台灣學生歷年來在國際數學評比中都有不錯的名次，但在深入探究這些評比背後的學習表現分布時，我們可以發現台灣學生數學能力表現兩極化的狀況日趨嚴重。國家教育研究院提供的各項國際數學能力評比結果顯示，台灣的名次一直在國際上名列前茅，但是數學學習表現兩極化的情形越來越明顯。
研究者為一名特殊教育教師，目前任教於國內某國中。有感於特殊教育需求領域的學生們，由於其先天條件限制，認知發展與抽象思考能力大部分較同儕落後，在數學科學習上實屬弱勢。有不少學生曾參加補救教學，但卻未見學習成效有明顯之提升，加上目前在特殊教育領域中，數學學習方面未有一套架構完整之教材，教學現場亦以直接教學法、工作分析法為主流，導致許多特殊教育學生的主動學習機會被忽略了。
本研究的目的在探究國中資源班學生，以摺紙活動學習幾何性質得觀察與推論之歷程，是否得因媒介教具的使用與教師適時的介入，增加其主動學習的機會與提升學習動機。研究者始終相信，只要在教學過程中給予適當鷹架與介入，數學學習對特殊需求學生並無想像中困難，這些學生們依然是可以主動學習的。
本研究以新竹縣某國中之資源班學生為例，分別為三名智能障礙學生與三名學習障礙學生，進行摺紙活動以學習幾何性質觀察與推論，過程中以錄音、錄影之方式蒐集資料，並以語料分析統整出學生之學習歷程。
研究結果顯示，不論是智能障礙或者學習障礙的學生，能夠具體操作模型是非常重要的。在抽象的觀察中，學生倚賴模型操作，且由於語言表達與字彙量受限，在說明時能以操作、手勢等非語言輔佐，讓研究者以及教師們能夠更清楚學生的學習程度與理解狀況，不會因其語言表達方面的限制而低估了學生的學習效果。雖然在觀察與對應的過程中會遭遇困難，也有看不見性質的狀況，但經研究者稍稍介入後，多能自己主動藉由操作模型的過程來回驗證自己的推測，且能在摺疊的過程中向研究者說明自己的想法與推論，並能搭配模型輔佐自己的說明，因此研究者認為，能夠藉由具體模型操作學習抽象概念，不論是在覺察或推論方面，都是學習上很好的媒介。
兩種障礙類別的學生在歷程中有特定差異存在，但是只要在幾何性質過程中能將邊與角的關係對應正確，那麼六位學生皆能在最後的推論階段以符合自己程度的語言及方式，推論出三角形的全等。
本研究結果可做為未來數學幾何學習課程設計在特教領域中的參考，最後提供對現場教學與未來研究更進一步之參考。

Over the years, Taiwanese students have been ranked well in international mathematics assessments and evaluations conducted by PISA (Programme for International Student Assessment) and the National Academy of Education; however, when analyzing the distribution of the students’ performance, the polarization of their mathematics performance is becoming larger and more obvious.
The researcher is a special education teacher currently teaching at a junior high school in Taiwan. Students are placed in special education classes due to their inherent limitations from delayed cognitive development and abstract thinking. In addition, these students tend to have a harder time in mathematics. The current curriculum uses didactic teaching methods and task analysis instead of active learning.
The purpose of this research is to explore the junior high school students’ process of observing and inferring the geometric properties during origami activities. It is hypothesized teaching aids and appropriate intervention from teachers can increase their opportunities for active learning and enhance their learning motivation. It is believed that if appropriate interventions are provided during the teaching process, mathematics learning will not be as difficult for students with special needs and they can still learn actively.
In this case study, there were six subjects who are students from a junior high school in Hsinchu County. Out of the six students, three students had intellectual disabilities and the other three students had learning disabilities. The six subjects performed paper origami activities to learn geometric observations and inferences. Throughout the study, data was collected with voice and video recording.The results of this study show that there were differences between the learning process characteristics for students with learning and intellectual disabilities; however, they were all able to come to the correct conclusion using proper reasoning.
Students with learning disabilities showed changes in their learning process. Their ability to mentally imagine and see corresponding shapes and angles improved. The students also showed an improvement in their observation of geometric properties without prompting from the researcher. Their ability to generalize the lesson improved as well.
When compared to the students with learning disabilities, the students with intellectual disabilities improvement was not as great. However, these students still showed improvement in their learning process. They showed similar improvements in their ability to mentally imagine corresponding shapes and generalize information from the lesson showed. These students’ ability to observe and learn autonomously were inferior compared to the other students. They were more dependent on the researcher for additional prompting and support.
Despite the different learning processes, the students were able to come to the conclusion that the shapes are congruent. The six subjects can use their own language and methods to understand the similarities between the angles and sides of the shapes to come to the conclusion they are identical shapes.
The results of this research can be used as a reference for future mathematics and geometry learning curriculum design for special education, and also provide a further reference for teaching and future research.

第一章 緒論 1
第一節 研究背景與動機 1
第二節 研究目的與問題 3
第三節 名詞解釋 4
第四節 研究限制 5
第二章 文獻探討 7
第一節 資源班學生 7
第二節 幾何概念的發展與迷思 12
第三節 摺紙活動應用在數學課程中的相關研究 15
第四節 教材設計理念 20
第三章 研究設計與實施 25
第一節 研究架構 25
第二節 研究情境 27
第三節 研究流程 32
第四節 研究工具設計說明 33
第五節 資料蒐集與整理分析 39
第四章 研究結果 41
第一節 特殊需求學生學習歷程之語料分析 41
第二節 學習障礙學生學習歷程統整分析 126
第三節 智能障礙學生學習歷程統整分析 132
第五章 結論與建議 141
第一節 研究結論 141
第二節 研究建議 144
參考文獻 147
中文部分 147
英文部分 148

中文部分：
何華國(1999)。特殊兒童心理與教育。台北：五南。
何華國(2003)。啟智教育研究。台北：五南。
李翠玲(2005)。特殊教育教學設計 (初版六刷)。台北：心理.
李祐宗(2014)。談幾何扣條在國中相似三角形單元的應用。科學教育月刊，(368)，35-40。
邱上真(2002)。特殊教育導論-帶好班上每位學生。台北：心理。
吳彥瑾(2012)。國中一般生與學習障礙生之視覺空間工作記憶，空間能力與數學幾何學習表現之相關研究。國立台南大學輔助科技研究所，碩士論文，未出版。
孟瑛如、陳麗如(2000)。學習障礙學生在魏氏兒童智力量表上顯現之特質研究。 特殊教育季刊。
孟瑛如(2013)。資源教室方案-班級經營與補救教學(第三版)。台北市。五南圖書。
洪儷瑜、陳淑麗、陳心怡(2003)。學習障礙國中學生的智力特質之研究。師大學報，48(2)，215-238。
洪儷瑜（2007）。學習障礙學生的教育與輔導。載於國立台灣師範大學特殊教育中心編，如何發現及協助特殊學生(90-99)。
紐文英(2003)。啟智教育課程與教學設計。臺北：心理。
黃德華、羅家健(2009)。數學學習障礙與數學輔導教學。台灣數學教師電子期刊，(18)，3-17。
教育部(2008)。九年一貫課程綱要。
教育部(2011)。國民教育階段特殊教育課程發展共同原則及課程綱要。
教育部(2011)。國民教育階段身心障礙資源班實施原則。
教育部(2013)。身心障礙與資賦優異學生鑑定辦法。
蔡元胤(2012)。國中二年級學生對於幾何問題迷思之探討。中原大學應用數學研究所，碩士論文，未出版。
翰林出版事業（2017）。國中數學備課用書第三冊。台南：翰林出版事業。
翰林出版事業（2017）。國中數學備課用書第四冊。台南：翰林出版事業。

英文部分：
Algozzine, B., O'Shea, D. J., Crews, W. B., & Stoddard, K. (1987). Analysis of mathematics competence of learning disabled adolescents. The Journal of Special Education, 21(2), 97-107.
Arıcı, S., & Aslan-Tutak, F. (2015). The Effect of Origami-Based Instruction on Spatial Visualization, Geometry Achievement, and Geometric Reasoning. International Journal of Science & Mathematics Education, 13(1).
Badian, N. A. (1999). Persistent arithmetic, reading, or arithmetic and reading disability. Annals of Dyslexia, 45-70.
Boakes, N. (2008). Origami-mathematics lessons: Paper folding as a teaching tool. Mathidues, 1(1), 1-9.
Boakes, N. J. (2009). Origami instruction in the middle school mathematics classroom: Its impact on spatial visualization and geometry knowledge of students. RMLE Online, 32(7), 1-12.
Cakmak, S., Isiksal, M., & Koc, Y. (2014). Investigating effect of origami-based instruction on elementary students’ spatial skills and perceptions. The Journal of Educational Research, 107(1), 59-68.
Cawley, J. F., Parmar, R. S., Yan, W., & Miller, J. H. (1998). Arithmetic computation performance of students with learning disabilities: Implications for curriculum. Learning Disabilities Research & Practice.
Crowley, M. L. (1987). The van Hiele model of the development of geometric thought. Learning and teaching geometry, K-12, 1-16.
Dickerson Mayes, S., Calhoun, S. L., & Crowell, E. W. (1998). WISC‐III profiles for children with and without learning disabilities. Psychology in the Schools, 35(4), 309-316.
Fuchs, L. S., & Fuchs, D. (2001). Principles for the prevention and intervention of mathematics difficulties. Learning Disabilities Research & Practice, 16(2), 85-95.
Gur, H., & Kobak-Demir, M. (2017). Geometry Teaching via Origami: The Views of Secondary Mathematics Teacher Trainees. Journal of Education and Practice, 8(15), 65-71.
Kavale, K. A., & Reese, J. H. (1992). The character of learning disabilities: An Iowa profile. Learning Disability Quarterly, 15(2), 74-94.