引導式的遊戲式學習用於數學應用問題解題與錯誤類型分析-以二元一次方程式為例

Abstract

遊戲式的學習在教學上的應用日漸受到重視，也有很多的研究指出遊戲式的學習能有效提昇學習成效，但是目前的教學遊戲都著重於測驗而不是教學，是否能達到教學目標仍有待探討。 在數學的學習上，問題解決是非常重要的基本能力，在數學教學中，常以文字的應用問題訓練學生問題解決能力，而且學習應用問題的解題也有助於提昇學生的理解力及邏輯思考能力，另外根據眾多的研究指出引導式教學有助於提昇學生問題解決能力。 在本論文中，將引導式的教學理論結合遊戲式學習理論，發展三個引導式的遊戲來幫助學生學習二元一次聯立程式。以桃園縣某國中七年級三個班級的學生，共92人為研究對象，二個班級為課堂實驗組，在數學課去電腦教室，上機練習遊戲式的課程複習，一個班級為課堂控制組，採一般傳統式教學複習課程，三個班皆由同一位數學教師授課，且已學習完二元一次聯立方程式的課程。 在實驗前先進行前測，實驗課程結束後進行後測，收集實驗數據，進行研究分析，並在學生學習中紀錄學生的學習歷程，依此找出學生在數學學習中常犯的錯誤類型，最後針對常犯的錯誤，進行補救教學。 實驗結果顯示接受引導式的遊戲式學習的學習成效平均高於傳統式教學，但無統計上的差異，另外將學生依學習成就分成三組，低成就組在二元一次聯立方程式的學習成效，遊戲式學習優於傳統式學習，而中成就組在應用問題的學習成效，遊戲式學習優於傳統式學習。 觀察使用遊戲式學習的班級發現，在學生用遊戲學習的情況下，前、後測成績有顯著差異，且後測平均高於前測平均，表示學生在使用遊戲進行學習有助於提昇學習成效。 在分析學生的學習歷程檔，發現學生在學習二元一次聯立方程式，容易犯的錯誤類型有，錯誤的運算規則、等量公理的錯誤使用、對二元一次方程式的意義不清楚及未針對答案檢驗其合理性。

The game-based Learning pays high regard day after day in the teaching application, also has many research to point out that can promote the learning efficiency. But didactical game in present put emphasis on examination rather on teaching, whether could achieve the teaching goal still to wait for discussing. The problem-solving ability in mathematics study is very important basic capability. In math teaching often train student’s problem-solving ability with application problem in word expression, and it will promote the student’s ability in problem-solving and enhance student’s arithmetic comprehension and being logical. Besides according to many researches still point out inducing-mode teaching can help student’s problem-solving ability. In the thesis will integrate inducing-mode teaching theory with gamed-based theory to develop three guided game-based learning that help students study linear equation with two variables. Take the three class of Taoyuan County’s seven grade students, total as 92 objects of study, two classes are experimental groups, goes to the computer classroom in the mathematics courses, practice game's-like curriculum review; a class is the baseline group, picks the general traditional type teaching refresher course, three classes all teach by the identical mathematics teacher, and has studied the linear equation with two variables. Carries on first before the experiment measured, after experiment end of course, after carrying on measured, the collection empirical datum, carries on the research analysis, and, in the student studies records student's study course, discovers the student according to this in mathematics study habitual criminal's wrong type, finally aims at habitual criminal's mistake, carries on the recovery teaching. Experimental results show a guided game-based learning average of effect that is higher than traditional teaching, but it is no statistical difference. Furthermore student by learning achievement will be divided into three groups, and the low group in the linear equation with two variables of learning, game-based learning is superior to traditional learning, and the middle group in the application problems of learning, and game-based learning is superior to traditional learning. Observed using games-based learning classes found in students learning the game situation. Test scores has the significant difference on pretest and post-test ,and post-test mean than pretest mean that students learn to use the game help to improve the learning outcomes. Learning process in the analysis file, found that students in the learning of linear equation with two variables, error types of easy mistakes, errors of calculation rules, equal justice misuse, the meaning of linear equation with two variables is not clear and not for the answer to test its reasonableness.