數學創意類比與同儕評量及其網路案例設計之初探

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，並以活動方式讓學生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數學成就的影響。本研究採實驗研究法，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、十道類比題目的學習活動。根據實驗結果分析，本研究有如下發現：一、在某些評分項目中(如創意性)，同儕評比與專家評比間的相關係數不高，這也顯示學生評量分數與專家評量的分數有些差距。二、本實驗設計之活動對於學生的較高層次之數學應用題及分析題有顯著性幫助。本研究結果建議，學生在同儕互評與創意類比的過程中可促進學生較高層次的思考，並幫助學生建構較豐富之數學概念結構，也因此學生在較高層次的成就測驗題目中有較好之表現。

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 form this study indicated that: 1. 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. 2. students in the experimental group had higher achievement scores on the higher-order levels of knowledge (e.g., application and analysis), which indicating that students may construct knowledge structures through higher-order cognitive operations in the processes of mathematical creative analogy activities and peer assessment.