Making Learning Real: Design Principles and Evidence for Applied Learning in Schools
Category: Student Learning
Instrument Overview
The Teaching for a Robust Understanding (TRU) Mathematics framework is an observation and reflection tool used to examine the key dimensions of high-quality mathematics instruction. It identifies five areas that shape strong learning environments: the richness of the mathematical content, opportunities for students to engage in meaningful thinking, equitable access to that thinking, agency and identity development, and the quality of teacher–student interactions. Together, these dimensions give educators a clear picture of how instruction supports deep understanding and productive participation in mathematics.
TRU Mathematics is used in upper-elementary through high school settings for professional learning, coaching, and collaborative lesson analysis. It is not an evaluation tool; instead, it guides teachers and teams in looking closely at lessons and identifying where changes could strengthen student reasoning and engagement. The framework was developed through research at UC Berkeley and is widely used by districts and math education organizations to support continuous improvement. By offering a structured way to reflect on core features of ambitious, equitable math instruction, TRU helps schools design learning environments where all students can develop strong mathematical understanding and agency.
Organization
Collection Category(ies)
Content
Grades
Kindergarten,
1st Grade,
2nd Grade,
3rd Grade,
4th Grade,
5th Grade,
6th Grade,
7th Grade,
8th Grade,
9th Grade,
10th Grade,
11th Grade,
12th Grade
Languages
English
Respondent
Observer
Administration Information
Length
6 dimensions
Qualifications
None indicated
Access and Use
Developer
Alan H. Schoenfeld, Professor, School of Education, University of California, Berkley Robert Floden, Former Professor, College of Education, Michigan State University
Price
Free
Contact
Alan H. Schoenfeld: alans@berkeley.edu
Open Access
Yes
Psychometrics (additional guidance)
Psychometric References
None indicated
