小学最低公倍数与最大公因数学习障碍分析

Muhammad Rifqi Mahmud, T. Turmudi, W. Sopandi, S. Rohimah, I. M. Pratiwi
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摘要

本研究旨在发现学习LCM和GCF的学生的学习障碍,为编写能够克服这些障碍的教材提供参考。这项研究涉及印度尼西亚万隆三所公立学校的74名五年级学生。本研究使用的研究方法是案例研究研究数据收集技术,通过提供测试、访谈和文件。数据分析技术使用数据收集、简化、呈现和结论。结果显示学习障碍有三种类型:本体障碍、认识论障碍和教学障碍。在求解LCM和GCF问题时,学生理解了倍数、因子和自然数的算术运算,从而发现了本体障碍。由于学生理解LCM和GCF概念的语境有限,因此发现了认识论障碍,因此他们无法在诸如单词问题之类的语境中使用它们。在学习中发现了教学障碍,这些障碍是由老师程序性地使用因子分解方法,即质因数分解或因子树给出的。因此,必须通过设计学习设计来预测这些障碍,这些学习设计可以促进学习轨迹,关注概念,使学习更有意义。
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Learning obstacles analysis of lowest common multiple and greatest common factor in primary school
This research aims to find learning obstacles for students studying LCM and GCF as a reference in preparing teaching materials that can overcome these obstacles. This research involved 74 grade V students at three public schools in Bandung, Indonesia. The research method used in this study was case study research—data collection techniques using triangulation by providing tests, interviews, and documentation. Data analysis techniques use data collection, reduction, presentation, and conclusions. The results show three categories of learning obstacles: ontogenic, epistemological, and didactic. The ontogenic obstacle was found because the students understood multiples, factors, and arithmetic operations on natural numbers in solving LCM and GCF problems. Epistemological obstacles were discovered because of the limited context in which students understood the concepts of LCM and GCF, so they could not use them in contexts such as word problems. Didactical obstacles were found from learning that was given by the teacher procedurally using factoring methods, namely prime factorization or factor trees. Therefore, these obstacles must be anticipated by designing learning designs that can facilitate learning trajectories, focus on concepts, and make learning more meaningful.
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