what is problem solving chemistry

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How to Solve a Chemistry Problem

Last Updated: February 15, 2024

This article was co-authored by Anne Schmidt . Anne Schmidt is a Chemistry Instructor in Wisconsin. Anne has been teaching high school chemistry for over 20 years and is passionate about providing accessible and educational chemistry content. She has over 9,000 subscribers to her educational chemistry YouTube channel. She has presented at the American Association of Chemistry Teachers (AATC) and was an Adjunct General Chemistry Instructor at Northeast Wisconsin Technical College. Anne was published in the Journal of Chemical Education as a Co-Author, has an article in ChemEdX, and has presented twice and was published with the AACT. Anne has a BS in Chemistry from the University of Wisconsin, Oshkosh, and an MA in Secondary Education and Teaching from Viterbo University. This article has been viewed 19,293 times.

Chemistry problems can vary in many different ways. Some questions are conceptual and others are quantitative. Each problem requires its own approach, and each has a different way to solve it correctly. What you can do is make a set of steps that can help us with any problems that you come across in the field of chemistry. Using these steps should help give you a guideline to working on any chemistry problem you encounter.

Starting the Problem

Finishing the Problem

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Thanks for reading our article! If you’d like to learn more about chemistry, check out our in-depth interview with Anne Schmidt .

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• Research Matters — to the Science Teacher

Problem Solving in Chemistry

One of the major difficulties in teaching introductory chemistry courses is helping students become efficient problem solvers. Most beginning chemistry students find this one of the most difficulty aspects of the introductory chemistry course. What does research tell us about problem solving in chemistry? Just why do students have such difficulty in solving chemistry problems? Are some ways of teaching students to solve problems more effective than others? Problem solving in any area is a very complex process. It involves an understanding of the language in which the problem is stated, the interpretation of what is given in the problem and what is sought, an understanding of the science concepts involved in the solution, and the ability to perform mathematical operations if these are involved in the problem. The first requirement for successful problem solving is that the problem solver understand the meaning of the problem. In order to do so there must be an understanding of the vocabulary and its usage in the problem. There are two types of words that occur in problems, ordinary words that science teachers generally assume that students know and more technical terms that require understanding of concepts specific to the discipline. Researchers have found that many students do not know the meaning of common words such as contrast, displace, diversity, factor, fundamental, incident, negligible, relevant, relative, spontaneous and valid. Slight changes in the way a problem is worded may make a difference in whether a students is able to solve it correctly. For example, when "least" is changed to "most" in a problem, the percentage getting the question correct may increase by 25%. Similar improvements occur for changing negative to positive forms, for rewording long and complex questions, and for changing from the passive to the active voice. Although teachers would like students to solve problems in whatever way they are framed they must be cognizant of the fact that these subtle changes will make a difference in students' success in solving problems. From several research studies on problem solving in chemistry, it is clear that the major reason why students are unable to solve problems is that they do not understand the concepts on which the problems are based. Studies that compare the procedures used by students who are inexperienced in solving problems with experts show that experts were able to retrieve relevant concepts more readily from their long term memory. Studies have also shown that experts concepts are linked to one another in a network. Experts spend a considerable period of time planning the strategy that will be used to solve the problem whereas novices jump right in using a formula or trying to apply an algorithm. In the past few years, science educators have been trying to determine which science concepts students understand and which they do not. Because chemistry is concerned with the nature of matter, and matter is defined as anything that has mass and volume, students must understand these concepts to be successful problem solvers in chemistry. Research studies have shown that a surprising number of high school students do not understand the meaning of mass, volume, heat, temperature and changes of state. One reason why students do not understand these concepts is because when they have been taught in the classroom, they have not been presented in a variety of contexts. Often the instruction has been verbal and formal. This will be minimally effective if students have not had the concrete experiences. Hence, misconceptions arise. Although the very word "misconception" has a negative connotation, this information is important for chemistry teachers. They are frameworks by which the students view the world around them. If a teacher understands these frameworks, then instruction can be formulated that builds on student's existing knowledge. It appears that students build conceptual frameworks as they try to make sense out of their surroundings. In addition to the fundamental properties of matter mentioned above, there are other concepts that are critical to chemical calculations. One of these is the mole concept and another is the particulate nature of matter. There is mounting evidence that many students do not understand either of these concepts sufficiently well to use them in problem solving. It appears that if chemistry problem solving skills of students are to improve, chemistry teachers will need to spend a much greater period of time on concept acquisition. One way to do this will be to present concepts in a variety of contexts, using hands-on activities.

What does this research imply about procedures that are useful for helping students become more successful at problem solving?

Chemistry problems can be solved using a variety of techniques. Many chemistry teachers and most introductory chemistry texts illustrate problem solutions using the factor-label method. It has been shown that this is not the best technique for high school students of high mathematics anxiety and low proportional reasoning ability. The use of analogies and schematic diagrams results in higher achievement on problems involving moles, stoichiometry, and molarity. The use of analogs is not profitable for certain types of problems. When problems became complex (such as in dilution problems) students are unable to solve even the analog problems. For these types of problems, using analogs in instruction would be useless unless teachers are willing to spend additional time teaching students how to solve problems using the analog. Many students are unable to match analogs with the chemistry problems even after practice in using analogs. Students need considerable practice if analogs are used in instruction. When teaching chemistry by the lecture method, concept development needed for problem solving may be enhanced by pausing for a two minute interval at about 8 to 12 minute intervals during the lecture. This provides students time to review what has been presented, fill in the gaps, and interpret the information for others, and thus learn it themselves. The use of concept maps may also help students understand concepts and to relate them to one another. Requiring students to use a worksheet with each problem may help them solve them in a more effective way. The worksheet might include a place for them to plan a problem, that is list what is given and what is sought; to describe the problem situation by writing down other concepts they retrieve from memory (the use of a picture may integrate these); to find the mathematical solution; and to appraise their results. Although the research findings are not definitive, the above approaches offer some promise that students' problem solving skills can be improved and that they can learn to solve problems in a meaningful way.

For further information about this research area, please contact:

Dr. Dorothy Gabel Education Building 3rd and Jordan Bloomington, Indiana 47405

Problems and Problem Solving in Chemistry Education: Analysing Data, Looking for Patterns and Making Deductions

Problem solving is central to the teaching and learning of chemistry at secondary, tertiary and post-tertiary levels of education, opening to students and professional chemists alike a whole new world for analysing data, looking for patterns and making deductions. As an important higher-order thinking skill, problem solving also constitutes a major research field in science education. Relevant education research is an ongoing process, with recent developments occurring not only in the area of quantitative/computational problems, but also in qualitative problem solving.

The following situations are considered, some general, others with a focus on specific areas of chemistry: quantitative problems, qualitative reasoning, metacognition and resource activation, deconstructing the problem-solving process, an overview of the working memory hypothesis, reasoning with the electron-pushing formalism, scaffolding organic synthesis skills, spectroscopy for structural characterization in organic chemistry, enzyme kinetics, problem solving in the academic chemistry laboratory, chemistry problem-solving in context, team-based/active learning, technology for molecular representations, IR spectra simulation, and computational quantum chemistry tools. The book concludes with methodological and epistemological issues in problem solving research and other perspectives in problem solving in chemistry.

With a foreword by George Bodner.

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Problems and Problem Solving in Chemistry Education: Analysing Data, Looking for Patterns and Making Deductions, The Royal Society of Chemistry, 2021.

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• Front Matter
• Acknowledgments
• Author Biographies
• Chapter 1: Introduction − The Many Types and Kinds of Chemistry Problems p1-14 By Georgios Tsaparlis Georgios Tsaparlis University of Ioannina, Department of Chemistry Ioannina Greece [email protected] Search for other works by this author on: This Site PubMed Google Scholar Abstract Open the PDF Link PDF for Chapter 1: Introduction − The Many Types and Kinds of Chemistry Problems in another window
• Chapter 2: Qualitative Reasoning in Problem-solving in Chemistry p15-37 By Vicente Talanquer Vicente Talanquer Department of Chemistry and Biochemistry, University of Arizona Tucson AZ 85721 USA [email protected] Search for other works by this author on: This Site PubMed Google Scholar Abstract Open the PDF Link PDF for Chapter 2: Qualitative Reasoning in Problem-solving in Chemistry in another window
• Chapter 3: Scaffolding Metacognition and Resource Activation During Problem Solving: A Continuum Perspective p38-67 By Nicole Graulich ; Nicole Graulich Justus-Liebig-Universität Gießen Germany Search for other works by this author on: This Site PubMed Google Scholar Axel Langner ; Axel Langner Justus-Liebig-Universität Gießen Germany Search for other works by this author on: This Site PubMed Google Scholar Kimberly Vo ; Kimberly Vo Monash University Australia [email protected] Search for other works by this author on: This Site PubMed Google Scholar Elizabeth Yuriev Elizabeth Yuriev Monash University Australia [email protected] Search for other works by this author on: This Site PubMed Google Scholar Abstract Open the PDF Link PDF for Chapter 3: Scaffolding Metacognition and Resource Activation During Problem Solving: A Continuum Perspective in another window
• Chapter 4: Deconstructing the Problem-solving Process: Beneath Assigned Points and Beyond Traditional Assessment p68-92 By Ozcan Gulacar ; Ozcan Gulacar University of California, Davis, Department of Chemistry One Shields Avenue Davis CA 95616 USA [email protected] Search for other works by this author on: This Site PubMed Google Scholar Charlie Cox ; Charlie Cox Duke University, Department of Chemistry Box 90346, 128 Science Drive Durham NC 27708-0346 USA Search for other works by this author on: This Site PubMed Google Scholar Herb Fynewever Herb Fynewever Calvin University, Department of Chemistry 3201 Burton SE Grand Rapids MI 49546 USA Search for other works by this author on: This Site PubMed Google Scholar Abstract Open the PDF Link PDF for Chapter 4: Deconstructing the Problem-solving Process: Beneath Assigned Points and Beyond Traditional Assessment in another window
• Chapter 5: It Depends on the Problem and on the Solver: An Overview of the Working Memory Overload Hypothesis, Its Applicability and Its Limitations p93-126 By Georgios Tsaparlis Georgios Tsaparlis University of Ioannina, Department of Chemistry Ioannina Greece [email protected] Search for other works by this author on: This Site PubMed Google Scholar Abstract Open the PDF Link PDF for Chapter 5: It Depends on the Problem and on the Solver: An Overview of the Working Memory Overload Hypothesis, Its Applicability and Its Limitations in another window
• Chapter 6: Mechanistic Reasoning Using the Electron-pushing Formalism p127-144 By Gautam Bhattacharyya Gautam Bhattacharyya Missouri State University, Department of Chemistry 901 South National Avenue Springfield MO 65897 USA [email protected] Search for other works by this author on: This Site PubMed Google Scholar Abstract Open the PDF Link PDF for Chapter 6: Mechanistic Reasoning Using the Electron-pushing Formalism in another window
• Chapter 7: Scaffolding Synthesis Skills in Organic Chemistry p145-165 By Alison B. Flynn Alison B. Flynn Department of Chemistry and Biomolecular Sciences, University of Ottawa 10 Marie Curie Ottawa Ontario K1N 6N5 Canada [email protected] Search for other works by this author on: This Site PubMed Google Scholar Abstract Open the PDF Link PDF for Chapter 7: Scaffolding Synthesis Skills in Organic Chemistry in another window
• Chapter 8: Problem Solving Using NMR and IR Spectroscopy for Structural Characterization in Organic Chemistry p166-198 By Megan C. Connor ; Megan C. Connor Department of Chemistry, University of Michigan Ann Arbor Michigan USA [email protected] Search for other works by this author on: This Site PubMed Google Scholar Ginger V. Shultz Ginger V. Shultz Department of Chemistry, University of Michigan Ann Arbor Michigan USA [email protected] Search for other works by this author on: This Site PubMed Google Scholar Abstract Open the PDF Link PDF for Chapter 8: Problem Solving Using NMR and IR Spectroscopy for Structural Characterization in Organic Chemistry in another window
• Chapter 9: Assessing System Ontology in Biochemistry: Analysis of Students’ Problem Solving in Enzyme Kinetics p199-216 By Jon-Marc G. Rodriguez ; Jon-Marc G. Rodriguez University of Iowa, Department of Chemistry E355 Chemistry Building Iowa City Iowa 52242-1294 USA [email protected] Search for other works by this author on: This Site PubMed Google Scholar Sven J. Philips ; Sven J. Philips Purdue University, Department of Chemistry 560 Oval Drive West Lafayette IN 47907 USA Search for other works by this author on: This Site PubMed Google Scholar Nicholas P. Hux ; Nicholas P. Hux Purdue University, Department of Chemistry 560 Oval Drive West Lafayette IN 47907 USA Search for other works by this author on: This Site PubMed Google Scholar Marcy H. Towns Marcy H. Towns Purdue University, Department of Chemistry 560 Oval Drive West Lafayette IN 47907 USA Search for other works by this author on: This Site PubMed Google Scholar Abstract Open the PDF Link PDF for Chapter 9: Assessing System Ontology in Biochemistry: Analysis of Students’ Problem Solving in Enzyme Kinetics in another window
• Chapter 10: Problem Solving in the Chemistry Teaching Laboratory: Is This Something That Happens? p217-252 By Ian Hawkins ; Ian Hawkins Welch College Gallatin TN 37066 USA Search for other works by this author on: This Site PubMed Google Scholar Vichuda K. Hunter ; Vichuda K. Hunter Middle Tennessee State University, Department of Chemistry PO Box 68 Murfreesboro TN 37132 USA [email protected] Search for other works by this author on: This Site PubMed Google Scholar Michael J. Sanger ; Michael J. Sanger Middle Tennessee State University, Department of Chemistry PO Box 68 Murfreesboro TN 37132 USA [email protected] Search for other works by this author on: This Site PubMed Google Scholar Amy J. Phelps Amy J. Phelps Middle Tennessee State University, Department of Chemistry PO Box 68 Murfreesboro TN 37132 USA [email protected] Search for other works by this author on: This Site PubMed Google Scholar Abstract Open the PDF Link PDF for Chapter 10: Problem Solving in the Chemistry Teaching Laboratory: Is This Something That Happens? in another window
• Chapter 11: Problems and Problem Solving in the Light of Context-based Chemistry p253-278 By Karolina Broman Karolina Broman Umeå University Sweden [email protected] Search for other works by this author on: This Site PubMed Google Scholar Abstract Open the PDF Link PDF for Chapter 11: Problems and Problem Solving in the Light of Context-based Chemistry in another window
• Chapter 12: Using Team Based Learning to Promote Problem Solving Through Active Learning p279-319 By Natalie J. Capel ; Natalie J. Capel Keele University UK [email protected] Search for other works by this author on: This Site PubMed Google Scholar Laura M. Hancock ; Laura M. Hancock Keele University UK [email protected] Search for other works by this author on: This Site PubMed Google Scholar Chloe Howe ; Chloe Howe Keele University UK [email protected] Search for other works by this author on: This Site PubMed Google Scholar Graeme R. Jones ; Graeme R. Jones Keele University UK [email protected] Search for other works by this author on: This Site PubMed Google Scholar Tess R. Phillips ; Tess R. Phillips Keele University UK [email protected] Search for other works by this author on: This Site PubMed Google Scholar Daniela Plana Daniela Plana Keele University UK [email protected] Search for other works by this author on: This Site PubMed Google Scholar Abstract Open the PDF Link PDF for Chapter 12: Using Team Based Learning to Promote Problem Solving Through Active Learning in another window
• Chapter 13: Technology, Molecular Representations, and Student Understanding in Chemistry p321-339 By Jack D. Polifka ; Jack D. Polifka Department of Chemistry, Human Computer Interaction Program, Iowa State University Ames IA 50011 USA [email protected] Search for other works by this author on: This Site PubMed Google Scholar John Y. Baluyut ; John Y. Baluyut Math and Science Division, University of Providence Great Falls MT, 59405 USA Search for other works by this author on: This Site PubMed Google Scholar Thomas A. Holme Thomas A. Holme Department of Chemistry, Human Computer Interaction Program, Iowa State University Ames IA 50011 USA [email protected] Search for other works by this author on: This Site PubMed Google Scholar Abstract Open the PDF Link PDF for Chapter 13: Technology, Molecular Representations, and Student Understanding in Chemistry in another window
• Chapter 14: An Educational Software for Supporting Students’ Learning of IR Spectral Interpretation p340-360 By Maria Limniou ; Maria Limniou School of Psychology, University of Liverpool UK [email protected] Search for other works by this author on: This Site PubMed Google Scholar Nikos Papadopoulos ; Nikos Papadopoulos Department of Chemistry, Aristotle University of Thessaloniki Greece Search for other works by this author on: This Site PubMed Google Scholar Dimitris Gavril ; Dimitris Gavril Department of Chemistry, Aristotle University of Thessaloniki Greece Search for other works by this author on: This Site PubMed Google Scholar Aikaterini Touni ; Aikaterini Touni Department of Chemistry, Aristotle University of Thessaloniki Greece Search for other works by this author on: This Site PubMed Google Scholar Markella Chatziapostolidou Markella Chatziapostolidou Department of Chemistry, Aristotle University of Thessaloniki Greece Search for other works by this author on: This Site PubMed Google Scholar Abstract Open the PDF Link PDF for Chapter 14: An Educational Software for Supporting Students’ Learning of IR Spectral Interpretation in another window
• Chapter 15: Exploring Chemistry Problems with Computational Quantum Chemistry Tools in the Undergraduate Chemistry Curriculum p361-384 By Michael P. Sigalas Michael P. Sigalas Aristotle University of Thessaloniki, Laboratory of Quantum and Computational Chemistry, Department of Chemistry Thessaloniki 54124 Greece [email protected] Search for other works by this author on: This Site PubMed Google Scholar Abstract Open the PDF Link PDF for Chapter 15: Exploring Chemistry Problems with Computational Quantum Chemistry Tools in the Undergraduate Chemistry Curriculum in another window
• Chapter 16: Methodological and Epistemological Issues in Science Education Problem-solving Research: Linear and Nonlinear Paradigms p385-413 By Dimitrios Stamovlasis ; Dimitrios Stamovlasis Aristotle University of Thessaloniki Thessaloniki Greece [email protected] Search for other works by this author on: This Site PubMed Google Scholar Julie Vaiopoulou Julie Vaiopoulou Democritus University of Thrace Alexandroupolis Greece [email protected] University of Nicosia Nicosia Cyprus Search for other works by this author on: This Site PubMed Google Scholar Abstract Open the PDF Link PDF for Chapter 16: Methodological and Epistemological Issues in Science Education Problem-solving Research: Linear and Nonlinear Paradigms in another window
• Chapter 17: Issues, Problems and Solutions: Summing It All Up p414-444 By Georgios Tsaparlis Georgios Tsaparlis University of Ioannina, Department of Chemistry Ioannina Greece [email protected] Search for other works by this author on: This Site PubMed Google Scholar Abstract Open the PDF Link PDF for Chapter 17: Issues, Problems and Solutions: Summing It All Up in another window
• Chapter 18: Postscript – Two Issues for Provocative Thought: (a) The Potential Synergy Between HOTS and LOTS (b) When Problem Solving Might Descend to Chaos Dynamics p445-456 By Georgios Tsaparlis Georgios Tsaparlis University of Ioannina, Department of Chemistry Ioannina Greece [email protected] Search for other works by this author on: This Site PubMed Google Scholar Abstract Open the PDF Link PDF for Chapter 18: Postscript – Two Issues for Provocative Thought: (a) The Potential Synergy Between HOTS and LOTS (b) When Problem Solving Might Descend to Chaos Dynamics in another window
• Subject Index p457-467 Open the PDF Link PDF for Subject Index in another window

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Problem-Solving in Chemistry

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• George M. Bodner 19 &
• J. Dudley Herron 20  

Part of the book series: Science & Technology Education Library ((CTISE,volume 17))

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Bodner, G.M., Herron, J.D. (2002). Problem-Solving in Chemistry. In: Gilbert, J.K., De Jong, O., Justi, R., Treagust, D.F., Van Driel, J.H. (eds) Chemical Education: Towards Research-based Practice. Science & Technology Education Library, vol 17. Springer, Dordrecht. https://doi.org/10.1007/0-306-47977-X_11

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Scaffolding the development of problem-solving skills in chemistry: guiding novice students out of dead ends and false starts

First published on 6th May 2017

To scaffold the development of problem-solving skills in chemistry, chemistry educators are exploring a variety of instructional techniques. In this study, we have designed, implemented, and evaluated a problem-solving workflow – “Goldilocks Help”. This workflow builds on work done in the field of problem solving in chemistry and provides specific scaffolding for students who experience procedural difficulties during problem solving, such as dead ends (not being able to troubleshoot) and false starts (not knowing how to initiate the problem-solving process). The Goldilocks Help workflow has been designed to scaffold a systematic problem-solving process with a designation of explicit phases of problem solving, to introduce students to the types of questions/prompts that should guide them through the process, to encourage explicit reasoning necessary for successful conceptual problem solving, and to promote the development of metacognitive self-regulation skills. The tool has been implemented and evaluated over a two-year period and modified based on student and instructor feedback. The evaluation demonstrated a shift in students’ beliefs in their capacities to use the strategies required to achieve successful problem solving and showed their capacity to employ such strategies.

Introduction

Problem solving is a multifaceted activity, influenced by a variety of cognitive, motivational, and behavioural factors. Cognitive factors include content knowledge, understanding of concepts, and process skills. In this study, we focused on approaches for developing students’ problem-solving process skills. Specifically, we have designed, implemented, and evaluated the problem-solving workflow “Goldilocks Help” (GH), which builds on work done in the field of problem solving in chemistry and related fields. In particular, it provides specific scaffolding for students who experience procedural difficulties during problem solving, such as dead ends (not being able to troubleshoot) and false starts (not knowing how to initiate the problem-solving process).

For the purpose of this study, we are focusing on problem-solving research in the field of chemistry education with the emphasis on (i) student difficulties in problem solving, (ii) problem-solving approaches by different problem solvers, and (iii) problem-solving processes.

Prior research on student difficulties in solving chemistry problems

One of often cited manifestations of student difficulties exhibited during problem solving is the application of memorised algorithms, either successful or not, without clear understanding of why they are appropriate (“black boxes”, “plug ‘n chug”) ( Van Ausdal, 1988 ; Pushkin, 1998 ; Cohen et al. , 2000 ; Drummond and Selvaratnam, 2008 ; Gulacar et al. , 2014 ; Nyachwaya et al. , 2014 ). Students resort to rote memorisation when they are not motivated to tackle problems conceptually or when they are cognitively overloaded and thus cannot “afford” the mental capacity required for conceptual problem solving ( Overton and Potter, 2008 ; Gulacar et al. , 2014 ). Some students also think that they are supposed “to know” how to solve a problem, and if they do not know at the first read of the problem ( i.e. if they can not recall an appropriate algorithm) then there is no point trying ( Harper, 2005 ).

Orientation on declarative and procedural knowledge and poor understanding of meaning of mathematical representations ( Herron and Greenbowe, 1986 ) can cause students to superficially (sometimes, meaninglessly) manipulate mathematical equations ( Van Ausdal, 1988 ; Comeford, 1997 ; Cohen et al. , 2000 ; Drummond and Selvaratnam, 2008 ; Selvaratnam, 2011 ; Gulacar et al. , 2014 ). While they are able to correctly execute mathematical operations, they could be failing to make strong connections between mathematical forms and the physical reality. This issue arises particularly sharply when a problem requires integration of mathematics, chemistry, and reasoning.

Some students may experience one or more of the following challenges: an inability to extract relevant information from a problem ( Bodner and McMillen, 1986 ; Cohen et al. , 2000 ; Gulacar et al. , 2014 ) or recognise a need for additional information that may be required for solving a problem ( Van Ausdal, 1988 ), impediments in language comprehension resulting from a limited scientific vocabulary, confusions with word meaning ( Yuriev et al. , 2016 ), or misreading the problem ( Herron, 1996a ), an impaired ability to handle complexity ( i.e. multiple concepts) ( Gulacar et al. , 2014 ), and poor reasoning skills ( Cohen et al. , 2000 ). These issues often lead to ignoring assumptions and limitations associated with some algorithms ( Herron and Greenbowe, 1986 ; Van Ausdal, 1988 ; Nyachwaya et al. , 2014 ), rushing into the solution without first clarifying the problem ( Harper, 2005 ; Drummond and Selvaratnam, 2008 ; Selvaratnam, 2011 ), guessing based on irrelevant data ( Gulacar et al. , 2014 ), not knowing where to start ( Van Ausdal, 1988 ; Gulacar et al. , 2014 ), or giving up ( Harper, 2005 ; Drummond and Selvaratnam, 2008 ). The absence of a habit for checking and troubleshooting ( Herron and Greenbowe, 1986 ; Van Ausdal, 1988 ) and/or failure to use units correctly or at all ( Van Ausdal, 1988 ; Gulacar et al. , 2014 ) may manifest in the reporting of an incorrect or intermediate result ( Herron and Greenbowe, 1986 ) or an alternative result ( Herron, 1996a ) in place of the result called for in the problem.

Behavioural issues may also sometimes impede problem solving. These could manifest as negative attitudes and a lack of self-confidence in problem solving ( Harper, 2005 ; Drummond and Selvaratnam, 2008 ), focus on the “right answer” in preference to the problem-solving process ( Cohen et al. , 2000 ; Harper, 2005 ), and a reluctance to try a new approach to problem solving ( Van Ausdal, 1988 ; Comeford, 1997 ; Cohen et al. , 2000 ).

The causes of problem-solving difficulties are not only student-driven. The instructor-driven causes include classroom practices and instructional materials, expecting students to apply procedures without requiring them to demonstrate their reasoning ( Pushkin, 1998 ; Cohen et al. , 2000 ; Zoller, 2000 ; Nyachwaya et al. , 2014 ). While worked examples have their place, focusing purely on worked examples could inhibit the development of problem-solving skills ( Bodner and McMillen, 1986 ; Harper, 2005 ). Finally, the development of problem-solving skills could suffer due to an insufficient emphasis on (meta)cognitive strategies and a lack of integration between explicit and continuous training of (meta)cognitive strategies and content teaching in a range of contexts ( Cohen et al. , 2000 ; Drummond and Selvaratnam, 2008 ; Selvaratnam, 2011 ; Yu et al. , 2015 ). The main focus of this study is to address the latter issue along with a range of student-driven causes.

Problem-solving approaches

Algorithms are stepwise procedures for solving of well-defined tasks, guaranteeing arrival at a solution if the procedures are applied correctly. A range of algorithmic methods have been developed in chemistry to guide students through problem solving: “networks” ( e.g. , Waddling, 1988 ), “pathways” ( e.g. , McCalla, 2003 ), or “solution maps” ( e.g. , Selvaratnam and Canagaratna, 2008 ). Algorithms decrease the overload of the working memory ( Baddeley and Hitch, 1974 ) and allow individual steps in more complex sequences to be automated ( Johnstone and Al-Naeme, 1991 ). However, such methods are not applicable for solving complex chemistry problems since they are limited to specific problem types and lack the generality requisite for authentic tasks ( Bodner and McMillen, 1986 ).

On the other hand, strategic approaches give students a general direction, i.e. an overall sequence (not necessarily linear) of stages/phases of a solution process . While they do not guarantee arrival at a solution, they induce a systematic approach to problem solving ( De Corte et al. , 2012 ). They are useful for problem solving in the context of its definition by Wheatley: “what you do when you don’t know what to do” ( Wheatley, 1984 ). In accordance with this definition, problem solving requires trial and error, sometimes involving backwards or sideways steps. An “anarchistic” strategy to solving chemical problems, one that allows for trial and error, has been proposed by Bodner and co-workers ( Bodner, 2003 ). Bodner defined a successful problem solver as one who is able to extract relevant information from the problem statement, one who often uses drawing to represent a problem, is willing to “try something” when stuck, keeps track of the problem-solving process, and checks the answer to see if it makes sense ( Bodner, 2015 ).

Research on problem-solving processes

Whereas general problem-solving processes are very similar between different disciplines and reflect human problem solving ( Simon and Newell, 1971 ), each discipline implements these processes in a field-specific manner. Since chemistry problems require specific terminology and ways of prompting, instructional approaches need to foster discipline-specific problem-solving process skills.

Theoretical framework

Scaffolding.

A critical component of scaffolding is prompting . Prompts, embedded within learning environments, are seen by students as integral, not additional, structural elements ( Horz et al. , 2009 ). Successful prompts direct student attention to important information they may have overlooked, facilitate awareness of potential knowledge gaps, help them organise their thoughts, make their thinking “visible”, and recognise a need to evaluate the validity of their solutions ( Ge and Land, 2003 ). Guiding-through-questions, or Socratic questioning , effectively stimulates rational and logical thinking and reasoning and structures a problem-solving process. It promotes reflection and improves problem-solving skills ( Ge and Land, 2003 ; Rhee, 2007 ). Question prompts convey transcendent messages about what is important in problem solving, e.g. a question “what are you asked to determine?” conveys a message about the need to identify the goal ( Herron, 1996b ).

Metacognition and self-regulation

Self-regulated learning (SRL) represents proactive processes used by students to set goals, select and implement strategies, and self-monitor their effectiveness ( Zimmerman and Pons, 1986 ; Pintrich et al. , 1991 ; Zimmerman, 2008 ; Low and Jin, 2012 ). SRL is characterised by personal initiative, perseverance, and adaptive skill ( Zimmerman, 2008 ) and involves metacognitive, motivational, and behavioural engagement by students. Metacognitive self-regulation is enacted via planning, monitoring, and regulating ( Pintrich et al. , 1991 ). Planning activities, e.g. task analysis, activate prior knowledge and assist with organising information. Monitoring activities, e.g. self-questioning, help to integrate new information with prior knowledge. Regulating/controlling activities, e.g. evaluation and checking, assist in adjusting problem-solving behaviour.

Research questions

(1) Do students change their approach to problem solving when exposed to explicit and scaffolded instruction, using a specially designed problem-solving workflow?

(2) Does students’ metacognitive self-regulation, as related to problem solving, develop as a result of such instruction?

Design and development of “Goldilocks Help” workflow

The design of GH was informed by cognitive load ( Sweller, 1988 ; Sweller et al. , 2011a ) and information processing ( Roberts and Rosnov, 2006 ; St Clair-Thompson et al. , 2010 ) theories. Specifically, GH provides students with useful prompts while avoiding overloading their cognitive structures. This consideration was taken into account when designing the original version as described below ( Fig. 1 ), as well as when refining it, following the feedback from students and instructors (see Results section). Furthermore, we aimed for the right balance between prompts being useful ( i.e. going further than generic “analyse” or “plan” instructions) but not too specific so as to turn the workflow into an algorithm (hence, the name “Goldilocks” which alludes to The Story of Goldilocks and the Three Bears or the Goldilocks zone in astronomy). Finally, the prompts were designed to increase students’ awareness of their comprehension failures, and to trigger the use of additional information when necessary. The prompts were fashioned after the Socratic questioning used by the lead author in the actual face-to-face instruction over many years. The following paragraphs describe the structure and attributes of the problem-solving process as implemented in the “Goldilocks Help” workflow.

Understanding

The lack of knowledge, often not recognised by students, creates an obstacle at the very beginning of the problem-solving attempt (a false start of the first kind). In our workflow, students are encouraged to examine all the terms and concepts relevant to a given problem. In the first instance, it may simply entail reading a problem text and checking that all terms are clear, known, and their meaning understood. We have previously demonstrated the importance of a deep understanding of the terminology in promoting successful problem solving ( Yuriev et al. , 2016 ).

Misconceptions and alternative conceptions often do not manifest themselves until later in the process, where they may lead either to an incorrect solution or to getting stuck (a dead end of the first kind). An example of arriving at an incorrect solution is represented by solving this problem (presented in the context of reversible processes with no non-expansion work occurring): A sample containing two moles of oxygen gas is heated from 25.0 °C to 45.0 °C at atmospheric pressure. Predict enthalpy for this process . Unless students appreciate that the change in enthalpy is equal to energy absorbed or released as heat at constant pressure ( IUPAC, 2014 ), they may use the constant-volume heat capacity, rendering the answer incorrect.

To help avoid these common pitfalls, the GH workflow starts by asking students to define relevant terms present in the problem statement, as well as relevant relationships and principles. Students are then prompted to consider whether the meaning of all terms is clear and to consult the resources ( e.g. , textbook), if it is not.

Bodner and McMillen emphasised the critical importance of the early holistic stage of problem solving, to which they referred as cognitive restructuring ( Bodner and McMillen, 1986 ). Students need to recognise the initial and the goal states of the problem and then to use the results of this analysis for solving the problem. To quote Bodner and McMillen, these early steps “set the stage for the analytic thought processes that eventually lead to an answer”.

During problem analysis, any relevant assumptions need to be explicitly stated in order to select an appropriate course of action. For example, problems dealing with ionic equilibria of weak electrolytes often involve assuming a negligible extent of ionisation. If students do not explicitly make this assumption, they may internalise this concept as being a fact , characterising all solutions of weak electrolytes. This conjecture may be then inappropriately used in situations where it does not apply. For example, in problems where the extent of ionisation is known exactly or where it needs to be determined. Thus, ignoring the appropriateness/applicability of assumptions may lead to students embarking on an incorrect course of action (a dead end of the second kind) ( Nyachwaya et al. , 2014 ). To address these common pitfalls, the GH tool requires students to state the current and desired states ( i.e. , knowns and unknowns) and prompts students to consider their features.

To deal with these common pitfalls, the GH workflow directs students to establish the relationships between known parameters and the unknown(s) and then prompts them to consider whether all the relationships are clear and to consult the resources, if they are not. At this stage, it is also appropriate to prompt students as to whether all the information, required to determine the unknown(s), is available and to return to the analysis, if it is not. Unlike many practice and assessment problems that students encounter in their studies, authentic real-world problems are not posed with all the relevant data in a neat statement. The necessary information needs to be identified and sourced. Furthermore, real-world problem presentation often contains information that is actually not required to reach a solution. All these elements of complexity should be tackled at the planning stage.

Implementation

To deal with this lack of evaluation experience, the GH workflow prompts students to consider whether the answer is sensible and whether the units are correct. These two specific decision points have been selected based on common student difficulties. An example of a non-sensible answer is a numerically correct answer with a wrong sign: for example, confusing initial and final states of a process leads to a negative enthalpy for an endothermic process or vice versa (a dead end of the fourth kind). Another example of students producing non-sensible results is reporting negative temperature in Kelvin. Problem solving is impossible without making mistakes ( Martinez, 1998 ). It is important for students, on the one hand, to understand this and to accept mistakes and, on the other hand, develop methods to deal with mistakes as a necessary part of problem solving ( Herron, 1996b ; Kapur and Toh, 2015 ). To demonstrate evaluation strategies, GH contains a list of exemplar (but by no means comprehensive) troubleshooting prompts.

Ethics approval

Context and participants.

While some tasks involved simple mathematical manipulations of data, others had added elements of complexity. For example, one element of complexity involved data (such as compound properties) not being provided in the problem statement, with only system properties being given (such as mass, temperature, etc. ). Students were required to identify what information was required (as a result of early problem restructuring) and source it. The sources available to students (textbook tables, worksheet appendices) contained a wide range of data, so students needed to know what they were looking for rather than be guided by the data provided. Following is an example of such type of problem: Consider the chemical reaction 2H 2 O 2 (l) → 2H 2 O(l) + O 2 (g) in which liquid hydrogen peroxide decomposes into O 2 and water at 25 °C. Analyse available thermodynamic data, provided in the appendix, and determine the standard enthalpy change for this reaction, using TWO different methods. Suggest a reason why the two results are not identical . In this case students were able to access standard enthalpies of formation and mean bond enthalpies.

Another element of complexity involved including data that was not actually required for solving a given problem, for example: Extracts containing benzylpenicillin were prepared for analysis in buffer at pH 6.5 at 25 °C. The rate constant for the hydrolysis of benzylpenicillin under these conditions is 1.7 × 10 −7 s −1 . What is the maximum length of time (in hours) the solutions can be stored before analysis so that no more than 1% decomposition occurs?

Problem-solving workshop

Following this chemistry-unrelated task, students were presented with two chemistry questions. Q1: What is the concentration (% w/v) of a solution of 5 g of a salt dissolved in 200 mL of aqueous solution? Q2: A sample of 5 g of Ephedrine is dissolved in 200 mL of aqueous solution. What is the molar concentration of this solution? As expected, many students were able to solve Q1 almost instantly without a need to write anything down or use a calculator. For Q2, students came up with responses and queries that aligned with the problem-solving workflow.

Novice problem solvers often do not recognise that they are using a specific problem-solving procedure ( Herron, 1996a ). The tasks, presented to students in this workshop, are designed to make the process “more visible” and to encourage students to become aware of things they do when they solve problems (“problem solving behaviour” ( Herron, 1996a )), to pay attention to understanding problem terminology and to the early stages of problem analysis and solution planning.

Data collection and analysis

Each year, the inventory was administered twice, during the first and last weeks of the semester (pretest and posttest). The pretest was completed prior to the problem-solving activities of the workshop described above and prior to the introduction of the GH workflow. The inventory items were scored on a 5-point Likert scale (never, rarely, sometimes, often, and very often). From 93 to 115 students have participated in the four instances of the inventory administration. Matched data from 106 students was available for analysis.

In order to confirm that the component items in the modified scale were inter-correlated, the internal reliability of the modified scale was determined by calculating Cronbach's α on data obtained from the 2015 and 2016 cohorts. Cronbach's α was determined using the Statistical Package for Social Sciences (SPSS; IBM, Chicago). According to the results of the Cronbach's alpha analyses, all the included items measured different aspects of the same construct or sub-constructs, with alpha values consistently greater than 0.7 ( α [knowledge of cognition] = 0.75, α [regulation of cognition] = 0.83, α [overall] = 0.86). The calculated alpha values indicate that the desired level of internal consistency was achieved, and allows for the overall scores to be summed and analysed as a total, as an α value above 0.7 indicates that all of the items contained within a particular scale are measuring the same outcome, without unnecessary redundancy ( α values were all less than 0.9).

To determine the effect of a semester-long problem-solving approach on student metacognitive awareness, matched paired t -tests were performed to compare the data from before and after the intervention. The total and mean scores for the overall inventory, knowledge of cognition, regulation of cognition, and their sub-categories were determined. The pretest scores were compared with the posttest scores from the same students, identified by student-selected 4-character codes. Where students did not respond to a particular item, their data for that item was removed from the analyses, at the item, category, sub-construct and overall level. Descriptive statistics and paired t -tests were calculated using GraphPad Prism version 6 (La Jolla, California). Cohen's d , or effect size, was calculated for the overall inventory, knowledge of cognition and regulation of cognition, by subtracting mean pretest scores from mean posttest scores, and dividing by the average of the standard deviations (SD) of the two groups.

Workflow and instruction refinement based on student focus groups and academic feedback

Academic survey responses are summarised in Table 3 . The survey confirmed the construct validity of the GH workflow, demonstrated by positive responses to items 1–4 and 7 (52–71% agreement with only 1 or 2 respondents disagreeing). The instructors have also noted that, while the workflow is not confusing to expert problem solvers such as themselves (19 out of 21 responses), it could be confusing to students (19 out of 21 responses). Written comments related to (i) the need to add a loop from the evaluation phase back to analysis, (ii) the requirement to incorporate extra prompts for dimensional analysis, reflecting common problem-solving difficulties associated with units, and (iii) suggesting prompts for additional information sourcing.

These findings led to two instructional modifications in 2016. Firstly, the GH workflow was decluttered to reduce confusion and modifications suggested by academics were implemented ( Fig. 2 ). Secondly, modelling instruction was introduced into lectures and tutorials, where at least one of the problems allocated to each class period was worked through interactively, using explicit workflow prompts and colour-coding of the problem-solving stages.

End-of-semester reflections

With respect to the “Understand” phase, students noted the importance of this stage for the subsequent steps . They also commented about the importance of preparation and building conceptual knowledge for performing this step. However, some students had a limited perception of class preparation as just a “speeding-up” of the process (“Working on the problems beforehand made it easier to discuss as everyone had read the problems and therefore did not have to waste time rereading and trying to understand the questions”), indicating a need for further instructional attention to explaining to students the value of re-reading questions as a problem-solving technique.

Students repeatedly referred to various elements of the “Analysis” phase, such as relationships between concepts , restructuring the problem , and focusing on the data and the goals . Skipping the “Plan” phase is a known manifestation of novice problem solving ( Herron, 1996a ). Reflections showed that students learned to appreciate the slow-down that is involved in attending to planning a solution. Specifically, the consequences of the lack of planning and the value of a well written-out plan for later revision emerged as a strong notion. The timing of the planning was also mentioned. Regarding the “Evaluate” phase, students referred to specific checking strategies as well as critically assessing the overall processes . Students’ reflections showed not only that they learned what exactly to do to evaluate their solutions, but that they actually started doing it more regularly .

With respect to the workflow as a whole, some noted it helped them to commence , progress , and complete the problem-solving tasks. Adopting the GH workflow clearly required a change in some students’ approaches . Also, confusion caused by it was regularly mentioned, particularly in 2015, prior to the workflow refinement.

Two selected extensive quotes capture student development of the problem-solving approaches, influenced by the GH workflow:

– I have realised the importance of understanding exactly what a problem is asking and planning my solution. Instead of jumping straight into solving problems, I now more and more take the time to identify what I do and don't know and the process I need to go through to solve it. I used to just plug things into equations but I now have a greater understanding of why I am calculating something in this way and appreciating how something is derived. It not only means I am more likely to answer correctly but forces me to fully understand what I am doing and why, so this knowledge can be applied to many situations, including unfamiliar ones

– In the past it was routine for me to see a couple of numbers, find a formula that has all the variables, then to just put them in the calculator and get an answer. Although I might get the right answer or not it was the equivalent of a guess as I didn’t understand as to why I chose those numbers. However, as the semester progressed I have learned to slow down whilst attempting each question and to first analyze all the information before jumping to the calculator. It occurred to me that I first have to recognize any assumptions that are being made which may affect which formula I chose. Then to accurately write down all variables is essential and with all this in mind, at the end of the analysis and understanding of the question, is the time to pick the formula that has the necessary variables to solve what is being asked

In tutorials, students worked in small groups of 4–5 and, at the end of each class, a presenter from each group delivered a workshopped solution to the whole class. This setup provided students with multiple opportunities to experience the problem-solving approaches of others, within and between groups. Students talked about others’ way of thinking and strategising . They emphasised different ways of thinking rather than using different algorithms and discovered that different approaches may not be truly alternative, but rather complementary and integrative . Some students appreciated that it is useful not only to be exposed to other's solutions, but particularly others’ questions .

We have used students’ reflections to carry out a detailed thematic analysis of students’ perceptions of group work and the change in their teamwork skills as a result of the instructional design used in the course. This analysis is outside of the scope of the present work and will be published separately. Here, we are presenting themes associated with the effects of cooperation specifically on problem solving. Students reported enhanced understanding of concepts , disambiguation of misconceptions , consolidation of ideas , and complementarity . They appreciated the benefits from working with more knowledgeable peers as well as learning by teaching to those less proficient . Student resistance to group work is well known ( Hillyard et al. , 2010 ), so it was not surprising to come across negative comments about it (“I found this inefficient because everyone has their own way to solve the problems, so a lot of time was spent discussing rather than writing”). This last quote represents an instructional challenge in that some students do not appreciate the value of peer discussion for their learning and improvement of problem-solving skills.

While many students have declared that their problem-solving skills have improved as a result of this teaching and learning approach, some of them have done so in a self-critical, metacognitive manner. Specifically, they commented on their strengths and weaknesses and demonstrated a mature appreciation of the fact that learning problem-solving process and improving relevant skills is a process in itself . However, some have revealed their grade, rather than intrinsic, motivation when it comes to skills development as well as somewhat simplistic view of what problem solving is.

Students recognised challenges associated with problem-solving. Reported were general difficulties summarised vide supra such as not knowing where to start or verbalising the thought process . Many students expressed concerns over challenges associated with using a process-driven approach .

Metacognition and self-regulation inventory scores

Mean scores for the overall inventory, knowledge of cognition and regulation of cognition sub-constructs, and the categories are shown in Table 6 . The scores are provided as mean ± SEM, with N indicating the number of matched pairs, and p the significance reached after a paired t -test.

The primary aim of the intervention described in this paper was to support students in developing the metacognitive habit of self-questioning and in learning what type of questions to ask themselves during the problem-solving process. Furthermore, the use of the GH workflow was designed to encourage students to incorporate the prompts and questions into their problem-solving schema and, ultimately, to internalise them. These prompts capture what an experienced instructor would ask students if they were to get stuck during problem solving. Goldilocks Help problem-solving workflow provides these prompts to students themselves or arms a less experienced instructor with a specific mechanism to guide students.

Student engagement with the GH problem-solving workflow

The first theme represented the successful outcome of the intervention designed and implemented in this study. The second theme concerns students that have been previously exposed to structured problem solving. They show the internalisation of the process, the removal of the need for an explicit support ( Puntambekar and Hubscher, 2005 ), and therefore a student-controlled fading of scaffolding ( Wood et al. , 1976 ). The third theme is reminiscent of the earlier findings where students abandoned the problem-solving approach they were taught because they found it to be “too time consuming” ( Bunce and Heikkinen, 1986 ). It is also possible that the intervention presents a hurdle to students with low functional M-capacity and disembedding ability as well as low levels of scientific reasoning and working memory ( Tsaparlis, 2005 ). This theme demonstrated the need for workflow refinement and, together with feedback from instructors ( Table 3 ), led to a more streamlined version ( Fig. 2 ). The focus group and reflection comments about confusion also prompted us to implement an additional action in 2016, i.e. an emphasis on the steps within the process (gathering information, analysis, planning, and reflective evaluation) and explicit explanation and demonstration of what they entail, through modelling instruction.

How much structure and guidance is optimal? There are those who argue that providing excessive support structures confuses some learners, interferes with their own problem-solving schema, and leads to a decrease in performance ( Horz et al. , 2009 ; Nuckles et al. , 2010 ), mostly due to cognitive overload ( Sweller et al. , 2011b ). Others have argued that minimal structure and guidance do not work ( Kirschner et al. , 2006 ). Moreover, prompts may be too structured to be useful for some learners while others may be redundant once students have established their own internal schemas ( Belland, 2011 ). The challenge of over-structuring was actually found to be greater for high-achieving students ( Kalyuga, 2007 ). To address the issues of over-structuring, we have refined the original workflow to reduce excessive scaffolding. For example, we removed the planning prompt that asked students to consider the distinction between system properties ( e.g. , standard enthalpy of combustion) and process parameters ( e.g. , enthalpy for a given process with a specified mass of a compound being combusted). The concept of system-specific properties is an important one and is still included into the workflow, under the evaluation phase.

Importantly, when modifying the workflow, we did not aim to entirely eliminate possible confusion. Instead we used the instances of confusion, incidental as well as anticipated, to improve students’ problem-solving skills and metacognitive awareness. Specifically, one of the primary goals of presenting students with the GH workflow was to expose them to what expert problem-solving processes and expert thinking entail. Not unexpectedly, it is a long jump from algorithmic problem solving to conceptual thinking. It is challenging and, therefore, confusing and frustrating.

Contrary to how it is often perceived by students, confusion is not an entirely negative aspect of learning. Confusion, alongside flow, is an affective state that positively correlates with learning ( Craig et al. , 2004 ). Occasional complication of tasks by implementing specific scaffolds could be productive ( Reiser, 2004 ). In other words, disciplined struggle is good for learning. However, failure to resolve confusion and struggle could also promote frustration and decrease learning ( D’Mello and Graesser, 2010 ). Comments of the type “If you’d just tell me what equation to use, I’d be able to solve a problem” ( Harper, 2005 ) or “there must be an easier way” ( Van Ausdal, 1988 ) are not uncommon and convey frustration associated with problem solving. What we, instructors and students, do with that frustration makes the difference between learning and avoidance of learning. As instructors, we should take these instances of confusion and frustration to explain to students that problem solving is indeed a process and not a recall task and that the ability to see connections between initially abstract and seemingly disconnected pieces of information develops with practice and rests on organised, not memorised, knowledge.

Change in metacognitive awareness after one semester of the intervention

The increased scores for regulation of cognition are congruent with themes that emerged from students’ qualitative comments ( Table 4 ). Specifically, the increased planning scores were illustrated by students appreciating the detrimental consequences of not attending to the planning stage and the value of a well written-out plan for later revision, and the importance of attending to planning before plunging into calculations. The scores for the evaluation, debugging, and monitoring were reflected in students’ comments about specific checking strategies, critical assessment of the overall processes, and the significance of evaluating each time a problem-solving cycle is undertaken. The items within the information management strategies category deal with such aspects of problem solving as focusing on important information and on overall meaning rather than specifics and organising and linking information. These aspects align well with student notions related to understanding and analysis of problems: importance of preparation and building conceptual knowledge, relationships between concepts, and restructuring the problem.

Limitations of the study and future work

This study was carried out in an authentic classroom setting with the cohorts of students taught by one of the authors (E. Y.). This context prevented the use of an experimental control vs. treatment design, which would not have been ethical. In keeping with within-subject design, independent variables (such as prior academic ability) were not manipulated. And finally, it should be noted that problem-solving abilities of students are likely to be affected by factors outside of the unit of study where the Goldilocks Help tool was implemented. Thus, rather than making any claims about cause and effect, we present possible relationships based on the collected data.

In this paper, we have described the design of a problem-solving workflow intended for use in general and physical chemistry courses. We have now implemented it for analytical and formulation chemistry courses (without any modifications), as well as developed versions for use in spectroscopy, organic chemistry, and pharmacology subject areas, and pilot studies were undertaken in 2016. Future work will evaluate their effectiveness. Furthermore, we are collecting data on the problem-solving skill development of the cohorts described in this paper in the context of a longitudinal study.

Finally, in this study, the problem-solving process was used by first-year students to develop problem-solving skills, while tackling essentially closed, numerical problems. The literature shows that open-ended and complex problems require a much less linear and more iterative approach. However, skills acquired by novice students, when dealing with simpler problems, form the foundation for solving open-ended and complex problems.

Conclusions

Problem-solving metacognition and self-regulation inventory.

○ Declarative knowledge

■ I understand my intellectual strengths and weaknesses.

■ I am a good judge of how well I understand something.

○ Procedural knowledge

■ I have a specific purpose for each strategy I use.

■ I am aware of what strategies I use when I solve problems.

■ I find myself using helpful problem-solving strategies automatically.

■ I try to use strategies that have worked in the past.

○ Conditional knowledge

■ I learn best when I know something about the topic.

■ I use different problem-solving strategies depending on the situation.

■ I use my intellectual strengths to compensate for my weaknesses.

• Regulation of cognition

■ I ask myself questions about the material before I begin.

■ I think of several ways to solve a problem and choose the best one.

■ I read instructions carefully before I begin solving a problem.

■ To solve a problem, I first develop a plan with the sequence of steps necessary for completion.

■ I define each problem carefully before attempting to solve it.

○ Information management strategies

■ I consciously focus my attention on important information.

■ I create my own examples/diagrams and/or write my own notes to make information more meaningful.

■ I ask myself if the information in the problem is related to other information I know.

■ I focus on overall meaning rather than specifics.

■ Before solving a problem, I assemble and organize all the necessary information.

○ Monitoring

■ I consider several alternatives to a problem.

■ I periodically review to help me understand important relationships.

■ I find myself analysing the usefulness of strategies I use for solving problems.

■ I find myself pausing regularly to check my comprehension.

■ While solving a problem, I consider various aspects of the problem.

○ Debugging strategies

■ I change strategies when I fail to understand.

■ I re-evaluate my assumptions when I get confused.

■ After a problem is solved, I look for improvements on the solution process.

○ Evaluation

■ I summarize what I have learned after I finish.

■ I ask myself if I have considered all options after I solve a problem.

■ After a problem is solved, I reflect on it and on how its solution could help to solve future problems.

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• 1.1 Organic Chemistry
• 2 Stoichiometry

Chemistry is the study of interactions between atoms at a macroscopic or microscopic (molecular) level.

Organic Chemistry

Organic chemistry is a branch of chemistry that focuses on molecules that contain carbon. Although most of organic chemistry is nonliving, organic chemistry is the basis of life.

Stoichiometry

Stoichiometry is about calculating the amount of certain substances in a chemical reaction.

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A model approach to solving problems

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Use models in your teaching to help students learn how to find solutions

Source: © Tobatron

Models help students solve problems in the science classroom, a skill they will take into the wider world

In science, as in everyday life, there are many problems to solve. As science teachers, we use models all the time in our lessons, not just because they are explicitly mentioned in exam board specifications, but also because they help make abstract concepts more concrete. How do we help our students use models to problem solve in their science education?

Problem solving in everyday life

As a starting point, we can link models and problem solving to everyday life. In class, a student can successfully neutralise an acid using an alkali. We can gain student buy-in by applying this to situations outside the classroom, for example the need to brush our teeth.

Introduce routines around problem solving to motivate students

Taking it further, we can use their classroom experience of models when thinking about future careers. We can emphasise that problem solving is a fundamental skill in all jobs. We can embed the idea that problem solving isn’t simply something being learned in the classroom. Rather, it is a skill that will help them be successful in their later lives. To help them understand this concept, ask students to name a job and then explain how problem solving would be successfully used in that job.

Introduce routines around problem solving to motivate students into believing they have a strategy to attempt a task. Teach your students to use a textbook if they’re stuck. Teach them how to use the contents and index pages. This reinforces a skill that encourages independence and will benefit them if they run out of mobile data.

Promote engagement with students needing more encouragement by using a simple rhyme and choral response: ‘What do we do if we’re stuck?’ – ‘We look in a textbook’. If students find a task too hard and can’t solve the problem, motivation will fall and possibly lead to behavioural issues. While this approach needs a big input of teacher direction to begin with, over time the skill will embed.

Download this

Evaluate multiple models activity, for age range 14–16

Enhance your learners' skills interpreting and evaluating models with this set of examples showing a hydrogen molecule.

Download the teacher notes as MS Word or pdf , slides as PowerPoint or pdf and student worksheet as MS Word or pdf.

Multiple-models activity, for age range 14–16 years

Enhance your learners’ skills interpreting and evaluating models with this set of examples showing a hydrogen molecule, including classroom slides and a worksheet.

Download the activity from the Education in Chemistry website: rsc.li/3x7j2KW

Using models

While models are scattered throughout the curriculum, there are some best bets of where they routinely apply. When discussing JJ Thomson’s plum pudding model, students could choose a different model that represents the same idea, for example, a chocolate chip cookie. After a chromatography practical, students can be encouraged to identify an unknown substance based on different Rf values.

Acronyms are a useful model that students can learn to apply to similar questions. For example, to aid students in successfully drawing covalent bonding , introduce them to GROSO:

• g roup number
• r equired shared pairs
• o verlap circles
• s hared pairs drawn in
• o ther outer electrons

Acronyms are a useful model that students can learn to apply to similar questions. For example, to aid students in successfully drawing covalent bonding, introduce them to GROSO:  g roup number;  r equired shared pairs;  o verlap circles;  s hared pairs drawn in;  o ther outer electrons.

Initially, this would need lots of practice and quick checks using mini whiteboards. Once the routine is embedded though, students can take this model and apply it to other covalent questions.

Worked examples also support students by providing a scaffold of how to answer a question. By referencing a completed question, students can attempt a question by following the steps.

More recommended resources

• Use Johnstone’s triangle to help learners of all ages and stages model their thinking.
• Our online Problem solving tutor  will help your 16–18 learners to structure and develop their problem solving skills in quantitative chemistry.
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• Show your students how models can help to predict reactions and influence the taste and texture of chocolate and biscuits, by sharing a profile of food scientist, Robert .
• Use Johnstone’s triangle to help learners of all ages and stages model their thinking: rsc.li/3mLA282
• Our online Problem solving tutor will help your 16–18 learners to structure and develop their problem solving skills in quantitative chemistry: rsc.li/3DJRJtG
• Find out how to use post-16 models to inform 14–16 understanding: rsc.li/3HYxHy6
• Show your students how models can help to predict reactions and influence the taste and texture of chocolate and biscuits, by sharing a profile of food scientist, Robert: rsc.li/3RCMMZl

Focusing on problem solving is also a brilliant opportunity to work with other departments. If multiple departments are using the same routine, students are more likely to commit this to long-term memory, thus reducing cognitive load.

The Ofsted research review into science contains a section on coherence between the mathematics and science departments describing how to share similar language around tackling equations. If students can problem solve in maths, we can show them how to carry that skill across by using the same method in science. Many maths departments teach the balance method to solve equations. You can apply this to many chemistry calculations, such as titration.

The Ofsted research review into science contains a section on coherence between the mathematics and science departments describing how to share similar language around tackling equations (rsc.li/3Yx4yjf). If students can problem solve in maths, we can show them how to carry that skill across by using the same method in science. Many maths departments teach the balance method to solve equations. You can apply this to many chemistry calculations, such as titration.

By using these strategies and questions with our students, we can teach them the importance of problem solving. These are skills, once learned, that students can carry with them for future success.

This article is part of our Teaching science skills series, bringing together strategies and classroom activities to help your learners develop essential scientific skills, from literacy to risk assessment and more.

More Holly Walsh

Using multiple models in science | 14–16 years

Atoms, molecules and compounds quiz | 11–14 years

How is carbon cycled? | 11–14 years

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Chemistry Assistant

Ai-powered chemistry problem solver.

• Homework Help: Students can use the Chemistry Assistant to help understand and work through chemistry problems in their homework.
• Teaching Aid: Teachers can use this tool to generate solutions to chemistry problems, aiding in lesson planning and student instruction.
• Exam Preparation: Use the Chemistry Assistant to prepare for chemistry exams by solving practice problems and getting explanations of chemistry terms and principles.
• Research Assistance: Researchers can use this tool to help work through chemistry problems in their work.

Yes, the Chemistry Assistant is designed to handle a wide range of chemistry problems, from basic to advanced. However, it's always important to cross-verify the solutions provided by the AI with trusted resources or professionals in the field to ensure accuracy and understanding, especially with more complex problems and principles.

While the Chemistry Assistant is specifically designed for chemistry problems, HyperWrite offers other AI tools for different subjects and needs. You can explore more tools at app.hyperwriteai.com/tools .

New & Trending Tools

Ai christmas card message generator, ai chemistry research assistant.

Module 5: Thinking and Analysis

Problem-solving with critical thinking, learning outcomes.

• Describe how critical thinking skills can be used in problem-solving

Most of us face problems that we must solve every day. While some problems are more complex than others, we can apply critical thinking skills to every problem by asking questions like, what information am I missing? Why and how is it important? What are the contributing factors that lead to the problem? What resources are available to solve the problem? These questions are just the start of being able to think of innovative and effective solutions. Read through the following critical thinking, problem-solving process to identify steps you are already familiar with as well as opportunities to build a more critical approach to solving problems.

Problem-Solving Process

Step 1: define the problem.

Albert Einstein once said, “If I had an hour to solve a problem, I’d spend 55 minutes thinking about the problem and five minutes thinking about solutions.”

Often, when we first hear of or learn about a problem, we do not have all the information. If we immediately try to find a solution without having a thorough understanding of the problem, then we may only be solving a part of the problem.  This is called a “band-aid fix,” or when a symptom is addressed, but not the actual problem. While these band-aid fixes may provide temporary relief, if the actual problem is not addressed soon, then the problem will continue and likely get worse. Therefore, the first step when using critical thinking to solve problems is to identify the problem. The goal during this step is to gather enough research to determine how widespread the problem is, its nature, and its importance.

Step 2: Analyze the Causes

This step is used to uncover assumptions and underlying problems that are at the root of the problem. This step is important since you will need to ensure that whatever solution is chosen addresses the actual cause, or causes, of the problem.

Asking “why” questions to uncover root causes

A common way to uncover root causes is by asking why questions. When we are given an answer to a why question, we will often need to question that answer itself. Thus the process of asking “why” is an  iterative process —meaning that it is a process that we can repeatedly apply. When we stop asking why questions depends on what information we need and that can differ depending on what the goals are. For a better understanding, see the example below:

Problem: The lamp does not turn on.

• Why doesn’t the lamp turn on? The fuse is blown.
• Why is the fuse blown? There was overloaded circuit.
• Why was the circuit overloaded? The hair dryer was on.

If one is simply a homeowner or tenant, then it might be enough to simply know that if the hair dryer is on, the circuit will overload and turn off.  However, one can always ask further why questions, depending on what the goal is. For example, suppose someone wants to know if all hair dryers overload circuits or just this one. We might continue thus:

• Why did this hair dryer overload the circuit? Because hair dryers in general require a lot of electricity.

But now suppose we are an electrical engineer and are interested in designing a more environmentally friendly hair dryer. In that case, we might ask further:

• Why do hair dryers require so much energy?

As you can see from this example, what counts as a root cause depends on context and interests. The homeowner will not necessarily be interested in asking the further why questions whereas others might be.

Step 3: Generate Solutions

The goal of this step is to generate as many solutions as possible. In order to do so, brainstorm as many ideas as possible, no matter how outrageous or ineffective the idea might seem at the time. During your brainstorming session, it is important to generate solutions freely without editing or evaluating any of the ideas. The more solutions that you can generate, the more innovative and effective your ultimate solution might become upon later review.

You might find that setting a timer for fifteen to thirty minutes will help you to creatively push past the point when you think you are done. Another method might be to set a target for how many ideas you will generate. You might also consider using categories to trigger ideas. If you are brainstorming with a group, consider brainstorming individually for a while and then also brainstorming together as ideas can build from one idea to the next.

Step 4: Select a Solution

Once the brainstorming session is complete, then it is time to evaluate the solutions and select the more effective one.  Here you will consider how each solution will address the causes determined in step 2. It is also helpful to develop the criteria you will use when evaluating each solution, for instance, cost, time, difficulty level, resources needed, etc. Once your criteria for evaluation is established, then consider ranking each criterion by importance since some solutions might meet all criteria, but not to equally effective degrees.

In addition to evaluating by criteria, ensure that you consider possibilities and consequences of all serious contenders to address any drawbacks to a solution. Lastly, ensure that the solutions are actually feasible.

Step 6: Put Solution into Action

While many problem-solving models stop at simply selecting a solution, in order to actually solve a problem, the solution must be put into action. Here, you take responsibility to create, communicate, and execute the plan with detailed organizational logistics by addressing who will be responsible for what, when, and how.

Step 7: Evaluate progress

The final step when employing critical thinking to problem-solving is to evaluate the progress of the solution. Since critical thinking demands open-mindedness, analysis, and a willingness to change one’s mind, it is important to monitor how well the solution has actually solved the problem in order to determine if any course correction is needed.

While we solve problems every day, following the process to apply more critical thinking approaches in each step by considering what information might be missing; analyzing the problem and causes; remaining open-minded while brainstorming solutions; and providing criteria for, evaluating, and monitoring solutions can help you to become a better problem-solver and strengthen your critical thinking skills.

iterative process: one that can be repeatedly applied

• Problem solving. Authored by : Anne Fleischer. Provided by : Lumen Learning. License : CC BY: Attribution
• College Success. Authored by : Matthew Van Cleave. Provided by : Lumen Learning. License : CC BY: Attribution
• wocintech stock - 178. Authored by : WOCinTech Chat. Located at : https://flic.kr/p/FiGVWt . License : CC BY-SA: Attribution-ShareAlike
• Five whys. Provided by : Wikipedia. Located at : https://en.wikipedia.org/wiki/Five_whys . License : CC BY-SA: Attribution-ShareAlike

Analyzing the Impact of Time Spent on Practice Questions on General Chemistry Students' Problem-Solving Performance

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37 Problem-Solving Products That’ll Basically Erase Eyesores In Your Home

All those things you've wanted to fix in your home...we've got a solution, right here.

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1. A sleek and discreet  shoe-storage cabinet  for the pile of shoes quickly becoming a hazard in your entryway. Not to mention, you can even put a catchall tray or mail folder for an additional surface!

And sure, it's designed for shoes, but some reviewers even use it as a media console for games and other electronics!

Promising reviews: "I love this piece. Before, everyone in the family would come in and throw their shoes off and the area was a mess. Now everyone takes time to put their shoes in this and the area looks so nice. I’ve had many compliments on it." — Vicki Davis

"I’ve had open shoe racks and the shoes were always falling out. Now all my shoes are contained and organized and hidden in a nice cabinet that’s low profile ." — Kirsten Soquel

Get it from Amazon for $139.99 (be sure to clip the $20 off coupon for this price)

2. A faux book display  that'll ingeniously hide all your cords and electronics to make your media console, desk, or bookshelf look waaaayyyy tidier and organized!

Promising review : "We absolutely love our CovoBox. It fits perfectly into our cabinet, and the cable modem/router, AppleTV, and external hard drive, and their various cables are now cleverly disguised as Harry Potter books 1–7. Great customer service, quick delivery, and a fabulous product. Two thumbs way, way up!" — John Grace

Get it from Covogoods on Etsy for $12+ (originally $24+; available in various customizations and sizes) OR from Amazon Handmade for $29+ (you'll choose customizations before adding to your cart).

Covogoods is a woman-founded small business based in Utah creating unique storage products from up-cycled books.

3. A large  woven storage basket  that's a perfect option for storing all those extra throw blankets until guests come over to cozy up for a movie or Netflix marathon. It takes organization to the next level with a minimalist knit design that effortlessly blends in with your living space.

Promising review : "This organizing basket is just what I was looking for to store our warm winter throws in our family room. It’s absolutely beautiful! The two-tone colors match my space perfectly! The basket material is very thick and sturdy. It easily holds its shape, even when empty. I am so pleased with the quality and the craftsmanship. I will definitely look into other sizes and styles." — Sky

Get it from Amazon for $24.99+ (available in three sizes and two styles/colors).

4. Some  brick whitewash paint  to transform your current fireplace into one that looks like it'd be the focal point in a home on Apartment Therapy. Plus, it'll brighten up your room!

Promising review: "This is amazing!!!!! It looks like a different fireplace. I have been looking at a horrible grout repair that the previous owners did for 20 years. I did this in about two hours!!!!!! This product is fast, it's easy to use, easy to clean up, and inexpensive ." — Denise

Get a pint from Amazon for $29.95 .

5. A ventilated  cable management box , so you can put all those tangled cords out of sight without having to rearrange all your electronics. Trust, your household will be so grateful to not be tripping over cords every time they walk into your WFH office or living space.

And grab a sleek  cable sleeve  (aka a wire cover) while you're at it!

Promising review : "My cords look so much neater now. I also used a cord protector to bind up my cords. My surge protector fit nicely in the box. Very happy with my purchase." — Amazon Customer

Get a two-pack from Amazon for $36.99+  (available in four colors).

6. Orrr an  under-desk cable management tray in case your desk is a cluster of dangling cords and you want to keep them and  the surge protector they're plugged into organized and concealed.

Zero tools are required, and it's designed with a two-way clamp for both horizontal and vertical surfaces. It can be used on desks up to 3.1 inches thick.

Promising review:  "First impression of the CarryUp, the build of it is solid and felt heavy. The weight of it made me confident it will hold up well and last me a long time.  Overall, setup was a breeze. No tools needed at all. One sentence that sums up this product for me...Simple and effective!!!!!  If you have messy cords underneath your desk then don't think, just buy this product." — Eddie Sadiwa

Get it from Amazon for   $24.99  (also available in cream).

BadShelfie is a POC-owned small business creating space-saving storage and organization solutions.

7. A  bathroom storage tower  with a slim design, so you can make use of that awkward space between your toilet and sink or wall. It's also designed with a toilet paper dispenser, a small shelf, and a storage door if you want to hide your plunger, toilet brush, and cleaner!

Promising review: "So easy to put together I could put it together with my eyes closed. Fit amazingly perfectly between the tub and the toilet and it has created so much more space, and my bathroom is no longer cluttered because of this product." — COS45B

Get it from Amazon for $35.68+ (available in three colors and checkout the storefront for more size options).

8. Some concrete paint  in case you've been wanting to redo your floors, garage, pool deck, or get creative with a DIY project. If you love to paint and have the time for a moderately difficult home upgrade, get ready to show off those before and after photos to everyone (even if they've never stepped foot in your home)!

It dries with a satin finish!

Promising review: "Works great. Used it in the basement for a quick, simple, inexpensive upgrade to brighten up the floor a bit and give the cement a clean look. Did a fairly good job filling in some of the hairline cracks as well." — T

Get a gallon from Amazon for $35+  (available in two colors).

9. A litter box enclosure , so you can hide the much-needed litter box from being the focal point of your living space whenever your adorable feline traipses over. It looks decorative and can even be used as surface for potted plants, pictures, and more, so no one has to know it's specifically for your kitty's business.

Promising reviews:  "I absolutely, LOVE this litter box cabinet. I used to keep it in my closet until noticing my clothes would have a chalky film on them. This is perfect! ! Not only does it hide the box itself, but it helps contain any smells that are beginning to emanate from the box.  I clean it out every other day and have never noticed any odors. I also took out the divider, because my box was a few inches too long. All changing supplies are kept inside, so it works out great! I HIGHLY recommend this litter box cabinet!!" — Angie

"This is the perfect way to conceal a litter box as well as the odors and dust that come with them.  I have noticed a significant difference in the air quality in my home, it is as if I don't even have a litter box." — Annie

Get it from Wayfair for  $74.99+  (available in three colors).

10. A finish restorer  to wipe on your faded, worn furniture or floors to bring them back to their newly installed glory! If you're sick of staring at antique furniture that simply needs a refresh, you won't regret this.

You won't completely be restoring a piece, but this is a quick way to make your furniture,  floors ,  front doors , and  kitchen cabinets  look brand-spankin' new for less.

Promising review:  "Very easy to get results. I applied to eight dining room chairs that had scrapes, scuffs, and white paint marks. An amazing transformation so quickly.  I finished eight chairs in 90 minutes without rushing.  I bought two pints, but only one was necessary. I used a cotton cloth for most of the application but also used 0000 steel wool for the scrapes and paint removal." — Grumpy Neanderthal

Get it from Amazon for  $9.99+  (available in nine wood finish colors; also available in  larger sizes ). Many reviewers follow up with the same brand's wood polish and conditioner (they're meant to be used together!), which you can get for  $9.98  from Amazon.

11. Or a set of wood repair markers  for those smaller scratches and scuffs that don't require a full replacement or refinish — seriously, it'll take only a few minutes to make your furniture or floor look like new!

Former BuzzFeed Shopping editor  Abby Kass  says:  "I used a similar kit on my TV stand after moving it into my current apartment, and it worked great! It was super easy to use — you just color in the scratch. And you can't tell the difference. It's amazing! And next time I move, I'm def hiring movers."

Promising reviews:  "I can’t believe how well these work! Much better than I was expecting. I just had my home interior painted, and the painters damaged a fiberboard medicine cabinet when they removed the masking tape. It ripped off the fake-wood veneer.  These markers completely filled in the ugly spots, and the colors blended well. I love that it appears to have some clear coat in it, too, as it dries with a slight shine that makes it look more like wood stain rather than marker.  I also used them to stain wood filler in two spots in my maple kitchen cabinets where a previous homeowner had hung a paper towel holder, and I really struggle to see the hole! It looks fantastic. I highly recommend this set. It’s a good value and works very well." — Shane

"These are great. I have several finishes on different pieces of furniture, and after several years, they were showing lots of scratches. Not anymore.  Super easy to use and covered everything.  Wasn't sure after paying such a minimal price that they'd work, but they really do." — Kindle Customer

Get a set of 13 markers from Amazon for  $9.99 .

12. A roll of  faux ivy , which adds a certain  je ne sais quoi  to your boring fence, railing or trellis. It's giving, "you no longer have the privilege to view me and my bougie lifestyle" and your neighbors better respect it.

Promising review:  "This was exactly what we needed for the backyard.  It definitely provides enough privacy, and it gives the backyard a very nice ambiance!  The leaves completely blend in with the other trees and plants we have in the backyard, and it looks like we made a huge upgrade in our gardening game. I'm now just hoping it can withstand the AZ summer and not fade with the sun (product description does state fade-resistant). Don't be hesitant with purchasing; it's totally worth it!!" — Amazon Customer

Get a roll from Amazon for  $44.99+  (available in three sizes). You'll need some  green zip ties  to secure them, too.

13. A set of  under-bed storage bags  for anyone who needs a place to put those off-season clothes or extra towels and bedding when not in use. Just pack them up and slide them out of sight!

Promising review:  " These storage bags are fantastic. I live in a small apartment where storage space is at a premium.  I use these to store my Costco toilet paper and paper towels so I don't need to make as many trips to the store. It keeps them in pristine condition and out of sight. The handles make them easy to pull in and out, and they fold up nicely when not in use. I'm thinking about getting two more since four will fit under my queen bed." — Kimberly Dorn

Get a two-pack from Amazon for  $13.97+  (available in three colors and in packs of four).

14. A pleated bed skirt , which will hide whatever is under your bed, be it storage, a snoozing pet and their horde of toys, shoes, or nothing at all.

Promising review: "Looks great — really ‘finishes’ off the look. Ironed very easily and looks really nice. Material is very soft and holds the pleat." — AM

Get it from Target for $23.99+ (originally $28.99+ available in seven sizes and 13 colors).

15. A TV cord cover  in case you decided to mount your TV and hate the way the cords look hanging down the wall — with this, you can keep things neat, tidy, and matching your room aesthetic, and no one will even notice! (Seriously, can you see it below?)

Promising review : "These look great and are super easy to apply. This is the perfect solution for hiding a cord! It looks like it is just a part of the baseboard. Mine is covering a cable wire only, but I think they are big enough to hide more than one cord if needed. I didn’t cut mine, and I bought two. You can tell where the two meet if you look closely. However, I do not think anyone would notice. I can’t believe I let our cable cord sit across the floor for this long. I wish I would have found these sooner! " — Amazon Customer

Get it from Amazon for $19.99+ (available in three sizes, five colors, and in multipacks).

16. A miniature bottle of touch-up paint  to help you disappear those scuffs, scratches, and stains that cleaning doesn't seem to get rid of. It's so renter-friendly, you can use it on your furniture, walls, and floors without your landlord getting wise.

Promising review: "I usually don't leave reviews, but I have to with this touchup paint. I had cheap Command hooks on my wall to hang up my curtains in my apartment, and they ended up falling off and damaging the wall. I brought this to cover it up since it was an eyesore, and this worked perfectly! Thankfully, I matched the right shade, and you can't even tell. It's easy to use and not messy at all. Once it dries, it instantly blends in. I'm glad it worked so well because now I can put more stuff on my walls and fix it with the paint so it won't affect my security deposit, LOL." — N.D.

Get it from Amazon for $18.95 (available in three sizes, 24 colors, and in sets of three).

17. Some splurge-worthy  self-priming paint  so you can make your room the one of your dreams with these bold, beautiful colors. Plus, it's created without any toxic solvents, meaning you don't have to air out the room overnight afterward!

The paint is low-odor, washable, scrubbable, and self-priming! See their entire selection of interior paints  here .

And if you're not sure what colors to go with, take Clare's Color Genius Quiz !

Get a gallon from Clare for $74+ (also available as a quart for $28, a sample for $3, and with or without the seven-piece paint kit).

Clare is a Black and woman-owned paint company founded by interior designer Nicole Gibbons. They offer a wide assortment of colors to make paint shopping an effortless experience. Plus, their swatches are peel-and-stick, which is perfect for renters!

18. An electrical cord cover  that'll hide the not-so-cute chain keeping your chandelier or pendant light in place without detracting from the vibes of the room.

Promising review:  "This is a great product. [It]  serves the purpose of covering ugly cords and looks beautiful. Also easy to install.  Got lucky and the color I chose from the chart offered matched exactly to our wall color!" — Deborah Smith

Get it from Amazon for  $20.13+  (available in 14 colors and as a two-pack).

19. An electric pressure washer  because the exterior of your home has to make a good first impression, too! Restore your stone, brick, wood, and concrete surfaces to their original glory with this washer that generates up to 2,030 psi, getting rid of dirt, grime, and more.

Promising review:  "Power washer was delivered Monda. It’s Wednesday and  I have washed two cars, cleaned the driveway and sidewalks, cleaned back fence, and the work keeps piling up.  Everything I see now needs to be cleaned! This little dude does not back down, plenty of power and it's surprisingly not too loud. Soap dispensers work great, and the tips are easy to change." — MAR

Get it from Amazon for  $199 .

20. A semi-transparent deck and stain sealer , which keeps your patio, deck, and other outdoor wood surfaces looking good as new while preventing further damage from the elements.

Promising review:  "This was recommended to me by a guy who sold us redwood boards from his mill. It went on easily and it looks gorgeous! I stained a fence and two decks in the last three years, and this product is far superior right off the bat. Love the richness of the color and the wood is soaking it up consistently." — I Know Jack

Get a 1-gallon can from Amazon for  $32.99   (available in four stain colors).

21. A flat outlet plug , so you can hide cluttered cords while still making sure all your electronics are getting the juice they need. Plus, it's perfect if you have furniture against the wall blocking access to a much-needed outlet.

Promising review: "This was very easy to install to hide all the messy wires. This is life-changing to create a nice, sleek space." — Martha Ashley

Get it from Amazon for $23.95+ (available in eight different lengths/configurations).

22. A pendant light  if you've been thinking about upgrading the lighting in your living room, bedroom, kitchen, or home office. These offer a modernized look to your space that'll you probably become obsessed with and start doing more to add to the aesthetic!

The adjustable cord measures 5.5 feet. Bulbs aren't included, but you can get a set of compatible Edison bulbs  here .

Promising review:  "Love these green pendants above our island. The color is a perfect muted olive green and the wood accent just elevates the look. For reference, our island is 8-feet long and three of these lights fit perfectly." — Jay Stanford

Get it from Amazon for  $59.95+  (available in four colors).

23. Orrr a  recessed light conversion kit  in case the tenants before you decided canned lighting was the move — it's no longer 2006, so time to upgrade to a more luxe look with chic pendant lights, a ceiling lamp, or even a chandelier!

Promising reviews:  "Bought a house with canned lights everywhere. I wanted a few semi-flush pendants and chandeliers so I tried this product. Very easy to install and works like a charm. " — PJG123

"It may take a bit of finessing and maybe an extra hole drilled here or there but it will eventually do what it is supposed to do. I now have a surface-mounted light on my front porch instead of the can light the builder supplied.  We turned a dark, ugly space into a wonderfully lit beautiful space.  We are amazed at the transformation this lighting change made to our home. Would do this again in a second." — TDC

Get it from Amazon for  $24.93 .

24. A set of metal furniture leg replacements  just perfect for upgrading the wobbly, wooden legs on your current furniture, so you don't have to break the bank on replacing it entirely! As someone whose dog chewed up the wooden legs of my couch...this is going into my cart, ASAP.

Promising review: "Quality is very good. Easy to attach with provided screws. We replaced wooden legs that were not strong with these beautiful gold metal legs and really complemented the piece." — sherry case

Get a set of four from Alfa Modern Furnishing on Etsy for $47.95+ (available in brushed gold or black).

Alfa Modern Furnishing is an LA-based small business creating unique, modernized home and furniture accents.

25. A 35-quart  slide-out trash can , which is *super* stealthy and conceals the horrible, smelly eyesore that is the kitchen garbage.

It even includes all the necessary mounting hardware!

Promising review:  "I hesitated to trade existing storage space for a trashcan but I am so glad I did. The Rev-A-Shelf was easy to install and worked exactly as I expected. The instructions were a bit lacking but a quick check on YouTube is all you need. Just four easily placed screws to your cupboard bottom and project complete.  The fact that the kitchen trash is not the first thing guests see when they enter my house is awesome. I should have done this upgrade years ago!  You won't be sorry if you purchase this unit. I love it!" — daisy

Get it from Amazon for  $61.99+  (available in seven colors, or check out other options/sizes for the  Rev-A-Shelf trashcan storage ).

26. A roll of self-adhesive  toilet sealant tape  because are you really going to caulk your toilet or has it been on your to-do list for weeks, if not months? Finally, cross it off the list and enjoy how tidy your "throne room" looks!

Promising reviews: "Boy does this tape pretty up an otherwise boring toilet. Way better than a bead of caulk. Clean...clean...clean before installation. Also helps to warm the product. Can be stretched during installation to better fit around tight bends. Been in place for a few weeks; still holding fine." — Selaretus

"Went on easily around the toilet, [it] looks so much better. Covered discoloration around the base, highly recommend." — Jerry

Get it from Amazon for $9.99 (available in four sizes/styles).

27. A  vinyl transition floor strip  in case someone didn't finish the job on your floors and there's an awkward, unappealing threshold between two rooms. Literally cover up the gap and make that transition on your floor or wall look seamless!

Promising review:  "I have a weirdly tall transition to my bathrooms and struggled with getting a normal threshold to stay in the entrance to my other bathroom after laying vinyl tile, so I hesitated on doing the hall bath until I found this product. Problem solved!  Looks great and doesn’t budge! And affordable!  I will definitely be ordering more for the long gap between my laminate and marble flooring in another area that I have hated for years."— m. white

Get it from Amazon for  $9.99+  (available in two sizes and six colors).

28. An  oil stain remover  because even thinking about replacing the driveway will be a headache! This no-scrub remover deeply penetrates any petroleum-based stain and removes it so well you'll forget it was ever there!

Promising review:  "Changed the oil on my girlfriend's car and some oil spilled on my NEW driveway...which I didn't notice 'til four days later. Four spots all about the size of a dollar bill baking in the Arizona sun for four days.  Put the stuff on (sits on the stain like pancake batter — don't be afraid to pour liberally) and let it sit from 6 p.m. 'til about 9 a.m. the next day. It dried and the instructions said to just sweep the stuff up. It broke apart with the broom and the stains were gone, just swept up the powder pieces — took about a minute. I WAS SHOCKED! Something that actually works on oil and it's easy.  Absolutely NO sign of anything that was there. My driveway is smooth concrete so I can't vouch for what would happen with a rougher surface but whoever makes this stuff is a genius. If they tried to take on World Peace, Earth would be a better place." — AmazonBob

Get it from Amazon for  $17.97  (also available in a larger size)

29. A unique switch plate cover  to transform your current, boring beige switch plates and truly make your home your own (even if you're renting).

Promising review:  "These plates are very beautiful. They match perfectly with the decor of my house. Very happy with this purchase." — Ingrid Hogan

Get it from  Farmhouse Iron Co.  on Etsy for  $13+  (available in five styles).

Farmhouse Iron Co. is a California-based small business creating unique home decor.

30. A ceiling-mount shelf  just perfect for decluttering your garage and making use of all that ✨ vertical space! ✨ Not to mention, they'll barely be noticeable once installed.

These shelves measure 45" x 45" and can hold up to 250 lbs of evenly distributed weight.

Promising review:  "These are a great way to open up more storage potential in the garage. This is actually my third home when I've used these in my garage. If you have lots of room between your garage door and your ceiling, these can be used up there to allow you to store stuff in a space you would otherwise not be able to use.  They're great for being able to store stuff way up high and not take up any floor space . We store all of our Christmas lights and other holiday decorations on them. They hold up the weight of four or five big bins full of Christmas light strings, no problem." — Buster

Get it from Amazon for  $91.98+  (available in two colors/styles).

31. A macramé tapestry , which makes the perfect decorative cover for an electric panel or random pre-war house fixture that doesn't even work. It's an artsy and chic conversation-starter, so no one will even know what's hiding underneath.

This tapestry measures 18" x 40" so make sure it'll be a good fit to cover your electrical panel!

Promising review:  "I bought this to cover the electric panel in our mudroom. It covers it perfectly so now it's not the first thing you see when you walk in. Had to brush out the tassels a little bit but it is good quality!" — J. Underwood

Get it from Amazon for  $45.99 .

32. Some  metallic spray paint  to update your favorite metal fixtures, furniture, or accessories instead of buying brand new ones. Doorknobs, faucets, mirrors, lights — new home, who this?

Promising review: "Best-looking metal spray paint I have seen. It took me 90 minutes to prepare, mask, and paint my bathroom faucet. I used about 1/2 a can of this paint." — OC-Adam

Get it from Amazon for $14.79+ (available in eight metallic finish colors).

33. A must-have  privacy screen  for hiding that bulky AC in the backyard, trash cans, pool equipment, or whatever else in your yard is messing up your lawn aesthetic.

Promising review: "Super easy to install and took less than 30 minutes to put together, level out, and hammer in the stakes. My HOA doesn’t allow the trash bins to be visible from the street, so this fixed that issue, plus it matches my house trim." — Joseph and Anne Sawyer

Get it from Amazon for $145.15 . 

34. A  create-your-own countertop paint kit  that'll get you one step closer to your dream kitchen within a single weekend without having to pay for a contractor or stonemason. This kit has everything you need to transform your current laminate, tile, or butcher block countertop into a luxe-looking granite finish — you just need to block out the time to DIY!

Each kit includes a can of primer, three cans of mineral paints, a can of acrylic topcoat, a roller arm and two pads, a paint sponge, and a foam brush.

Promising review: "Easy to put on. You just have to let the base coat dry and then start sponging the colors on. I am not crafty at all and I still can't believe what my countertop looks like. I am glad I gave it a try. So far it seems very durable. I do not cut on my counters or place hot pots or pans on there — I always use pot holders. I LOVE MY NEW COUNTERS. It was much cheaper and easier than replacing them ." — Sharon

Get it from Amazon for $99.95  (available in five finishes and in a marble version ).

35. A decorative air vent cover  to add a chic flair to your home, unlike those regular-degular registers currently catching your eye whenever you walk into the room.

Promising review:  "I bought these to replace the ugly, plain registers that were on my ceiling. Installed in less than 10 minutes and they look beautiful. I ordered white and spray painted them nickel to match my ceiling fan. Couldn't be happier." — AsMeow

Get one from Amazon for  $16.12+  (available in two sizes and four finishes).

36. Some flexible baseboard trim  that you can simply trim, peel, and stick to update the molding in *any* room with a clean, looks-like-new finish.

This roll of self-adhesive trim measures 4 inches by 20 feet.

Promising review:  "This was very easy to apply and make sure you have it where you want it before sticking because it REALLY sticks to the wall. I laid out the roll and let it relax for a day before cutting and applying. Love the easy-to-clean material. Made trimming out my bathroom/ laundry room quick and easy." — Cassie

Get it from Amazon for  $28.99+  (available in nine sizes and three colors).

37. A 30-gallon  deck storage box  designed with a waterproof exterior to keep your cushions, gardening supplies, and other outdoor must-haves safe from the elements without having to tote them back and forth inside.

Promising review : "Put together in less than five minutes by myself and no tools needed. This is a nice little box, holds the lumbar pillows along with other things I need for my backyard on a regular basis . The box fits nicely on my small patio." — ALM329

Get it from Amazon for $35.99+ (available in two sizes and four colors).

Reviews have been edited for length and/or clarity. 

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Quantum Physics

Title: solving an industrially relevant quantum chemistry problem on quantum hardware.

Abstract: Quantum chemical calculations are among the most promising applications for quantum computing. Implementations of dedicated quantum algorithms on available quantum hardware were so far, however, mostly limited to comparatively simple systems without strong correlations. As such, they can also be addressed by classically efficient single-reference methods. In this work, we calculate the lowest energy eigenvalue of active space Hamiltonians of industrially relevant and strongly correlated metal chelates on trapped ion quantum hardware, and integrate the results into a typical industrial quantum chemical workflow to arrive at chemically meaningful properties. We are able to achieve chemical accuracy by training a variational quantum algorithm on quantum hardware, followed by a classical diagonalization in the subspace of states measured as outputs of the quantum circuit. This approach is particularly measurement-efficient, requiring 600 single-shot measurements per cost function evaluation on a ten qubit system, and allows for efficient post-processing to handle erroneous runs.

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Sail the Seven C’s Voyage Logbook by Robert Bear Instructs Teams on Creative Problem Solving Amid Organizational Storms

Today’s business environment is incredibly fast-moving and complicated, with problems arising left and right, like waves in a storm battering a ship. This can lead to organizations and team members feeling overwhelmed and helpless because they don’t know where and how to start dealing with these problems. Drawing on his more than four decades of experience in teaching, business, art, and the military, Robert E. Bear has authored Sail the Seven Cs Voyage Logbook , a workbook that guides members of corporate teams and other organizations on how to creatively solve problems while supporting each other. 

Written from the standpoint of a sailor, Sail the Seven Cs uses various maritime terminologies and metaphors to drive its points. According to Bear, the book and its forms function as a tool for a team, committee, task force, or a group to work together in a systematic, organized approach that can solve problems of any size. The eBook, which will soon be available on Amazon, also has a section that can help individuals and organizations secure funding for their projects by teaching them how to write grant requests. 

As outlined by the book, the seven Cs are: 

• Conviction , or a problem that one is passionate about solving. This could be an unfair practice at work, increasing productivity, taking care of employees’ interests, or filling a market niche. 
• Courage is the fortitude to step forth and become involved. Courage is the fortress of character that will sustain you through to the success of a positive change. 
• Counsel may involve more than just seeking advice from friends or peers. This also includes advice and services from professionals, such as attorneys or accountants, as well as gathering as much pertinent data as possible within the business. 
• Creativity involves crafting a map of solutions to the problem to pass through the doldrums of apathy and indifference, as well as strategies to overcome the hurricanes of skepticisms and tsunamis of intolerance. 
• Cooperation integrates as many individuals, organizations, and businesses as possible, each having a stake in the outcome of the resolved problem. It also involves leaders being able to properly allocate tasks and responsibilities. 
• Communication must be a multi-directional, fluid process throughout your network, Bear says. Teams must be able to effectively disseminate objectives, articulate ideas, impart information, and share feelings and feedback. 
• Commitment , the final C, maybe the hardest C to navigate. It may entail a return to one or more of the previous Cs for continued buoyancy and not sinking from the onslaught of the monsters of doubt and new problems that have surfaced. 

According to Bear, each team member should have their own copy of Sail the Seven C’s , to ensure that everyone is on the same page. The team should also confirm a time when they can regularly assemble and work on and review each other's efforts and logbooks.  

In addition to the exercises provided by Sail the Seven C’s , Bear also holds half-day and full-day corporate creative problem-solving workshops that reinforce these lessons and provide an even more potent start to an organization’s journey toward positive change. 

Bear recommends teams hold free word association exercises to develop their creative problem-solving skills. This encourages members to not be afraid of voicing ideas that may sound silly at first, because there may be something in there that actually works. As different people have different skills and different knowledge sets, encouraging each member to speak up when they believe they have something to contribute is vital to organizational success. 

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OSP Hosted Webinar: The RPPR Matrix – Decoding and Problem Solving the NIH Progress Report System

The Office of Sponsored Programs will be hosting the upcoming NCURA webinar:

The RPPR Matrix – Decoding and Problem Solving the NIH Progress Report System

September 30, 2024 12:00 – 1:30 pm MT * Webinar 1:35 – 2:30 pm ET * After the Show * Talk with the Faculty Directly!

Completing an RPPR can be a daunting challenge especially if one is new to the process. This session will go through an actual Progress Report (RPPR), section by section in detail explaining the requirements that NIH will review. The session will go over addressing the common errors and warnings and how to avoid the common pitfalls that result in a late submission or a non-compliant RPPR that can result in further inquiry from NIH. This session will go over the difference between SNAP and Non-SNAP RPPRs, Multiple component RPPRs, completion of the Budget Section H for applicable activity codes and dive into HSS/ASSIST for Human Subjects reporting requirements. Difference between Annual, Interim, and Final reports will also be discussed.

Learning Objectives

By the end of this webinar, participants will be able to:

• Navigate and become familiar with each section of the RPPR
• Troubleshoot error and warning messages
• Correctly report personnel effort and unobligated balance
• Advise PI on other reporting components
• Understanding the process of preparing budgets in section H

Format of webinar: 90-minute presentation, followed by 55 minutes of discussion.

If you, another faculty member, or your department administrator or business manager are interested in attending this webinar, please complete this sign-up form . You do not need to be an NCURA member in order to register. We look forward to learning alongside you!