數學創意類比與同儕評量及其網路案例設計之研究

Abstract

本研究之目的在於將創意、類比、與同儕評量的理念相結合，並以一活動方式讓學生進行發揮數學創意類比聯想與同儕交互評量，以檢驗對於中學學生的數學態度、數學成就，及降低學生之數學焦慮的影響。 研究中首先根據文獻的分析，以創意活動題目設計之原則，設計一系列適合讓中學學生進行創意類比聯想之題目，之後經過答案整理，進行同儕互評活動以讓學生從同儕評量活動中學習批判與思考，之後再輔以網路案例設計，利用WWW的便利性讓同學於網路上進行活動，以期能結合時尚流行之科技媒體，讓學生更容易獲得同儕回饋以獲得更大之學習成效。 本研究採準實驗研究法，實驗樣本取自新竹某中學二年級學生實驗組與對照組兩班各36人，實驗組進行了為期約一個月、四次活動、十道類比題目之的研究活動，在實驗之前、之後兩班各進行活動單元數學成就測驗與數學態度測驗問卷，並在最後以語意流程圖析法，兩班各抽取8人進行晤談，以了解學生於活動單元數學認知結構之差別。 最後根據實驗結果分析，本研究有如下發現：一、本實驗設計之活動對於學生的數學應用能力及分析能力有顯著性幫助。二、實驗設計之活動對於學生之數學成功態度之提昇有不可忽視的影響。三、實驗活動對於拓展學生認知結構之豐富度與概念範疇有顯著性的幫助。四、中學學生之評量能力尚未成熟，與專家評量之間相關性不高。

This study was inspired by the ideas of creative analogy in mathematics and peer assessment. This study further designed a web-based environment to implement the ideas, where students could express their creative analogy thoughts in mathematics and process peer assessment. The subjects involved in this study included two classes (thirty-six for each) in a junior high school in Hsinchu. A class was assigned into an experimental group, which received four-time research treatments (i.e., mathematical creative analogy activities) within a month, while another class was assigned into a control group. The research findings derived from this study indicted that: 1. Students in the experimental group had higher achievement scores on the higher-order levels of knowledge (e.g., application and analysis), 2. The research treatment had an undeniable impact on students' attitudes toward success in mathematics, 3. The research treatment helped students construct larger and richer cognitive structures on the mathematical concepts. However, the results also revealed that the peers' assessment scores on these activities were not necessarily related to the experts' evaluations, possibly due to the immaturity of student knowledge development, or the complexity of inter-relationships among peers.