以眼球追蹤法分析國中數學幾何試題的解題歷程

Abstract

為能瞭解不同數學幾何學習經驗的學生如何解題，本研究以Usiskin在1982年發展的Van Hiele幾何思考層次測驗做為前測問卷，以得知學生之先備幾何能力與經驗，透過眼球追蹤技術可以瞭解各區閱讀比重情況，以探究不同幾何能力學生的解題歷程。本研究以28位非理工科大學生為受試者，蒐集其解決數學幾何問題時的眼動資料，隨後進行晤談。結果發現，(1)區域內閱讀時間百分比(PTSZ)而言，「幾何圖形與尺規作圖」中，幾何思考層次較高的學生因對於幾何性質更為清楚明確，相對分配較少時間處理選項區域內的訊息，在「三角形的基本性質」單元中，幾何思考層次較高的者，分配較多時間在求解標的與附圖中所提供的線索，「相似形」、「圓」和「幾何與證明」，幾何思考達第三層次的學生通常花時間在問題及題幹區域百分比較高。高思考層次組較能在解題過程中，分配較多時間在解題資訊所在之處。(2)區域內首次閱讀凝視時間(FPFDZ)而言，幾何思考層次較高的學生，會花較多時間在關鍵資訊上建構問題表徵。(3)區域內總凝視時間(TFDZ)而言，整體而論，高幾何思考的學生，會花較多時間在處理附圖區域的資訊。(4)圖文交互閱讀次數和回視而言，在「圓」單元中，低思考層次者嘗試在問題和正解返回題幹區域間搜尋相關線索的交互閱讀次數較高思考層次者多，且從正解回視問題區域的次數明顯多於高思考層次者，表低思考層次者可能因對於圓的幾何性質不熟悉，需反覆確認及搜尋題目所提供的線索，此過程中亦可能對於題幹中的資訊仍有部分尚未理解。(5)此結果部分與過去研究相符，論文最後提供此研究對於數學教學上的建議。

In order to understand how students with different mathematical geometry learning experiences solve problems, this study use the Van Hiele Geometry Test developed by Usiskin in 1982 as pretest questionnaire to preliminarily know students’ geometry ability and experience. In this study, we used eye tracking method to collect 28 non-science undergraduate students’ eye movement patterns when they were solving national standardized examination on the topic of geometry. Having interview immediately afterwards. After data processing, the following conclusions were drawn from this study: (1) With regard to PTSZ, in Geometry and Ruler Charting chapter, students with higher levels of geometric thinking spent relatively less time on processing of the option area; In Triangle chapter, those with higher levels of geometric thinking spent more time on processing the clues from figures. In Similarity chapter, students who reached the third level of geometric thinking often spent more time on question and statement area. (2) In terms of FPFDZ, high geometric thinking students spent more time constructing problem representation on key information. (3) In terms of TFDZ, high geometric thinking students generally spent more time dealing with the information from figure area. (4) With regard to ISC and regression, in Circle chapter, those with low thinking level tried to search more often for relevant clues between statement and problem as well as correct answer area. Moreover, the number of regression from correct answer to question is higher than high thinking level. (5) The result is consistent with the previous researches. In the end of this study provides some suggestions for mathematics teaching.