| 摘要: | 本研究旨在探討國中生的數學同儕互教學習成效、高低分群學生的同儕互教學習成效差異、以及國中生在同儕互教中的準備、講解、互動品質與程度，並透過分析準備、講解、互動程度與考試成績之關聯，初探「教中學」產生歷程。
研究對象為桃園市某國中七年級班級23位學生，依數學能力分為12位高分群學生與11位低分群學生。分別於「指數記法與科學記號」、「因數與倍數」、「最大公因數與最小公倍數」、「指數律」、「代數式的化簡」及「一元一次方程式」六個單元實施同儕互教，每單元流程皆相同。數學老師教完單元內容後，進行單元前測，接著實施含準備、講解、互動三個階段的同儕互教，最後進行單元後測。研究工具包含六個數學單元前後測考卷、教學準備學習單（紀錄準備過程）、錄音筆（紀錄講解與互動過程）、及研究者發展之「準備品質」、「講解品質」、「互動品質」評分方法。由於學生進行教學的題數與難易度不一，因此「品質」後續被轉換為「程度」（指某學生在其最多可以獲得的品質分數中，實際達到多少程度），以標準化每位學生的表現。資料分析方法包含以二因子混合設計MANOVA探討六個單元的同儕互教效果（前後測差異）、及數學能力與同儕互教交互作用效果，並以盒鬚圖描述高低分群學生之準備、講解與互動程度分數分布等。研究結果如下：
一、同儕互教後，整體而言，國中生的後測成績顯著高於前測成績，且高、低分群學生提升相似幅度的分數。也就是說，同儕互教有益於國中生的數學學習，且對高、低分群學生有相似的學習成效。
二、同儕互教中，高分群學生平均準備程度高（60%–70%）、內部差異小，低分群學生平均準備程度低（30%）、但內部差異大。高分群學生平均講解程度高（60%–70%）、但內部差異大；低分群學生平均講解程度低（30%）、內部差異亦大。高、低分群學生平均互動程度皆低（高分群：30%；低分群：10%–20%），但高分群學生內部差異大，而低分群學生內部差異小。
三、與後測成績最相關者仍是前測成績；但在準備、講解、互動中，與後測成績最相關者為講解程度，亦即講解程度可能是預測「教中學」效果的重要指標。
最後，綜合研究結果與對現有文獻之探討，提出國中數學同儕教學實施建議與對未來研究之展望。
;The study aimed to examine the effectiveness of reciprocal peer tutoring (RPT) on the academic performance of middle school students in mathematics, the differences in the effectiveness of RPT between high and low math-proficiency students, and the qualities/levels of students’ preparation, explanation, and interaction. The study also attempted to explore the learning-by-teaching effect by analyzing the relationships between the levels of preparation, explanation, interaction, and the test scores.
The study was conducted in a seventh-grade math classroom at a public middle school in Taiwan, involving 23 students (12 high math-proficiency students and 11 low math-proficiency students). Six RPT sessions were implemented for six math topics: Introduction to Exponents and Scientific Notation, Factors and Multiples, Greatest Common Factor and Least Common Multiple, Laws of Exponents, Simplification of Algebraic Expressions, and Algebraic Equations. The procedure for each of the six RPT sessions was identical: after the math teacher covered the topic, a pretest was conducted, followed by RPT session with preparing-to-teach, explanation, and interaction phases. Finally, all students completed the posttest. Pretest and posttest scores, students’ preparing-to-teach worksheets, and audio recordings of students’ verbal explanations and interactions were collected. Self-developed criteria for assessing the qualities of preparation, explanation, and interaction were applied. Since the number and difficulty of questions taught by students varied, qualities were later converted into levels (the extent to which a student reached the maximum achievable quality scores) to standardize students’ performance. A two-way mixed design MANOVA was applied to explore the effects of RPT and the interaction effect between students’ math proficiency and the RPT effect. Box plots were also used to illustrate the distribution of students’ preparation levels, explanation levels, and interaction levels. The results are as follows:
Firstly, overall, after the RPT sessions, middle school students’ posttest scores showed a significant improvement compared to their pretest scores, and this improvement was similar for both high and low math-proficiency students.
Second, during the RPT sessions, students with high math proficiency achieved high preparation levels (60%-70%) with low internal variation, while students with low math proficiency had low preparation levels (30%) with high internal variation. High math proficiency students attained high explanation levels (60%-70%) with high internal variation, while low math proficiency students had low explanation levels (30%) with high internal variation. Both high and low math proficiency students exhibited low interaction levels (high: 30%; low: 10%-20%), with high internal variation among high math proficiency students and low internal variation among low math proficiency students.
Last but not least, among preparing-to-teach, explanation, and interaction, explanation levels had the highest correlation with posttest scores, indicating that explanation level may be a crucial indicator for predicting learning-by-teaching effect. |
