Math Instruction

Mathematics skills and ways of thinking are central to students’ long-term academic, economic, and civic opportunities. Yet many classrooms still emphasize a narrow set of skills^{1, 2}, leaving fewer chances for students to engage in the kinds of rich problem-solving and reasoning that support deeper learning and future access to advanced coursework. At the same time, schools and districts face complex decisions about curriculum adoption, instructional support, and professional development—decisions that are stronger when informed by high-quality data on what is happening in classrooms and how students are experiencing mathematics.

Collecting data on math instruction is essential for understanding which classroom practices genuinely support student learning and for identifying where instructional improvement is most needed. High-quality measures of instructional quality and student experience give researchers clearer insight into the features of teaching that matter most. For educational leaders, these data illuminate how curricula are being implemented across classrooms and highlight gaps in support, especially at key transition points such as the move into middle school or Algebra I. Together, such information strengthens efforts to ensure all students have access to rigorous, engaging, and equitable mathematics instruction.

History: Systematic measurement of belonging, cultural responsiveness, rigor, and discourse in math classrooms has grown significantly over the past decade. A key turning point was the Effective Mathematics Teaching Practices in the National Council of Teachers of Mathematics (NCTM)’s 2014 report³, which highlighted the importance of mathematical discourse and high-cognitive-demand tasks and helped spur new observation tools. Equity-focused work—such as Schoenfeld’s TRU framework⁴, further developed in 2019⁵, and the 2025 NASEM Equity in K–12 STEM Education report⁶—reinforced the need to understand students’ identities, experiences, and sense of belonging. At the same time, the rise of improvement science^{7, 8} encouraged the creation of practical, easy-to-use measures that could support continuous instructional improvement. Together, these developments shifted data collection in mathematics education beyond achievement alone toward richer evidence about how students experience and engage with mathematics.

Respondent types: Data on mathematics instruction can come from several perspectives—for example, from students reflecting on their classroom experiences, from observers documenting a lesson in real time, or from teachers describing their instructional approaches. Student surveys are especially helpful for understanding how welcomed, challenged, and included students feel in math class. Observation tools offer a different lens by capturing what actually happens during instruction, such as the rigor of tasks or the quality of classroom discussions. Teacher surveys can add useful context, though it’s best not to rely on the same person to report on both the factors influencing instruction and the outcomes of interest. CRSE research often tends to over-rely on teacher self-report surveys. Choosing whose perspective to gather ultimately depends on the goals of the study or improvement effort and helps ensure that the information collected about math instruction is accurate and meaningful.

Ethical and equity implications: Students data that is shared with instructors (e.g., PMRR) should be presented anonymously and used to further inquire about improvement, rather than to evaluate or assess students.

Timing and frequency: Many of the research instruments in this collection are designed to capture big-picture patterns, not week-to-week changes in instruction. Because of that, they are usually administered only a few times during a school year. In contrast, practical measurement tools—often shorter and easier to use—can be given more regularly to help teachers and leaders track progress and make quick adjustments. For observation tools, especially when they are used to evaluate or support professional development, it’s important to schedule multiple observations each year (at least two) and to continue this over several years. This helps show whether instructional practices are truly shifting over time.

This curated list of instruments with validity and reliability concerns four areas related to mathematics instruction: (1) Belonging in Mathematics; (2) Culturally Responsive and Sustaining Education; (3) Rigor and Cognitive Demand; and (4) Discourse.

The first two areas are primarily about how students experience their mathematics learning. There is a growing consensus that students’ affective responses to their learning environments and sense of relevance influence learning^6. The last two areas are more concerned about the quality of students’ opportunities for learning that have been linked to supporting students' learning.

There are other areas prevalent in the mathematics education research literature that are not in this curated list. For instance, there are valid and reliable measures related to teachers’ mathematical knowledge for teaching (MKT)⁹ which has been documented to mediate the quality of instruction. Information about teachers’ MKT is not readily actionable by practitioners; however, any robust set of professional development efforts should seek to strengthen all teachers’ MKT¹⁰.

Another set of constructs that are discussed widely in the literature, and for which there exist an abundance of measures, is students’ mathematical motivation and engagement, which have been linked to achievement. Students’ sense of belonging predicts students’ motivation and engagement^{11, 12}. Since creating an environment that fosters a sense of belonging is an actionable way to enhance motivation and engagement, only the former is included in this list.

For similar reasons, measures of student learning, while abundant, do not appear on this list. The National Science Foundation funded project “Validity Evidence for Measurement in Mathematics Education” has an extensive repository of measures that includes constructs not included at this list (see: mathedmeasures.org).

[1] Burdman, P. (2018). The Mathematics of Opportunity: Rethinking the Role of Math in Educational Equity. Just Equations, Opportunity Institute. https://www.justequations.org/resource/the-mathematics-of-opportunity-rethinking-the-role-of-math-in-educational-equity 

[2] The New Teacher Project. (2018, September 25). The Opportunity Myth: What students can show us about how school is letting them down—and how to fix it. https://tntp.org/publication/the-opportunity-myth/ 

[3] National Council of Teachers of Mathematics. (2014). Principles to Actions: Ensuring Mathematical Success for All. Reston, VA: NCTM. https://www.nctm.org/PtA/ 

[4] Schoenfeld, A. H. (2014). What makes for powerful classrooms, and how can we support teachers in creating them? Educational Researcher, 43(8), 404–412. 

[5] Schoenfeld, A. H. (2019). Video analyses for research and professional development: The Teaching for Robust Understanding (TRU) Framework. ZDM Mathematics Education, 50(4), 491–506. https://doi.org/10.1007/s11858-017-0908-y 

[6] National Academies of Sciences, Engineering, and Medicine. (2025). Transforming Undergraduate STEM Education: Supporting Equitable and Effective Teaching. Washington, DC: The National Academies Press. https://doi.org/10.17226/28268 

[7] Bryk, A. S., Gomez, L. M., Grunow, A., & LeMahieu, P. G. (2015). Learning to improve: How America’s schools can get better at getting better. Harvard Education Press. 

[8] Lewis, C. (2015). What is improvement science? Do we need it in education? Educational Researcher, 44(1), 54–61. https://doi.org/10.3102/0013189X15570388 

[9] Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic‑specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372–400. https://doi.org/10.5951/jresematheduc.39.4.0372 

[10] Cobb, P., & Jackson, K. (2021). An empirically grounded system of supports for improving the quality of mathematics teaching on a large scale. Implementation and Replication Studies in Mathematics Education, 1(1), 77-110. 

[11] Goodenow, C. (1993). Classroom Belonging among Early Adolescent Students: Relationships to Motivation and Achievement. Journal of Early Adolescence, 13(1), 21–43. https://doi.org/10.1177/0272431693013001002 

[12] Matthews, J.S. (2018). When am I going to use this in the real world? Cognitive flexibility and urban adolescents’ negotiation of the value of mathematics. Journal of Educational Psychology, 110(5), 726–746. https://doi.org/10.1037/edu0000242