Instruction and Cognitive Change in Mathematics: Learning Decimal Numbers

该项目考察了教学干预导致的认知过程的变化，并将这些信息应用于开发一个原型教学计划。感兴趣的认知过程是指构建十进制数字符号的意义和使用该意义来解决十进制数字任务的过程。先前的研究表明，对于许多学生来说，书写符号缺乏意义是一系列数学任务表现不佳的原因。课堂教学旨在促进为符号创造意义的认知过程，并在小数的背景下实施和评估。四年级和五年级的学生将在整个课堂环境中接受指导。笔试和一系列个人面谈将提供有关关键认知过程的变化以及特定教学事件如何引发这些变化的信息。通过一系列教学研究收集的关于认知变化和教学有效性的信息将被翻译成一个原型教学计划，以发展数学中书面符号的意义。从研究转向实践，从描述学生的表现到制定教学计划，是这项研究计划的主要目标。除了提供新的知识和产品成果外，该项目还提供了一个基于一连串调查概念的模型，用于将研究转化为实践。

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.