多元表徵應用於二元一次聯立方程式文字題列式教學之研究

Abstract

本研究目的在分析不同表徵之教學設計模式對於常態編班學生其學習成效及認知負荷之影響，並以整體學生、學過與未學過學生及不同數學學習成就學生作為樣本區隔，針對國中七年級「二元一次聯立方程式文字題列式」進行研究，進而對教學現場中不同的教學對象提出其適用之教學設計模式建議。 本研究採準實驗研究設計，以研究者任教之常態編班國中七年級四個班的學生為研究對象進行實驗，依據不同的教學設計模式分為四組進行實驗，分別為(1)串流式教學組、(2)代數教材設計原則組、(3)動態圖像組、(4)代數教材設計原則輔以動態圖像組。 實驗結果分析得到：(1)將結合代數教材設計原則及動態圖像之教學設計教材運用於常態編班中整體學生、未學過之學生及中學習成就、低學習成就學生之教學，能有效提升其學習成效，並降低認知負荷；(2)代數教材設計原則能降低學生在搜尋相關訊息之認知負荷；(3)動態圖像表徵有助於低學習成就學生理解題意，進而正確的將文字表徵轉化為代數表徵；(4)將僅有動態圖像表徵而未具代數教材設計原則之教材設計運用於常態編班中整體學生、未學過學生及中學習成就、高學習成就學生之教學，其學習成效表現不佳且認知負荷較高；(5)在實驗教材中皆未產生專業知識反轉效應。

The purpose of this study was to analyze the effects of four different instructional design models on learning effectiveness and cognitive load among students in a normal grouping system. The experimental lesson was about translate word problems of two variables into a system of linear equations. The sample was divided by experience of learning the lesson and math learning achievement into various groups to find the suitable instructional design model for each group of students. The quasi-experimental research design was adopted. Four seventh-year classes of students from the school where the researcher served as a teacher participated in the experiment. The students were divided into four groups based on four instructional design models, including (1) streaming instruction, (2) algebra lesson design principles, (3) dynamic graphic represrntations teaching, and (4) algebra lesson design principles with dynamic graphic represrntations teaching. The experimental results showed: (1) the instruction based on algebra lesson design principles with dynamic graphic represrntations teaching could effectively enhance the learning effectiveness and reduce the cognitive load among overall students, students who have never learnt the experimental lesson, students with intermediate math learning achievement, and students with low math learning achievement in a normal grouping system; (2) the instruction based on algebra lesson design principles could reduce the cognitive load on students in seeking related information; (3) dynamic graphical representations were helpful for students with low learning achievement in comprehension of problems and translation of word representations into algebraic representations; (4) the instruction designed with dynamic graphic representations but without algebra lesson design principles caused poor learning effectiveness and higher cognitive load among overall students, students who have never learnt the experimental lesson, students with intermediate math learning achievement, and students with high math learning achievement in a normal grouping system; (5) no expertise reversal effect was found in this study.