Cognitive Effects of Multiple Representations of Mathe- matical Concepts: An Exploratory Study

数学概念多重表示的认知效应：一项探索性研究

• 批准号: 8751381
• 负责人: Patrick Thompson
• 金额: $ 10.05万
• 依托单位: Board of Trustees of Illinois State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-08-01 至 1989-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8751381&HistoricalAwards=false
• 关键词: Cognitive; Effects; Multiple; Representations; Mathe

Mathematics learning consists of more than simply memorizing rules and procedures. Unfortunately, much of the mathematics currently being learned is of this type. A concensus is emerging, however, that a necessary condition for students to understand important mathematical concepts is that they posess multiple representational systems for those concepts and be able to translate smoothly and efficiently among them. This project will study how we can teach effectively for students' development of multiple representational systems and how such instruction affects their development of concepts and skills. Two computer programs will be designed for this project; one for decimal numeration and one for algebra. Both programs will present simultaneous, "linked" representational systems. Students will solve problems by acting directly upon one representational system with their actions being automatically reflected in the other. Operations on decimals numbers will be studied for five weeks with a class of seventh graders. Concepts of expression, identity, linear equation, and solving linear equations will be studied with pre-algebra eighth graders over a school year. The basic research methodology will be that of the constructivist teaching experiment. Through carefully planned individual and small group interview protocols, a model (models) of student knowledge will be constructed which describes the relationship beween the representations taught. Curriculum materials to facilitate mathematical understanding will also be developed. The proposed research is challenging and should lead to significant advances in mathematics and science education. The Principal Investigator is highly regarded in the mathematics education community and this is reflected in this well conceived research project.

数学学习不仅仅是简单的记忆 规则和程序。 不幸的是，大部分的数学 目前正在学习的是这种类型。 共识是 然而，出现了一个必要条件，学生 理解重要的数学概念是他们拥有 这些概念的多个代表系统， 在他们之间顺利有效地翻译。 这个项目将研究我们如何有效地教学， 学生发展多种表征系统， 这种教学如何影响他们的概念发展， skills.将为该项目设计两个计算机程序; 一个用于十进制计数，一个用于代数。 两个程序 将呈现同时的、“链接的”代表性系统。 学生将通过直接对一个问题采取行动来解决问题 代表性系统，他们的行动自动 反映在另一个。 对小数的运算将是 在一个七年级的班级里学习了五个星期。 概念 表达式、恒等式、线性方程和解线性方程 方程将研究与前代数八年级学生超过一个 学年 基本的研究方法将是建构主义 教学实验通过精心策划的个人和 小组访谈协议，学生模型（模型） 将构建描述关系的知识 在所教的表征之间。课程材料， 促进数学理解也将得到发展。 拟议的研究具有挑战性，应导致 数学和科学教育的重大进步。 的 首席研究员在数学方面受到高度评价 教育界，这反映在这个精心构思的 研究项目。