以分段方式降低任務複雜度對專家與生手閱讀幾何證明的影響

Impact of Reducing Task Complexity by Segmentation on Experts'and Comprehension of Novices' Reading Geometric Proof Problems

本研究旨在探討將一個複雜的幾何證明用分段方式呈現，以降低任務的複雜度對專家與生手在認知負荷感受與閱讀理解之影響。依據數學結構及Duval（1998）的推理資訊組織層次將幾何證明分成分段與未分段兩種文本方式呈現，並將專家（亦即，28 位準中學數學教師和21 位中學數學教師）與生手（66 位八年級學生）隨機分派於不同呈現方式的組別中，以瞭解其認知負荷感受與閱讀理解的情形。研究結果顯示：（1）不論是對專家或對生手而言，證明文本以分段方式呈現，有助於提高其閱讀意願以及降低其閱讀證明時的困難度和所花費的心力，但對他們在閱讀理解的表現上，則未造成顯著差異。（2）不論證明文本以分段或未分段呈現，專家的閱讀意願與信心指數皆顯著高於生手，而其閱讀證明時的困難度和所花費的心力則顯著低於生手；且專家的閱讀理解表現也顯著優於生手。本研究依據研究結果，對幾何證明的後續研究與教學提出可能的教學策略與建議，以做為學術研究與教學實務工作者參考之用。

This study aimed to investigate whether reducing task difficulty by segmenting a complex geometric proof would have a differential influence on experts' and novices' cognitive load and reading comprehension. Based on mathematical structures and the theory of reasoning with organization (Duval, 1998), two versions (i.e., segmented and nonsegmented) of a print-based geometric proof were created. Forty-nine experts (i.e., 28 pre-service and 21 in-service math teachers) and sixty-six novices in their eighth-grade year were randomly assigned to either a segmented or non-segmented group. Results showed that for both experts and novices, segmentation helped increase their reading willingness and to lower their perceived task difficulty and cognitive demandingness of task. Segmenting or not, however, would not make a statistical difference with respect to participants' reading comprehension. Additionally, irrespective of versions of text read, experts' reading willingness and confidence level were significantly higher than those of the novices. Experts' perceived task difficulty and cognitive demandingness of task were significantly lower than those of the novices. Also, experts were found to comprehend the geometric proof significantly better than novices. Based on results of the study, future research and instructional strategies for teaching geometric proofs were proposed.