Instruction and Cognitive Change in Mathematics: Learning Decimal Numbers

该项目研究了认知过程的变化， 教学干预，并将这些信息应用于开发一个 原型教学程序。 兴趣的认知过程 是那些参与构建十进制数字符号的意义 并利用其意义解决十进制数问题。 以前的工作 表明，对于许多学生来说，缺乏意义的书面符号， 是在一系列数学任务中表现不佳的根源。 课堂教学旨在促进认知过程， 为符号创造意义是在上下文中实现和评估的 十进制分数。 四年级和五年级的学生将在整个课堂上进行指导 设置.笔试和一系列的个人面试将 提供有关关键认知过程变化的信息，以及如何 这种变化是由特定的教学事件引起的。 的 关于认知变化和教学效果的信息， 通过一系列的教学研究收集，将被翻译成 转化为一个原型教学程序， 数学中的符号 从研究到实践，从对学生生活的描述， 执行处方的教学计划，是一个主要的 这个研究项目的目的。 除了提供新的 知识和产品成果，该项目提供了一个模型，基于 探索概念链，将研究转化为实践。

The project examines changes in cognitive processes resulting from instructional interventions and applies this information in developing a prototype instructional program. The cognitive processes of interest are those involved in constructing meaning for decimal number symbols and using the meaning to solve decimal number tasks. Previous work suggests that for many students, the lack of meaning for written symbols is the source of low performance across a range of mathematical tasks. Classroom instruction designed to promote cognitive processes that create meanings for symbols is implemented and evaluated in the context of decimal fractions. Students in grades 4 and 5 will be instructed in whole classroom settings. Written tests and a series of individual interviews will provide information on changes in key cognitive processes and on how such changes are induced by specific instructional events. The information on cognitive change and instructional effectiveness, gathered through a sequence of instructional studies, will be translated into a prototype instructional program for developing meaning for written symbols in mathematics. Moving from research to practice, from descriptions of students' performance to prescriptions of instructional programs, is a major objective of this program of research. In addition to providing new knowledge and product outcomes, the project provides a model, based on chain of inquiry notions, for translating research into practice.