不岡等號概念之基模導向解題教學實驗研究

Abstract

本研究旨在針對不同等號概念之教材，進行基模導向解題教學實驗，以探索學生等號概念的表現﹒並歸納合宜之學習路徑，以做為日後改善代數推理教學與課程設計的依據。研究樣本為公立小學12 名一年級學生·2 人一組，參與研究者設計之不同順序等號概念的教學實驗與測驗，資料分析與說明則採取質、量併陳方式來呈現。綜合研究發現，獲得以下結果﹒經不同等號概念之教學情境實驗後，學生能獲得等號反身性、單邊運算與雙邊運算相等關係的觀念;學生等號概念的學習以路徑「單邊運算→反身性→雙邊運算」之教學效果最佳，其次為「反身性→單(雙)邊運算→雙(單)邊運算」之教學順序;等號概念之間的轉化與連結，依學生認知能力不同而有不同表現。研究者根據發現結果提出建議，提供未來等號概念之教學與研究參考。

The goal of this study was to reevaluate the concept of the equal sign and implement schema-based problem-solving instruction experiment to understand theprocess of solving equation problems and the means of learing it. When taking a test, twelve first graders completed three sequential tasks specifying a concept related to the equal sign. The collected data were analyzed according to descriptive statistics with a qualitative approach. The results showed that most of the students were capable of acquiring the three concepts represented by the equal sign after such an experiment,. The best method of learning the concepts of the equal sign involved the following sequences: I) one-side operation → reflection → two-side operation; 2) reflection → one-side operation → reflection → two-side operation; or 3) reflection → two-side operation → one-side operation. Students of different cognitive abilities showed different degrees of performance in the transformation and connection of their concepts of the equal sign. These findings could support teachers engaging students in opportunities to learn the concepts of the equal sign, by demonstrating how instruction can be used to improve and guide the design of curricula.