以眼動追蹤技術探討專家、生手進行數學證明確認之差異

Exploring Differences Between Expert and Novice in Mathematical Proof Validation Using Eye-Tracking Technology

本研究使用眼動追蹤技術探討專家、生手在數學證明確認任務上的注意力分布與眼動行為表現，並以兩類證明文本（符號比例多、寡）作為組內因子。本研究的參與者有19位數學家及24位修習過數論課程之數學系在學學生。研究工具為八題數學證明確認任務，在實驗過程中會請參與者直接回答他們的答案及判斷的理由。所採用的眼動指標為凝視次數與總凝視時間。研究結果顯示，在答題結果方面，專家組整體表現優於生手組；在眼動指標數據方面，文本的符號比例多寡對專家並無差異，但對於生手而言，符號比例較多的文本其資訊較複雜，閱讀上也需花費較多的認知心力。此結果顯示符號使用較少的素材或許能讓數學系生手的學習負擔減輕並增進學習效果，可提供教材或課程設計者作為參考。

This study used eye-tracking technology to explore the attention allocation and the eye-movement behavior of experts and novices on the task of mathematical proof validation, and we considered the two proof types (amounts of symbol ratio) as a within subjects factor. Participants were 19 mathematicians, and 24 mathematics undergraduates who had all completed the course of number theory. The research materials were 8 proofs in the proof validation task. During the experiment, the participants were asked to directly answer and give the reason for judgement. Two eye-movement indicators were used for analysis: Fixation counts and dwell time. This study found that, in the proof validation tasks, experts performed better than novices. The amount of symbol ratio within proofs had no effect on experts’ eye-movement indicators; however for novices, proofs with a higher proportion of symbol owned more complex information, and required more cognitive effort to read. This result showed that the use of proofs with a lower proportion of symbol would reduce the burden and improve their learning effect for the novice students, which can be used as a reference for textbooks or curriculum designers.