The problem of improving school students' mathematical understanding is too complex to approach from any one research perspective. Learning, teaching, and curriculum influence each other in significant ways. The proposed project will extend a current research effort in order to investigate the development of students' algebraic reasoning in grades 5 through 7 as they are taught for three years from a curriculum infused with instruction emphasizing quantitative reasoning. The project's first year will be devoted to assessing 5th-grade students' concepts of quantity and quantitative operations, developing cognitive objectives of instruction and materials to support experimental instruction aimed at achieving those objectives, developing evaluation instruments and aligning them with experimental instruction, and instructing classroom teachers on the objectives of teaching for quantitative reasoning. The subsequential three years will focus on effects of instruction on student' quantitative and algebraic reasoning and effects of teachers' participation on their knowledge of mathematical content and pedagogy. Experimental instruction will incorporate advanced software and materials developed for research on teaching and learning quantitative reasoning by use of multiple, linked representational systems. The proposed study should have a significant impact on research on mathematics learning, research on mathematics teaching, and research on curriculum development.
