运用Gardner的三平方问题在数学解题模块中的小组作业

IF 0.3 Q4 MATHEMATICS
Jonathan Hoseana
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引用次数: 0

摘要

:考虑一个1 × 3的网格,其左上顶点连接到每个单元正方形的右下顶点。三个锐角的和是多少?这三个锐角是由单位平方的底边组成的?这就是所谓的三方问题,通常被认为是加德纳的问题。在最近的一个学年里,作者使用了一个由YouTube频道Numberphile制作的关于这个问题的视频,作为本科第一学期模块的一个小组项目:数学问题解决。这个项目包括合作撰写问题和个人完成一份同行评估表。我们报告了这个项目的结果,这引起了理论和教学上的讨论。理论讨论包含了该问题的七个备选解决方案,以及对形成任意大小网格的相同平行四边形的推广,其左上顶点连接到每个平行四边形的右下顶点。教学讨论强调了同伴评价表在发现小组成员不平等贡献以及学生沟通技巧不足方面的有效性。后者一直引起人们的关注,随后导致该模块被开发并更名为数学写作与推理,并于下一学年开始实现。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Using Gardner's Three-Squares Problem for a Group Project in a Mathematical Problem Solving Module
: Consider a 1 × 3 grid whose top-left vertex is connected to the bottom-right vertex of each of the unit squares. What is the sum of the three acute angles formed by the connecting segments with the unit squares’ bases? This is the so-called three-squares problem, often attributed to Gardner. In a recent academic year, the author used a video on this problem, produced by the YouTube channel Numberphile, for a group project in a first-semester undergraduate module: Mathematical Prob-lem Solving. The project involved collaborative writing on the problem and individual completion of a peer-assessment form. We report the outcomes of this project, which give rise to both theoretical and pedagogical discussions. The theoretical discussion comprises seven alternative solutions to the problem, as well as a generalisation to the case of identical parallelograms forming an arbitrary-sized grid whose top-left vertex is connected to the bottom-right vertex of each parallelogram. The pedagogical discussion highlights the peer-assessment form’s effectiveness in detecting unequal group members’ contribution, as well as the students’ inadequate communication skills. The latter, which has consistently raised concerns, subsequently led to the module being developed and renamed as Mathematical Writing and Reasoning, whose realisation commenced the following academic year.
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来源期刊
Mathematics Enthusiast
Mathematics Enthusiast MATHEMATICS-
CiteScore
1.40
自引率
0.00%
发文量
43
期刊介绍: The Mathematics Enthusiast (TME) is an eclectic internationally circulated peer reviewed journal which focuses on mathematics content, mathematics education research, innovation, interdisciplinary issues and pedagogy. The journal exists as an independent entity. The electronic version is hosted by the Department of Mathematical Sciences- University of Montana. The journal is NOT affiliated to nor subsidized by any professional organizations but supports PMENA [Psychology of Mathematics Education- North America] through special issues on various research topics. TME strives to promote equity internationally by adopting an open access policy, as well as allowing authors to retain full copyright of their scholarship contingent on the journals’ publication ethics guidelines. Authors do not need to be affiliated with the University of Montana in order to publish in this journal. Journal articles cover a wide spectrum of topics such as mathematics content (including advanced mathematics), educational studies related to mathematics, and reports of innovative pedagogical practices with the hope of stimulating dialogue between pre-service and practicing teachers, university educators and mathematicians. The journal is interested in research based articles as well as historical, philosophical, political, cross-cultural and systems perspectives on mathematics content, its teaching and learning. The journal also includes a monograph series on special topics of interest to the community of readers.
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