Learning Mathematics through Representations (LMR)
Overview
Learning Mathematics through Representations (LMR) is a research-based curriculum unit for the teaching and learning of integers and fractions in the elementary grades (26 lessons). The curriculum uses the number line as the principal representational context and builds upon two core ideas: (a) mathematical representations are fundamental to mathematical communication and learning and (b) curriculum units should be designed as well-orchestrated lesson sequences that support insight and understanding rooted in systematic research.
The LMR team is led by Geoffrey B. Saxe and includes additional faculty and (now former) graduate students in the Graduate School of Education, University of California, Berkeley. The members of the LMR staff bring expertise in developmental and educational research, curriculum development, pre-service education and professional development, and elementary classroom teaching.
On our website, you can explore the research and development process that led to LMR as well as a listing of our project-based publications. You can also download the lesson guides and auxiliary materials. The descriptions and links below will point you to the appropriate pages.
- Staff: Includes a list of the researchers, developers, and designers who contributed to the LMR curriculum.
- Research & Development: Provides background information and the design principles, which guided the development of the LMR curriculum.
- Curriculum: Offers various ways of exploring and downloading the LMR curriculum.
- Publications: Includes lists of LMR publications and presentations.
Most recent (in press) publications:
- Saxe, G. B., & Sussman, J. (2019). Mathematics learning in language inclusive classrooms: Supporting the achievement of English learners and their English proficient peers. Educational Researcher, 48(7), 452–465. https://doi.org/10.3102/0013189X19869953
- Saxe, G. B., & Sussman, J. (2019). Online Supplement to Mathematics Learning in Language Inclusive Classrooms: Supporting the Achievement of English Learners and their English Proficient Peers. Educational Researcher.
Who can use the LMR curriculum materials? The LMR curriculum is free for non-commercial use. You may address inquiries about commercial use or derived works to lmr@berkeley.edu.
Note: If you are interested in exploring Geoffrey Saxe's research on mathematical cognition with the Oksapmin in Papua New Guinea and people's use of their 27-body part counting system, click here.