Rational Number Project: Research on Teaching and Learning in Multiplicative Structures

这五个地点的项目旨在实现以下六个目标 目标： 1)进行数学/心理/教学分析， 乘法结构的内容域。 该分析将 确定所包括的许多主题内部和之间的关系 在这个领域，并将形成课程的框架 发展、评估、教师教育和研究组成部分 本项目 2)制定目标框架以及范围和顺序， 中小学数学课程教材 乘法结构域：由乘法- 有效的概念、关系、操作和问题情境 包括：乘法，除法，有理数 概念包括分数（部分整体），比率，小数，运算符， 测量和比例性，直至并包括缺失值 数字比较的情况下，定性推理和 线性函数的图形描述和解释。 3)概述一个完整的评估计划，以配合项目 目标. 该评估程序将包括一个计算机自适应 学习者概况测试和基于计算机的临床模拟 采访 4)开发、试点和实施简化教学实验 旨在探索学生的“逻辑概念发展”。" 其中几个迷你单位也将在6-10进行实地测试 完整的教室。 教师将接受采访。 5)提炼，再开发和扩展，有理数相关材料 从我们以前的工作，以反映更近期的项目 理解。 材料将被格式化，以便使用 由中学的老师们来教。 6)开发并验证一个理性信念改变的模型， 用于帮助教师获得有关多方面的知识， 和评价教师对以下方面的知识 这个域。

This five site project is designed to accomplish the following six objectives: 1) Conduct a mathematical/psychological/instructional analysis of the content domain of multiplicative structures. This analysis will identify relationships within and between the many topics included in this domain, and will form the framework for the curriculum development, assessment, teacher education, and research components of the project. 2) Develop an objectives framework and a scope and sequence for elementary and middle school mathematics curriculum material for the domain of multiplicative structures: to consist of multiplica- tive concepts, relationships, operations, and problem situations and will include: multiplication, division, rational number concepts including fraction (part whole), ratio, decimal, operator, measurement and proportionality up to and including missing value numerical comparisons situations, qualitative reasoning and the graphical depiction and interpretation of linear functions. 3) Outline a complete assessment program to coincide with project goals. This assessment program will include a computer adaptive learner profile test and computer based simulations of clinical interviews. 4) Develop, pilot, and implement abbreviated teaching experiments designed to explore students' "logical conceptual development." Several of these mini units will also be field tested in 6-10 intact classrooms. Teachers will be interviewed. 5) Refine, redevelop and extend, rational number related materials from our previous work so as to reflect more recent project understandings. Materials will be formatted so as to be usable by middle school classroom teachers. 6) Develop and validate a model of rational belief change, which will used for both helping teachers acquire knowledge about multi- plicative structures, and for evaluating teachers' knowledge about this domain.