基于认知风格的学生微积分解题数学错误的结构

In Hi. Abdullah, Hery Suharna, Mustafa AH. Ruhama
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引用次数: 0

摘要

数学概念的理解是课堂学习中学生在解决数学问题时经常出现的错误。对学生来说,最难的是解题,因为解题需要运算能力、对概念的高度掌握以及良好的语言表达能力等,这样学生在做数学题时才不会再出错。学生在解决数学问题时出现的错误有:(1)概念连接错误;(2)运算错误;(3)概念建构错误。问题是基于认知风格的学生数学解题错误概念的结构是什么。本研究的方法,即探索性描述方法,旨在确定学生在解决数学问题时基于认知风格的错误结构。研究数据分析,即:(1) 数据还原;(2) 数据暴露;(3) 数据三角测量;(4) 得出结论。所提到的认知风格有领域依赖型和独立型之分。结论是:(1) 应用领域依赖型认知风格的概念性错误的结构首先是不平衡,然后通过联系适用的概念来解决;(2) 应用领域独立型认知风格的概念性错误的结构首先是不平衡,然后通过分析来解决。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Structure of Students’ Mathematical Errors in Solving Calculus Problems Based on Cognitive Style
The understanding mathematical concept is an error that often occurs in classroom learning among students when solving mathematical problems. The most difficult part for students is solving problems, because it requires numeracy skills, high concept mastery, as well as the ability to use good language, and so on so that students don’t make any more mistakes when working on math problems. Student errors in solving mathematics problems are (1) errors in connecting concepts, (2) errors in operations and (3) errors in constructing concepts. The problem is what is the structure of students’ mathematical misconceptions in solving mathematical problems based on cognitive style. The method in this research, namely an exploratory descriptive approach, aims to determine the structure of students’ errors based on cognitive style in solving mathematical problems. Analysis of research data, namely: (1) Data reduction, (2) Data exposure, (3) data triangulation and (4) drawing conclusions. The cognitive styles referred to are field dependent and independent. The conclusions are (1) the structure of conceptual errors with an applied field dependent cognitive style begins with disequilibrating, then solving by linking applicable concepts, and (2) the structure of conceptual errors with a field independent cognitive style begins with disequilibrating, then solving using analyse.
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