Students’ Combinatorial Thinking Error in Solving Combinatorial Problem

Gusti Uripno, Tatag Yuli Eko Siswono, Endah Budi Rahaju, Arief Budi Wicaksono
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Abstract

Combinatorial thinking errors describe students’ difficulties and obstacles in solving combinatorial problems. This study aims to describe the errors experienced by students in solving combinatorial problems in terms of combinatorial thinking processes. This research involved two subjects who were 12th grade high school students at a school in Gresik, Indonesia. The students have already taken a combinatorics course. Data collection was conducted using the think-aloud observation method and task-based interviews. Both methods of data collection were conducted to validate the data using the triangulation method. The two subjects experienced similar errors. The research shows that the filling slots method is a simple and easy way for students to understand, but problems arise when students cannot understand the meaning of the questions and input the correct numbers for the problem. The combinatorial thinking error includes the general counting process and vertical upward formulas or expressions. The general counting process error is generating a number that represents the given aspects of the problem and the vertical upward formula/expression is identifying the concept that fits the problem. This research suggests enhancing students understanding of number representation when teaching the filling slot method. The teacher should illustrate some of the multiplication rule and addition rule examples to help students distinguish between these two fundamental rules. Further research is needed to provide solutions to the constraints experienced by students in solving combinatorial problems.
学生解决组合问题时的组合思维错误
组合思维错误描述了学生在解决组合问题时遇到的困难和障碍。本研究旨在从组合思维过程的角度描述学生在解决组合问题时所经历的错误。这项研究涉及印度尼西亚Gresik一所学校的两名12年级高中生。学生们已经上了一门组合学课程。数据收集采用出声思考观察法和任务型访谈法。对两种数据采集方法进行了验证,采用三角测量法对数据进行了验证。这两个实验对象都经历了类似的错误。研究表明,填槽法对学生来说是一种简单易行的理解方式,但当学生无法理解问题的含义并为问题输入正确的数字时,就会出现问题。组合思维错误包括一般计数过程和垂直向上的公式或表达式。一般的计数过程错误是生成一个代表问题给定方面的数字,而垂直向上的公式/表达式是识别适合问题的概念。本研究建议在教授填槽法时,加强学生对数字表示的理解。教师应举例说明乘法规则和加法规则的一些例子,以帮助学生区分这两个基本规则。为解决学生在解决组合问题时遇到的限制,需要进一步的研究。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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