從眼動型態探討閱讀幾何文本的視覺化與推理歷程   全文下載

Examining Eye Movement to Explore Visualization and Reasoning During the Reading of Geometric Texts

幾何文本富含空間表徵與推理，本研究藉由比較不同類型幾何文本的眼動型態來探討幾何閱讀，尤其是Duval所揭示的視覺化與推理歷程。本研究的有效樣本為50位大學生，每位受試者閱讀九題幾何敘述及兩題幾何證明，其中幾何證明分成已知求證、示範證明兩部分分析，三者的推理成分依序由低而高。結果發現：幾何敘述、已知求證、示範證明之讀圖凝視時間占總凝視時間比率分別為 .36、.41和 .51，示範證明的讀圖比率顯著較高，顯現文本差異影響讀者仰賴圖的程度。幾何閱讀的總凝視時間劃分為初始理解與回視兩階段，由三類文本兩階段的時間比率與各興趣區域（AOI）凝視時間等資料，推論初始理解階段與視覺化的關係較密切，而回視則與推理較有關。最後，以馬可夫轉移機率分析眼動軌跡發現，幾何符號是指引成人讀者到圖參照的線索，尤其是文本主體的幾何符號有高比率參照圖的型態。相對而言，讀者讀到一般文字、幾何名詞，以及背景脈絡出現的幾何符號，則傾向繼續閱讀下文，而較少有到圖參照的眼動型態。

Geometric texts carry rich spatial information and arguments. This study examined the eye movement of adults reading different types of geometric text to explore Duval’s model of visualization and reasoning. A total of 50 participants were requested to read two geometry proof items and nine geometric description items. Eye movements during proof reading were categorized into “given,” “prove,” and “proof examples.” Three types of geometric text comprised different proportions of reasoning components. Answers to the question of to what extent reasoning elements are involved in the three types of geometric text were ranked in the following order: “geometric description,” “given and prove,” and “proof example.” First, we found that the total fixation duration ratios of the graph for these three types of geometric text were 36%, 41% and 51%, respectively. The ratio of proof examples was significantly higher than that of the other two types of geometric text, indicating that the extent to which readers rely on figures when reading geometric texts is influenced by differences between the three types of geometric text. Second, according to the total fixation time, the process of reading comprehension for a geometric text can be divided into two phases: initial comprehension and rereading. As indicated from the reading time ratios and average reading time for areas of interest (AOIs), we observed that initial comprehension could be related to Duval’s visualization, and that rereading could be related to Duval’s reasoning. Finally, based on an analysis of the Markov transition matrix, geometric symbols—particularly keynote geometric symbols—were regarded as clues that guide the reader from the text to the figures; however, word description, geometric terms, and geometric symbols embedded in the background were proven to direct readers to move onto subsequent AOIs in the text, but rarely onto figures.