國二學生閱讀數學幾何證明問題之視覺行為特徵

Eighth Graders’Visual Behavior Characteristics When Reading Mathematical Geometry Proof Problems

本研究旨在利用眼動追蹤技術追蹤國二學生閱讀數學幾何證明問題時的閱讀歷程，探討視覺行為特徵和學習成效之間的關係。本研究採眼動實驗研究方法，從90名國二學生依數學段考成績，篩選出17名已認識基本幾何符號，但未學過幾何證明的學生，參與幾何證明教材閱讀的眼動實驗。受試者在實驗中需要閱讀九頁關於三角形全等性質（SSS、ASA、SAS）的學習教材，每個全等性質皆含有三個頁面（概念說明頁、簡單例題頁、困難例題頁），每個頁面皆含有三個興趣區塊（主旨區（T）、說明區（S）、圖形區（G））。本研究採資料為本的研究取向，根據後測成績將學生分成高低學習成效兩組，比較兩組學生在不同教材頁面和不同興趣區塊的所有眼動指標，並運用遲滯序列分析（Lag Sequential Analysis [LSA]）辨識出兩組學生在教材閱讀歷程中的視覺行為特徵。研究結果發現：在概念說明頁的圖形區塊，高學習成效組具有顯著較長的總閱讀時間、總凝視時間、平均凝視時間、閱讀時間比例、凝視次數比例、重複閱讀時間、和重複凝視時間，顯示高學習成效的學生在理解概念時會花費較多的心力處理圖形資訊；而在簡單例題頁的說明區的文字，高學習成效學生的平均凝視時間則顯著較短，代表較易於理解簡單例題的文字說明。此外，LSA結果顯示，高學習成效組在三個頁面均無明顯的注意力轉移特徵，然而，低學習成效組的學生在概念說明頁和困難例題頁的主旨區皆與空白區有顯著的來回反覆思考的視覺行為特徵，顯示理解主旨訊息有一定的困難，且其在概念說明頁說明區的注意力會明顯地轉移到圖形區，顯示低學習成效學生在理解概念說明文字時，可能很需要圖片訊息的輔助。本研究透過眼動資料的探勘分析，找出學習成效高低的學生，尤其有學習困難的學生，在閱讀數學幾何證明教材歷程中，有關注意力分布和注意力轉移的視覺行為特徵。本研究發現應可提供未來促進個別化數學學習的數位學習平台的開發。

This study aims to track the reading process of eighth-grade students when reading mathematical geometry proof problems using eye-tracking technology and to explore the visual behavior characteristics associated with different learning outcomes. Using an eye-tracking experimental research method, this study selected 17 subjects from 90 Taiwanese eighth-graders based on their mathematics midterm exam scores. These students had a basic knowledge of geometric symbols but had not yet studied geometric proofs. They participated in an eye-tracking experiment while reading geometry-proof materials. During the experiment, participants were asked to read learning materials on triangle congruence properties (SSS, ASA, SAS). Each congruence property consisted of three pages: a concept explanation page, a basic example page, and an advanced example page. Each page contained three information zones: Main Idea Zone, Explanation Zone, and Diagram Zone. Based on a data-driven approach, this study divided the subjects into high and low learning outcome groups based on post-test scores. The study then compared all eye-tracking metrics among different information zones across different material pages. Additionally, for each group, Lag Sequential Analysis (LSA) was applied to identify visual behavior characteristics of students' reading processes. The results revealed that, on the concept explanation page’s Diagram Zone, the high-performance group exhibited significantly longer total reading time, total fixation duration, average fixation duration, percent of reading time, percent of fixation count, secondary passing time, and revisited fixation duration, suggesting that students with higher learning outcomes invested more effort in processing graphical information when comprehending the concepts. On the simple example page’s Explanation Zone, high-performance students showed a significantly shorter average fixation duration, indicating that they perceived it easier than the low-performance group to understand the textual explanations of simple examples. On the other hand, LSA results surprisingly indicated that high-performance students exhibited no significant attentional shifts among different information zones. In contrast, low-performance students displayed frequent back-and-forth inter-scanning between the Main Idea Zone and blank spaces on both the concept explanation and difficult example pages, suggesting difficulty in understanding the core information. Moreover, low-performance students shifted their attention from the Explanation Zone to the Diagram Zone on the concept explanation page, indicating a greater reliance on visual aids to comprehend textual explanations. Through the learning analytics of eye-tracking data, this study identified the visual behavior characteristics of attentional distributions and attentional shifts for students with different learning outcomes, especially for students with learning difficulties, in reading mathematical geometry proof materials. The findings of this study may contribute to the future development of personalized digital learning platforms to improve students’mathematics learning.