inspired by the design of most role-playing games, Chen et al. ( 2012a , 2012b ) proposed a three-tiered framework of game-based learning—a game world, quests, and learning materials—for supporting elementary students’ enjoyment and goal setting in mathematics learning. Furthermore, while a game world may facilitate students’ exploration and participation, quests are the containers of learning materials with specific goals and rewards. In the game world, students receive quests from nonplayer virtual characters, who may enhance social commitments. To complete the quests, students have to make efforts to undertake learning materials. Today, quests have been widely adopted in the design of educational games (e.g., Azevedo et al. 2012 ; Hwang et al. 2015 ).

However, in educational games with quests, students still play the role of receivers rather than active learners. To facilitate elementary students’ initiative, Lao et al. ( 2017 ) designed digital learning contracts, which required students to set weekly learning goals at the beginning of a week and checked whether they achieved the goals at the end of the week. More specifically, when setting weekly goals, students had to decide on the quantity of learning materials that they wanted to undertake in the coming week. Furthermore, they also had to decide the average correctness of the tests that followed the learning materials. To help them set reasonable and feasible goals, the system provided statistics from the past 4 weeks. As a result, the students may reflect on how well they learned and then make appropriate decisions. After setting goals, students are provided with a series of learning materials for attempting to accomplish those goals. At the end of the week, they may reflect on whether they achieved their learning goals in the contracts. In a sense, learning contracts may not only strengthen the sense of commitment but also empower students to take more control of their learning.

In textbooks or classrooms, learning is usually predefined as a specific sequence, which students must follow to learn. Nevertheless, the structure of knowledge is not linear, but a network. If we could reorganize these learning materials according to the structure of knowledge, students could explore knowledge and discover the relationships among different pieces of knowledge when learning (Davenport and Prusak 2000 ). Knowledge mapping has the advantage of providing students concrete content through explicit knowledge graphics (Ebener et al. 2006 ). Previous studies have shown that the incorporation of knowledge structures into educational games could effectively enhance students’ achievement without affecting their motivation and self-efficacy (Chu et al. 2015 ). For this reason, this study attempted to visualize the structure of knowledge in an educational game. In other words, a knowledge map was visualized and gamified so that students could make decisions to construct their own knowledge map in games.

To enhance students’ mathematics achievement and interests, we designed the Math-Island online game by incorporating a gamified knowledge map of the elementary mathematics curriculum. More specifically, we adopt the mechanisms of a construction management game , in which every student owns a virtual island (a city) and plays the role of the mayor. The goal of the game is to build their cities on the islands by learning mathematics.

System architecture

The Math-Island game is a Web application, supporting cross-device interactions among students, teachers, and the mathematics content structure. The system architecture of the Math-Island is shown in Fig.  1 . The pedagogical knowledge and learning materials are stored in the module of digital learning content, organized by a mathematical knowledge map. The students’ portfolios about interactions and works are stored in the portfolio database and the status database. When a student chooses a goal concept in the knowledge map, the corresponding digital learning content is arranged and delivered to his/her browser. Besides, when the student is learning in the Math-Island, the feedback module provides immediate feedback (e.g., hints or scaffolded solutions) for guidance and grants rewards for encouragement. The learning results can also be shared with other classmates by the interaction module. In addition to students, their teachers can also access the databases for the students’ learning information. Furthermore, the information consists of the students’ status (e.g., learning performance or virtual achievement in the game) and processes (e.g., their personal learning logs). In the Math-Island, it is expected that students can manage their learning and monitor the learning results by the construction management mechanism. In the meantime, teachers can also trace students’ learning logs, diagnose their weaknesses from portfolio analysis, and assign students with specific tasks to improve their mathematics learning.

The system architecture of Math-Island

• Knowledge map

To increase students’ mathematics achievement, the Math-Island game targets the complete mathematics curriculum of elementary schools in Taiwan, which mainly contains the four domains: numerical operation , quantity and measure , geometry , and statistics and probability (Ministry of Education of R.O.C. 2003 ). Furthermore, every domain consists of several subdomains with corresponding concepts. For instance, the domain of numerical operation contains four subdomains: numbers, addition, and subtraction for the first and second graders. In the subdomain of subtraction, there are a series of concepts, including the meaning of subtraction, one-digit subtraction, and two-digit subtraction. These concepts should be learned consecutively. In the Math-Island system, the curriculum is restructured as a knowledge map, so that they may preview the whole structure of knowledge, recall what they have learned, and realize what they will learn.

More specifically, the Math-Island system uses the representational metaphor of an “island,” where a virtual city is located and represents the knowledge map. Furthermore, the island comprises areas, roads, and buildings, which are the embodiments of domains, subdomains, and concepts in the curriculum, respectively. As shown in Fig.  2 , for example, in an area of numeral operation in Math-Island, there are many roads, such as an addition road and a subtraction road. On the addition road, the first building should be the meaning of addition, followed by the buildings of one-digit addition and then two-digit addition. Students can choose these buildings to learn mathematical concepts. In each building, the system provides a series of learning tasks for learning the specific concept. Currently, Math-Island provides elementary students with more than 1300 learning tasks from the first grade to the sixth grade, with more than 25,000 questions in the tasks.

The knowledge map

In Math-Island, a learning task is an interactive page turner, including video clips and interactive exercises for conceptual understanding, calculation, and word problem-solving. In each task, the learning procedure mainly consists of three steps: watching demonstrations, practicing examples, and getting rewards. First, students learn a mathematical concept by watching videos, in which a human tutor demonstrates examples, explains the rationale, and provides instructions. Second, students follow the instructions to answer a series of questions related to the examples in the videos. When answering questions, students are provided with immediate feedback. Furthermore, if students input wrong answers, the system provides multilevel hints so that they could figure out solutions by themselves. Finally, after completing learning tasks, students receive virtual money according to their accuracy rates in the tasks. The virtual money is used to purchase unique buildings to develop their islands in the game.

Game mechanisms

In the Math-Island game, there are two game mechanisms: construction and sightseeing (as shown in Fig.  3 ). The former is designed to help students manage their learning process, whereas the latter is designed to facilitate social interaction, which may further motivate students to better develop their cities. By doing so, the Math-Island can be regarded as one’s learning portfolio, which is a complete record that purposely collects information about one’s learning processes and outcomes (Arter and Spandel 2005 ). Furthermore, learning portfolios are a valuable research tool for gaining an understanding about personal accomplishments (Birgin and Baki 2007 ), because learning portfolios can display one’s learning process, attitude, and growth after learning (Lin and Tsai 2001 ). The appearance of the island reflects what students have learned and have not learned from the knowledge map. When students observe their learning status in an interesting way, they may be concerned about their learning status with the enhanced awareness of their learning portfolios. By keeping all activity processes, students can reflect on their efforts, growth, and achievements. In a sense, with the game mechanisms, the knowledge map can be regarded as a manipulatable open learner model, which not only represents students’ learning status but also invites students to improve it (Vélez et al. 2009 ).

Two game mechanisms for Math-Island

First, the construction mechanism allows students to plan and manage their cities by constructing and upgrading buildings. To do so, they have to decide which buildings they want to construct or upgrade. Then, they are required to complete corresponding learning tasks in the building to determine which levels of buildings they can construct. As shown in Fig.  4 , the levels of buildings depend on the completeness of a certain concept, compared with the thresholds. For example, when students complete one third of the learning tasks, the first level of a building is constructed. Later, when they complete two thirds of the tasks, the building is upgraded to the second level. After completing all the tasks in a building, they also complete the final level and are allowed to construct the next building on the road. Conversely, if students failed the lowest level of the threshold, they might need to watch the video and/or do the learning tasks again. By doing so, students can make their plans to construct the buildings at their own pace. When students manage their cities, they actually attempt to improve their learning status. In other words, the construction mechanism offers an alternative way to guide students to regulate their learning efforts.

Screenshots of construction and sightseeing mechanisms in Math-Island

Second, the sightseeing mechanism provides students with a social stage to show other students how well their Math-Islands have been built. This mechanism is implemented as a public space, where other students play the role of tourists who visit Math-Island. In other words, this sightseeing mechanism harnesses social interaction to improve individual learning. As shown in Fig.  4 , because students can construct different areas or roads, their islands may have different appearances. When students visit a well-developed Math-Island, they might have a positive impression, which may facilitate their self-reflection. Accordingly, they may be willing to expend more effort to improve their island. On the other hand, the student who owns the island may also be encouraged to develop their island better. Furthermore, when students see that they have a completely constructed building on a road, they may perceive that they are good at these concepts. Conversely, if their buildings are small, the students may realize their weaknesses or difficulties in these concepts. Accordingly, they may be willing to make more effort for improvement. On the other hand, the student who owns the island may also be encouraged to develop their island better. In a word, the visualization may play the role of stimulators, so that students may be motivated to improve their learning status.

This paper reported a 2-year study in which the Math-Island system was adopted in an elementary school. The study addressed the following two research questions: (1) Did the Math-Island system facilitate students’ mathematics achievement in terms of conceptual understanding, calculating, and word problem-solving? In particular, how was the mathematics achievement of the low-achieving students? (2) What was students’ levels of interest in mathematics and the system, particularly that of low-achieving students?

Participants

The study, conducted from June 2013 to June 2015, included 215 second graders (98 females and 117 males), whose average age was 8 years old, in an elementary school located in a suburban region of a northern city in Taiwan. The school had collaborated with our research team for more than 2 years and was thus chosen as an experimental school for this study. In this school, approximately one third of the students came from families with a low or middle level of socioeconomic status. It was expected that the lessons learned from this study could be applicable to other schools with similar student populations in the future. The parents were supportive of this program and willing to provide personal tablets for their children (Liao et al. 2017 ). By doing so, the students in the experimental school were able to use their tablets to access the Math-Island system as a learning tool at both school and home. To compare the students’ mathematics achievement with a baseline, this study also included 125 second graders (63 females and 62 males) from another school with similar socioeconomic backgrounds in the same region of the city as a control school. The students in the control school received only conventional mathematics instruction without using the Math-Island system during the 2-year period.

Before the first semester, a 3-week training workshop was conducted to familiarize the students with the basic operation of tablets and the Math-Island system. By doing so, it was ensured that all participants had similar prerequisite skills. The procedure of this study was illustrated in Table  1 . At the beginning of the first semester, a mathematics achievement assessment was conducted as a pretest in both the experimental and the control school to examine the students’ initial mathematics ability as second graders. From June 2013 to June 2015, while the students in the control school learned mathematics in a conventional way, the students in the experimental school learned mathematics not only in mathematics classes but also through the Math-Island system. Although the teachers in the experimental school mainly adopted lectures in mathematics classes, they used the Math-Island system as learning materials at school and for homework. At the same time, they allowed the students to explore the knowledge map at their own pace. During the 2 years, every student completed 286.78 learning tasks on average, and each task took them 8.86 min. Given that there were 344 tasks for the second and third graders, the students could finish 83.37% of tasks according to the standard progress. The data also showed that the average correctness rate of the students was 85.75%. At the end of the second year, another mathematics achievement assessment was administered as a posttest in both schools to evaluate students’ mathematics ability as third graders. Additionally, an interest questionnaire was employed in the experimental school to collect the students’ perceptions of mathematics and the Math-Island system. To understand the teachers’ opinions of how they feel about the students using the system, interviews with the teachers in the experimental school were also conducted.

Data collection

Mathematics achievement assessment.

To evaluate the students’ mathematics ability, this study adopted a standardized achievement assessment of mathematics ability (Lin et al. 2009 ), which was developed from a random sample of elementary students from different counties in Taiwan to serve as a norm with appropriate reliability (the internal consistency was 0.85, and the test-retest reliability was 0.86) and validity (the correlation by domain experts in content validity was 0.92, and the concurrent validity was 0.75). As a pretest, the assessment of the second graders consisted of 50 items, including conceptual understanding (23 items), calculating (18 items), and word problem-solving (9 items). As a posttest, the assessment of the third graders consisted of 60 items, including conceptual understanding (18 items), calculating (27 items), and word problem-solving (15 items). The scores of the test ranged from 0 to 50 points. Because some students were absent during the test, this study obtained 209 valid tests from the experimental school and 125 tests from the control school.

Interest questionnaire

The interest questionnaire comprised two parts: students’ interest in mathematics and the Math-Island system. Regarding the first part, this study adopted items from a mathematics questionnaire of PISA and TIMSS 2012 (OECD 2013 ; Mullis et al. 2012 ), the reliability of which was sound. This part included three dimensions: attitude (14 items, Cronbach’s alpha = .83), initiative (17 items, Cronbach’s alpha = .82), and confidence (14 items Cronbach’s alpha = .72). Furthermore, the dimension of attitude was used to assess the tendency of students’ view on mathematics. For example, a sample item of attitudes was “I am interested in learning mathematics.” The dimension of initiatives was used to assess how students were willing to learn mathematics actively. A sample item of initiatives was “I keep studying until I understand mathematics materials.” The dimension of confidences was used to assess students’ perceived mathematics abilities. A sample item was “I am confident about calculating whole numbers such as 3 + 5 × 4.” These items were translated to Chinese for this study. Regarding the second part, this study adopted self-made items to assess students’ motivations for using the Math-Island system. This part included two dimensions: attraction (8 items) and satisfaction (5 items). The dimension of attraction was used to assess how well the system could attract students’ attention. A sample item was “I feel Math-island is very appealing to me.” The dimension of satisfaction was used to assess how the students felt after using the system. A sample item was “I felt that upgrading the buildings in my Math-Island brought me much happiness.” These items were assessed according to a 4-point Likert scale, ranging from “strongly disagreed (1),” “disagreed (2),” “agreed (3),” and “strongly agreed (4)” in this questionnaire. Due to the absences of several students on the day the questionnaire was administered, there were only 207 valid questionnaires in this study.

Teacher interview

This study also included teachers’ perspectives on how the students used the Math-Island system to learn mathematics in the experimental school. This part of the study adopted semistructured interviews of eight teachers, which comprised the following three main questions: (a) Do you have any notable stories about students using the Math-Island system? (b) Regarding Math-Island, what are your teaching experiences that can be shared with other teachers? (c) Do you have any suggestions for the Math-Island system? The interview was recorded and transcribed verbatim. The transcripts were coded and categorized according to the five dimensions of the questionnaire (i.e., the attitude, initiative, and confidence about mathematics, as well as the attraction and satisfaction with the system) as additional evidence of the students’ interest in the experimental school.

Data analysis

For the first research question, this study conducted a multivariate analysis of variance (MANOVA) with the schools as a between-subject variable and the students’ scores (conceptual understanding, calculating, and word problem-solving) in the pre/posttests as dependent variables. Moreover, this study also conducted a MANOVA to compare the low-achieving students from both schools. In addition, the tests were also carried out to compare achievements with the norm (Lin et al. 2009 ). For the second research question, several z tests were used to examine how the interests of the low-achieving students were distributed compared with the whole sample. Teachers’ interviews were also adopted to support the results of the questionnaire.

Mathematics achievement

To examine the homogeneity of the students in both schools in the first year, the MANOVA of the pretest was conducted. The results, as shown in Table  2 , indicated that there were no significant differences in their initial mathematics achievements in terms of conceptual understanding, calculating, and word problem-solving (Wilks’ λ  = 0.982, F (3330) = 2.034, p  > 0.05). In other words, the students of both schools had similar mathematics abilities at the time of the first mathematics achievement assessment and could be fairly compared.

At the end of the fourth grade, the students of both schools received the posttest, the results of which were examined by a MANOVA. As shown in Table  3 , the effect of the posttest on students’ mathematics achievement was significant (Wilks’ λ  = 0.946, p  < 0.05). The results suggested that the students who used Math-Island for 2 years had better mathematics abilities than those who did not. The analysis further revealed that the univariate effects on calculating and word problem-solving were significant, but the effect on conceptual understanding was insignificant. The results indicated that the students in the experimental school outperformed their counterparts in terms of the procedure and application of arithmetic. The reason may be that the system provided students with more opportunities to do calculation exercises and word problems, and the students were more willing to do these exercises in a game-based environment. Furthermore, they were engaged in solving various exercises with the support of immediate feedback until they passed the requirements of every building in their Math-Island. However, the students learned mathematical concepts mainly by watching videos in the system, which provided only demonstrations like lectures in conventional classrooms. For this reason, the effect of the system on conceptual understanding was similar to that of teachers’ conventional instruction.

Furthermore, to examine the differences between the low-achieving students in both schools, another MANOVA was also conducted on the pretest and the posttest. The pretest results indicated that there were no significant differences in their initial mathematics achievement in terms of conceptual understanding, calculating, and word problem-solving (Wilks’ λ  = 0.943, F (3110) = 2.210, p  > 0.05).

The MANOVA analysis of the posttest is shown in Table  4 . The results showed that the effect of the system on the mathematics achievement of low-achieving students was significant (Wilks’ λ  = 0.934, p  < 0.05). The analysis further revealed that only the univariate effect on word problem-solving was significant. The results suggested that the low-achieving students who used Math-Island for 2 years had better word problem-solving ability than those students in the control school, but the effect on conceptual understanding and procedural fluency was insignificant. The results indicated that the Math-Island system could effectively enhance low-achieving students’ ability to solve word problems.

Because the mathematics achievement assessment was a standardized achievement assessment (Lin et al. 2009 ), the research team did a further analysis of the assessments by comparing the results with the norm. In the pretest, the average score of the control school was the percentile rank of a score (PR) 55, but their average score surprisingly decreased to PR 34 in the posttest. The results confirmed the fact that conventional mathematics teaching in Taiwan might result in an M-shape distribution, suggesting that low-achieving students required additional learning resources. Conversely, the average score of the experimental school was PR 48 in the pretest, and their score slightly decreased to PR 44 in the posttest. Overall, both PR values were decreasing, because the mathematics curriculum became more and more difficult from the second grade to the fourth grade. However, it should be noted that the experimental school has been less affected, resulting in a significant difference compared with the control school (see Table  5 ). Notably, the average score of word problem-solving in the posttest of the experimental school was PR 64, which was significantly higher than the nationwide norm ( z  = 20.8, p  < .05). The results were consistent with the univariate effect of the MANOVA on word problem-solving, suggesting that the Math-Island system could help students learn to complete word problems better. This may be because the learning tasks in Math-Island provided students with adequate explanations for various types of word problems and provided feedback for exercises.

To examine whether the low-achieving students had low levels of interest in mathematics and the Math-Island system, the study adopted z tests on the data of the interest questionnaire. Table  5 shows the descriptive statistics and the results of the z tests. Regarding the interest in mathematics, the analysis showed that the interest of the low-achieving students was similar to that of the whole sample in terms of attitude, initiative, and confidence. The results were different from previous studies asserting that low-achieving students tended to have lower levels of interest in mathematics (Al-Zoubi and Younes 2015 ). The reason was perhaps that the low-achieving students were comparably motivated to learn mathematics in the Math-Island system. As a result, a teacher ( #T-301 ) said, “some students would like to go to Math-Island after school, and a handful of students could even complete up to forty tasks (in a day),” implying that the students had a positive attitude and initiative related to learning mathematics.

Another teacher ( T-312 ) also indicated “some students who were frustrated with math could regain confidence when receiving the feedback for correct answers in the basic tasks. Thanks to this, they would not feel high-pressure when moving on to current lessons.” In a sense, the immediate feedback provided the low-achieving students with sufficient support and may encourage them to persistently learn mathematics. Furthermore, by learning individually after class, they could effectively prepare themselves for future learning. The results suggested that the system could serve as a scaffolding on conventional instruction for low-achieving students. The students could benefit from such a blended learning environment and, thus, build confidence in mathematics by learning at their own paces.

The low-achieving students as a whole were also attracted to the system and felt satisfaction from it. Teacher ( #T-307 ) said that, “There was a hyperactive and mischievous student in my class. However, when he was alone, he would go on to Math-Island, concentrating on the tasks quietly. He gradually came to enjoy learning mathematics. It seemed that Math-Island was more attractive to them than a lecture by a teacher. I believed that students could be encouraged, thus improve their ability and learn happily.” Another teacher ( #T-304 ) further pointed out that, “For students, they did not only feel like they were learning mathematics because of the game-based user interface. Conversely, they enjoyed the contentment when completing a task, as if they were going aboard to join a competition.” In teachers’ opinions, such a game-based learning environment did not disturb their instruction. Instead, the system could help the teachers attract students’ attention and motivate them to learn mathematics actively because of its appealing game and joyful learning tasks. Furthermore, continuously overcoming the tasks might bring students a sense of achievement and satisfaction.

Discussion on some features of this study

In addition to the enhancement of achievement and interest, we noticed that there are some features in this study and our design worth some discussion.

The advantages of building a long-term study

Owing to the limitations of deployment time and sample sizes, it is hard for most researchers to conduct a longitudinal study. Fortunately, we had a chance to maintain a long-term collaboration with an experimental school for more than 2 years. From this experiment, we notice that there are two advantages to conducting a long-term study.

Obtaining substantial evidence from the game-based learning environment

The research environment was a natural setting, which could not be entirely controlled and manipulated like most experiments in laboratories. However, this study could provide long-term evidence to investigate how students learned in a game-based learning environment with their tablets. It should be noted that we did not aim to replace teachers in classrooms with the Math-Island game. Instead, we attempted to establish an ordinary learning scenario, in which the teachers and students regarded the game as one of the learning resources. For example, teachers may help low-achieving students to improve their understanding of a specific concept in the Math-Island system. When students are learning mathematics in the Math-Island game, teachers may take the game as a formative assessment and locate students’ difficulties in mathematics.

Supporting teachers’ instructions and facilitating students’ learning

The long-term study not only proved the effectiveness of Math-Island but also offered researchers an opportunity to determine teachers’ roles in such a computer-supported learning environment. For example, teachers may encounter difficulties in dealing with the progress of both high- and low-achieving students. How do they take care of all students with different abilities at the same time? Future teachers may require more teaching strategies in such a self-directed learning environment. Digital technology has an advantage in helping teachers manage students’ learning portfolios. For example, the system can keep track of all the learning activities. Furthermore, the system should provide teachers with monitoring functions so that they know the average status of their class’s and individuals’ learning progress. Even so, it is still a challenge for researchers to develop a well-designed visualization tool to support teachers’ understanding of students’ learning conditions and their choice of appropriate teaching strategies.

Incorporating a gamified knowledge map of the elementary mathematics curriculum

Providing choices of learning paths.

Math-Island uses a representational metaphor of an “island,” where a virtual city is located and represents the knowledge map. Furthermore, the island comprises areas, roads, and buildings, which are the embodiments of domains, subdomains, and concepts in the curriculum, respectively. Because the gamified knowledge map provides students with multiple virtual roads to learn in the system, every student may take different routes. For instance, some students may be more interested in geometry, while others may be confident in exploring the rules of arithmetic. In this study, we noticed that the low-achieving students needed more time to work on basic tasks, while high-achieving students easily passed those tasks and moved on to the next ones. As a result, some of the high-achieving students had already started to learn the materials for the next grade level. This was possibly because high-achieving students were able to respond well to challenging assignments (Singh 2011 ). Therefore, we should provide high-achieving students with more complex tasks to maintain their interest. For example, Math-Island should provide some authentic mathematical problems as advanced exercises.

Visualizing the learning portfolio

In this study, we demonstrated a long-term example of incorporating a gamified knowledge map in an elementary mathematical curriculum. In the Math-Island game, the curriculum is visualized as a knowledge map instead of a linear sequence, as in textbooks. By doing so, students are enabled to explore relationships in the mathematics curriculum represented by the knowledge map; that is, the structure of the different roads on Math-Island. Furthermore, before learning, students may preview what will be learned, and after learning, students may also reflect on how well they learned. Unlike traditional lectures or textbooks, in which students could only follow a predefined order to learn knowledge without thinking why they have to learn it, the knowledge map allows students to understand the structure of knowledge and plan how to achieve advanced knowledge. Although the order of knowledge still remains the same, students take primary control of their learning. In a sense, the knowledge map may liberate elementary students from passive learning.

Adopting the mechanisms of a construction management game

This 2-year study showed that the adaptation of two game mechanisms, construction and sightseeing, into the elementary mathematical curriculum could effectively improve students’ learning achievement. The reason may be that students likely developed interests in using Math-Island to learn mathematics actively, regardless of whether they are high- and low-achieving students.

Gaining a sense of achievement and ownership through the construction mechanism

Regardless of the construction mechanism, Math-Island allows students to plan and manage their cities by constructing and upgrading buildings. Math-Island took the advantages of construction management games to facilitate elementary students’ active participation in their mathematical learning. Furthermore, students may manage their knowledge by planning and constructing of buildings on their virtual islands. Like most construction management games, students set goals and make decisions so that they may accumulate their assets. These assets are not only external rewards but also visible achievements, which may bring a sense of ownership and confidence. In other words, the system gamified the process of self-directed learning.

Demonstrating learning result to peers through the sightseeing mechanism

As for the sightseeing mechanism, in conventional instruction, elementary students usually lack the self-control to learn knowledge actively (Duckworth et al. 2014 ) or require a social stage to show other students, resulting in low achievement and motivation. On the other hand, although previous researchers have already proposed various self-regulated learning strategies (such as Taub et al. 2014 ), it is still hard for children to keep adopting specific learning strategies for a long time. For these reasons, this study uses the sightseeing mechanism to engage elementary students in a social stage to show other students how well their Math-Islands have been built. For example, in Math-Island, although the students think that they construct buildings in their islands, they plan the development of their knowledge maps. After learning, they may also reflect on their progress by observing the appearance of the buildings.

In brief, owing to the construction mechanism, the students are allowed to choose a place and build their unique islands by learning concepts. During the process, students have to do the learning task, get feedback, and get rewards, which are the three major functions of the construction functions. In the sightseeing mechanism, students’ unique islands (learning result) can be shared and visited by other classmates. The student’s Math-Island thus serves as a stage for showing off their learning results. The two mechanisms offer an incentive model connected to the game mechanism’s forming a positive cycle: the more the students learn, the more unique islands they can build, with more visitors.

Conclusion and future work

This study reported the results of a 2-year experiment with the Math-Island system, in which a knowledge map with extensive mathematics content was provided to support the complete elementary mathematics curriculum. Each road in Math-Island represents a mathematical topic, such as addition. There are many buildings on each road, with each building representing a unit of the mathematics curriculum. Students may learn about the concept and practice it in each building while being provided with feedback by the system. In addition, the construction management online game mechanism is designed to enhance and sustain students’ interest in learning mathematics. The aim of this study was not only to examine whether the Math-Island system could improve students’ achievements but also to investigate how much the low-achieving students would be interested in learning mathematics after using the system for 2 years.

As for enhancing achievement, the result indicated that the Math-Island system could effectively improve the students’ ability to calculate expressions and solve word problems. In particular, the low-achieving students outperformed those of the norm in terms of word problem-solving. For enhancing interest, we found that both the low-achieving and the high-achieving students in the experimental school, when using the Math-Island system, maintained a rather high level of interest in learning mathematics and using the system. The results of this study indicated some possibility that elementary students could be able to learn mathematics in a self-directed learning fashion (Nilson 2014 ; Chen et al. 2012a , b ) under the Math-Island environment. This possibility is worthy of future exploration. For example, by analyzing student data, we can investigate how to support students in conducting self-directed learning. Additionally, because we have already collected a considerable amount of student data, we are currently employing machine learning techniques to improve feedback to the students. Finally, to provide students appropriate challenges, the diversity, quantity, and difficulty of content may need to be increased in the Math-Island system.

Abbreviations

Program for International Student Assessment

The percentile rank of a score

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The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors would like to thank the Ministry of Science and Technology of the Republic of China, Taiwan, for financial support (MOST 106-2511-S-008-003-MY3), and Research Center for Science and Technology forLearning, National Central University, Taiwan.

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CYCY contributed to the study design, data acquisition and analysis, mainly drafted the manuscript and execution project. HNHC was involved in data acquisition, revision of the manuscript and data analysis.ZHC was contributed to the study idea and drafted the manuscript. CCYL of this research was involved in data acquisition and revision of the manuscript. TWC was project manager and revision of the manuscript. All authors read and approved the final manuscript.

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Charles Y.C. Yeh is currently an PhD student in Graduate Institute of Network Learning Technology at National Central University. The research interests include one-to-one learning environments and game-based learning.

Hercy N. H. Cheng is currently an associate professor and researcher in National Engineering Research Center for E-Learning at Central China Normal University, China. His research interests include one-to-one learning environments and game-based learning.

Zhi-Hong Chen is an associate professor in Graduate Institute of Information and Computer Education at National Taiwan Normal University. His research interests focus on learning technology and interactive stories, technology intensive language learning and game-based learning.

Calvin C. Y. Liao is currently an Assistant Professor and Dean’s Special Assistant in College of Nursing at National Taipei University of Nursing and Health Sciences in Taiwan. His research focuses on computer-based language learning for primary schools. His current research interests include a game-based learning environment and smart technology for caregiving & wellbeing.

Tak-Wai Chan is Chair Professor of the Graduate Institute of Network Learning Technology at National Central University in Taiwan. He has worked on various areas of digital technology supported learning, including artificial intelligence in education, computer supported collaborative learning, digital classrooms, online learning communities, mobile and ubiquitous learning, digital game based learning, and, most recently, technology supported mathematics and language arts learning.

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Yeh, C.Y.C., Cheng, H.N.H., Chen, ZH. et al. Enhancing achievement and interest in mathematics learning through Math-Island. RPTEL 14 , 5 (2019). https://doi.org/10.1186/s41039-019-0100-9

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There are 2 common types of action research: participatory action research and practical action research.

• Participatory action research emphasizes that participants should be members of the community being studied, empowering those directly affected by outcomes of said research. In this method, participants are effectively co-researchers, with their lived experiences considered formative to the research process.
• Practical action research focuses more on how research is conducted and is designed to address and solve specific issues.

Both types of action research are more focused on increasing the capacity and ability of future practitioners than contributing to a theoretical body of knowledge.

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Action research is often reflected in 3 action research models: operational (sometimes called technical), collaboration, and critical reflection.

• Operational (or technical) action research is usually visualized like a spiral following a series of steps, such as “planning → acting → observing → reflecting.”
• Collaboration action research is more community-based, focused on building a network of similar individuals (e.g., college professors in a given geographic area) and compiling learnings from iterated feedback cycles.
• Critical reflection action research serves to contextualize systemic processes that are already ongoing (e.g., working retroactively to analyze existing school systems by questioning why certain practices were put into place and developed the way they did).

Action research is often used in fields like education because of its iterative and flexible style.

After the information was collected, the students were asked where they thought ramps or other accessibility measures would be best utilized, and the suggestions were sent to school administrators. Example: Practical action research Science teachers at your city’s high school have been witnessing a year-over-year decline in standardized test scores in chemistry. In seeking the source of this issue, they studied how concepts are taught in depth, focusing on the methods, tools, and approaches used by each teacher.

Action research differs sharply from other types of research in that it seeks to produce actionable processes over the course of the research rather than contributing to existing knowledge or drawing conclusions from datasets. In this way, action research is formative , not summative , and is conducted in an ongoing, iterative way.

As such, action research is different in purpose, context, and significance and is a good fit for those seeking to implement systemic change.

Action research comes with advantages and disadvantages.

• Action research is highly adaptable , allowing researchers to mold their analysis to their individual needs and implement practical individual-level changes.
• Action research provides an immediate and actionable path forward for solving entrenched issues, rather than suggesting complicated, longer-term solutions rooted in complex data.
• Done correctly, action research can be very empowering , informing social change and allowing participants to effect that change in ways meaningful to their communities.

Disadvantages

• Due to their flexibility, action research studies are plagued by very limited generalizability  and are very difficult to replicate . They are often not considered theoretically rigorous due to the power the researcher holds in drawing conclusions.
• Action research can be complicated to structure in an ethical manner . Participants may feel pressured to participate or to participate in a certain way.
• Action research is at high risk for research biases such as selection bias , social desirability bias , or other types of cognitive biases .

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Normal distribution
• Degrees of freedom
• Null hypothesis
• Discourse analysis
• Control groups
• Mixed methods research
• Non-probability sampling
• Quantitative research
• Inclusion and exclusion criteria

Research bias

• Rosenthal effect
• Implicit bias
• Cognitive bias
• Selection bias
• Negativity bias
• Status quo bias

Action research is conducted in order to solve a particular issue immediately, while case studies are often conducted over a longer period of time and focus more on observing and analyzing a particular ongoing phenomenon.

Action research is focused on solving a problem or informing individual and community-based knowledge in a way that impacts teaching, learning, and other related processes. It is less focused on contributing theoretical input, instead producing actionable input.

Action research is particularly popular with educators as a form of systematic inquiry because it prioritizes reflection and bridges the gap between theory and practice. Educators are able to simultaneously investigate an issue as they solve it, and the method is very iterative and flexible.

A cycle of inquiry is another name for action research . It is usually visualized in a spiral shape following a series of steps, such as “planning → acting → observing → reflecting.”

Sources in this article

We strongly encourage students to use sources in their work. You can cite our article (APA Style) or take a deep dive into the articles below.

George, T. (2024, January 12). What Is Action Research? | Definition & Examples. Scribbr. Retrieved August 4, 2024, from https://www.scribbr.com/methodology/action-research/

Cohen, L., Manion, L., & Morrison, K. (2017). Research methods in education (8th edition). Routledge.

Naughton, G. M. (2001).  Action research (1st edition). Routledge.

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Tegan George

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