幾何證明文本閱讀的眼動研究：圖文比重及圖示著色效果

Eye Movements During Geometry Proof Reading: Text Contrasting With Figure and the Colored Effects

幾何證明的文本具有圖示參照的特性。透過眼動追蹤技術可以瞭解圖文的閱讀比重以及圖示著色對閱讀歷程與理解的影響，以探究閱讀幾何證明的圖文整合歷程。本研究採四道國中的幾何證明為材料，操弄附圖上是否著色，以學過但不熟稔幾何證明的31 位大學生為受試者，蒐集其閱讀幾何證明時的眼動資料，隨後立即進行紙筆回憶測驗。結果發現，(1)受試者有一半的凝視時間落在圖區，且單位畫素凝視時間圖區較文區長，閱讀幾何證明相當依賴讀圖的現象，說明了圖示提供建構與整合各幾何元件空間關係之訊息，且此訊息因空間工作記憶的限制而需重複閱讀。此外，圖示也提供憶取幾何性質之線索，有助於讀者進行橋接論證，顯示讀圖的教學是個值得著力之處。(2)圖示著色縮減關鍵區的初始理解時間，但不影響其回視時間，也未造成回憶表現的差異，顯示著色影響大學生閱讀幾何證明的視覺化歷程，但對幾何推理歷程以及最終的理解記憶影響不大。亦即圖示著色是個可以影響幾何證明閱讀效率的表徵方式，在文本呈現與教學上有其意義。(3)結論處也指出幾何閱讀的眼動研究尚須確認數學詞彙單位、處理圖文來回時意外落點的技術，以及閱讀軌跡的分析方式等基礎研究。

The reading comprehension of geometry proofs necessitates a coherent mental representation of all the information conveyed in the figure and text. Eye movements can be used to assess the perceptual and cognitive processes, and how colored figures affect the integration of text and figures during comprehension. For our experiment, we used four junior high school level geometry proofs with colored/uncolored figures to examine 31 undergraduate students who had learned but have not mastered geometry proofs. First, the participants' eye movements were recorded during reading. A paper-and-pencil recall test was then administered to the participants after the reading procedure. The data reveal that half of the fixations were located on figures, and the proportion of fixations to the pixels of the figures was greater than that of the texts. The results suggested that the reading of geometry proofs depended more on figures that organized the statements using a specific status and provided cues for the geometry proof properties compared to text. Working memory limitations increased the regression time for figures. Additionally, figures provided utility cues for recalling geometric properties, which assisted readers in performing deductions and verifications. Colored figures influenced the visualization of undergraduate students when reading geometry proofs. This reduced the initial reading comprehension time of one theorem, but did not affect the regression time and comprehension exhibited in the recall tests. Valid analyses of eye movements when reading geometry proofs must be supported by definitions of mathematical words and data-screening skills.