視覺障礙學生的數學學習困難與輔助需求：從表徵角度之分析

Mathematics Learning Difficulties and Support Needs of Students with Visual Impairments: An Analysis from the Perspective of Representation

本研究旨在探討視障生在缺乏視覺輔助與適當表徵支持的情況下，會遭遇哪些數學學習上的困難。由於視障生極需使用多種表徵作為理解與操作數學概念的中介工具，當表徵不足時，其所產生的困難樣態與歷程，更為目前研究尚待釐清的重要議題。本研究採深度訪談法，以立意取樣對15位平均年齡為20歲的視障生進行半結構式訪談，並以錄音筆與訪談札記紀錄訪談過程，之後將其轉化為回溯式訪談資料，使用主題分析法進行分析，了解視障生在數學學習上所遇到之困難。本研究發現，在缺乏視覺輔助的情況下，若無適合視障生之教學支持，會導致其難以使用表徵理解數學圖表與數學概念，使學習數學發生困難。具體而言，在視障輔具部分，點字由左至右之線性機制與原先具空間性的數學符號不相容，以及大部分教材依賴視覺經驗，導致視障生在使用符號表徵與計算上產生困難，且觸覺「下而上」的認知歷程，使其難以建立正確的圖像表徵。在教學方式上，教師通常使用模糊代詞或手勢，以及教學未補足不同感官資訊落差，都會導致表徵缺失並耗費大量溝通成本。最後，本研究建議：為降低視覺不利所造成之數學學習困境，在設計課程時應融入適合視障生之教學支持，協助其建立數學表徵，提升視障生在學習數學上的經驗。

This study aims to investigate the mathematical learning difficulties encountered by students with visual impairments in the absence of visual support and adequate representational scaffolding. Given that such students rely heavily on multiple forms of representation as mediating tools for understanding and manipulating mathematical concepts, the nature and processes of the difficulties arising from insufficient representations remain critical issues that warrant further clarification in the existing literature. A qualitative approach was adopted, employing in-depth interviews with a purposive sample of 15 visually impaired students with a mean age of 20. Semi-structured interviews were conducted, and the data were collected using audio recordings and interview notes. These data were subsequently transformed into retrospective interview transcripts and analyzed using thematic analysis to explore the challenges visually impaired students faced in learning mathematics. The findings indicate that, in the absence of visual support, insufficient or inappropriate instructional assistance significantly hinders students’ability to utilize representations to comprehend mathematical graphs and concepts, thereby impeding their mathematical learning. Specifically, regarding assistive tools, the linear structure of Braille is incompatible with the spatial nature of many mathematical symbols. In addition, most instructional materials rely heavily on visual experiences, which results in substantial difficulties for visually impaired students in processing symbolic representations and performing calculations. Furthermore, the predominantly“bottom-up”nature of tactile cognitive processing makes it challenging for these students to construct accurate mental imagery. In terms of instructional practices, teachers’frequent use of ambiguous pronouns and gestures, along with the lack of compensation for gaps across sensory modalities, contributes to representational deficiencies and increases the communicative burden. Based on these findings, this study suggests that, to mitigate the disadvantages caused by the lack of vision, instructional design should incorporate appropriate supports tailored to visually impaired students. Such supports can facilitate the construction of mathematical representations and enhance their overall learning experiences in mathematics.