Quantitative Concepts as a Foundation for Algebra

提高中学生数学素养的问题 理解是太复杂了，从任何一个研究方法 perspective. 学习、教学和课程相互影响， 重要的方式。 拟议的项目将扩大目前的研究 努力，以调查学生的代数发展 推理在5年级到7年级，因为他们被教导了三年， 一门充满了强调定量的教学的课程 推理 该项目的第一年将致力于评估五年级 学生数量概念和数量运算概念的培养 教学的认知目标和支持材料 实验教学旨在实现这些目标，发展 评估工具，并将其与实验教学相结合， 并指导课堂教师的教学目标， 定量推理 接下来的三年将集中在 教学对学生数量推理和代数推理的影响 教师参与对教师知识的影响 数学内容和教学法。 实验教学将 采用先进的软件和材料， 教与学定量推理的使用多，链接 代表系统。 拟议的研究将对以下方面的研究产生重大影响： 数学学习，数学教学研究，数学教学研究 课程开发

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.