Research & Development

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Geoffrey Saxe
Professor of the Graduate School
Graduate School of Education
University of California, Berkeley


The LMR team used a research-based approach to curriculum development in order to address three concerns that have been frequently raised about elementary mathematics materials.

Mathematically Coherent Curriculum
Many curriculum units treat integers and fractions separately, and children do not recognize the deep mathematical connections. In consultation with mathematicians and mathematics educators, the LMR team developed a lesson sequence for 4th and 5th grades that coordinates lessons on integers and fractions using the number line as the principal representational context. 

Research Foundation and Contribution
Curriculum materials are often developed without the necessary research base on mathematical learning to inform the design of the materials and instructional methods. The LMR team conducted multiple phases of research on mathematical development and instructional practices to guide the design of our curriculum unit.

Supports for Lesson Implementation
Curriculum materials are frequently missing a clear model of the teaching practices that enable all students to learn.  Therefore the LMR team has developed specific lesson structures along with a lesson guide for each lesson.

Several design principles guided the development of the LMR curriculum to address these concerns.

Design Principles

  • Communication: eliciting student thinking and building on student ideas, affording students opportunities to contribute mathematical ideas
  • Connection: provoking cognitive conflict and engaging students in analysis and resolution, affording students opportunities to make connections among mathematical ideas
  • Equity: differentiating instruction in shared mathematical contexts, affording all students opportunities to engage with core mathematical content