math research ideas for high school students

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• My name is Rebecca, and I know that many high school math teachers struggle to find the time to create engaging lessons and resources appropriate for their students' levels.
• I've been teaching for 25+ years, and I know that struggle well! My resources will alleviate that overwhelming feeling while giving you the tools to feel confident and empowered in your teaching so that you can focus on inspiring your students.

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• Best Math Project for High School Students

If you're looking for a math project idea for your high school students, keep reading.

By far, the most exciting thing I do in my high school math classes is to give my students my How to Adult Project . Students select a profession with a salary and monthly student loan payment out of a hat. Working with a partner, they have to budget their money with the help of a spreadsheet to "buy" a house and a car in our metro area.

I love to do this project with my students because we only do a few projects, and I like the change from the usual routine and the students learn a bit about adulting in a fun but structured way. This project could work just as well with high school students as it does with middle school students.

You may also be interested in:

• Exponential Functions Project (for Algebra 2 or Precalculus)
• Trig Graphs Project | Sine Graph Sunset Project (for Precalculus)
• Conic Sections Project (for Precalculus)
• Optimization Project (for Calculus)
• Vase Project (for Calculus)

A couple of years ago, I was looking for a project to do with my second-semester seniors in my on-level calculus class. If you teach high school seniors, then you know the struggle it is to get them to come to class at all, to come on time, or to do anything during class besides complain about how awful it is to be in school or how the administration has it out for them. 😕

The beauty of teaching this calculus class is that it is full of seniors, there is no external exam at the end of the year (like for the AP classes), and there is no set curriculum, so I can move as fast or as slow as I want.  

Once we cover all of the pertinent calculus topics, we have about 3 to 4 weeks remaining. In the past, we did an extended unit of algebra and trigonometry in an effort to prepare them for a potential placement test at the students’ future colleges.

(click here to read more about what I teach in my on-level calculus class .)

But one day, I cut the algebra and trigonometry unit in half and used some of that time for a mini financial math project. And so, the How to Adult Project was born.

STUDENT FEEDBACK

Some of the things that my students have said about this project:

"This project was very useful/helpful. The most useful project that any of my teachers have given me."

"Awesome project; very relevant, really appreciate the idea in prep for the future."

"I thought the project was great and straightforward!"

So what exactly do the students do?

PROJECT INSTRUCTIONS

Students work with a partner. If you have an odd number of students, have one group of 3. I once allowed a group of 4 students, which was a mistake; there was not enough work to go around.

Each student will draw a profession and salary out of a hat. Most students will also receive a monthly payment toward student loan debt.

On the first day I spend about 20 to 30 minutes giving direct instructions for setting up an Excel spreadsheet to create a budget.   Most students have little to no experience with Excel. It would certainly be easier for me to share my master spreadsheet directly with the students, but I want the setting up of the spreadsheet to be part of the “adulting” experience. Google Sheets also works here.

I give them guidelines such as:

• Assume the average take-home pay (after taxes, social security, etc.) is 76%.
• Partnerships should spend no more than 1/3 of your combined monthly take-home pay on a house payment (mortgage, taxes, and insurance).
• Individuals should not let their total monthly vehicle expenses (car payment and insurance) exceed 10% of their monthly gross income.

After the students set up the spreadsheet, they shop online on real-estate and car sales websites to find a house and car they like.

Next, they visit "the bank" (that’s me!) to ask for a (fake) loan. Below, I discuss the fun I have playing the role of the banker. 😄

If you want my version of the project , which is EDITABLE, and includes the rubric and the list of professions and salaries,  click on the link .

STUDENT FINAL PRODUCT

The students create a Google Slides presentation where they first introduce themselves and share the backstory of their make-believe future selves. I encourage them to get creative, embellish and have fun with it. (For example, one student’s profession is a personal trainer. He embellished by saying he is a personal trainer for a celebrity athlete.)

The presentation must include a photo and specifications (price, square feet, etc.) of their three favorite houses  and the same for the cars. U ltimately, the students must narrow their choices down to one house and one car per person. 

Students must also include a screenshot of the spreadsheet showing their calculations for the monthly payments.

Students write summary paragraphs about why they chose that house and that car and what they gained from the experience.

All I require from the students is the Google Slides presentation and that they complete a peer and self-evaluation.   I have never required that they stand in front of the class and share their presentation with their classmates, but that certainly could be done if there was time.

CAN BE USED WITH VIRTUAL STUDENTS

In the spring of 2020, when we were virtual because of the coronavirus pandemic, in addition to the Google Slides presentation, I also required that each group make a video of them talking through their Google Slides presentation. Students posted their videos on Padlet.com. Each student must also watch and comment on at least two other groups’ videos.

I did not take the time to walk through the creation of the spreadsheet when we were virtual; I didn’t want to keep them on Google Meet for that length of time. (The morale of the seniors was low, and I was doing my best to be gracious.)    I posted my master spreadsheet on my class website for them to download and use. I also did not require the students to visit "the bank" to ask for a loan. I gave every group the same terms for the loans.

It was trickier in 2020 for the groups to work together, and they told me later it was more challenging to keep up with the deadline. But I was pleased with the final projects they produced.

THE CONSTRAINTS

When designing the project, I knew I had to include some limitations. I wanted to allow the students some freedom, but I also needed a rubric so that I could grade them all the same, even though everyone’s final product would be different.

Every year, at least one student says they wish they could buy a house anywhere in the world. I do not allow that much freedom because the cost of living in every city differs.

Hence, I only allow them to shop for houses in our metro area. Students quickly discover that houses are less expensive further from downtown, and the property taxes are lower.

Students ask if they can buy a condominium or a townhouse instead of a single-family home. I allow that as long as they are buying and not renting.

Students always want to know if they can go over budget on the car as long as they go under budget for the house. I call this the Lance Rule. One year, a student named Lance wanted to do precisely this, and I allowed it. He and his partner chose a shack that, based on the photos, would not pass a health inspection, let alone a building inspection. And yet he chose an $80,000 car. 🙄

Now, I tell the students that they *can* go over budget on the car, but if they go over by more than $100/month, they will be penalized on the rubric.

For most of the out-of-the-box questions, they ask (can I buy an RV instead of a house and a car? Can’t I just ride my bike or use public transportation?) I say, “In life, yes, but in this project, no. There are instructions, and you need to follow them. You’re getting a grade for this."

GRADING THE PROJECT

I have a rubric with 14 different criteria. Most of the criteria are regarding “did you include all required components? Photos, specifications, etc.” The students are given 0, 1, or 2 points for most criteria.

The total number of possible points is around 30. I use a square root curve to get the final score. In other words, I take the points they earned, divide by 30, then take the square root of that number. For example, if a group earned 29 out of 30 points, I do the square root of 29/30, which is about 0.983; in the gradebook, I put 98%. If a group earned 15 out of 30 points, I put 71% in the gradebook.

If you want  my version of the project ,  which is EDITABLE, and includes the rubric and the list of professions and salaries,  click on the link .

ROLE-PLAYING

One of the most fun things about this project is that I get to role-play as the banker. I put on fake glasses (old plastic sunglasses with lenses removed) and have a nametag and a brochure.

The bank is my desk. I put the name of the bank on the wall behind me. I call it People’s Championship Bank. I put two chairs near my desk, and when they’re ready to visit the bank, I introduce myself using my first name. I ask them what their names are and how I can help them. They always find that part very amusing. Some of them even play along and give me a fake name.

Here are some fun interactions I have had with my students at "the bank": 😁

• I stepped out to go to the bathroom, and when I came back, two students were waiting at "the bank" and complained about the service.
• I picked up my phone and pretended to be talking to someone. I might have even given the students the side-eye while I said (to no one) on my phone, "Yeah, there are some young-looking guys here probably wanting a loan or something."
• I closed the bank 10 minutes before class was over. One student asked, "Is the bank still open?" No. "Aw, I guess we can come back tomorrow."
• When the first group came to the bank, I noticed my brochure was folded incorrectly, so I blamed the (fake) intern.
• A student referred to me as a teller, and I got angry and said, “I am not a teller! I am an account manager! This is my daddy’s bank, and if you are rude to me one more time, I will call security and have you kicked out of here!”

AREN'T TEENAGERS FUNNY?

Here is a collection of some of the funniest conversations I have overheard while they worked on the project.

• “I want to spend less on a house so that I can spend more on Xbox.”
• "We don't need two bedrooms. We can share a bed."
• "Well, that was a stressful day - why don't we go car shopping tomorrow?"
• "Is this a bad time to tell you I am a hoarder? ... I need a basement just for my cats..."
• "We can't carpool; as a paralegal, I could get called in anytime."
• "What is wrong with me looking at 21 million dollar houses?"
• “People don’t have to see your house, but people will see your car.”
•   “We don’t want to buy a house. We are going to live in my car for a year and save money.” How are you going to shower? “Gym membership.”
•   “I want to spend my money on clothes and entertainment, not food.”
• The girl of one partnership was absent. Her male partner said she was absent because “she had to take the kids to the doctor.”
• One year, two boys found a lovely house listed for $3000 or $11/month.   They called the number on the listing and talked to the real estate agent. They claimed they were recent college graduates. She said there was a mistake in the listing. It was supposed to say $3000/month. She then recruited them as clients and emailed them other listings.   One of the boys told me, “I feel so grown up. I have a realtor.”

SUGGESTIONS FOR CHANGES:

Most of these suggestions come from the students themselves. I don't implement most of these because I want to spend at most 3 class days on the project.

But if you wanted to expand this project, you could

• do a more structured lesson on Excel
• go into detail about the mortgage formula
• allow the students to decide on their own profession and do the research for the salary
• give some groups some make-believe children and a monthly daycare expense
• let the students make a decision on how much of a down payment they want to put on the house (I have them randomly draw a percentage (5%, 10%, or 20%) out of a hat)
• allow the students to create a complete budget, including food, utilities, entertainment, etc.

CAUTIONARY TALE

Below are some common questions or misunderstandings by students as we go through this process.

• If a group doesn't score 100% on this project, it is usually because they did not thoroughly read the instructions and the rubric.
• When students come to "the bank," they are nervous about taking out a 30-year loan. They think they have to commit to keeping the house for 30 years.
• Students want to use the mortgage calculators advertised on real-estate websites. I tell them to ignore those because I want them to use the spreadsheet. One student even asked me, "Do we have to put a down payment?" because a real-estate site said, "No down payment is required." 😐
• Students want to get the property tax information from the real-estate website instead of searching the government website. In recent years, students have had trouble with this part, so I *do*, let them use the property tax info on the real-estate website.

If you want  my version of the project , which is EDITABLE, includes the rubric, and the list of professions and salaries,  click on the link .

• Trig Graphs Project | Sine Graph Sunset Project
• Exponential Functions Project
• Optimization Project   (for Calculus)
• Vase Project   (for Calculus)
• Conic Sections Project

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100+ Amazing Algebra Topics for Research Papers

Many students seek algebra topics when writing research papers in this mathematical field. Algebra is the study field that entails studying mathematical symbols and rules for their manipulation. Algebra is the unifying thread for most mathematics, including solving elementary equations to learning abstractions like rings, groups, and fields.

In most cases, people use algebra when unsure about the exact numbers. Therefore, they replace those numbers with letters. In business, algebra helps with sales prediction. While many students dislike mathematics, avoiding algebra research paper topics is almost impossible at an advanced study level.

Therefore, this article lists topics to consider when writing a research paper in this academic field. It’s helpful because many learners struggle to find suitable topics when writing research papers in this field.

How to Write Theses on Advanced Algebra Topics

A thesis on an algebra topic is an individual project that the learner writes after investigating and studying a specific idea. Here’s a step-by-step guide for writing a thesis on an algebra topic.

Pick a topic: Start by selecting a title for your algebra thesis. Your topic should relate to your research interests and your supervisor’s guidelines. Investigate your topic: Once you’ve chosen a topic, research it extensively to know the relevant theories, formulas, and texts. Your thesis should be an extension of a particular topic’s analysis and a report on your research. Write the thesis: Once you’ve explored the topic extensively, start writing your paper. Your dissertation should have an abstract, an introduction, the body, and a conclusion.

The abstract should summarise your thesis’ aims, scope, and conclusions. The introduction should introduce the topic, size, and significance while providing relevant literature and outlining the logical structure. The body should have several chapters with details and proofs of numerical implementations, while the conclusion should restate your main arguments and tell readers the effects. Also, it should suggest future work.

College Algebra Topics

You may need topics to consider if you’re in college and want to write an algebra research paper. Here’s a list of titles worth considering for your essay.

• Exploring the relationship between Rubik’s cube and the group theory
• Comparing the relationship between various equation systems
• Finding the most appropriate way to solve mathematical word problems
• Investigating the distance formula and its origin
• Exploring the things you can achieve with determinants
• Explaining what “domain” and “range” mean in algebra
• A two-dimension analysis of the Gram-Schmidt process
• Exploring the differences between eigenvalues and eigenvectors
• What the Cramer’s rule states, and why does it matter
• Describing the Gaussian elimination
• Provide an induction-proof example
• Describe the uses of F-algebras
• Understanding the number problems in algebra
• What’s the essence of abstract algebra?
• Investigating Fermat’s last theorem peculiarities
• Exploring the algebra essentials
• Investigating the relationship between geometry and algebra

These are exciting topics in college algebra. However, writing a winning paper about any of them requires careful research and analysis. Therefore, prepare to spend sufficient time working on any of these titles.

Cool Topics in Algebra

Perhaps, you want to write about an excellent topic in this mathematical field. If so, consider the following ideas for your algebra paper.

• Discussing a differential equation with illustrations
• Describing and analysing the Noetherian ring
• Explain the commutative ring from an algebra viewpoint
• Describe the Artin-Weddderburn theorem
• Studying the Jacobson density theorem
• Describe the four properties of any binary operation from an algebra viewpoint
• A detailed analysis of the unary operator
• Analysing the Abel-Ruffini theorem
• Monomorphisms versus Epimorphisms: Contrast and comparison
• Discus Morita duality with algebraic structures in mind
• Nilpotent versus Idempotent in Ring theory

Pick any idea from this list and develop it into a research topic. Your educator will love your paper and award you a good grade if you research it and write an informative essay.

Linear Algebra Topics

Linear algebra covers vector spaces and the linear mapping between them. Linear equation systems have unknowns, and mathematicians use vectors and matrices to represent them. Here are exciting topics in linear algebra to consider for your research paper.

• Decomposition of singular value
• Investigating linear independence and dependence
• Exploring projections in linear algebra
• What are linear transformations in linear algebra?
• Describe positive definite matrices
• What are orthogonal matrices?
• Describe Euclidean vector spaces with examples
• Explain how you can solve equation systems with matrices
• Determinants versus matrix inverses
• Describe mathematical operations using matrices
• Functional analysis of linear algebra
• Exploring linear algebra and its fundamentals

These are some of the exciting project topics in linear algebra. Nevertheless, prepare sufficient resources and time to investigate any of these titles to write a winning paper.

Pre Algebra Topics

Are you interested in a pre-algebra research topic? If so, this category has some of the most exciting ideas to explore.

• Investigating the importance of pre-algebra
• The best way to start pre-algebra for a beginner
• Pre-algebra and algebra- Which is the hardest and why?
• Core lessons in pre-algebra
• What follows pre-algebra?
• The first things to learn in pre-algebra
• Investigating the standard form in pre-algebra
• Provide pre-algebra examples using the basic rules to evaluate expressions
• Differentiate pre-algebra and algebra
• Describe five pre-algebra formulas

Consider exploring any of these ideas if you’re interested in pre-algebra. Nevertheless, choose a title you’re comfortable with to develop a winning paper.

Intermediate Algebra Topics for Research

Perhaps, you’re interested in intermediate algebra. If so, consider any of these ideas for your research paper.

• Reviewing absolute value and real numbers
• Investigating real numbers’ operations
• Exploring the cube and square roots of real numbers
• Analysing algebraic formulas and expressions
• What are the rules of scientific notation and exponents?
• How to solve a linear inequality with a single variable
• Exploring relations, functions, and graphics from an algebraic viewpoint
• Investigating linear systems with two variables and solutions
• How to solve a linear system with two variables
• Exploring linear systems applications with two variables
• How to solve a linear system with three variables
• Gaussian elimination and matrices
• How to simplify a radical expression
• How to add and subtract a radical expression
• How to multiply and divide a radical expression
• How to extract a square root and complete the square
• Investigating quadratic functions and graphs
• How to solve a polynomial and rational inequality
• How to solve logarithmic and exponential equations
• Exploring arithmetic series and sequences

These are exciting topics in intermediate algebra to consider for research papers. Nevertheless, learners should prepare to solve equations in their work.

Algebra Topics High School Students Can Explore

Are you in high school and want to explore algebra? If yes, consider these topics for your research, they could be a great coursework help to you.

• Crucial principles and formulas to embrace when solving a matrix
• Ways to create charts on a firm’s financial analysis for the past five years
• How to find solutions to finance and mathematical gaps
• Ways to solve linear equations
• What is a linear equation- Provide examples
• Describe the substitution and elimination methods for solving equations
• How to solve logarithmic equations
• What are partial fractions?
• Describe linear inequalities with examples
• How to solve a quadratic equation by factoring
• How to solve a quadratic equation by formula
• How to solve a quadratic equation with a square completion method
• How to frame a worksheet for a quadratic equation
• Explain the relationship between roots and coefficients
• Describe rational expressions and ways to simplify them
• Describe a cubic equation roots
• What is the greatest common factor- Provide examples
• What is the least common multiple- Provide examples
• Describe the remainder theorem with examples

Explore any of these titles for your high school paper. However, pick a title you’re comfortable working with from the beginning to the end to make your work easier.

Advanced Topics in Algebra and Geometry

Maybe you want to explore something more advanced in your paper. In that case, the following list has advanced topics in geometry and algebra worth considering.

• Arithmetical structures and their algorithmic aspects
• Fractional thermoentropy spaces in topological quantum fields
• Fractional thermoentripy spaces in large-scale systems
• Eigenpoints configurations
• Investigating the higher dimension aperiodic domino problem
• Exploring math anxiety, executive functions, and math performance
• Coherent quantiles and lifting elements
• Absolute values extension on two subfields
• Reviewing the laws of form and Majorana fermions
• Studying the specialisation and rational maps degree
• Investigating mathematical-pedagogical knowledge of prospective teachers in ECD programs
• The adeles I model theory
• Exploring logarithmic vector fields, arrangements, and divisors’ freeness
• How to reconstruct curves from Hodge classes
• Investigating Eigen points configuration

These are advanced topics in algebra and geometry worth investigating. However, please prepare to explore your topic extensively to write a strong essay.

Abstract Algebra Topics

Most people study abstract algebra in college. If you’re interested in research in this area, consider these topics for your project.

• Describe abstract algebra applications
• Why is abstract algebra essential?
• Describe ring theory and its application
• What is group theory, and why does it matter?
• Describe the critical conceptual algebra levels
• Describe the fundamental theorem of the finite Abelian groups
• Describe Sylow’s theorems
• What is Polya counting?
• Describe the RSA algorithm
• What are the homomorphisms and ideals of Rings?
• Describe integral domains and factorisation
• Describe Boolean algebra and its importance
• State and explain Cauchy’s Theorem- Why is it important?

This algebra topics list is not exhaustive. You can find more ideas worth exploring in your project. Nevertheless, pick an idea you will work with comfortably to deliver a winning paper.

Get Professional Math Homework Help!

Perhaps, you don’t have the time to find accurate algebra homework solutions. Maybe you need math thesis help from an expert. If so, you’ve no reason to search further. Our thesis writing services in USA can help you write a winning assignment. We offer custom help with math assignments at cheap prices.

If you want to get a quality algebra dissertation without sweating, place an order with us. We’re an online team providing homework help to students across educational levels. We guarantee you a top-notch service once you approach us, saying, “Please do my math assignment.” We’re fast and can beat even a tight deadline without compromising quality. And whether you’re in high school, university, or college, we will write a paper that will compel your teacher to award you the best grade in your class. Contact us now!

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11 Math Programs for High School Students

If you are a high-achieving and ambitious high school student, the prospect of pursuing math or STEM at a university level is an exciting opportunity to explore your passion and potential.

How to choose a high school math program?

Start by defining your objective - whether it is to increase your understanding of math or add prestige to your college application. For the former, a good summer school should suffice, but for the latter, prepare for a competitive application process for internships and research mentorship programs. Look for programs that are highly selective, free, or offer a stipend.

Conduct thorough research on the host organization and the mentors you’ll be working with.

Read program reviews, and consult with your counselors and math teacher.

Evaluate factors such as location, eligibility, and cost before making a decision.

How we have picked math programs for you

Participating in a highly selective math program can make you an outstanding and competitive applicant. In this article, we will explore some of the best math programs for high school students looking to enhance their skills and stand out in the competitive field of mathematics and STEM. Most of these programs are highly or moderately selective.

Even if the program is not highly selective, it can demonstrate your dedication and interest in pursuing your interests beyond a classroom setting and help you build more skills. You can find more of these opportunities by looking up colleges and exploring their summer offerings.

1. Program in Mathematics for Young Scientists (PROMYS)

The PROMYS program runs for six weeks and is designed for exceptional high school students passionate about math. The curriculum focuses on encouraging exploration and discovery. You will attend thought-provoking lectures and advanced seminars, collaborate with peers on problem sets, and engage in mathematical research.

Each year, PROMYS accepts around 80 high school students aged 14 and up and 25 undergraduate counselors. PROMYS is committed to promoting diversity in STEM fields and strongly encourages applications from students who identify as female, African American, Hispanic, or other underrepresented groups.

Location: Residential, Boston University

Cost: The program is free for students whose annual family income is under $80,000.

For students whose family income surpasses this amount, the program tuition ranges from $2000-$6000, depending on the program’s predetermined income brackets.

Application deadline: March 5, 2023

Program dates: July 2 – August 12, 2023

Eligibility: High school students that are at least 14 years old, have completed 9th grade, and are not yet enrolled as a full-time college or university student

2. Stanford University Mathematics Camp (SUMaC)

If you're a high school student with a talent for math, consider applying to SUMaC. With an acceptance rate of less than 10%, this program hosts only 40 students each year for an academically rigorous three-week experience. Additionally, there is an online cohort of 64 students.

The 2023 curriculum at SUMaC will focus on two main topics: Abstract Algebra & Number Theory and Algebraic Topology . You get to explore a range of fascinating concepts in Abstract Algebra, including the limitations of straight-edge and compass constructions, the classification of patterns in two dimensions, error-correcting codes, cryptography, and the analysis of symmetry in structures. In Algebraic Topology, you will learn various techniques for analyzing topological properties of shapes using algebraic concepts.

During the program, you will work collaboratively on advanced mathematical problems, participate in academically challenging classes and sessions, and gain exposure to important research areas in mathematics.

Location: Residential, Stanford University; Online

Online: $3,550

Residential: $8,250

Application deadline: Applications for the 2023 sessions are already closed. Based on this year’s deadlines, the applications close in early February each year.

Program dates:

Online: June 19 – July 10, 2023

Residential: June 25 – July 21, 2023

Online: July 17 – August 4, 2023

Eligibility: All high school sophomores and juniors, including international applicants

3. Research Science Institute Program at MIT

The Research Science Institute (RSI) at MIT provides a unique opportunity for high school students who have demonstrated exceptional aptitude in mathematics, science, and engineering to participate in a six-week program. Only a select group of about 100 talented students worldwide are chosen to participate in this program.

During the program, you will engage in a combination of on-campus coursework in STEM theory and off-campus work in science and technology research. In the first week, you will take STEM coursework and then spend the remaining five weeks conducting research projects under the mentorship of experienced researchers and scientists. Throughout the program, you will be involved in the entire research cycle, from reading the most current literature in your chosen field to drafting and executing a detailed research plan to delivering conference-style oral and written reports on your findings. This immersive experience will allow you to gain hands-on experience with the research process and develop valuable skills that will serve you well in your academic and professional pursuits.

One of 2022’s ‘most distinguished’ oral presentations was on Computing the Mosaic Number of Reduced Projections of Knots and Links under the direction of faculty from the MIT Department of Mathematics.

Location: Residential, MIT

Cost or stipend: None

Application deadline: Applications for the 2023 sessions are already closed. Based on this year’s deadlines, the applications close in early December each year.

Program dates: July - August 2023 (tentatively, based on last year’s schedule)

Eligibility: High school juniors (international applicants are welcome)

4. Lumiere Research Scholar Program – Mathematics Track

Lumiere Research Scholar Programs provide a platform for ambitious high school students to conduct research in mathematics under the guidance of renowned PhD mentors. The program was founded by researchers at Harvard and Oxford, and it is entirely virtual, allowing you to engage in research from anywhere in the world. You will be matched with a top PhD mentor and collaborate one-on-one with them to produce a high-quality, university-level research paper.

The program's duration varies based on your research goals and how deeply you would like to explore the subject. As mathematics is a broad subject, the Lumiere Research Scholar Program offers research opportunities across a wide range of topics and encourages students to combine their mathematical interests with other disciplines.

You can find the application form here .

Also, check out the Lumiere Research Inclusion Foundation , a non-profit research program for talented, low-income students.

Location: Virtual

Application deadline: There are four cohorts throughout the year. Applications are due in February, May, September, and December, respectively. Apply here !

Program dates: There are four cohorts throughout the year in spring, summer, fall, and winter.

Eligibility: All high school students may apply.

Horizon offers trimester-long research programs for high school students across subject areas such as data science, machine learning, political theory, biology, chemistry, neuroscience, psychology, and more! It is one of the very few research programs for high school students that offers a choice between quantitative and qualitative research!  

Once you select a particular subject track and type of research you’ll be paired with a professor or Ph.D. scholar (from a top university) who will mentor you throughout your research journey.  You’ll work to create a 20-page, university-level research paper that you can send to prestigious journals for publication as a high school student. 

This program is a solid opportunity for you to pursue a research program in highly specialized fields, under the guidance of a top scholar.  The program also provides a letter of recommendation for each student, as well as detailed project feedback that you can use to work on future projects and on college applications. Apply here !

Location : Virtual 

Application Date: May 21, 2024 for the summer cohort, and September 25, 2024 for the fall cohort 

Program Dates: 

Summer seminar - June 24, 2024 - September 2, 2024

Fall seminar - October 23, 2024 - February 19, 2025

Lab dates are flexible, but you must apply 4 weeks in advance.

Eligibility: High school students with good academic standing (>3.67/4.0 GPA) can apply. Most accepted students are 10th/11th graders! Only a couple of tracks require formal prerequisites, more details of which can be found here .

6. Summer Academy for Math and Science (SAMS)

If you are a high-school junior from an underrepresented background, SAMS is a great opportunity for you to earn college credit while mastering fundamental concepts in higher-level math and science. The program runs for six weeks and is completely free. You'll be taught by Carnegie Mellon University faculty and will participate in a challenging curriculum that includes classroom training, hands-on research projects, and professional and academic development courses. At the end of the program, you'll present your STEM research projects at a day-long Symposium.

To be selected for SAMS, you should have a strong interest in math, extra-curricular activities, and/or community engagement, as well as a dedication to diversity and inclusion in education. Students from low-income families, underrepresented communities, and those who have never attended a high school with a long history of admissions to top-tier institutions are highly encouraged to apply.

Location: Residential, Carnegie Mellon University

Application deadline: March 15, 2023

Program dates: July 1, 2023 – August 5, 2023

Eligibility: Must be a current high school junior

7. Mathroots

Mathroots is a 14-day summer program hosted by MIT-PRIMES designed for high school students from underrepresented backgrounds or underserved communities who have a passion for math and want to explore creative topics in the field. During the program, you'll have the opportunity to discover new mathematical ideas and hone your problem-solving skills. You'll participate in a variety of activities, including classes, group sessions, and lectures led by a team of experienced instructors who have taught both research and competition math. Throughout the program, you'll discover new mathematical ideas and gain a deeper understanding of the subject.

Application deadline: Applications for the 2023 sessions are already closed. Based on this year’s deadlines, the applications close in early March each year.

Program dates: June 23, 2023 – July 7, 2023

Eligibility: US citizens or students attending high school in the US (before the last year of high school) who are between the ages of 14-18

8. UC Santa Barbara’s Research Mentorship Program - Mathematics Track

If you're a highly motivated high school student looking to gain university-level research experience, the Research Mentorship Program is an excellent choice. This highly selective summer program allows you to choose a research project in the discipline of your choice, including a Mathematics track.

During the program, you'll receive training on how to conduct research, write professional papers, and present your findings at formal conferences. You'll be matched with a mentor who will guide you as you work on your research project. Additionally, the Research Mentorship Program offers the opportunity to earn university credits that will be added to your permanent record at UCSB.

If you’re interested in this program, we’ve also written an in-depth piece detailing everything you need to know about RMP 2023 !

Location: Residential, UC Santa Barbara

Commuter option: Around $5,000

Residential Option: Around $12,000

Program dates: June 20 – August 4, 2023

Eligibility: Students all over the world who are in 10th and 11th Grade with a minimum GPA of 3.8

9. California State Summer School for Mathematics & Science (COSMOS)

If you're a high school student with an aptitude for STEM subjects, including math, consider applying to COSMOS. This four-week summer residential program is designed to challenge mathematically gifted and motivated students while providing them with the opportunity to work with renowned faculty, researchers, and scientists. Through hands-on and lab-intensive curricula, COSMOS fosters students' interests, skills, and awareness of educational and career options in STEM fields.

COSMOS offers several 'Clusters' at campuses located at UC Davis, UC Irvine, UC San Diego, or UC Santa Cruz. Some of the math-specific clusters include advanced STEM topics like Tissue and Tumor Biology and Mathematical/Computational Modeling, Computation and Machine Learning, Number Theory and Discrete Math, and Mathematical Modeling of Biological Systems.

Location: Residential, choice between UC Davis, UC Irvine, UC San Diego, and UC Santa Cruz

Cost or stipend: $4,770 program tuition

Application deadline: Applications for the 2023 sessions are already closed. Based on this year’s deadlines, the applications open in January and close in early February each year.

Program dates: All clusters will run between July 9, 2023 – August 5, 2023

Eligibility: California State students who are rising 8th-11th graders

10. PRIMES USA

PRIMES-USA is a one-year research program focused on mathematics, which is free for high school students. The program is accessible to students from all over the United States, and every selected student is mentored by graduate students and faculty from various universities, including MIT.

The program is divided into four distinct phases that take place throughout the year. During Phase 1, you engage in advanced reading. In Phase 2, you conduct active research with the guidance of mentors. In Phase 3, you engage in independent study. In the final phase, Phase 4, you finalize your project with the help of your mentor and present your findings at the Fall-Term PRIMES conference held in mid-October. In addition to presenting, you are required to write a final paper that summarizes your research results. This paper can be submitted to professional research journals and competitions for publication.

Application deadline: Applications for 2024 will open on October 1, 2023. Based on this year’s deadlines, the applications close at the end of November each year.

Program dates: Year-Round, from January 1 to December 31 of the calendar year.

Eligibility: High school juniors and sophomores (including home-schooled) residing in the United States are eligible if they live no closer than 50 miles from Boston (Students residing within driving distance from Boston should apply to the MIT section of PRIMES ).

11. UC Irvine’s Math ExpLR Summer Research Program

Math ExpLR is a 6-week program focused on the intersection of mathematics and biology. This program offers students a unique opportunity to gain insight into the world of mathematical research and university studies. You will collaborate with undergraduate students and work on a computational biology research project under the guidance of a principal investigator.

The program also includes weekly skill development activities that cover a range of topics, including how to effectively deliver presentations, how to write math using computer software, the basics of Matlab, and principles of mathematical modeling. Upon completion of the program, each team will present their research findings and submit an expository paper that describes their work in detail.

Location: Residential, UC Irvine

Cost or stipend: Free

Application deadline: Applications for the 2023 sessions are already closed. Based on this year’s deadlines, the applications close in February each year.

Program dates: June 26, 2023 – August 4, 2023

Eligibility: All high school students

Bonus entry:

The Ross Mathematics Program at Ohio State University

The Ross Mathematics Program is a great opportunity for highly motivated high school students with a love for mathematics. This intensive six-week residential summer experience is designed to help you explore the subject with a focus on Number Theory.

During the program, you'll attend ten hours of class per week, consisting of five hours of lectures and five hours of small-group meetings . The rest of your time will be spent working independently on the challenging mathematical ideas presented in class and on problem sets. You'll have the opportunity to study a range of topics, including Euclid's Algorithm, Quadratic Number Fields, Polynomials, Gaussian integers, and more. The Ross Program is an ideal setting for you to deepen your knowledge of mathematics in a supportive and collaborative environment.

Location: Residential, Otterbein University or the Rose-Hulman Institute of Technology (depending on which session you choose)

Cost: $6,000 program tuition

Application deadline: March 31, 2023

Otterbein University: June 11, 2023 – July 21, 2023

Rose-Hulman Institute of Technology: June 18, 2023 – July 28, 2023

Eligibility: High school students aged 15-18 years

There are plenty of other great program opportunities in math, so here are a few other paid and free math programs you can consider:

Summer Workshop in Math (SWiM) at Duke University

IMA-MathCEP Math Modeling Camp at The University of Minnesota

Simons Summer Research Program

Rutgers Young Scholars Program in Discrete Mathematics

Illinois Tech Mathematics Camp

Michigan Math & Science Scholars Summer Program (MMSS)

UPenn Mathematics Academy

If you're looking for a real-world internship in math and related fields that can help boost your resume while applying to college, we recommend Ladder Internships!

Ladder Internships  is a selective program equipping students with virtual internship experiences at startups and nonprofits around the world!  

The startups range across a variety of industries, and each student can select which field they would most love to deep dive into. This is also a great opportunity for students to explore areas they think they might be interested in, and better understand professional career opportunities in those areas. The startups are based all across the world, with the majority being in the United States, Asia and then Europe and the UK. 

The fields include technology, finance, environmental science and sustainability, business and marketing, healthcare and medicine, media and journalism and more.

You can explore all the options here on their application form . As part of their internship, each student will work on a real-world project that is of genuine need to the startup they are working with, and present their work at the end of their internship. In addition to working closely with their manager from the startup, each intern will also work with a Ladder Coach throughout their internship - the Ladder Coach serves as a second mentor and a sounding board, guiding you through the internship and helping you navigate the startup environment. 

Cost : $1490 (Financial Aid Available)

Location:   Remote! You can work from anywhere in the world.

Application deadline:  April 16 and May 14

Program dates:  8 weeks, June to August

Eligibility: Students who can work for 10-20 hours/week, for 8-12 weeks. Open to high school students, undergraduates and gap year students!

Additionally, you can also work on independent research in AI, through Veritas AI's Fellowship Program!

Veritas AI focuses on providing high school students who are passionate about the field of AI a suitable environment to explore their interests. The programs include collaborative learning, project development, and 1-on-1 mentorship.  These programs are designed and run by Harvard graduate students and alumni and you can expect a great, fulfilling educational experience. Students are expected to have a basic understanding of Python or are recommended to complete the AI scholars program before pursuing the fellowship. 

The   AI Fellowship  program will have students pursue their own independent AI research project. Students work on their own individual research projects over a period of 12-15 weeks and can opt to combine AI with any other field of interest. In the past, students have worked on research papers in the field of AI & medicine, AI & finance, AI & environmental science, AI & education, and more! You can find examples of previous projects   here . 

Location : Virtual

$1,790 for the 10-week AI Scholars program

$4,900 for the 12-15 week AI Fellowship 

$4,700 for both

Need-based financial aid is available. You can apply   here . 

Application deadline : On a rolling basis. Applications for fall cohort have closed September 3, 2023. 

Program dates : Various according to the cohort

Program selectivity : Moderately selective

Eligibility : Ambitious high school students located anywhere in the world. AI Fellowship applicants should either have completed the AI Scholars program or exhibit past experience with AI concepts or Python.

Application Requirements: Online application form, answers to a few questions pertaining to the students background & coding experience, math courses, and areas of interest. 

Stephen is one of the founders of Lumiere and a Harvard College graduate. He founded Lumiere as a PhD student at Harvard Business School. Lumiere is a selective research program where students work 1-1 with a research mentor to develop an independent research paper.

Image source: MIT PRIMES website

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Ideas for high school pure maths projects

I am thinking of giving my high school students some pure maths projects to do. It is a lot easier to think of some interesting stats projects but not in pure maths. The students' maths background are weak, they might not really understand the relationship between integration and area finding. I am planning of giving a short project that could be done in 1-2 weeks time (for 1-2 pages long) that emphasises on conceptual understanding but if possible exciting and upon completing the projects students should feel more confident tackling more problems.

From my experience when I studied maths back then in high school, I preferred to understand the concepts first before trying to do any problems. But nowadays, I think it is a common phenomenon that students tend to jump straight into doing problems without bothering the purposes, motives, and relationships from one concept to the other. In other words, students are not interested in connecting the dots, they just want to do and pass the tests.

The topics that we are discussing now are: differential and integral calculus of trigonometric and logarithmic functions.

Here are some ideas that I have in mind: 1. Summarise different interpretations of derivatives (for example: geometric interpretation, algebraic interpretation, physical interpretation, etc) 2. Relate the idea of (definite) integration (continuous) and summation (discrete) and give some properties or equations which are very similar in both cases. 3. Summarise common trig identities and prove them. For example, $sin^2\theta+cos^2\theta=1$ can be proved using Pythagoras.

I would really appreciate if anyone could share some other ideas or examples which might be helpful in enhancing students' understanding of concepts, I have a very limited knowledge on the current research, maybe there are some exciting research topics which do not require tons of advanced maths. Many thanks!

• secondary-education

• $\begingroup$ Can basic elementary number theory be handled by them? $\endgroup$ –  Git Gud Commented Mar 30, 2014 at 11:55
• $\begingroup$ @Git Gud: Some really basics stuff yeah I think, like divisibility, prime factorisation, gcd, etc.. But we don't want to go to far to something like Fermat's Little Theorem, Chinese Remainder Theorem etc. But I would like to know some ideas in elementary number theory which might be useful in some other occasions. Thanks! :) $\endgroup$ –  user71346 Commented Mar 30, 2014 at 12:03
• 1 $\begingroup$ You've made your issues clear, but not in the form of a question. Putting it into a question, with a question mark, focuses the post and makes it easier for people to answer well. $\endgroup$ –  user173 Commented Mar 30, 2014 at 12:47
• 1 $\begingroup$ Would something like asking them to provide primality certificates of some given prime numbers be feasible (i.e. I'm not asking about this particular question, but its character)? $\endgroup$ –  dtldarek Commented Mar 30, 2014 at 13:29
• 2 $\begingroup$ ams.org/programs/students/high-school/emp-student-research $\endgroup$ –  David Ebert Commented Jun 4, 2014 at 6:14

13 Answers 13

Joseph Malkevitch , based out of CUNY York College but also a visiting professor at Columbia University Teachers College, has a fair bit on his website about (high school) student research.

Depending on the student's mathematical level, one could point to Malkevitch's pages on Mathematics Research Projects or a couple other pages directed at undergraduate students (1) (2) .

Other helpful links and pieces of writing can be found on his main site (click his linked name above).

• 3 $\begingroup$ Very good, substantive answer. A good standard to set. :) $\endgroup$ –  paul garrett Commented Mar 30, 2014 at 23:13

Just a list of some cool things:

• Recurrent relations There are a lot of different ways to find solutions for recurrent relations. Logistic maps are also very neat way to illustrate what's going on.
• Bernoulli numbers This is what I gave a short presentation on. It may be a bit boring for highschoolers sinec there is not really a cool way to explain or illustrate what you're doing, but maybe for the students who are more interested in pure math.
• Linear algebra
• Complex numbers Some very basic complex analysis can be suited for high-schoolers (of course, formal proofs for all the theorems that are commonly used is way too much, but maybe some arguments or some informal proofs would be feasible).
• Infinite series There was an excellent pdf on this, which presented the difference between the different types on convergence for infinite series, together with some convergence tests, all in a very intuitive way very suited for highschoolers, but unfortunately I can't find it now.
• Cardano's formula for solving (some) cubic equations this can be done geometrically like the quadratic formula, but probably requires guidance.
• Fourier theory An illustrated approach could be really cool, together wth an explanation of some of the basic concepts of Fourier analysis.
• Calculus some semi-rigorous proofs using limits and limits of summations can probably made by high school students and can be very interesting.
• Trigonometric identities like cos and sin addition and multiplication formulas
• Platonian solids There is a very nice proof that there are only 5 platonian solids, and there are some nice properties for 3-dimensional solids as well (F + V = E + 2), and some basic linear algebra for calculating areas, volumes and angles would be appropriate.
• Ramsey theory This can be explained quite nicely by using the analogy of people in a group who are either friends or not. Also, the proofs have a nice graphical representation. Graph theory in general has some really cool topics for high school students, so there are definitely more topics here.
• Programming an AI for a simple game It's always fun to play a game against a computer, and it's impressive when you can program a computer in such a way that it performs better in a game then most humans can.
• Maps and projections Things like the Mercator projection and stuff. I don't know the specifics, but I know a guy who did this as his high school project.
• Non-euclidian geometry I don't know too much about this, so this may be too hard, but this is a really cool demonstration of how axiomatic systems work and a fun mind-experiment that, suprisingly, can be embedded in a picture.
• Game theory Game theory provides a lot of interesting question. For example, I was just playing that 2048 game, and I found myself repeating: right, down, right, down, ... until i got stuck, then I did left or up, and started over again. Provided you have the probabilities of the new blocks appearing (else you could estimate them or just create your own variant in which the probabilities are known) you can, for example, try to analyze the average score. Then you could also try to find a pattern that ends the game as quickly as possible, or one that ends the game with the lowest average score (and are these patterns the same?). The nice thing is that even when a mathematical analysis is not feasible, you can just let your computer play for a day and come up with a very good estimate.

I've taken some subjects that I found interesting myself, and some others from a course where everybody had to give a presentation on a mathematical subject. Some of these subjects may be too hard or maybe too specialized to write a 100-page paper about, but I'll let you be the judge of that.

I've mainly focussed on things that have either a nice geometric representation (because a picture usually makes things more interesting and easier to understand) or some nice things that are not to hard to understand but still are considered interesting and/or nontrivial. I think all but the first three have elements that allow for a nice graphical explanation.

That being said, the students probably require a considerable amount of guidance. Most of the material they'll find is not suited for them, so the teacher either needs to have some material that is appropriate, or help out in another way that allows the students to do the research relatively independent.

• 2 $\begingroup$ Note that this is one of the theorems mentioned in my link above. The specific site is york.cuny.edu/~malk/high-school-research/… and includes as recommended reading: O'Rourke, Joseph, Art Gallery Theorems and Algorithms, Oxford U. Press, Oxford, 1987. $\endgroup$ –  Benjamin Dickman Commented Mar 31, 2014 at 18:42
• 3 $\begingroup$ My Art Gallery book is online at this link . $\endgroup$ –  Joseph O'Rourke Commented Jun 4, 2014 at 20:03

Here are a few projects done at my high school:

1) Given a quadratic in the form $y=ax^2+bx+c$, determine what changing $a$, $b$ and $c$ does to the turning point (vertex) of the parabola and prove your answer. Most students are able to figure out $a$ and $c$ relatively quickly, and they are good practice for $b$, which turns out to be much harder.

2) Prove that 7 congruent circles form 12 points of tangency as shown in the diagram below. Challenge students to prove this at least two ways using separate branches of maths.

3) Taxicab Geometry . Resources and questions abound online. This is one example of a good guiding worksheet. I haven't done Taxicab Geometry with my students, but I think it's an interesting way to challenge students to rethink all of their basic geometry definitions and axioms.

4) Have students revisit every maths theorem and formula used in high school. Have them summarise the theorem in their own words and give two examples of how it is used. (This project was given to the "bottom set" of students, with the feeling that they needed more practice, whereas the top students were more prepared for an extension.)

• $\begingroup$ For (2) it looks like 12 points of tangency, how do you count 18? $\endgroup$ –  JTP - Apologise to Monica Commented Jun 4, 2014 at 2:59
• $\begingroup$ @JoeTaxpayer Oops. You're right. $\endgroup$ –  David Ebert Commented Jun 4, 2014 at 6:15

Solving quadratic and cubic equations. At least for cubics, this really does require that your students have seen complex numbers.

Solving the quadratic by completing the square is simple, clever, and you may not have ever shown them the proof in class.

For the ambitious, Cardano's method for solving the cubic is quite straight forward, based on the lemma that for any two numbers $S$ and $P$, there are two (possibly complex) numbers whose sum is $S$ and whose product is $P$.

Staying within the realm of algebra, some basic things about complex numbers could make for a decent two-page project. Students could prove the basic geometrical facts about complex numbers:

• Addition corresponds to vector addition on an Argand diagram.
• Multiplication correponds to multiplying the lengths and adding the angles.

Proving those facts could be page 1. Page 2 could be using them to prove another geometrical fact about complex numbers:

• There are exactly $n$ $n$-th roots of $1$, and they form the vertices of an $n$-gon centered at $0$. From this you can deduce that there are exactly $n$ $n$-th roots of any number.
• You can use complex numbers to prove certain trig identities.

As a professional mathematician, I certainly appreciate the projects listed above, and this might not be exactly the kind of answer you're looking for. The projects below will definitely help students understand a particular concept (dimension and proof-writing, respectively) but will not directly help them solve any problems.

When I used to teach high school, I would usually try to develop projects that connected mathematics to other disciplines. I would focus especially on the humanities and arts, since students whose interests leaned in those disciplines were often the most challenging to motivate and engage. Two projects with which I had some success:

• In a geometry class, I had students read Flatland and then asked that they come up with a creative project based on what they read. One student turned it into an analysis of women's rights in Victorian England; another painted, on a thin strip of wood, what an inhabitant of Flatland might see; another made the argument that cubist paintings were a 2-d rendering of what a 4-d person might see looking at a 3-d person and then made some paintings in that style.
• Also in the same geometry class, I tried to make an analogy between proof-writing (even though this was only ten years ago, we were still teaching proofs at this school) and editorial writing. What are your givens/the editorial writer's biases and assumptions? What are you trying to prove/the editorial writer trying to say? Can you/the editorial writer justify each step in your argument? I then had the students take an editorial in a local newspaper and attempt to decompose it into a two column proof.

At my daughters high school, last year every student must do a project of student research. They can choose the subject themselves (my daughter choose biology). Some math projects which have been done: -Fractals, programming fractals. -determinants and the eight-queen-problem

• 1 $\begingroup$ Can you maybe add some details about how deep the projects have been studied? $\endgroup$ –  Markus Klein Commented Mar 31, 2014 at 11:33
• 1 $\begingroup$ surpringly deep! The expectation is that should be used >100hr,and final report about 100 pages. My daughters project was studying birds during winter months in a park nearby our house, detailing which species visited, how many, etc, what they were eating, writing detailed observation protocol. The maths project I found surpringly deep! for the age. $\endgroup$ –  kjetil b halvorsen Commented Mar 31, 2014 at 11:38

If you understand some French, you can go to the site of Math en Jeans and look at the subjects other people have worked at with high school students.

Continued fractions can produce a vast range of good projects, which you can give at any age from (willing) middle school to (reluctant) high school students. One simple way to motivate the concept is to ask students to discover approximations to pi that were in wide use in ancient world . Sure, everybody knows $\pi \approx 22/7$, but can you do better than that? How do you proceed from $22/7$ to the next approximation? How do you convert continued fractions to "regular" ones, and vice versa? What if you allow not only the fractions like $1/a_n$, but also $2/a_n$, $3/a_n$, etc? E.g., if your first approximation is $\pi \approx 3.14 = 157/50 = 3 + 7/50$, how can you improve it using the continued fractions approach? Has anybody discovered this approximation? Can you produce a reasonably looking approximation that is not listed on Wikipedia?

You might also want to read Euclidlab - http://euclidlab.org/unsolved . They have many interesting projects, which should appeal to high-schoolers (I am a high-schooler myself and am thus speaking from ``experience''). In fact, I am planning on joining Camp Euclid, which other high-school students might find interesting (it costs a lot, though).

COMAP (The Consortium for Mathematics and Its Applications) publishes a newsletter for its members called Consortium. The current issue of Consortium can be downloaded for free from the web page below (which also includes other free COMAP materials) until the next issue appears, at which time the "current" issue goes behind a firewall.

https://www.comap.com/Free/

Consortium has many articles that can inspire student research (middle school to graduate school) research, In particular, the last couple of issues of Consortium have featured a "new column" that I edit, that discusses research problems specifically designed for (but not limited to) pre-college students. There problems appear under the title: "Student Research Corner." If you use the COMAP search feature you can find the titles of these research problems which are quick starting but all are geometrical questions nearly all involving graph theory and polyhedra.

Ask them to show that the following procedure constructs all rhombuses (rhombi?) of a fixed side length: take two circles of the same radius. Let them be placed to intersect at two distinct points. Now the two centres and the intersection points together form vertices of a rhombus. Now 'pull the circles apart' slightly or push them closer and obtain more of them.

Maybe something with 3D point groups (not all the details of the group theory, but describing the types of them (mirror plane, rotation, etc.) and classifying some common objects. (E.g. it is interesting that octahedron and cube have same symmetry. also, 2-D tiling patterns (but not 3d space groups...too complicated).

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6 Ways to Improve Students’ Math Literacy

Middle and high school math teachers can use these ideas to build students’ reading comprehension and reasoning skills using real tasks like budgeting.

While a lot has changed in math instruction over the years, the idea that students need to be math literate has been constant. Being math literate means much more than calculations. Life events such as buying a home, paying taxes, or even estimating how much you’ll spend on groceries require modeling and reasoning skills.

State and district tests often include problems that are real-world based, and that means that students will need to use reading comprehension, along with math skills, in order to show proficiency. This can be particularly difficult for students with learning disabilities, those who have had interrupted schooling, and/or emergent multilingual learners. It’s imperative that math teachers develop a tool kit to help students decipher the math moves needed for such problems.

Through my dissertation research and my many years of teaching mathematics with great math teachers, I have found simple ways to help students become more math literate. Here are some practical ideas on how teachers can help students become math literate, from the perspective of Algebra 1 teachers from various backgrounds.

6 Ways to Help Students Gain Math Literacy

1. Use sentence frames. Sentence frames are a simple way to help students of all backgrounds learn how to state their answers and ask any questions they have about a word problem. Teachers can post sentence frames on a board or even on students’ desks for easy access. Here are some examples:

• “I agree with this answer because ____.”
• “I believe the answer is ____ because ____.”
• “I showed my work by ____.”
• “One strategy that may be helpful is ____ because ____.”

2. Bring back the highlighter. Many Algebra 1 teachers agree that the highlighter is a great way to help emphasize learning in mathematics. The highlighter gives students control of the parts of the problem that they find important. A good suggestion is to demonstrate the use of highlighting key words and have highlighters available for every task and assessment. It also helps students see the patterns in math problems.

3. Speak “algebra.” Students in all math classes need to be speaking math in their classes. It’s important to use the appropriate vocabulary words that pertain to the lesson. This is particularly important as students see formal math language in textbooks and standardized tests. Yes, breaking down the vocabulary for comprehension is a great tactic, but bringing it back to the standard math vocabulary is how we make connections.

4. Use word walls. The word wall was an important part of many math classrooms a few decades ago. They made sure that students saw math words that related to a particular topic being taught. For example, when introducing a polynomial unit, teachers would often put words such as monomial , trinomial , and polynomial on the word wall.

Many Algebra 1 teachers feel that having the visual is most important as students learn about new topics. Students need visual reminders. One suggestion was for students to “own” the word wall by passing out the words in advance and having them hang up each word as it was introduced throughout the unit. Students can make the words artsy and creative in an effort to personalize the resource.

5. Provide foldables or graphic organizers. The use of foldables in the math classroom is a game changer for many students, especially in the post-pandemic era. These low-tech student- or teacher-made “books” constructed out of folded paper provide learners with a handy place to write down the main concepts introduced in a unit. Students have been so used to math technology that there is a need to bring them back to tactile methods.

Providing a foldable to sum up or even begin a unit is a cost-effective method and allows students to use paper and scissors in a creative way to refer to math vocabulary and common word problems. You can find lots of free ideas for foldables online , and there are sites that sell them as well. Some of the designs are very creative and bring a bit of visual art into your math classroom.

6. Have students write relevant word problems. Every time there’s a new curriculum or textbook, word problems get a refresher to connect with the current generation, but there’s no reason why students can’t make up their own. Allow them to write their own word problems, using the context you’re teaching. Not only will students own their own learning, but also they will be able to use critical thinking skills to combine math, vocabulary, and everyday life to further their understanding.

Making the math classroom become a laboratory of reading and math enables students to become owners of the learning process. Students can be math literate, which will allow teachers to facilitate learning processes with all types of word problems, and consequently improve math scores and prepare students for the world of infusing mathematics into their everyday lives.

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25 Math Summer Programs for High Schoolers in 2024

What’s covered:, 25 math summer programs for high school students.

• How Impressive are Math Summer Programs in High School Admissions?

Other Ways to Spend Your Summer 

Are you a high school student who loves mathematics? Are you looking for ways to test your skills against other bright young students? Consider spending this summer with one of these 25 math summer programs for high school students.  

1. IMA-MathCEP Math Modeling Camp at The University of Minnesota

Dates: June 24 – 28 

Location: University of Minnesota Application Deadline: May 31

The Math Modeling Camp is a free program where high schoolers use mathematical models to analyze real-world situations like the effect of traffic on a bridge or the climate’s estimated impact on natural resources. The program tests participants’ problem-solving skills, ability to collaborate with others, and attention to detail for extended periods. This is a non-residential program and preference is given to students from Minnesota, especially those who live in the Twin Cities area.

To apply, you must have completed Calculus and present a recommendation letter from a math teacher.

2. SUMaC (Stanford University Math Camp)

• Online session 1: June 17 – July 5
• Online session 2: July 8 – 26
• Residential session: June 23 – July 19

Location: Stanford University and online Application Deadline: February 1 

Cost: $3,550 – $8,250 

SUMaC offers two different formats of its SUMaC program that high school students can choose from, either a three-week virtual experience or a four-week residential experience. All participants immerse themselves in advanced mathematics through activities like lectures, guided research, and group problem-solving. Space in the program is limited; just 64 students are chosen for the virtual program and 40 are selected for the residential program. 

3. Idea Math Camp

• Plano, Texas: June 4 – 14
• Nashua, New Hampshire: June 23 – July 4 

Location: John Paul II School and Rivier University  

Application Deadline: N/A

Cost: $1,935 – $3,895

IDEA MATH is a two-week program for high school students that provides in-depth enrichment in important mathematical areas. The program combines an interactive teaching approach with group learning as well as seminars-style lectures. Students will participate in a variety of courses that add up to 65 academic hours and will cover subjects including algebra, combinatorics, geometry, and number theory. 

4. Canada/USA Mathcamp

Dates: June 30 – August 4

Location: University of Puget Sound Application Deadline: March 6

Cost: $5,500 

Canada/USA Mathcamp is a five-week-long summer camp for high school students with demonstrated potential and aptitude in mathematics to enhance their abilities, skills, and confidence in the subject. Mathcamp enrolls 65 new students each summer, as well as 55 returning alumni. The Qualifying Quiz, a personal essay, recommendation letters, and prior mathematical knowledge are used to determine whether applicants are accepted. 

5. Summer Academy for Math and Science (SAMS) at Carnegie Mellon University

Dates: June 22 – August 3

Location: Carnegie Mellon University Application Deadline: March 1

SAMS (Summer Academy for Math and Science) camp is a free, residential, six-week intensive program for high-school Juniors. SAMS selects students who have shown a strong interest in mathematics, extra-curricular activities, and/or community engagement as well as a dedication to diversity and inclusion in education.

Students from low-income families, underrepresented communities, and individuals who have never attended a high school with a long history of admissions to top-tier institutions are encouraged to apply. 

6. AlphaStar In-Person Academy Summer Math Camp

• Session 1: June 17 – July 5 
• Session 2: July 15 – August 2

Location: Mission College Application Deadline: N/A

Cost: $1,350 – $3,050 

AlphaStar Summer Math Camp is an intensive, three-week-long program for high-school students geared towards training for prestigious math competitions. The camp provides fundamental math courses such as algebra, counting, geometry, and number theory. Students are taught mathematical skills by subject-matter experts and participate in engaging national and international competitions throughout the course of the program. 

AlphaStar encourages students with proven mathematical talent and analytical problem-solving skills to apply, as well as those who would like to push themselves outside of their comfort zones. 

7. AwesomeMath Summer Program

• Session 1: June 10 – 28
• Session 2: July 1 – 19 
• Session 3: July 22 – August 9

Location: Online Application Deadline: Varies 

Cost: $1,175 – $1,475, depending on date of payment

The AwesomeMath Summer Program is a three-week intensive online course for talented high school pupils who want to improve their problem-solving abilities and enhance their mathematics education in general. The AwesomeMath Summer is particularly unique in that it helps students practice and prepare for contests such as AMC10/12, USAMO, and AIME.

Aim to register by February 2 for this program, to get the lowest price per course rate.

8. The Ross Mathematics Program

• Otterbein University : June 9 – July 19 
• Rose-Hulman Institute of Technology : June 16 – July 26

Location: Otterbein University and Rose-Hulman Institute of Technology Application Deadline: March 15

Cost: $7,000

The Ross Program is an intensive six-week residential summer experience designed to encourage motivated 15- to 18-year-old students to explore mathematics. Admission decisions are based on several criteria, including school transcripts, teacher recommendations, a personal applicant essay, and proof of the applicant’s previous work on challenging math problems. 

9. Research Science Institute Program at MIT

Dates: June 23 – August 3 

Location: Massachusetts Institute of Technology (MIT) Application Deadline: December 3 

MIT’s Research Science Institute (RSI) selects approximately 100 of the world’s most accomplished high school juniors to attend this six-week program that exposes students to advanced theory and research in mathematics, science, and engineering. Participants spend the first week of RSI taking STEM coursework and the last five weeks conducting projects under the mentorship of experienced researchers and scientists. 

10. MathILy at Bryn Mawr College

Dates: June 30 – August 3 

Location: Bryn Mawr College Application Deadline: April 30 

Cost: $5,300 

MathILy is a five-week residential summer math program for high schoolers. The math lessons are inquiry-based, interactive, and operate on the principle that combining smart people with mathematics results in learning and fun. Math class takes place for about seven hours—six days a week—in two morning shifts and two evening shifts. Instructors are Ph.D.s in math, as well as undergraduate math students.  

11. Michigan Math & Science Scholars Summer Program (MMSS)

• Session 1: June 23 – July 5
• Session 2: July 7 – 19 
• Session 3: July 21 – August 2 

Location: University of Michigan Application Deadline: Rolling 

Cost: $1,300 – $2,300 

The Michigan Math and Science Scholars (MMSS) summer program exposes high school sophomores, juniors, and seniors to current mathematical developments and research while encouraging future generations of mathematicians to engage in and enjoy the subject. The residential program also provides participants with a sample of what it’s like to attend a major university—living in a residence hall, working in labs, taking classes, and learning from faculty, graduate students, and advanced undergraduates.  

Three two-week courses are offered, with students having the option to attend one, two, or all three. 

12. Math Skills Camp at Hofstra University 

Dates: July 29 – August 9 

Location: Hofstra University 

Application Deadline: N.A

Cost: $2,250 

The Math Skills Camp at Hofstra University is designed for 6th through 10th graders who want to improve their math abilities and consolidate classroom learning before the start of the new academic year. The program’s objective is to foster students’ current math abilities while motivating them to improve their skills. 

Hofstra University’s program, unlike the others on this page, does not focus on mathematically gifted students. It is intended for everyone. 

13. HCSSiM (Hampshire College Summer Studies in Mathematics) 

Dates: June 30 – August 10 

Location: Hampshire College Application Deadline: N/A

Cost: $5,882

HCSSiM is a six-week program for talented and highly motivated high school students that includes college-level mathematics instruction. For the majority of the day, participants are actively engaged in doing mathematics (rather than merely learning about the outcomes of mathematics).

The curriculum is made up of lectures, study sessions, math workshops (general-knowledge classes), maxi-courses (three-week classes taught by senior management personnel), and mini-courses (specialized shorter classes).

The program is free for domestic students from families with household incomes beneath $85,000. 

14. PROMYS (Program in Mathematics for Young Students)

Location: Boston University Application Deadline: April 30 

Cost: $6,100 

PROMYS is a residential six-week summer program at Boston University that aims to encourage exceptionally driven high school students to delve deeply into the creative world of mathematics in a positive learning environment with peers, counselors, research mathematicians, and visiting scientists.

Approximately 80 high school students over the age of 14 are chosen to participate annually along with 25 undergraduates to work as counselors. Students who are female, African American, Hispanic, or from other underrepresented groups in STEM are strongly encouraged to apply.  

The program is free for domestic students from families who earn under $80,000 per year. 

15. UPenn Mathematics Academy

Dates: July 6 – 27 

Location: University of Pennsylvania (UPenn) Application Deadline: N/A

Cost: $9,700 

This residential program exposes high school students to mathematical complexes rarely offered at the high school level, including: 

• Combinatorics
• Generating functions and partitions
• Graph theory
• Combinatorial game theory
• Galois theory
• Linear algebra
• Euclidean and non-Euclidean geometries
• Point-set topology
• Knot theory

Participants engage in lectures, workshops, group work, computer simulations, and problem sessions. One year of high school algebra II or trigonometry is required. 

Students attending a public or charter school in the School District of Philadelphia may qualify to participate in the academy for free.  

16. Rutgers Young Scholars Program in Discrete Mathematics

Dates: July 8 – August 2

Location: Rutgers University Application Deadline: Rolling 

Cost: $4,500

This residential four-week program encourages talented high school students to consider careers in mathematics. Participants use mathematical concepts to solve problems, work with professional mathematicians, and learn about careers in the field. Participants also sample college life by living and studying at Rutgers University during the week, while getting to return home on the weekends for downtime.  

17. Illinois Tech Mathematics Camp

Dates: June 10 – 14

Location: Online Application Deadline: May 3

Cost: $350 

This online program seeks to expose rising 9th through 12th graders to mathematical problems they rarely encounter in high school. Participants will bolster their abstract reasoning and problem-solving skills and learn to better communicate mathematical ideas. Students will also gain a greater appreciation for the usefulness, power, and beauty of mathematics.

18. AI/Machine Learning Research Bootcamp

Dates: June 17 – 26 

Location: Online

Application Deadline: June 5

Cost: $1,975 

This six-week virtual program exposes students in grades 8 through 12 to the mathematics behind AI, machine learning, and deep learning models. Engineers from MIT and Stanford teach classes while students work in teams of two to three under their supervision to train their own AI models from scratch. No prior experience is required to attend this program.  

19. Summer Math Program for Young Scholars

Dates: August 12 – 30

Location: New York University (NYU)

Application Deadline: May 1

Cost: $1,750

Mathematically inclined high schoolers are introduced to undergraduate-level math topics in this three-week summer program. Participants explore topics like number theory, graph theory, knots and surfaces, and computer science through problem-solving activities, lectures, and mathematical games and puzzles. They’ll also explore careers in mathematics and gain firsthand experience with college-level coursework.

High schoolers in grades 9 through 12 are eligible to participate.

20. Young Scholars Program (YSP) at the University of Chicago

Dates: July 1 – 26

Location: University of Chicago

Application Deadline: April 12

Cost: $250 – $1,000

Chicago area students in grades 7 through 12 can sharpen their math skills in this selective four-week camp. Participants are broken into three cohorts (grades 7-8, grades 9-10, and grades 11-12) and exposed to mathematics not often found in high school curricula. The focus of 2024’s program is number theory.

The program has a unique fee structure based on income, and students from lower-income households pay less than those from higher-income families.

21. Stony Brook Mathematics Summer Program

Dates: July 15 – 19

Location: Stony Brook University

This week-long program explores several mathematical fields including knot theory, number theory, cryptography, the mathematics of finance, and statistics for the biological sciences. In addition to being exposed to advanced mathematical topics, students will attend lectures, work on projects, and participate in mathematical games. They’ll also connect with other students interested in math and work closely with professors.

The program is open to rising sophomores, juniors, and seniors.

22. New York Math Circle (NYMC) Summer Program

Dates: July 22 – August 8

Location: New York University (NYU) and online

Application Deadline: May 17

Cost: $875 – $995

Students who enjoy math, want to challenge themselves, and want to explore new mathematical topics and problems will want to check out New York Math Circle. Participants must take a qualifying exam, which is used to place them into one of three sections based on their skills.

23. California State Summer School for Mathematics & Science (COSMOS)

Dates: July 7 – August 3

Location: UC Davis , UC Irvine , UCLA , UC San Diego , and UC Santa Cruz

Cost: $5,007

This four-week, STEM-focused summer program is held concurrently on five University of California campuses. Participants tackle challenging hands-on, lab-intensive curricula not commonly found in high school—helping build skills and awareness of career paths in STEM.

The program is open to students in grades 8 through 12 with a minimum 3.5 GPA. It’s also competitive—just 160 to 200 students per campus are selected to participate.

24. LSU Math Circle

• Session 1: June 10 – 29
• Session 2: July 15 – August 3

Application Deadline: February 9

Cost: $1,200

Students work in small mentored groups in this three-week program, meeting for two to three hours a day to learn mathematical material not commonly taught in high school and build a foundation of college-level math skills. The program culminates with a capstone project and then the presentation of a colloquial-style poster.

High schoolers in grades 9 through 12 are eligible to participate in the program.

25. My Introduction to Engineering (MITE)

• Session 1: June 23 – 27
• Session 2: July 7 – 11

Location: The University of Texas at Austin

Application Deadline: March 25

This five-day program introduces participants to life as an engineering student at UT Austin . Students participate in hands-on engineering activities, sit for lectures, go on tours, and explore a variety of careers in engineering. As a residential program, it also allows students to experience a slice of college life.

The program is open to current high school juniors and is limited to just 50 participants per session.

How Impressive are Math Summer Programs in High School Admissions? 

A college is looking for students who have a wide range of interests. Summer math programs allow you to show your abilities and enthusiasm for learning, which is highly valued by academic institutions. 

Extracurricular activities are divided into four tiers . The four tiers are divided into more and less distinctive activities, with Tier 1 representing the most unique programs and Tier 4 covering more common activities. You should aim to include a few of each when applying. 

Math summer programs generally fall into Tier 3 or 4, but could be considered Tier 1 or 2 if they are particularly prestigious and selective. For example, Tier 1 might be PROMYS and a Tier 4 might be MathILY. 

How does a math summer camp or an outside activity influence your chances of acceptance? CollegeVine’s free chancing engine will let you see your true chances of getting into 1500+ colleges in the United States, as well as offer tips for enhancing your profile! 

Math summer programs are an excellent way to improve your admissions chances, but there are other options, including internships, volunteering, and independent study. 

• Internships can help you explore career options and gain valuable professional experience.
• Volunteering offers the chance to do good work in your community, which will impress admissions officers.
• Independent study can provide an opportunity to pursue a topic of personal interest outside the classroom.  

Overall, math summer programs are a great way to improve your chances of admission, but only one factor in an entire application.

Related CollegeVine Blog Posts

80 Impactful Research Topics for High School Students

By Rebekah Pierce

Educational writer and former teacher

3 minute read

Choosing the right research topic can be the secret ingredient to making your high school student paper not only impressive but also fun to write. Let's face it - no one wants to slog through a boring topic that has been done a million times before. 

A good research topic is like the foundation of a strong building. It sets the stage for everything else - not to mention that it helps you develop critical thinking and analytical skills that you’ll need as you move into college and beyond. 

Here are some of the best research paper ideas (and some tips to help you get started with writing about these fun research topics for high school projects).

How to Choose the Right Research Paper Topic

Begin by identifying what interests you most. What do you want to learn more about? These don’t necessarily have to be controversial topics. Just think about what might be a good research topic for your interests.

Once you have a few ideas for a good topic, start the research process to hunt down resources and relevant literature. Aim for the best research paper topics that will allow for a comparative study, such as analyzing different perspectives on a social issue or contrasting historical events. 

Make sure your chosen topic is neither too broad nor too narrow. Finding the right balance is incredibly important if you want to produce a focused and impactful paper.

Do your own research through Polygence!

Polygence pairs you with an expert mentor in your area of passion. Together, you work to create a high quality research project that is uniquely your own.

How to Get Started with Your Research Paper Writing

First up, do a thorough literature review to gather existing research and insights relevant to your topic. This may even inspire new angles for you to explore!

Organize your findings and outline the structure of your paper to keep things clear, tight, and tidy. Write an abstract to break down your intentions.

As you write a research paper , critically analyze the information and present your arguments coherently, allowing your voice to shine through (objectively) while incorporating scholarly evidence. In the introduction , grab the reader with an enticing bit of information, like a hook, quote, or stat.

Edit, edit, and edit some more - then, get ready to publish!

Need some inspiration to get the creative juices flowing? Keep reading to discover the best research topics for high school students.

Technology Research Paper Topics

The Influence of Artificial Intelligence on Modern Society: Artificial Intelligence (AI) is no longer just a concept from sci-fi movies. What are the ethical considerations? 

Cybersecurity Threats and Measures in the Digital Age: With the rise of digital technology, cybersecurity is more important than ever. 

The Future of Renewable Energy Technologies: Solar panels, wind turbines, and electric cars are just the beginning. 

Impact of Social Media on Youth Behavior: Social media platforms like Instagram, TikTok, and Snapchat dominate the lives of teenagers - for better or worse.

The Role of Technology in Modern Education : How are digital tools and online platforms enhancing learning experiences? 

Health and Medicine Topics

The Effects of Diet and Nutrition on Mental Health: What we eat doesn't just affect our physical health.

Advances in Cancer Research and Treatment: Explore the latest advances in cancer research.

The Impact of Vaccines on Public Health: Are vaccines safe? What does the future hold?

Mental Health Issues Among Teenagers: For these psychology research paper topics for high schoolers, explore the many factors leading to an increased incidence of mental health issues in teens, from academics to Snapchat and everything in between.

The Role of Genetics in Personalized Medicine: Take a closer look at how genetic studies are being used to create personalized, in-depth treatment plans for patients.

Making a difference starts with you

Interested in Environmental Science? We'll match you with an expert mentor who will help you explore your next project.

Environment Topics

Climate Change and Its Impact on Global Ecosystems: Climate change is affecting us all. Take a look at how melting ice caps and rising temperatures are impacting ecosystems around the world. 

Sustainable Practices in Urban Development: To minimize our environmental impact, we need to think green. But what does this mean for urban development?

The Effects of Pollution on Marine Life: How can we reduce the impact of pollution on marine life?

Renewable Energy Sources: Benefits and Challenges: Renewable energy sources like wind, solar, and hydroelectric power offer numerous benefits but also come with challenges. Explore these.

The Importance of Biodiversity Conservation: How can we incorporate strategies to protect endangered habitats?

Social Issues and Sociology Research Topics

The Impact of Social Media on Interpersonal Relationships: Social media is shaking up the way we interact with others. 

The Role of Education in Reducing Inequality: Education is the number one way to reduce inequality. Explore strategies and policies that can help with this.

Gender Equality in the Workplace: Gender equality remains a significant issue in workplaces worldwide - talk about why and how to address this.

The Effects of Poverty on Community Health: Explore how poverty has far-reaching impacts on nutrition, healthcare access, and overall health and well-being.

Immigration Policies and Their Social Implications: Immigration policies are far-reaching, impacting more than just immigrant communities. 

History Argumentative Essay Topics

The Causes and Effects of World War II: Research the causes and ripple effects of the Second World War.

The Impact of the Civil Rights Movement on Modern Society: Ask how the Civil Rights Movement impacted racial equality today - and look at the continuing challenges.

Ancient Civilizations and Their Contributions to the Modern World: How do these ancient achievements influence us today?

The History of Space Exploration: Space exploration has captivated humanity for decades - but what’s the background?

The Evolution of Democracy Throughout History: Democracy has evolved significantly over the centuries - detail this evolution.

Science Research Topics

The Exploration of Space: Past, Present, and Future: What are the scientific and societal benefits of exploring space?

Genetic Engineering and Its Ethical Implications: Are there ethical considerations (or risks) of genetic engineering? Take a look at them. 

The Impact of Climate Change on Natural Disasters: Climate change is increasing the frequency and severity of natural disasters. 

Advances in Renewable Energy Technology: Renewable energy technology is advancing rapidly - what innovations hold the most promise?

The Role of Science in Solving Global Problems: How can science help solve problems related to disease, poverty, and climate change? 

Literature Research Topics

The Influence of Classic Literature on Modern Writing: Ever wondered how Shakespeare still affects today's bestsellers? A research paper on how classic literature influences modern writing can uncover fascinating parallels and divergences.

Themes of Dystopia in Contemporary Literature: From "The Hunger Games" to "1984," dystopian themes have captivated readers for ages. 

The Role of Literature in Social Change: Literature has the power to inspire revolutions. Explore books like "Uncle Tom's Cabin" and "To Kill a Mockingbird" and how they created societal shifts.

Comparative Analysis of Major Literary Movements: Compare the themes, styles, and impacts on society of different literary movements like Romanticism, Realism, and Modernism. 

The Impact of Digital Media on Reading Habits: Is the Kindle killing books? If so, research how and why in this essay topic.

Economics Topics

The Effects of Globalization on Local Economies: Globalization is reshaping economies worldwide -explore its impacts on local businesses and job markets.

The Role of Technology in Transforming the Job Market: From AI to automation, technology is revolutionizing jobs. 

Economic Impacts of Climate Change: Climate change isn't just an environmental issue; it's an economic one too.

The Influence of Consumer Behavior on Market Trends: Ever bought something because it was trending? Study how consumer behavior shapes market trends.

The Future of Cryptocurrencies in the Global Economy: Bitcoin, Ethereum, Dogecoin - what's the deal? 

Education Research Paper Topics

The Impact of Online Learning on Student Performance: Online learning is more relevant now than ever, which you’ll explore in this education research topic.

The Role of Technology in Modern Education: How are smart boards and tablets changing classrooms for public schools? How can they improve academic achievement?

Comparative Analysis of Education Systems Around the World: Why do some countries excel in education while others lag? Compare different education systems to see what works and doesn’t.

The Effects of Standardized Testing on Student Learning: Standardized tests are controversial; research their impacts on student learning and whether they accurately measure academic performance and predict academic success, particularly related to special education, elementary school, and early childhood education.

Innovations in Educational Methodologies: From flipped classrooms in elementary education to gamification for middle school, explore different teaching methods with this research question.

Arts Research Project Ideas

The Evolution of Visual Arts Through Different Periods: Study how visual arts have evolved from the Renaissance to Postmodernism.

The Influence of Digital Media on Traditional Arts: Analyze how digital media is affecting traditional arts like painting and sculpture.

The Role of Art in Cultural Preservation: Art isn’t just for aesthetics; it preserves culture too. 

Comparative Study of Art Movements: Compare movements like Impressionism and Cubism.

The Impact of Public Art on Community Identity: Murals, sculptures, and public installations - how do they shape community identity and pride? 

Athletics Topics

The Impact of Sports on Academic Performance: Do athletes perform better academically? 

The Role of Athletics in College Admissions: Sports can be a ticket to higher education. Research how athletics influence college admissions and scholarships for current college students.

The Effects of Physical Activity on Mental Health: Exercise isn’t just for the body; it’s also for the mind. Explore that in these research ideas.

The Influence of Sports on Leadership Skills

Sports teach more than physical skills. Analyze how participation in sports cultivates leadership qualities.

The Future of Technology in Sports Training: From wearable tech to virtual reality, technology is revolutionizing sports training. 

Music Research Paper Topics

The Influence of Classical Music on Modern Genres: Ever heard classical elements in pop songs? Explore how classical music influences modern genres.

The Role of Music in Cultural Identity: Music defines cultures. Study how different genres contribute to cultural identity.

The Effects of Music Therapy on Mental Health: Music heals. Research why that is.

Evolution of Music Technology: From vinyl to Spotify, music tech has come a long way. 

The Impact of Music Education on Academic Performance: Does music make you smarter? 

Government and Politics Persuasive Essay Topics

The Impact of Government Policies on Economic Growth: Government policies can make or break economies. 

Comparative Analysis of Political Systems: Democracy, autocracy, and everything in between - compare different political systems and their effectiveness.

The Role of Youth in Political Movements: Young people are powerful when it comes to historical and current political movements. 

Government Response to Climate Change: How are governments tackling climate change? 

The Influence of Lobbying on Legislation: Lobbying shapes laws. Investigate how.

Writing and Communication Topics

The Evolution of Writing Styles Over the Centuries: Writing styles have changed dramatically. Study their evolution and what influenced these changes.

The Impact of Digital Media on Writing and Communication: Digital media is reshaping communication. 

Creative Writing Techniques for Young Authors: Explore techniques and tips to enhance creative writing.

The Role of Writing in Personal Expression: Research how writing can be a powerful tool for self-expression.

The Importance of Effective Communication Skills: Study why effective communication skills are crucial in various aspects of life.

Society, Culture, and Social Science Topics

The Effects of Social Media on Cultural Norms: Social media is changing culture. Research its impacts on cultural norms and behaviors.

The Role of Tradition in Modern Society: Traditions persist in modern times. Study the role of ancient traditions in contemporary society.

Comparative Analysis of Cultural Practices Around the World: Different cultures, different practices. Compare cultural practices and their meanings worldwide.

The Influence of Media on Public Perception: Media shapes how we see the world. 

The Impact of Globalization on Cultural Identity: Globalization is blending cultures. Research its effects on cultural identities.

Business and Entrepreneurship Topics

The Impact of Startups on the Economy: Startups are economic powerhouses. Study their impacts on local and global economies.

The Role of Innovation in Business Success: Research how innovation influences business achievements.

Ethical Considerations in Business Practices: Investigate ethical considerations and their impacts on business practices.

The Influence of Digital Marketing on Consumer Behavior: Analyze the effects of digital marketing on consumer behavior and purchasing decisions.

Strategies for Successful Entrepreneurship: Want to start a business? Explore strategies.

Polygence Scholars Are Also Passionate About

Engaging in research with polygence's core program.

Picking the right research topic can set the tone for your entire project. It's not just about getting a good grade—it’s about developing critical thinking and enhancing your analytical skills. Your high school research paper topics can even set the stage for future academic pursuits or careers. 

Polygence’s Core Program offers a variety of resources to help you nail every aspect of your research paper. Sign up today!

By selecting an impactful research topic , you're not just writing a paper - you're developing research skills that will serve you for a lifetime. These skills can enhance your understanding of your current school curriculum and prepare you for the rigorous demands of higher education, setting a strong foundation for your academic future.

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Math enrichment for all: 3 ways to engage all learners in deep mathematical thinking

As with many things in education, the term “enrichment” has come to mean different things to different people. For some, enrichment refers to supplemental classroom content or after-school activities that go beyond the standard curriculum. For others, it means a group of students who get pulled from the regular class to engage in more challenging content or gifted and talented activities. Math enrichment in particular can mean a lot of things.

When I first started teaching, I thought of enrichment as the puzzles and activities that I had on hand for fast finishers. I used these frequently in math when I thought I needed something to challenge kids who clearly (or so I thought) understood the math. Both of those assumptions—that what I was giving those students was enrichment and that finishing quickly meant students understood math deeply—were among the many things that I misunderstood as a beginning teacher. So, what is a better model for enrichment in math?

Math enrichment for all

There are several issues with my original approach to enrichment. First, it provided students who might actually have been ready for more challenge with glorified busywork that didn’t deepen their understanding of math. Second, it created a delineation between regular (aka “boring”) math work and “fun” enrichment work. Finally—and most importantly—it reinforced the assumption that not all students were capable of deeper understanding of math or worthy of enrichment. If indeed there had been an activity of value, it would only have been offered to a select few students (and usually the same few), denying others the opportunity to explore math in a richer way. As Jennifer Piggott of the University of Cambridge’s NRICH Mathematics Project puts it, “Enrichment should pervade the curriculum as a whole and not simply be available to those who work fastest.”

Ironically, it wasn’t until I became an enrichment teacher that I was introduced to the concept of enrichment for all. My school had a two-tiered enrichment program. In addition to a traditional pull-out program, every class got multiple one-week enrichment sessions each year where I worked with the grade-level classroom teachers to create a unit that deepened on-grade content. The lessons were designed so that all students could participate in all activities but were purposefully open-ended enough to allow students to explore the content at different depths. In these whole-class sessions, I saw both high levels of engagement and an incredible depth of thinking by all students.

Setting things straight

Before digging further into enrichment, I want to clarify some terminology. First, let’s address the difference between “enrichment” and “acceleration.” Researchers Susanne Schnell and Susanne Prediger nicely distinguish the two concepts in their study “Mathematics enrichment for all—Noticing and enhancing mathematical potentials of underprivileged students as an issue of equity” : “Acceleration means learning mathematics in accelerated pace (mainly by taking special courses ahead of the normally scheduled year). Enrichment means to expand students’ experiences and skills by exposing them to rich learning processes.” They further distinguish two approaches to enrichment: enrichment by “broadening,” or the learning of extra topics or subjects, often via extracurricular programs, and enrichment by “deepening,” which focuses on greater depth and complexity with the current topic. I’m going to focus on enrichment by deepening.

Why math enrichment for all?

Numerous research studies have highlighted the fact that African American, Latino, and Native American students , English learners, students with disabilities , and students from lower socioeconomic backgrounds are significantly underrepresented in traditional gifted and talented programs. This can be attributed to multiple factors , ranging from biased or flawed entry criteria to lack of equal educational opportunities for all students. Couple this with inequitable access to on-grade instruction and high-quality instructional materials and you can see that some students face real barriers to accessing anything beyond low-level content.

NCTM’s position on Access and Equity in Mathematics Education calls out that “To increase opportunities to learn, educators at all levels must focus on ensuring that all students have access to high-quality instruction, challenging curriculum, innovative technology, exciting extracurricular offerings, and the differentiated supports and enrichment necessary to promote students’ success at continually advancing levels.” Schnell and Prediger propose that an enrichment for all approach is necessary to expose the potential of traditionally underserved students: “Only if the situation has a potential of becoming mathematically rich, then the student can show some potentials. And in longer-term perspectives: if the student experiences his or her mathematical potential in a mathematically rich learning situation, then the potential can become a stable characteristic of the student in the long run.”

Students who are perpetually underchallenged have little opportunity to showcase their potential. I also appreciate Schnell and Prediger’s use of the term “potential,” as it implies a more fluid and dynamic characteristic, which may appear situationally but can be nurtured and developed. By contrast, labels like “gifted” and “talented” tend to be approached as more static and “given by nature.”

Furthermore, studies have shown that access to enriching math content has a positive impact on students’ engagement and attitudes. One study examined the Secondary Mathematics Masterclass program in the UK, which is designed to “inspire and engage young people in the art and practice of mathematics.” Students in the program reported enjoying learning “through experimenting rather than just being told something.” Over 60% felt the program improved their attitude toward and confidence in math, as well as their mathematical ability. John Hattie’s Visible Learning project cites attitude toward content domain as a factor with the potential to accelerate learning. All students need access to opportunities that support such positive experiences in math.

Getting started with math enrichment for all

Now that you understand the why behind enrichment for all, it’s time to get down to the nitty gritty of how to provide it. In their paper, Schnell and Prediger propose seven design principles for fostering all students’ mathematics potential :

• Provide enrichment in whole-class settings
• Enrich and deepen topics related to the on-grade curriculum
• Utilize low-floor/high-ceiling problems to allow for differentiation and challenge
• Engage students with rich mathematical problems
• Use open-ended problems to give students experiences of autonomy and competence
• Value cognitively demanding processes over “perfect products”
• Support positive engagement through discussion of students’ ideas and thinking

Below are three specific ways to put some of these principles in action. The good news is you may already be doing some of these!

1. Support positive engagement through discussion of student’s ideas and thinking

Many college- and career-ready standards include practice standards requiring students to articulate their thinking and critique others’ reasoning. Thus, many teachers already include mathematical conversations as a regular part of their classroom. The importance of this cannot be understated. In his research on high-growth strategies , Chase Nordengren states that “Student conversation is the most concrete representation of students’ higher order thinking. By introducing student discourse early and often, high-growth teachers create opportunities for all students to engage in higher-order thinking around grade-level topics.”

But not all student conversations are alike. To be effective, the discourse should be focused on high-level questions and big topics rather than solely on procedural questions. Research has shown that high-level questions that prompt students to reflect on and consolidate their learning improve student performance. While students may start by explaining their approach to a problem, they can be prompted with high-level questions to see connections to previous problems and big mathematical ideas. Delving into big mathematical ideas supports the design principle of deepening and enriching on-grade topics.

When planning questions for a unit or lesson, think about the mathematical ideas that underlie the topic of the lesson and what you might ask to help students make these connections. For example, when discussing a problem about dividing fractions, students can be directed to discuss larger topics like the meaning of division, the relationship between division and multiplication, as well as fundamental fraction concepts. NWEA’s free Formative Conversation Starters provide a great model for using a single problem as a jumping-off point for a deeper discussion of big math ideas. For tips on how to implement these conversations, check out my colleague Kailey Rhodes’s post “Formative conversations and the pursuit of equity in math instruction: 4 light bulb moments.” Or read my colleague Ted Coe’s post on student discourse to learn more about the connection between high-level questions and strategies for high growth for all .

Open-ended, general questions like “How does that work?” “Is that always true?” and “What do you notice/wonder about…” also help promote deeper thinking over quick responses.

2. Engage students with rich mathematical problems

Problem-solving is a standard part of all math classes. Traditionally, this takes the form of routine word problems where students apply the skill learned in the previous lesson to a real-world context . Such problems rarely demand deep thinking of students.

In his TED Talk , math teacher Dan Meyer talks about how he revises the problems in his textbook to support “patient problem-solving,” where students must ask questions, rely on their intuition, build the problem themselves, and actively and iteratively make decisions. His Three-Act Tasks present students with limited information, usually in multimedia form, and a question to answer. Through discussion, students ask questions, generate ideas, determine what information they need, gather that information and then work on answering the original question, self-monitoring, and changing course as needed. They are actively engaging in mathematical thinking in a way that they don’t when solving a rote problem with a straightforward solution path.

Fermi problems are another example of problems that support creative thinking. Named after physicist Enrico Fermi, these are open-ended problems that push solvers to determine a solution path, make and test assumptions, and sometimes make reasonable estimates to solve. They also support a collaborative group approach and mathematical modeling. An example of a Fermi problem is, “How much water does your household use in a week? Can you answer this without looking at a water bill?” As with Three-Act Tasks, students must determine what information they need and determine a solution path, which they must monitor and change as needed.

3. Utilize low-floor, high-ceiling problems to allow for differentiation and challenge

Low-floor, high-ceiling tasks are designed to allow all students to participate and contribute to the conversation while giving those with deeper understanding something chewier to wrestle with. Or as described on NRICH’s site , “everyone can get started and everyone can get stuck.” Problems are structured so that there is more than one way to solve them, and there is room for students to explore different approaches and wrestle with bigger mathematical concepts.

Educator and researcher Marian Small has created a type of low-floor, high-ceiling task that she calls open questions. These types of questions allow for natural differentiation and, like the Formative Conversation Starters, also use a single question to explore big ideas in math through rich classroom discussions. Here’s an example of an open middle question: ____ is 4/5 of ____. This presentation allows all students entry to the problem. Every student can respond in some way, and the variety of responses can be leveraged to raise the level of the discussion for the entire class. The blanks can be filled with various types of numbers: whole numbers (4 is 4/5 of 5 or 72 is 4/5 of 90), fractions (12/25 is 4/5 of 6/10), or decimals (0.8 is 4/5 of 1). Students who show deeper understanding can easily be asked to stretch their thinking.

Small recommends circulating around the room to monitor student work. If you feel a student isn’t stretching themselves as much as they could, tell them that many people have similar answers and request that they find an answer with, say, greater numbers or a different type of number. All of this can lead to conversations about different types of numbers as well as the meaning of multiplication and scaling. Open questions like these help students understand that not all of math is about following a single path to an answer but, instead, can be about flexible thinking and creativity.

A note about technology

Technology has become an integral part of education. As with all educational tools, its uses should be carefully considered . While online programs can support math enrichment for all, care must be taken to ensure that they do not either become digital versions of the puzzles I gave to my fast finishers or claim to accelerate learning without building solid conceptual understanding. Online communication and collaboration tools can be a great way for students to model, map, and share their mathematical thinking with others. Check out “75 digital tools and apps teachers can use to support formative assessment in the classroom” to find some that might work for your class.

Whenever students are learning online, have them explicitly connect that work to whole-class content and teach them to think metacognitively about the material they are interacting with. Both strategies support higher-order thinking and retention of knowledge.

Changing minds

Shifting to an enrichment-for-all approach can unlock the mathematical potential of all students. To get started, think about how you can build on what you already do in your classroom to provide open-ended, rich explorations of math for all students. Feel like you need some more support? We’ve got you covered with the high-quality resources listed below.

• 3 Act Task File Cabinet . Educator Graham Fletcher has a host of resources on his site, including links to Three-Act Tasks for a wide array of grades organized by big ideas and standards.
• Dan Meyer’s Three-Act Math Tasks . This Google Sheet contains links to Three-Act Tasks, primarily for middle and high school, filterable by CCSS standard and mathematical practice.
• Formative Conversation Starters . This is our free resource for grades 2–8. Each grade-level document provides an overview of how to implement the conversations, problems to get the conversations started, questions, and possible student responses.
• Geogebra Open Middle Exercises . This site provides online, interactive problems similar to Marian Small’s open problems, organized by domain and grade band.
• NCTM Asking Questions and Promoting Discourse . This site provides a list of strategies and resources for supporting rich questions and conversations in your classroom. Links are provided to K–12 Notice and Wonder lesson plans designed to broaden student thinking and elicit conversations and creative thinking. A PowerPoint also provides tips for promoting discourse, including an overview of the five practices for orchestrating productive mathematical discussions .
• NCTM’s Game of the Year . Each year, NCTM creates a long-term, open-ended math challenge based around the numbers in the year. For 2024, the challenge is to use the digits in the year 2024, plus operational and grouping symbols, to write expressions representing the counting numbers 1 through 100.
• NCTM Notice and Wonder . This site contains a host of resources designed to support mathematical curiosity and engagement. Note that some resources require NCTM membership.
• NRICH . This site, developed by the mathematics faculty of the University of Cambridge, offers free curriculum-linked resources and challenging math problems plus low-floor, high-ceiling problems designed to engage students ages 3–18. There are teacher, student, and parent sections of the site, all of which contain problems and activities organized by grade ranges and content.
• One, Two…Infinity . Marian Small’s website lists her various publications related to enriching math activities and open questions. The presentations section provides copies of PowerPoints organized by grade band or mathematical topics, and there is also an open problem of the week. These presentations are loaded with free examples of open questions. You can also watch a free webinar where she discusses open problems on NCTM’s website .
• Openmiddle.com . This site contains a large number of printable K–12 open problems searchable by grade, domain, and Common Core standard. Student sheets can be printed in English, Spanish, and French.

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Don't say math is hard: How parents can help children succeed at math

by University of British Columbia

Students are heading back to school and university next week but many may be feeling nervous about tackling mathematics, thanks to its fearsome reputation.

Parents can help by not vocally dreading the subject and instead helping their kids have fun with math, according to Dr. Melania Alvarez (she/her), outreach and education coordinator at the Pacific Institute for the Mathematical Sciences and the UBC department of mathematics, and Dr. Lindsey Daniels (she/her), assistant professor of teaching in the department of mathematics.

We asked them how to set children up for success.

Why do you think some young people are scared of math?

MA: Most children like math when they are very young, but as they hear from their teachers, parents and people around them that math is hard or difficult, a fear of math or anxiety sets in.

It's important for parents to instead talk about the importance of math and how fun and interesting it can be.

LD: One of the issues for students leaving high school and entering university is uncertainty. At university, classes are much bigger and the pace is often faster.

What can parents do to set their children up for math success?

MA: Parents can expose their children to fun and interesting math activities at all ages. For instance, did you know you can earn a living doing origami for NASA ?

There are a lot of games you can play, and they don't have to cost money. For example, when you're out driving, use the numbers on license plates to get to a specific number. We've put together a resource with more of these sorts of games.

Lead by example and show an interest in math. When children see their parents reading, they read. Math is the same. Teach them how to think like a mathematician by asking them, how did you use math today?

LD: It's important to be consistent. Math is like stacking LEGOs—it's OK if there's one missing brick when building a wall, but if there are multiple missing bricks, it will crumble. We want strong foundations before moving on to new concepts.

Be a cheerleader for your child: If they come home with a low test score, help them identify what topics they need to work on and a successful study strategy for moving forward. Everyone has gotten a bad grade—even those of us with Ph.D.s in math! It's an opportunity to identify where there's a missing brick and plug that gap.

How can parents help young people heading to university?

LD: Parents can support their kids in asking for help, whether that's from the instructor, the teaching assistant or the math help center on campus, including UBC's center . Offer to go with them, or to watch some YouTube videos like Numberphile and 3Blue1Brown and take notes together.

Encourage your child to set themselves up for success: They should attend class, take notes, go to office hours, find a study strategy that works for them and apply it consistently. This will look different for every student. It might take a term or two, so it's best to start figuring this out early.

A great strategy is to ask them to teach the concept or terminology to you, because to coherently explain something, you have to really know it. Ask with enthusiasm to show you're interested.

What can parents do if they notice their child is struggling?

MA: Making mistakes is part of learning. Talk about the mistake and work on it together to find a way forward.

LD: It's 100-per-cent OK to tell your kid, "I don't know, but I'm going to start asking questions."

Validate your child's feeling: It's OK that this is challenging. Offer to work through a problem together, or find an easier problem to tackle first. Write out questions together for their teacher. And ask about available resources at school you can look at together.

Provided by University of British Columbia

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