分組合作之精熟學習策略對八年級學生數學科 學習成就與學習經驗之影響 －以一元二次方程式為例

Abstract

本研究探討不同分組合作學習之精熟學習策略對國中八年級學生學習「一元二次方程式」單元時，對學生數學學習成就與數學學習經驗之影響。本研究採取準實驗研究之不等組前測－後測，研究對象為桃園市某國中八年級三個班級，共84位學生為研究對象。其中，隨機分派三個班分別為：實驗組（一）27人，採分組合作學習精熟學習策略之「認知師徒制（CA）」；實驗組（二）28人，採分組合作學習精熟學習策略之「學生小組成就區分法（STAD）」；控制組29人，採「講述式教學法」。教學實驗研究為期四週，研究的主要工具為「數學學習成就測驗」與「數學學習經驗問卷（量表）」，並藉由描述性統計、成對樣本t檢定及變異數分析之方法予以分析探討，以了解分組的合作技巧對學生數學學習成就與學習經驗之影響。研究主要結果論述如下： 一、 學生數學學習成就方面 (一) 透過三種不同的教學方法後，三組學生的數學學習成就測驗後測成績無顯著差異（p＞0.05）。然而，認知師徒制（CA）與學生小組成就區分法（STAD）皆有效提升學生之數學成就並降低班級內學生的數學成就差異程度。 (二) 在教學後，三組學生之前測－後測都能呈現顯著的學習效果（p＜0.05），表示三種教學方法都有助於學生在數學科的學習成就。 (三) 學生小組成就區分法（STAD）有效提升高成就學生數學學習成就；認知師徒制（CA）有效提升中成就學生數學學習成就；認知師徒制（CA）與學生小組成就區分法（STAD）皆較講述式教學法有效提升低成就學生數學學習成就。 二、 學生數學學習經驗方面 (一) 透過三種不同的教學方法後，認知師徒制（CA）與學生小組成就區分法（STAD）的學生在數學學習經驗上，皆達到統計考驗上的顯著差異（ｐ＜0.05），而控制組所實行的講述式教學法並未達到顯著差異（ｐ＞0.05）。 (二) 認知師徒制（CA）、學生小組成就區分法（STAD）皆較講述式教學法有效提升學生的數學學習經驗三個層面：「學習動機與態度」、「合作技巧與同儕互動」與「師生關係」，並達到統計考驗上的顯著差異（ｐ＜0.05）。 (三) 透過認知師徒制（CA）與學生小組成就區分法（STAD）此兩種教學法，對學生之數學學習經驗並未帶來顯著差異（ｐ＞0.05）。 最後，研究者根據研究結果提出具體建議，以作為數學科教學及未來研究之參考。

This study aims to investigate the effects of cooperative learning on eighth-grade students’ mathematical learning achievements and learning experiences using mastery learning strategy by taking “Quadratic Equation of One Variable” as an example. This study was a quasi-experiment with nonequivalent pretest-posttest control group design. The subjects of the study were 84 eighth-graders from three classes in Taoyuan. These three groups of students were randomly divided into three groups, which were the experimental group (Ⅰ) (27 students) using “Cognitive Apprenticeship (CA)” mastery learning strategy of cooperative learning, the experimental group (Ⅱ) (28 students) using “Student Teams-Achievement Division( STAD)” mastery learning strategy of cooperative learning, and the control group (29 students) using the Lecturing Method. It was a four-week teaching experiment and the main instruments employed in this study were the Mathematical Learning Achievement Test and the Mathematical Learning Experience Questionnaire (scale). Intended to explore the impact of the cooperative skills on students’ mathematical learning achievements and mathematical learning experiences, the statistic techniques we used including descriptive statistics, paired-sample t test and analysis of variance. The conclusions of this research are shown as follows : 1. Aspects of learning achievements in mathematics： a. In terms of the post-test results of Mathematical Learning Achievement Test, there are no significant differences under three different instruction methods（p＞0.05）. However, both of the mastery learning strategies of cooperative learning, CA and STAD, effectively improved students’ mathematical achievements and reduced the differences among students in one class. b. After the teaching experiment, the mathematical achievements of students in these three groups were improved significantly on the pre-and post-test of Mathematical Learning Achievement Test（p＜0.05）. It means that three kinds of teaching methods can help students improve their mathematical learning achievements. c. The mastery learning strategies of cooperative learning, STAD, can improve higher-level students’ mathematical learning achievements effectively. The mastery learning strategies of cooperative learning, CA, can improve medium-level students’ mathematical learning achievements effectively. Both of STAD and CA can improve lower-level students’ mathematical learning achievements more effectively than the Lecturing Method.

2. Aspects of learning experiences in mathematics： a. In terms of the post-test results of Mathematical Learning Experience Questionnaire (scale), by these three different teaching methods, there are significant differences for the groups using CA and STAD（p＜0.05）；however, there are no significant differences for the Lecturing Method of the control group（p＞0.05）. b. The mastery strategies of cooperative learning , CA and STAD , both can significantly improve students' learning experiences in mathematica on three aspects：motivation and attitude, skills of collaboration and peer interactions, and relationships between teacher and students（p＜0.05）. c. Through CA and STAD , the mastery learning strategies of cooperative learning, there are no significant differences in mathematic learning experiences（p＞0.05）. Based on the results of the experiments, we proposed concrete suggestions for the teaching and the future studies in mathematica.