同儕交互指導數學解題方案對國小學童數學解題表現、數學焦慮及后設認知影響之實驗研究

An Experimental Study for the Effects of RPT Program on Elementary Students' Performance, Anxiety and Metacognition of Mathematical Problem Solving

陸正威(Chen-Wei Lu) ； 王慧豐(Hui-Feng Wang)

《花蓮師院學報》 10期 (2000/10) Pp. 273-298

摘要

本研究旨在探討「同儕交互指導數學解題方案」對不同程度別國小學童數學解題表現的提升，數學焦慮的降低，以及解題後設認知的增強所能產生的立即與保留效果是否會隨編組情境方式而有所不同。本研究以台北縣永和國小五年級154名學生（四個班級）爲研究樣本，並以班級爲單位，隨機分派在異質編組、同質編組、不編組與控制組的情境下。各班學生依數學解題能力測驗前測成績分為高低不同程度別的受試者，以不等組前後測設計進行為期十週之實驗處理。研究結果顯示：
一、異質編組的「同儕交互指導數學解題方案」能顯著提升受試學童的數學解題表現，且提升的程度明顯高於不編組與控制組情境所能達到的。另外，異質編組同儕交互指導情境有助於降低高程度學童的數學焦慮，以及可增強受試學童數學解題的後設認知。
二、同質編組的「同儕交互指導數學解題方案」能顯著提升受試學童的數學解題表現，且提升的程度明顯高於不編組與控制組情境所能達到的。另外，同質編組同儕交互指導情境有助於降低低程度學童的數學焦慮，但卻未能增強受試學童數學解題的後設認知。
三、不編組的「數學解題方案」能顯著提升受試學童的數學解題表現，且提升的程度明顯高於控制組情境所能達到的。然而，不編組情境卻未能有效降低受試學童的數學焦慮。更值得注意的是，此不編組情境明顯降低受試學童數學解題的後設認知（研究者認為此下降的幅度是出自於學童對自己原本認知重新修正的結果，而非單純降低學童後設認知的程度）。
四、在控制組情境下（沒有接受任何數學解題教學），受試學童的數學解題表現、數學焦慮與後設認知，經過十週後都没有明顯的改變，顯示這些變項不容易因時間而發生太大改變。依此研究結果，本研究進一步探討「同儕交互指導數學解題方案」對國小學童數學解題表現、數學焦慮及後設認知的影響。並對國小教學及後續研究，提出建議。

關鍵字

同儕交互指導數學解題方案 ； 數學解題表現 ； 數學焦慮 ； 后設認知

並列摘要

The main purpose of this study was to investigate the immediate and maintenance effects of different types of ”RPT Mathematical Problem Solving Program” on promoting elementary students' performance, decreasing their anxiety and enhancing their metacognition in mathematical problem solving. The subjects in this study were 154 students in four fifth-grade classes of Yong-Hoelementary school in Taipei County. The subjects, by class unit, were randomly assigned into ”dyadic-different”, ”dyadic-same”, ”non-dyadic” and ”control” groups. Subjects in each group were divided into high-level and low-level subgroup by their mathematical problem solving scores inpre-test. Each group was treated by different experimental program as assigned for ten weeks. And, subjects were given post-test and post-delay-test after program.
Based on the results of this study, the effects of ”RPT Mathematical Problem Solving Program” on elementary students' performance, anxiety and metacognition of mathematical problem solving were explored, and implications for teaching and further research were addressed.

並列關鍵字

RPT Mathematical Problem Solving Program ； performance of mathematical problem solving ； anxiety in mathematics ； metacognition in mathematical problem solving