The Effects of Proof Features and Question Probing on Understanding Geometry Proof

Abstract

本研究主要探討的問題是：不同寫法、不同複雜度和不同種類的理解問題對學生理解幾何證明有何影響？在理論上，採用Duval的組織敘述之3種層次做為不同種類的理解，依此設計工具測驗153位國三學生對幾何證明的理解。研究結果顯示：1.不同寫法、不同複雜度和不同種類的理解問題之間沒有交互作用；2.局部理解是最容易的；3.不同複雜度會影響學生在局部理解和整體理解問題的表現。以上結果的一般性仍受限在沒有給命題的證明文本之測驗情境。在安排閱讀幾何證明的學習序列時，編輯者應該要考慮混合證明步驟數和命題熟悉度的複雜度因子。最後，本文將會提出進一步的研究議題。

This study aims to investigate how the written formats, complexity of proofs and the types of understanding questions affect students’ understanding of geometry proof. Theoretically, Duval’s three levels of organizing statements - micro, local and global, are applied to assess 153 ninth graders’ understanding of geometry proof. The results show (a) there was no interaction among written formats, complexity of proofs, and types of understanding questions in terms of students’ understanding of geometry proof; (b) local understanding is the easiest for students; (c) the effects of the complexity of proofs on local and global understanding were statistically significant. It is noted that the generalizability of the results is limited by the task of proof texts without their corresponding propositions. The factor mixing proof steps and familiarity of propositions should be taken into account while arranging learning sequence of reading proofs. Afterward, further research is proposed in this paper.