教材教法與成就水準對 數學學習成效、認知負荷及數學態度之研究 －以九年級圓與角單元為例

Abstract

本研究在國中九年級圓與角單元中，以「離散型脈絡」及「推導型脈絡」兩種教學方式在圓與角單元中有關圓心角、圓周角、圓內角、圓外角及弦切角五種角的教學，對不同成就學習者之學習成就、認知負荷感受及數學學習態度的比較。本實驗採用準實驗研究法，以桃園市某國中六個常態編班共 159 位學生為研究對象。不同教材脈絡設計及不同學習成就之學生為本實驗自變項，後測、延後測，認知負荷感受及數學學習態度為依變項，進行Two-Way ANOVA量化分析。研究結果顯示如下： (1) 教學脈絡與成就水準兩個變項在後測知識性題目及數學學習態度動機感受有顯著交互作用；其餘各項目在後測、延後測、認知負荷及數學學習態度各部分之表現均沒有顯著的交互作用。 (2) 教學脈絡在後測總分及後測理解性題目的主要效果中，離散組顯著優於推導組。 (3) 教學脈絡在後測知識性題目低成就學習者之單純主效果中，離散組顯著優於推導組。 (4) 延後測成就表現各變項中兩組教學脈絡均無顯著差異。 (5) 教學脈絡在認知負荷感受的上課理解程度變項的主要效果中，離散組優於推導組；其餘四個向度主要效果未達到顯著差異。 (6) 教學脈絡在數學學習態度之學習樂趣之主要效果中，離散組顯著優於推導組。 (7) 教學脈絡在數學學習態度之學習動機在中成就與低成就學習者之單純主效果中顯示離散組亦優於推導組；其餘各項未達到顯著差異。

The theme of this study is based on the "Angles Relating to Circles " unit discussing relationships with radians and angles to 5 angles which are Central Angle, Inscribed Angle, Chord Tangent Angle, Interior Angle of a Circle and Exterior Angle of a Circle in the Math Textbook for the ninth-grade students. In this study, the attitude, perceptions of cognitive load and effort in Math learning from various achievable students between discrete and derivative teaching contexts would be investigated. This experiment was based on a quasi-experimental design and 159 ninth-grade students from 6 average classes in a junior high school in Taoyuan city was adopted as participants. Various teaching contexts and students with different learning achievements were the independent variables while attitude in Math learning, perceptions of cognitive load and scores in post-test as well as delayed post-test were the dependent variables in this test. The investigative result was analyzed through a two-way ANOVA and showed in the following conclusions. 1. About teaching context and learning level, the significant interaction could be found of these 2 independent variables in the motivation of Math learning attitude and the knowledge dimension of post-test. The other dimension of post-test , delayed post-test ,cognitive load and Math learning attitude were failed to be found significant interaction. 2. The main effect about teaching context in the comprehension dimension of post-test as well as the total scores of the post-test, the discrete type group was obviously superior than the derivative type group. 3. The simple main effect about teaching context in the knowledge dimension of post-test of low achievement learner, the discrete type group was obviously superior than the derivative type group. 4. The two teaching contexts revealed no obvious differences in every independent variables of the delayed post-test achievement performance. 5. The main effect about teaching context in the class understanding of the perceptions of cognitive load, the discrete type group was obviously superior than the derivative type group; the main effect of the rest four dimensions were failed to reveal visible differences. 6. The main effect about teaching context in the learning pleasure of the Math learning attitude, the discrete type group was obviously superior than the derivative type group. 7. The simple main effect about teaching context in the learning motivation of the Math learning attitude to the middle and low achievement learners, the discrete type group was obviously superior than the derivative type group; the rest items were failed to reveal visible differences.