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Research & practice

Research that shapes
how we teach.

Math Cases draws on research around math anxiety, motivation, guided exploration, and tactile learning. These papers inform the choices behind our lessons and workshops.

The connections below describe how we apply the research. These papers did not evaluate Math Cases itself.

01 / Personal relevance

Give students a reason to care.

Randomized classroom study · high school scienceClassroom trial · high school science

Hulleman & Harackiewicz · 2009

Students with low expectations of success showed greater interest and earned higher course grades when they wrote about connections between their lives and their science coursework.

Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. Science, 326(5958), 1410–1412.

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Randomized classroom study · 82 ninth-grade classrooms, 1,916 studentsClassroom trial · 82 classes · 1,916 students

Gaspard et al. · 2015

A 90-minute mathematics relevance intervention helped students see more value in math. Both versions produced more positive value beliefs six weeks and five months later, with the specific benefits differing by activity.

Gaspard, H., Dicke, A.-L., Flunger, B., Brisson, B. M., Häfner, I., Nagengast, B., & Trautwein, U. (2015). Fostering adolescents’ value beliefs for mathematics with a relevance intervention in the classroom. Developmental Psychology, 51(9), 1226–1240.

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Three laboratory experiments · learning a mental math techniqueThree lab experiments · mental math

Canning & Harackiewicz · 2015

For participants with low confidence, generating their own reasons a math technique could be useful supported interest and performance. Simply being told its usefulness could have the opposite effect. Everyday examples were more helpful for these participants than career or school examples.

Canning, E. A., & Harackiewicz, J. M. (2015). Teach it, don’t preach it: The differential effects of directly-communicated and self-generated utility-value information. Motivation Science, 1(1), 47–71.

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How this informs Math Cases

Cases begin with a question students can care about. In “Connect to Your World,” students make their own connections between the mathematics and their lives. Everyday decisions give relevance a concrete starting point.

02 / Hands-on exploration

Making abstract ideas tangible.

Meta-analysis · 55 studies, kindergarten through collegeMeta-analysis · 55 studies · K–college

Carbonneau et al. · 2013

Instruction using physical math materials produced better learning on average than instruction using abstract symbols alone. Benefits varied by the outcome measured and how instruction was designed.

Carbonneau, K. J., Marley, S. C., & Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380–400.

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How this informs Math Cases

Students handle cubes, packages, room models, and data before connecting what they notice to measurements, graphs, or equations.

03 / Guided exploration

Curiosity works with support.

Meta-analysis · 72 studies of inquiry learningMeta-analysis · 72 inquiry studies

Lazonder & Harmsen · 2016

Students benefited from guidance during inquiry activities, with positive average effects on learning processes, task success, and learning outcomes.

Lazonder, A. W., & Harmsen, R. (2016). Meta-analysis of inquiry-based learning: Effects of guidance. Review of Educational Research, 86(3), 681–718.

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Task-design paper · inclusive secondary mathematicsTask design · secondary mathematics

Calleja · 2024

Low-floor, high-ceiling tasks encourage several strategies for tackling a task, making them inherently accessible (not easy!) regardless of a student’s mathematical starting point. Calleja illustrates how such tasks foster student-generated questions and multiple representations of the same topic, which supports complex mathematical thinking.

Calleja, J. (2024). Features in task design for inclusion: An example of a mathematical investigation. Educational Designer, 5(17), Article 68.

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Three-year comparative study · two English schools, students aged 13–16Two-school study · ages 13–16

Boaler · 1998

In a comparison of two schools, students learning through open-ended projects used mathematics more flexibly in unfamiliar and applied situations. Their teachers introduced mathematical tools as projects created a need for them.

Boaler, J. (1998). Open and closed mathematics: Student experiences and understandings. Journal for Research in Mathematics Education, 29(1), 41–62.

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How this informs Math Cases

We start with an interesting, open-ended question so students can enter through a prediction, an observation, or an idea. This is the low floor. The high ceiling comes from comparing strategies, building models, and defending increasingly precise explanations. Prompts, worked examples, and focused mini-lessons support students as they go deeper.

04 / Math anxiety

How students feel about math matters.

Meta-analysis · childhood through adulthoodMeta-analysis · childhood–adulthood

Barroso et al. · 2021

Across 747 estimates from earlier research, higher math anxiety was associated with lower math achievement on average. The relationship varied across ages and measures.

Barroso, C., Ganley, C. M., McGraw, A. L., Geer, E. A., Hart, S. A., & Daucourt, M. C. (2021). A meta-analysis of the relation between math anxiety and math achievement. Psychological Bulletin, 147(2), 134–168.

View the paper ↗

How this informs Math Cases

We give students an accessible way to begin: a prediction, an observation, or something they can build. Supporting participation and attending to how math feels are part of the workshop design.

See the ideas in action.

Explore the questions, materials, and mathematics inside each case.

Explore the cases