教學脈絡與成就水準對基本尺規作圖學習成效之研究

Abstract

本研究以「運用以中垂線為模組之模組化教學脈絡」對照「先教作圖步驟，再以線對稱圖形進行說明之一般教學脈絡」為焦點，旨在探討這兩種教學脈絡在與中垂線有關之四種基本尺規作圖的教學中，對於學生的學習表現以及認知負荷感受的影響。本實驗採用準實驗研究法，以新北市某國中七年級四個常態班共120位學生為研究對象，實驗組之教學脈絡為「以中垂線為模組」，對照組之教學脈絡為「線對稱圖形」。以二因子變異數進行實驗資料分析，自變項為教學脈絡與成就水準，依變項為後測表現、延後測表現與認知負荷感受，後測與延後測均區分為總分、中垂線概念、基本作圖與應用作圖四個部分進行分析；以認知負荷量表之花費心力檢測認知負荷感受；另以學習效率與學習投入分數綜合判斷學習情形，以及對於高學習成就學生是否發生專業知識反轉效應。研究結果顯示：(1)教學脈絡與成就水準兩個變項在後測、延後測各部分之表現及認知負荷感受均沒有顯著的交互作用。(2)教學脈絡變項對後測表現的主要效果，在總分、基本作圖與應用作圖達到顯著；成就水準變項對後測表現的主要效果，在總分、中垂線概念、基本作圖與應用作圖均達到顯著。(3)教學脈絡變項對延後測表現的主要效果，在總分、中垂線概念、基本作圖與應用作圖均達到顯著；成就水準變項對延後測表現的主要效果，在總分、中垂線概念、基本作圖與應用作圖均達到顯著。(4)教學脈絡變項對認知負荷感受的主要效果未達顯著差異；成就水準變項對認知負荷感受的主要效果達顯著差異。(5)綜合學習效率與學習投入分數判斷學習情況，實驗組為高投入高效率，對照組為低投入低效率，兩組教材對於高學習成就學生均未產生專業知識反轉效應。

This study focuses on the teaching context using perpendicular bisector module in comparison with the more common teaching context where construction procedures are taught first and then followed by explanation with line symmetric graphs. It is intended to investigate the effect of these two teaching contexts on students’ learning achievement and perceptions of cognitive load in the four types of ruler and compass construction instruction concerning perpendicular bisector. The experiment was based on a quasi-experimental deign, and the participants were120 seven graders from 4 average classes in a junior high school in New Taipei city. The teaching context of the experimental group was based on the perpendicular bisector module while students in the control group were instructed in a line symmetric graph teaching context. The result of the experiment was analyzed through two-way ANOVA, with teaching context and achievement level being independent variables and scores in post-test and delayed post-test and cognitive load being the dependent variables. Scores in both post-test and delayed post-test were analyzed as four individual parts, including total scores, perpendicular bisector concept, basic construction, and applied construction. The participants’ perceptions of cognitive load are measured through cognitive load measurement, while scores of instructional efficiency and instructional involvement were used to synthetically determine their learning achievement and whether the expertise reversal effect had been observed in the high achievers. The results of the study showed that :(1) In terms of the individual scores in post-test and delayed post-test as well as the perceptions of cognitive load, there was no significant interaction between the two independent variables, teaching context and learning level. (2)The major effect the variable of teaching context had on scores in post test was found to be significant in total scores, basic construction, and applied construction; the major effect the variable of achievement level had on scores in post test was found to be significant in total scores, perpendicular bisector concept, basic construction, and applied construction . (3) The major effect the variable of teaching context had on scores in delayed post-test was found to be significant in total scores, perpendicular bisector concept, basic construction, and applied construction; the major effect the variable of achievement level had on scores in delayed post-test was also found to be significant in total scores, perpendicular bisector concept, basic construction, and applied construction. (4) The major effect the variable of teaching context had on scores in perceptions of cognitive load was discovered to be insignificant; however, the major effect the variable of learning achievement had on scores in perceptions of cognitive load was found to be significant. (5) Judging from the synthesis of instructional efficiency and instructional involvement score, participants in the experimental group belonged to learners of high involvement high achievement learning style while in the control group participants were described as learners of low involvement and low achievement learning style. Both teaching materials did not lead to the expertise reversal effect in high achievers.