以直角三角形為模組對兩圓公切線尺規作圖學習成效之影響

Abstract

一般尺規作圖教學是採「步驟化」教學方式，學生需記憶大量且互動性高的作圖步驟，因而產生相當大的認知負荷。因此本研究試圖用「模組化」教學方式，也就是將教材內具有高互動關係的步驟切割出來，並組合成具有某一特定的功能，因而使得作圖步驟減少，期望藉此方式降低內在認知負荷，得到良好的學習效果。本研究採準實驗研究法，探討以直角三角形為模組對兩圓公切線尺規作圖學習成效之影響。以模組化教材及成就水準為自變項，後測、延後測及認知負荷為依變項。其中後測、延後測均細分為總分、計算、作圖三部分進行分析；認知負荷則是以上課感受量表中之花費心力進行檢測，以了解學生的學習效率及學習投入分數，目的是綜合此兩種分數來判斷模組化教材是否產生專業知識反轉效應。研究結果顯示：1.在後測部分，實驗組與對照組無顯著差異。2.在延後測部分，實驗組在總分、作圖表現皆顯著優於對照組。3. 在認知負荷部分，實驗組與對照組無顯著差異。4.綜合學習效率及學習投入分數，在後測部分，實驗組高成就水準為高效率、低投入，實驗組低成就水準為低效率、低投入；在延後測部分，實驗組高成就水準為高效率、高投入，實驗組低成就水準為低效率、低投入。故模組化教材並未產生專業知識反轉效應。應用模組化於高內在認知負荷之尺規作圖教學，雖然在近遷移(後測)無顯著差異，但遠遷移(延後測)則有顯著差異。表示模組化教材設計能降低內在認知負荷，產生較佳的學習效果。

The general teaching method for ruler and compass is step-by-step; students need to memorize a large quantity and highly interactive constructing step, resulting in a considerable cognitive load. Therefore, this study attempts to use "modular" method, that is, to separate the interaction between the steps from the teaching materials then combine the specific function, which reduces the construction steps. The purpose is to decrease the intrinsic cognitive load to improve students’ learning results. This study uses a quasi-experimental research method, to explore the effect of the right triangle module on the learning performance in ruler and compass construction of the common tangent of two circles. The independent variables are the modular materials and learning outcomes. The dependent variables are post-test, delayed post-test and cognitive load. The post-test and delayed post-test are subdivided into three segments of total scores, calculations, and drawing for analysis. The cognitive load is based on the scale of how students prepare and how much effort have been taken into account for the class in order to acquire the scores to analyze the efficiency and engagement of students’ learning consequences. This design is an integration of the two results to determine whether to generate modular teaching will produce the expertise reversal effect. Here are the results: 1. In the post-test sector, there is no significant difference between the experimental group and the control group. 2. In the delayed post-test sector, the experimental group has a superior execution in total score and constructing performance than the control group. 3. In the cognitive load sector, the experimental group and the control group had no significant difference. 4. In the integration of learning efficiency and learning engagement of the students, the scores show that the high achievement experimental group in the post-test has produced high efficiency with high engagement effort. The low achievement experimental group reveals low efficiency due to low engagement effort. The measurement in the delayed post-test sector, the high achievement experimental group has high efficiency with high input effort. The low achievement experimental group, on the contrary, has low efficiency with low input effort. The study results do not generate evidence to comply that modular teaching produces the expertise reversal effect.The application of modular teaching in the high intrinsic cognitive load shows that although there are no significant differences in the post-test sector, there are significant differences in the delayed post-test sector. The test result shows that the modular design teaching method is able to reduce intrinsic cognitive load hence a better learning results.