數學魔術對國小六年級球隊學生學習影響之研究

Effect of Mathematic Magic Activities on the Learning of Sixth-grade Sport-team Students.

陳政瑜(Cheng-Yu Chen)

指導教授 ： 許慧玉

國立清華大學/竹師教育學院/數理教育研究所/碩士(2017年)

摘要

本研究係以新竹市一所市區國小運動代表隊的四位六年級學生為個案，採質性研究法，旨在探討個案於三個不同的數學魔術個案過程中所產生的策略及學習模式。首先我們挑選四位運動代表隊六年級學生為個案，四位學生皆為數學學習低興趣且低成就學生；其次三個數學魔術則參考林壽福老師與吳如皓老師所著之數學魔術書，挑選了數學魔咒、數字神蹟、混水摸幣等三個數學魔術進行研究，分別與四位學生進行三個數學魔術活動，於此同時以錄影、錄音及學習單等方式收集資料，整個活動期間只不斷重複進行數學魔術本身之內容，而不進行教學。研究結果如下：(1)整體結果與認知負荷理論相符合。個體從事特定工作所產生認知負荷量的多寡，受到工作的難易程度與個體本身所具備的專業知識兩方面的影響。(2)個別學生有其固定學習模式。面對不同數學魔術活動，學生容易出現固定的思維模式，例如有個案習慣於觀察魔術時將注意力放在數學魔術的『變與不變』。(3)學生遭遇困難與固定思維模式有關聯。是指學生的固定思維造成其面對不同的數學魔術卻遇到相似的問題。

　　根據本研究的發現與結論，文末針對數學魔術研究設計面向、未來教學面向以及未來研究面向提出相關的建議。

關鍵字

數學魔術 ； 遊戲 ； 學習低成就

並列摘要

This research aims at discussing individuals’ strategic and learning patterns during three different mathematics of magic activities, conducted by case study and qualitative research. Research subjects are targeting four sixth-graders of elementary school’s sports team in Hsinchu City.

　Firstly, four sixth-graders in sports team were chosen, who had shown low interests and underachievement in math learning. Then facilitators selected three different mathematics of magic activities to interact with each student, based on the book The Mathematics of Magic, written by Shou-Fu Lin and Ru-Hao Wu. Through the entire period of activities, only the repeated contents of the mathematics of magic itself were given, no teaching. Meanwhile, observers collected data by video taking, audio recording and worksheets distributing.

Research conclusions are as following:
1) Results are consistent with cognitive load theory. The amount of cognitive loading that individuals have depends on the difficulties of assignment and the professional knowledge that inherent in indiviauls.
2) Students tend to have their own fixed action patterns of learning when facing different mathematics of magics. For instance, a student used to focus on magics’ change or not when observing the process.
3) The challenges that students encountered are related to fixed action patterns of thinking, which may cause them having similar problems in each different mathematics of magics.

Based on the findings and research conclusion in this study, suggestions are made in the thesis regarding mathematics of magics research design, future teaching and tutoring directions as well as future research studies perspectives.

並列關鍵字

mathematics of magic ； game ； underachievement learning

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