以測驗表現和眼動型態探討圖示調整在不同幾何命題判讀作業之影響

Abstract

圖示在幾何文本閱讀歷程扮演著重要角色。本研究以中學生和大學生為對象，透過圖示調整對轉譯、簡單和多步驟推論三類型命題判讀之正確率、反應時間、眼動型態的影響，探究圖示在幾何文本閱讀歷程各階段扮演的角色。材料採20道國中幾何文本，共計110個命題。三個實驗分別針對397位九年級生進行紙本施測、46位中等程度國、高中生進行電腦化測驗，以及41位大學生進行眼動實驗。結果發現：（1）整體而言，三類命題正確率由高至低，反應時間、總凝視時間和單位畫素時間由短至長依序是簡單、轉譯和多步驟類，顯示了這三類命題的判讀歷程如預期的由簡至繁。（2）圖示調整最能提升轉譯類命題表現，其次是簡單類，但對多步驟類的影響僅在效率與眼動型態上，顯示圖示調整最能有助知覺辨識，而提升轉譯類命題判讀；也能觸發相關幾何定理，提升簡單類命題判讀；但對於涉及複雜邏輯論證的多步驟類，圖示調整效果僅在反應時間的縮短，與眼動指標所反應的判讀歷程改變上。（3）受試者在轉譯類命題判讀歷程中，對題幹訊息的仰賴多於簡單和多步驟類；相對的在多步驟類命題判讀歷程中，對圖示訊息的仰賴多於簡單和轉譯類。顯示轉譯類命題的判讀因與圖文訊息直接相關，對題幹訊息的仰賴較另兩類命題多；相對的，多步驟類的推理論證是藉著圖示具體空間結構來完成，因此對圖示訊息仰賴重。（4）圖示調整顯著減少已知條件閱讀階段的命題初始理解時間，但對後續回視時間影響不顯著。顯示圖示調整主要影響空間表徵的形成，較不影響推理歷程。（5）瞳孔大小可嘗試作為探究幾何文本閱讀歷程的指標之一。本研究同時依據研究結果提出「幾何命題判讀認知模式」，並對幾何教學和未來研究提出具體建議。Figures play an important role in geometric text reading. This study investigated the different roles of figures in geometric text reading processes, through the effects of adjusted figures on the transforming proposition, one-step inferential proposition, and multi-step inferential proposition validated by accuracy, response time and eye movements. In this study, the validated result of high school and undergraduate students was analyzed using twenty junior high school level geometry texts containing 110 proposition validations. Three experiments were conducted. Experiment 1 was paper-pencil group tests of 397 ninth grade students for the measurements of their accuracy. Experiment 2 was the computer-based testing of 46 average level ninth and tenth grade students for the measurements of the accuracy and response time. Experiment 3 was eye tracking of 41 college students for the measurements of their accuracy, response time and eye movements. Results indicated that: (1) generally, the accuracy from high to low was transforming proposition, one-step inferential proposition, and multi-step inferential proposition. The response time, dwell time, and gaze duration per pixel from short to long were transforming proposition, one-step inferential proposition, and multi-step inferential proposition. This implied that the most complicated proposition validations were the multi-step ones and the least were transforming ones. (2) The effects of adjusted figures depended on different proposition validation. The greatest effect of adjusted figures on accuracy was on transforming proposition validation, followed by one-step one. The effect on multi-step proposition validation was only found to have increased the efficiency. This implied that adjusted figures contributed to the perceptual organization, which led to the increased efficacy in transforming proposition validation. In addition, the adjusted figures also activated relevantly geometric theorems in long term memory which increased efficacy in one-step proposition validation. Furthermore, for the complex proving processes of multi-step proposition validation, in contrast, the effects of adjusted figures were on the increased efficiency and eye movements. (3) The subjects relied more on given information in transforming proposition validation than in one-step and multi-step ones. By comparise, they relied on more figure information in multi-step proposition validation than in one-step and transforming ones. This implied that the integration of the text and figure during transforming proposition validation depended on text more than the inferential processes of one-step and multi-step ones did. In contrast, the complex inferential processes went through the concrete spatial construction of figures, which resulted in the greatest dependency on figures of the multi-step proposition validation. (4) Adjusted figures significantly decreased the initial reading comprehension time of the given reading, but did not affect the regression time. This implied that adjusted figures affected the forming of spatial representations, but did not affect the inferential time. (5) Pupillary dilations might be an indication of the change in geometric text reading. According to the results, the researcher proposed a “geometric proposition validation cognitive model.” Implications for future research and the teaching relevance to geometric text reading are discussed.