利用眼球追蹤技術於大學生數學垂直與平行概念能力的探究

本研究在探討大學生進行垂直與平行的判斷時，空間能力試題在形體的「輔助邊線」數量與題目「文字語序」的分類下，其作答效率、眼動指標及解題原因的差異。研究中，第一階段透過van Hiele幾何思維模式進行平面能力的試題設計，發現對參與者來說對「有無垂直記號」、「線段與直線的交點狀態」及「等角記號下的垂直與平行條件判定」的問題迷思。接著，在第二階段「空間能力測驗」與第三階段「空間能力再理解」後，整體在不同的分類下，「輔助邊線」彼此存在差異，「文字語序」則是部分有差異，透過眼動指標的對應，綜合總訪問時間、訪問次數與平均訪問時間的結果，發現在「輔助邊線」的試題分類彼此間有顯著差異，而以「無輔助邊線」的類型最困難；在「文字語序」的試題類下在試題難度排序後相鄰的兩類型試題間無差異，其中「前起點與後終點相同」的類型最困難，「同向平行」的類型最簡單。此外，藉由眼動行為模式的觀察，試題辨識時會透過「邊」做為連結中心進行資訊的蒐集。透過高低分組的比較下，則僅在「無輔助邊線」的注視總時間上存在差異；而在解題方法上高分組多以整體的視角進行目標的分析，低分組則是透過部分的視角連結相關元素進行分析。因此，在教學上建議：一、透過難易度循序進行教學，二、適當介入輔助邊線的資訊進行提示或觀察，三、透過順向與逆向的邊線關係進行試題轉換，刺激視覺的辨識，四、可以擴增圖片辨識時的視角，促進學生在未來的空間幾何與向量學習得到良好發展。

關鍵字

眼動儀； van Hiele幾何思維模式；空間能力；解題策略；迷思概念

並列摘要

This study explores the differences in answer efficiency, eye movement measures, and reasons for problem-solving the spatial ability test questions of college students when they make vertical and parallel judgments in the classification of "auxiliary edge" and "word order". In the first stage of the research, we used the van Hiele model of thinking in geometry to design the test of plane ability. It was found that were judged on the conditions of "presence of vertical mark", "point of intersection of line segment and straight line", and "vertical and parallel conditions under equiangular notation" for the participants. In the second stage, there are differences in the "auxiliary side" and partially differences in the "word order" in the overall test the test of spatial ability. Through the correspondence of the eye movement measures, in the comprehensive results of total visit duration, visit count and average visit duration, it is found that there are significant differences in the classification of the "auxiliary edge" test questions. "No-assisted side " is the most difficult. Under the "Word Order" category, there is no difference between the two adjacent types of questions after the questions are sorted by difficulty. Among them, the type with "the same of front-starting point and back-ending point" is the most difficult, and the type with "parallel of orthodromic" is the simplest. In addition, by observing the pattern of eye movement behavior, the "side" is used as the link center to collect information when identifying the test questions. In addition, through the observation of eye movement behavior patterns, the "side" will be used as the link center to collect information during the identification of test questions. Under the comparison of high and low groupings, there is only a difference in the total gaze time of "No-assisted side". In terms of problem-solving methods, the high-group uses an overall-perspective to analyze the target, while the low-group uses a partial-perspective to connect related elements for analysis. Therefore, there some suggestion for teaching: 1. Teaching through the difficulty level in order. 2. It should be appropriate to intervene the information of auxiliary side to prompt or observe. 3. The test questions are converted through the orthodromic and antidromic relationship, which stimulates visual recognition. 4. Enlarging the viewing angle of image recognition. in the future, students will develop well in space geometry and vector learning.