以「固定一邊找第三點」概念於國中三角形全等性質教學之研究

Abstract

本研究以「固定一邊找第三點」對照「尺規作圖」之教學脈絡，旨在探討這兩種教學脈絡在「SSS」、「ASA」、「AAS」、「SAS」以及「RHS」等五種判斷兩個三角形全等性質的教學中，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，以新竹市某國中八年級四個常態班共120位學生為研究對象，實驗組之教學脈絡為「固定一邊找第三點」，對照組之教學脈絡為「尺規作圖」。以二因子變異數進行實驗數據分析，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、基本知識、理解概念與應用說明四個部分進行分析；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，以及對於高成就水準學生是否發生專業知識反轉效應。研究結果顯示：(1) 以「固定一邊找第三點」的教學脈絡對後測表現在總分、理解概念與應用說明有達到顯著;成就水準變項對後測表現在總分、基本知識、理解概念與應用說明均達到顯著。(2)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，兩組教材對於高成就水準學生均未產生專業知識反轉效應。

This study compares two teaching contexts – " Finding the Third Point for a Given Side " and " Ruler" – to investigate their effects on students’ learning achievement and perceptions of cognitive load in "SSS", "ASA", "AAS", "SAS "and" RHS " two triangles congruent determine the nature of teaching. Quasi-experimental in design, this study involves 120 participants from 4 8th-grade classes in a junior high school in Hsinchu city. The teaching context of the experimental group was based on " Finding the Third Point for a Given Side " while students in the control group were " Ruler " teaching context. The result 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, the basic knowledge, understanding of concepts, and application of concepts. The participants’ perceptions of cognitive load were 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 showed that: (1) Total scores, understanding and application of concepts are found to be siginifcant in the post test in the " Finding the Third Point for a Given Side " teaching context; the variable of achievement level had on scores in post test was found to be significant in total scores, basic knowledge, understanding and application of the concept. (2) Judging from the synthesis of instructional efficiency and ii 5 instructional involvement score, participants in the experimental group belonged to learners of high involvement high achievement learning style while participants in the control group were described as learners of low involvement and low achievement learning style. Neither teachin