Quantitative Concepts as a Foundation for Algebra

提高学生的数学理解能力的问题太复杂了，不能从任何一个研究角度来解决。学习、教学和课程在很大程度上相互影响。该项目将扩展目前的研究工作，以调查五年级至七年级学生的代数推理能力的发展，因为他们在三年的课程中被灌输了强调定量推理的教学。项目第一年将致力于评估五年级学生的数量概念和定量操作，制定教学的认知目标和材料，以支持旨在实现这些目标的实验教学，开发评估工具并将其与实验教学相结合。并指导课堂教师定量推理教学的目标。接下来的三年将侧重于教学对学生定量和代数推理的影响，以及教师参与对他们的数学内容和教学知识的影响。实验教学将采用先进的软件和材料，这些软件和材料是为使用多个相互关联的表征系统进行定量推理的教学和学习而开发的。本研究将对数学学习研究、数学教学研究、课程开发研究产生重大影响。

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.