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

这个五个站点的项目旨在实现以下六个目标：1)对乘法结构的内容域进行数学/心理/教学分析。这一分析将确定该领域所包括的许多主题内部和之间的关系，并将形成该项目的课程开发、评估、教师教育和研究组成部分的框架。2)发展乘法结构领域的中小学数学课程教材的目标框架、范围和顺序：由乘法概念、关系、运算和问题情境组成，将包括乘法、除法、有理数概念(包括分数(部分整)、比率、小数、运算符、测量和比例性直到并包括缺值数值比较情形)，定性推理和线性函数的图形描述和解释。3)勾勒出与项目目标一致的完整评估计划。该评估计划将包括计算机适应性学习者概况测试和基于计算机的临床访谈模拟。4)开发、试点和实施旨在探索学生“逻辑概念发展”的简明教学实验。其中几个迷你单元还将在6-10个完好的教室进行现场测试。老师们将接受采访。5)提炼、再开发和扩展我们以前工作中的合理数量的相关材料，以反映更新的项目理解。材料将经过格式化，以便中学课堂教师使用。6)构建并验证了教师理性信念转变模型，该模型既可以帮助教师获得关于多元结构的知识，也可以用于评估教师对这一领域的知识。

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.