本研究旨在探討運用計算機輔助國小五年級學習障礙學生的小數位值概念教學之成效並提出建議。採用行動研究的方法，探討研究過程中運用計算機輔助數學教學所遇到的困境和解決策略、運用計算機對學生的學習數學成效。透過四位五年級學習障礙學生收集課程表現紀錄表、教學後省思紀錄表、師生對話紀錄表、教學錄影檔案、課程發展會議紀錄表、學生學習單、學生評量資料等多元相關資訊，進行資料整理與分析，並於研究過程中透過與研究參與者進行反省及修正，綜合歸納結論如下：

一、 運用計算機於小數位值概念教學提升學生的學習成效
（一） 認知：透過兩次的教學循環，發現計算機輔助了學生對於小數單位量的化聚理解，更提供更多時間來讓學生聚焦於驗證小數化聚規則。
（二） 技能：運用計算機更直接觀察到小數進行分解及合成的改變，也消除計算的困難度，快速提供回饋來提升學習效率。
（三） 態度：運用計算機於數學課堂可以提升學生的學習動機，從被動的學習數學概念轉變為主動完成更加深難度的練習，將教學重點鎖定在思考解題、邏輯推理能力培養、強化概念形成，進而提高國小學習障礙學生對學習數學的動機。
（四） 注意力：運用計算機於數學課堂可以維持學生學習的良好注意力。
（五） 主動與被動回答：運用計算機可以增加主動回答的次數，減少引導或發問等被動回答次數，也逐漸增加主動敘述與表達數學概念的能力。
最後，根據上述研究結論，提出對教育實務以及未來研究相關建議。

The purpose of this study was to investigate the effects and recommendations of action research on integrating calculators into mathematics teaching of decimals place value for the fifth graders with learning disabilities. And this study adopts action research to explore the dilemmas and solutions of the researcher’s integration of calculators into teaching, the effects on the students’ learning effectiveness in the research process. Through the collection of the teaching observation records, teaching reflection forms, teacher-student dialogue records, teaching films, curriculum development minutes, student worksheets, student assessment data and other related materials, the researcher uses them to organizes, summarize, analyze, and constantly revise on the process of teaching. The findings of the study are as the following:

1. Providing calculators for students improving three aspects of the teaching process:
(1) Cognitive Domain: It was found that students focus on understanding of the aggregation of fractional units, and verifying the aggregation of decimals.
(2) Psychomotor Domain: Using calculators can observe the changes in the decomposition and synthesis of decimals, also eliminate the calculational difficulties , and quickly giving feedback for students with learning disabilities.
(3) Affective Domain: Using calculators to improve learning motivation, change from passive learning to active, focus on thinking and solving problems, develop logical reasoning ability, strengthen concept formation.
(4) Attention: Using calculators can let students with learning disabilities concentrate on decimal learning.
(5) Active and passive replication: Using calculators can increase the number of active replication, reduce the number of passive replication such as guidance or questioning, and increase the ability to actively describe and express mathematical concepts.

Based on the conclusions, there some suggestions for educational practice and researchers in the future.

一、 中文部分
王培如（2018）。從數學能力與核心內涵面向探討國小三年級學生數單元數學感之表現。臺北市立大學數學系數學教育碩士班碩士論文，臺北市。取自https://hdl.handle.net/11296/3ac954
台灣精神醫學會（2015）。DSM-5精神疾病診斷準則手冊。新北市；合記圖書出版社。
艾如昀（1994）。國小學生處理小數的歷程與困難。國立中正大學心理研究所碩士論文，未出版，嘉義縣。
吳宜蓁、蕭伊倫（2015）。自我教導策略對國小中年級學習障礙學生在多位數乘法運算題的學習成效。雲嘉特教，21，36-44。
吳昭容（1996）。先前知識對國小學童小數概念學習之影響。國立台灣大學心理學研究所博士論文，未出版，台北。
呂美娟、施青豐、李玉錦譯（2002）。特殊教育課程與教學。臺北：學富。
杜建台（1996）。國小中高年級學童「小數概念」理解之研究。國立臺中師範學院國民教育研究所，未出版，臺中。
周筱亭（1990）。電子計算器對於國民小學小數運算學習之影響（1）。台北：台灣省國民教師研習會。
孟瑛如（2013）。資源教室方案－班級經營與補救教學（三版）。臺北市：五南。
孟瑛如（2013）。學習障礙與補救教學：教師及家長實用手冊。臺北市：五南。
孟瑛如、簡吟文（2014）。由DSM-5的改變談學習障礙未來的鑑定與教學輔導趨勢。輔導季刊，50，028-034。
孟瑛如、簡吟文、邱佳寧、陳虹君、周文聿（2015）。國民小學三至四年級數學診斷測驗（MDA/G3-4）。臺北市：心理。
孟瑛如、簡吟文、邱佳寧、陳虹君、周文聿（2015）。國民小學五至六年級數學診斷測驗（MDA/G5-6）。臺北市：心理。
林勇吉、楊德清（2002）。電算器教學活動幫助兒童學習數字常識能力之個案研究。科學教育研究與發展，30，1-26。
袁媛（2005）。計算機（Calculator）適合應用於國小數學的學習嗎？—談如何使用計算機作為兒童探討數概念的學習工具。載於莊淇銘（主編），國立臺北教育大學94年度地方教育輔導叢書—「傳承與變革」（頁213-218）。臺北市：國立臺北教育大學。
張鎮華（2015年，11月29日）。臺大數學系教授：中小學該用計算機教學。翻轉教育：親子天下X教與學的對話。取自：https://flipedu.parenting.com.tw/article/1805
張鎮華（2017）。適用計算機的教學單元（數學素養系列之1）。高中數學學科中心電子報，120。
教育部（1993）。國民小學課程標準。臺北：教育部。
教育部（2003）。國民中小學九年一貫課程綱要—數學學習領域。臺北市：教育部。
教育部（2008）。國民中小學九年一貫課程綱要—數學學習領域修訂版。臺北市：教育部。
教育部（2013）。身心障礙及資賦優異學生鑑定辦法（2013年9月2日）。
教育部（2014）。十二年國民基本教育課程綱要總綱。臺北市：教育部。
教育部（2018）。十二年國民基本教育課程綱要國民中小學暨普通型高級中等學校—數學領域。臺北市：教育部。
陳宜良（2005）。中小學數學科課程綱要評估與發展研究。取自http://libai.math.ncu.edu.tw/~shann/article/report_full.doc
陳界山（2017）。教學與評量的議題—計算機融入數學。臺北市：南一書局。
陳淑惠（譯）（1997）。如何幫助孩子克服隱性障礙。（原作者：Gordon Serfontein）。臺北市：新苗文化。
黃智瑛（2007）。臺灣與大陸現行小學數學課程綱要之比較研究。銘傳大學教育研究所碩士論文，未出版，臺北。
黃瑋𤧟（2018）。計算機融入國小五年級小數教學之行動研究：以學習障礙及輕度智能障礙學生為例。中原大學教育研究所碩士論文，未出版，桃園。
楊德清（2002）。從教學活動中幫助國小六年級學生發展數常識能力之研究。科學教育學刊，10（3），233-260。
溫世展、呂玉琴（2004）。影響國小教師數學教學相關信念與教學是否一致之原因探討。國立臺北師範學院學報，17，23-52。
劉曼麗（1996）。師院生的小數知識。論文將發表於84學年度數學教育研討會。國立嘉義師範學院。
劉曼麗（2003）。從小數符號的問題探討學生之小數概念。屏東師院學報，18，459¬494。
劉曼麗（2005）。小數診斷教學研究。科學教育學刊，13(1)，29¬52。
劉曼麗（2006）。我國學童小數概念發展之調查研究。科學教育學刊，14(6)，663¬693。
劉祥通（1994）。整合電子計算器於小學數學教育的探究。嘉義師院學報，8，61，313-336。
劉祥通，吳美蓉、翁宜青（2003）。電算器教學對小數大小比較之成效-國小六年級之個案研究。國民教育研究學報，10，251-280。
蔡清田（2011）。行動研究的理論與實踐。T&D飛訊，118，1-20。
翰林出版社（2017）。國民小學數學課本第七冊。臺北：翰林出版社。
翰林出版社（2017）。國民小學數學課本第九冊。臺北：翰林出版社。
翰林出版社（2017）。國民小學數學課本第八冊。臺北：翰林出版社。
翰林出版社（2017）。國民小學數學課本第十一冊。臺北：翰林出版社。
翰林出版社（2017）。國民小學數學課本第十二冊。臺北：翰林出版社。
翰林出版社（2017）。國民小學數學課本第十冊。臺北：翰林出版社。
翰林出版社（2017）。國民小學數學課本第六冊。臺北：翰林出版社。

二、 英文部分
American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorder-V (5th ed.). Washington, DC: Author.
Beaton, A. E., Mullis, V. S., Martin, M. O., Gonzalez, E. J., Kelly, D. L., & Smith, T. A. (1996). Mathematics achievement in the middle-school years: IEA’s Third International Mathematics and Science Study. Chestnut Hill, MA: TIMSS International Study Center, Boston College.
Bitter, G. G., & Hatfield, M. M. (1993). Integration of the math explorer calculator into the mathematics curriculum: The calculator project report. Journal of Computers in Mathematics and Science Teaching, 12(1), 59-81.
Black, L. M., & Shaver, L. B. (1988). A mathematics Framework approach to integrating calculators into elementary classes (Doctoral dissertation).
Carpenter, T. P., Corbitt, M. K., Kepner, H. S., Lindquist, M. M., & Reys, R. E. (1981). Decimals: Results and implications from national assessment. The Arithmetic Teacher, 28(8), 34-37.
Chien, C. (1998). Sixth grade students’ knowledge structure of decimals in Taiwan. Unpublished doctor dissertation, University of Georgia.
Common Core State Standards Initiative. (CCSSI) (2010). Introduction to the common core state standards. Washington, DC: Author. Retrieved from http://www.corestandards.org/ assets/ccssi-introduction.pdf
Ekenstam, A. A. (1977). On children's quantitative understanding of numbers. Educational Studies in Mathematics, 8(3), 317-332. doi: 10.1007/BF00385928
Ellington, A. J. (2003). A meta-analysis of the effects of calculators on students' achievement and attitude levels in precollege mathematics classes. Journal for Research in Mathematics Education, 34, 433–463.
Forster, P. A. (2006). Assessing technology-based approaches for teaching and learning mathematics. International Journal of Mathematics Education in Science and Technology, 37(2), 145-164.
Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37(1), 4-15. doi: 10.1177/00222194040370010201
Graham, T., Headlam, C., Honey, S., Sharp, J., & Smith, A. (2003). The use of graphics calculators by students in an examination: What do they really do? International Journal of Mathematics Education in Science and Technology, 34(3), 319-334.
Groves, S., Mousley, J., & Forgasz, H. (2006). A primary numeracy: a mapping review and analysis of Australian research in numeracy learning at the primary school level: report. Centre for Studies in Mathematics, Science and Environmental Education, Deakin University.
Hembree, R. & Dessart, D. J. (1992). Research on calculators in mathematics educations, In J. Fey and C. Hirsch (Eds.), Calculators in Mathematics Educations: National Council of Teachers of Mathematics 1992 yearbook (pp. 23-32). Reston, VA: National Council of Teachers of Mathematics.
Hiebert, J. (1992). Mathematical, cognitive, and instructional analyses of decimal fractions. In G. Leinhardt, R. Putnam, & R. A. Hattrup (Eds.), Analysis of arithmetic for mathematics teaching (pp. 283-322). Hillsdale, NJ: LEA.
Hiebert, J., & Wearne, D. (1983). Students’ conceptions of decimal numbers. Paper presented at the annual meeting of the American Educational Research Association, Montreal. (ERIC Document Reproduction Service No. Ed 230415).
Hiebert, J., & Wearne, D. (1988). Instruction and cognitive change in mathematics. Educational Psychologist, 23(2), 105-117.
Huinker, D. M. (1992). Decimals and calculators. Make sense! In J. T. Fey, Hirsch, C. R. (Ed.), Calculators in Mathematics Education: National Council of Teachers of Mathematics 1992 Yearbook (pp. 56-64). Reston, VA: National Council of Teachers of Mathematics. Reston, VA: National Council of Teachers of Mathematics.
Huinker, D. M. (2002). Calculators as learning tools for young children’s explorations of number. Teaching Children Mathematics, 8(6), 316-321.
Kutzler, B. (2000). The algebraic calculator as a pedagogical tool for teaching mathematics. International Journal for Computer Algebra in Mathematics Education, 7(1), 5-23.
Manly, M. (1997). Calculators in the ABE/GED classroom: Gift or curse? Adult Learning, 9(2), 16-17. doi: 10.1177/104515959800900210
Meel, D. E. (1997). Calculator-available assessment: The why, what and how. Educational Assessment, 4(3), 149-174.
Miller, S. P., & Mercer, C. D. (1997). Educational aspects of mathematics disabilities. Journal of Learning Disabilities, 30(1), 47-56. doi: 10.1177/002221949703000104
Moskal, B. M., & Magone, M. E. (2000). Making sense of what students know: Examining the referents, relationships and modes students displayed in response to a decimal task. Educational Studies in Mathematics, 43, 313-335.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (2000). The principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (2015). Strategic use of technology in teaching and learning mathematics: A position of the National Council of Teachers of Mathematics. Reston, VA: Author.
Reys, R. E., & Yang, D. C. (1998). Relationship between computational performance and number sense among sixth- and eighth-grade students in Taiwan. Journal for Research in Mathematics Education, 29(2), 225-237. doi: 10.2307/749900
Russell, R. L., & Ginsburg, H. P. (1984). Cognitive analysis of children's mathematics difficulties. Cognition and instruction, 1(2), 217-244.
Scheuneman, J. D., Camara, W. J., Cascallar, A. S., Wendler, C., & Lawrence, I. (2002). Calculator access, use, and type in relation to performance on the SAT I: Reasoning test in mathematics. Applied Measurement in Education, 15(1), 95-112.
Southwell, B. (1988). The use of calculators to develop reasoning processes and achievement in problem solving. Paper presented at the annual conference of the international group for the psychology of mathematics education, Veszprem, Hungary.
Sparrow, L., & Swan, P. (2005). Decimals, denominators, demons, calculators and connections. Australian Primary Mathematics Classroom, 10(3), 21-26.
Thipkong, S. (1988). Preservice elementary teachers’ misconception in interpreting units and solving multiplication and division decimal word problems. Unpublished doctoral dissertation, University of Georgia.
van Garderen, D., Scheuermann, A., & Jackson, C. (2013). Examining how students with diverse abilities use diagrams to solve mathematics word problems. Learning Disability Quarterly, 36(3), 145-160.
Walcott, C. & Stickles, P. R. (2012). Calculator use on NAEP: A look at fourth- and eighthgrade mathematics achievement. School Science and Mathematics, 112(4), 241-254
Williams, D. E. (1987). A Calculator-integrated Curriculum: The Time is Now. Arithmetic Teacher, 34(6), 8-9.
Wittrock, M. C. (1985). Learning science by generating new conceptions from old ideas. In L. H. T. West & A. L. Pines (Eds.), Cognitive structure and conceptual change (pp.259-266). New York : Academic Press.
Yeo, K. K. J. (2008).Exploring the use of calculators in the singapore’s primary mathematics curriculum. Electronic-Journal-Mathematics-Technology, 2(1), 73-83.
Zawojewski, J. (1983). Initical decimal concepts：Are they really so easy？ Arithemetic Theacher, 30(7), 52¬56.