我們真的認識數學障礙嗎？－臺灣數學障礙20年研究回顧與問題探究

Understanding Mathematics Learning Disabilities: Two Decades of Research in Taiwan

10.6172/BSE.201903_44(1).0003

王宣惠(Wang, Hsuan-Hui)；洪儷瑜(Hung, Li-Yu)

內容分析 ； 文獻回顧 ； 數學障礙 ； 學習障礙 ； Mathematics learning disabilities ； learning disabilities ； content analysis ； review

特殊教育研究學刊

44卷1期（2019 / 03 / 31）

59 - 90

繁體中文

數學能力影響個體日常生活與就業品質，亦為學習障礙者常見困難，但相較於閱讀障礙，數學障礙研究較少。本研究旨在了解臺灣數學障礙研究的樣貌，對照當代數學障礙定義與研究發現作為反思，主要回顧1995至2017年刊登於國內學術期刊之26篇數學障礙期刊論文以及14筆科技部研究，共計40筆數學障礙研究，進行內容分析。結果發現，臺灣數學障礙研究大致包括特質診斷與教學介入二主題，且以後者為多，顯示數學障礙學生的教學服務較受關注。整體而言，國內期刊論文實徵研究數量不多，且僅有少數能連結當代腦神經科學與核心缺陷之實證。在數學障礙概念的採用上，科技部研究與期刊論文之間有差距，科技部研究多反映出數學障礙定義的流變，但多數期刊論文仍採取差距標準。概念的差距反映出多數期刊論文對特質診斷的探究較忽略國際趨勢，研究對象可能與當代定義有差異而難以比對。此外，教學介入實徵證據少，且核心能力教學研究比率偏低。在八項科技部教學研究中，僅有一項探討基礎計算能力的教學；而在五篇實徵性期刊論文中，則主要探討資訊多媒體的應用、後設認知解題策略與圖示表徵策略對數學障礙學生文字題解題表現的效果。另外，國內期刊論文與科技部研究皆偏重文字題解題表現，且較缺乏語言歷程相關因素之區辨。本文根據上述發現，反思國內累積之實徵證據是否能提供教育工作者對數學障礙有完整的認識、引導出適合數學障礙學生的學習介入之探討，並據此對未來研究提出相關結論與建議。

Purposes: Mathematical ability influences quality of life and employment opportunities. Mathematics learning difficulties are common among people with learning disabilities. However, the field of mathematics disabilities is an area notably lacking in research in comparison to reading disabilities. The aim of this study was to delineate the contours of the research field of mathematics learning disabilities (MLD) in Taiwan. Methods: This study explored research in MLD from 1995 to 2017 in Taiwan, including 26 journal articles obtained from Google Scholar and the federated search system of the National Taiwan Normal University Library and 14 studies funded by the Ministry of Science and Technology (MOST). Through content analysis, the contemporary definitions and research findings related to mathematics learning disabilities were concluded which provided the framework of the study. Results/Findings: According to the results, features or diagnosis and interventions were the two primary topics concerning MLD. The number of intervention studies was relatively higher than that of features- or diagnosis-related studies, indicating that intervention received more attention in the field. However, evidence-based research was limited, and studies using contemporary evidence related to neuropsychology or cognitive deficit were even rarer. The evolution of and changes to the concept of MLD could be found in research funded by MOST, but not in journal articles, thus indicating a research-publication gap. The gap indicated that concepts of MLD in most journal articles neglected international definition and research trends, which meant that research participants could be various. Therefore, the results of local studies might be difficult to compare with the contemporary international literatures. In intervention research, the evidence of effect instruction was limited. Specific intervention explorations were limited and basic mathematical abilities were neglected in intervention studies. In the eight MOST intervention studies, only one investigated basic calculation instruction; in the five empirical journal articles, investigation mainly addressed the solving of mathematics word problems with the application of computer science multimedia, metacognitive strategies, and schematic representation strategies. In addition, students' performance of mathematics word problems was the main focus in journal articles and in the research funded by MOST. However, relevant language-processing factors received insufficient recognition and clarification. Conclusions/Implications: Reflections on the contrast between the aforementioned findings and international MLD trends may inform regarding the comprehensiveness of MLD understanding in Taiwan and regarding the appropriateness of interventions used. Finally, to benefit future studies, numerous conclusions and suggestions concerning MLD were specified based on the findings of the study.

1. 王瓊珠, Chiung-Chu(2012)。台灣中文字詞教學研究之文獻回顧與展望。教育心理學報，44(2)，253-272。
   連結：
2. 江美娟, Mei-Chua,周台傑, Tair-Jye(2003)。後設認知策略教學對國小數學學習障礙學生解題成效之研究。特殊教育學報，18，107-151。
   連結：
3. 吳雅琪, Ya-Chi,孟瑛如, Ying-Ru(2005)。資訊融入解題策略教學對國小數學學習障礙學生乘除法文字題解題成效之研究。特殊教育學報，21，103-128。
   連結：
4. 柯華葳, Hwawei(2005)。數學學習障礙學生的診斷與確認。特殊教育研究學，29，113-126。
   連結：
5. 袁媛, Yuan,王淑芬, Shu-Fen,陳國龍, Kuo-Long(2016)。國小二年級學生在數值線段上的數字估計能力與數學學習成就之相關研究。臺灣數學教育期刊，3(1)，1-18。
   連結：
6. 梁明華, Ming-Hua(2009)。電腦輔助教學在學習障礙學生數學解題的應用之探討。國小特殊教育，48，41-51。
   連結：
7. 連文宏, Wen-Hung,洪儷瑜, Li-Yu(2017)。數學學障與數學合併閱讀障礙國中生計算能力表現之特徵及其差異分析。臺灣數學教育期刊，4(1)，35-62。
   連結：
8. Algozzine, B.,O'shea, D. J.,Crews, W. B.,Stoddard, K.(1987).Analysis of mathematics competence of learning disabled adolescents.Journal of Special Education,21,97-107.
9. American Psychiatric Association(1994).Diagnostic and statistical manual for psychiatric disorders.Washington, DC:Author.
10. American Psychiatric Association(1987).Diagnostic and statistical manual of mental health disorders.Washington, DC:Author.
11. Anderson, U.(2008).Mathematical competence in children with different types of learning difficulties.Journal of Educational Psychology,100(1),48-66.
12. Baker, S.,Gersten, R.,Lee, D. S.(2002).A synthesis of empirical research on teaching mathematics to low-achieving students.The Elementary School Journal,103(1),51-73.
13. Barbaresi, W. J.,Katusic, S. K.,Colligan, R. C.,Weaver, A. L.,Jacobsen, S. J.(2005).Math learning disorder: Incidence in a population-based birth cohort, 1976-82, Rochester, Minn.Ambulatory Pediatrics,5(5),281-289.
14. Brown, J. S.,Burton, R. R.(1978).Diagnostic models for procedural bugs in basic mathematical skills.Cognitive Science,2(2),155-192.
15. Butterworth, B.,Varma, S.,Laurillard, D.(2011).Dyscalculia: From brain to education.Science,332,1049-1053.
16. Cantlon, J. F.,Brannon, E. M.,Carter, E. J.,Pelphrey, K. A.(2006).Functional imaging of numerical processing in adults and 4-y-old children.PLoS Biology,4(5),844-854.
17. 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,13,68-74.
18. Dehaene, S.,Cohen, L.(1997).Cerebral pathways for calculation: Double dissociation between rote verbal and quantitative knowledge of arithmetic.Cortex,33(2),219-250.
19. Dehaene, S.,Piazza, M.,Pinel, P.,Cohen, L.(2003).Three parietal circuits for number processing.Cognitive Neuropsychology,20(3-6),487-506.
20. Dehaene, S.,Spelke, E.,Pinel, P.,Stanescu, R.,Tsivkin, S.(1999).Sources of mathematical thinking: Behavioral and brain-imaging evidence.Science,284(5416),970-974.
21. Eva, K. W.(2008).On the limits of systematicity.Medical Education,42(9),852-853.
22. Fleischner, J. E.,Garnett, K.,Shepherd, M. J.(1982).Proficiency in basic fact computation of learning disabled and nondisabled children.Focus on Learning Problems in Mathematics,4,47-55.
23. Fletcher, J.(2005).Predicting math outcomes: Reading predictors and comorbidity.Journal of Learning Disabilities,38,308-312.
24. Fuchs, L. S.,Compton, D. L.,Fuchs, D.,Paulsen, K.,Bryant, J. D.,Hamlett, C. L.(2005).The prevention, identification, and cognitive determinants of math difficulty.Journal of Educational Psychology,97(3),493-513.
25. Fuchs, L. S.,Fuchs, D.,Compton, D. L.,Powell, S. R.,Seethaler, P. M.,Capizzi, A. M(2006).The cognitive correlates of third-grade skill in arithmetic, algorithmic computation, and arithmetic word problems.Journal of Educational Psychology,98(1),29-43.
26. Fuchs, L. S.,Fuchs, D.,Powell, S. R.,Seethaler, P. M.,Cirino, P. T.,Fletcher, J. M.(2008).Intensive intervention for students with mathematics disabilities: Seven principles of effective practice.Learning Disability Quarterly,31(2),79-92.
27. Fuchs, L. S.,Fuchs, D.,Stuebing, K.,Fletcher, J. M.,Hamlett, C. L.,Lambert, W.(2008).Problem solving and computational skill: Are they shared or distinct aspects of mathematical cognition?.Journal of Educational Psychology,100(1),30-47.
28. Geary, D. C.(2004).Mathematics and learning disabilities.Journal of Learning Disabilities,37,4-15.
29. Geary, D. C.(1993).Mathematical disabilities: Cognitive, neuropsychological, and genetic components.Psychological Bulletin,114(2),345-362.
30. Geary, D. C.(1990).A componential analysis of an early learning deficit in mathematics.Journal of Experimental Child Psychology,49(3),363-383.
31. Geary, D. C.,Bow-Thomas, C. C.,Yao, Y.(1992).Counting knowledge and skill in cognitive addition: A comparison of normal and mathematically disabled children.Journal of Experimental Child Psychology,54(3),372-391.
32. Geary, D. C.,Hoard, M. K.,Byrd-Craven, J.,DeSoto, M. C.(2004).Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability.Journal of Experimental child Psychology,88(2),121-151.
33. Gersten, R.,Chard, D. J.,Jayanthi, M.,Baker, S. K.,Morphy, P.,Flojo, J.(2009).Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components.Review of Educational Research,79(3),1202-1242.
34. Hulme, C.,Snowling, M. J.(2009).Developmental disorders of language learning and cognition.Chichester, West Sussex:John Wiley & Sons.
35. Jordan, N. C.,Hanich, L. B.,Kaplan, D.(2003).A longitudinal study of mathematical competencies in children with specific mathematics difficulties versus children with comorbid mathematics and reading difficulties.Child Development,74(3),834-850.
36. Kavale, K. A.,Reece, J. H.(1992).The character of learning disabilities.Learning Disability Quarterly,15,74-94.
37. Kroesbergen, E. H.,Van Luit, J. E.(2003).Mathematics interventions for children with special educational needs: A meta-analysis.Remedial and Special Education,24(2),97-114.
38. Kucian, K.,Grond, U.,Rotzer, S.,Henzi, B.,Schönmann, C.,Plangger, F.(2011).Mental number line training in children with developmental dyscalculia.Neuroimage,57(3),782-795.
39. Kucian, K.,von Aster, M.(2015).Developmental dyscalculia.European Journal of Pediatrics,174(1),1-13.
40. LeFevre, J.-A.,Smith-Chant, B. L.,Fast, L.,Skwarchuk, S.-L.,Sargla, E.,Arnup, J. S.(2006).What counts as knowing? The development of conceptual and procedural knowledge of counting from kindergarten through Grade 2.Journal of Experimental Child Psychology,93,285-303.
41. Lerner, J.,Johns, B.(2009).Learning disabilities and related mild disabilities.Boston, MA:Houghton Mifflin.
42. National Council of Teacher of Mathematics(2000).Principles and standards for school mathematics.Reston, VA:Author.
43. Organisation Economic aand Co-operation Development(2010).Organisation Economic aand Co-operation Development. (2010). The high cost of low educational performance: The longrun economic impact of improving PISA outcomes. Retrieved from http://www.oecd.org/pisa/44417824.pdf.
44. Piazza, M.,Mechelli, A.,Butterworth, B.,Price, C. J.(2002).Are subitizing and counting implemented as separate or functionally overlapping processes?.Neuroimage,15(2),435-446.
45. Piazza, M.,Pinel, P.,LeBihan, D.,Dehaene, S.(2007).A magnitude code common to numerosities and number symbols in human intraparietal cortex.Neuron,53(2),293-305.
46. Pinel, P.,Dehaene, S.,Rivière, D.,LeBihan, D.(2001).Modulation of parietal activation by semantic distance in a number comparison task.Neuroimage,14(5),1013-1026.
47. Simon, O.,Mangin, J. F.,Cohen, L.,Le Bihan, D.,Dehaene, S.(2002).Topographical layout of hand, eye, calculation, and language-related areas in the human parietal lobe.Neuron,33(3),475-487.
48. Swanson, H. L.(2006).Cross-sectional and incremental changes in working memory and mathematical problem solving.Journal of Educational Psychology,98,265-281.
49. Swanson, H. L.,Beebe-Frankenberger, M.(2004).The relationshipbetween working memory and mathematical problem-solving in children at risk and not at risk for serious math difficulties.Journal of Educational Psychology,96,471-491.
50. Swanson, H. LR.(Ed.),Harris, K. R.(Ed.),Graham, S.(Ed.)(2013).Handbook of learning disabilities.New York, NY:Guilford Press.
51. Xin, Y. P.,Jitendra, A. K.(1999).The effects of instruction in solving mathematical word problems for students with learning problems: A meta-analysis.The Journal of Special Education,32(4),207-225.
52. Zheng, X.,Flynn, L. J.,Swanson, H. L.(2013).Experimental intervention studies on word problem solving and math disabilities: A selective analysis of the literature.Learning Disability Quarterly,36(2),97-111.
53. Zorzi, M.,Priftis, K.,Umiltà, C.(2002).Brain damage: Neglect disrupts the mental number line.Nature,417(6885),138-139.
54. 王淑惠, Shu-Hui(2008)。淺談數學學障學生的教學。雲嘉特教，7，36-41。
55. 王淑惠, Shu-Hui(2013)。國小數學學習障礙學生的教學策略。雲嘉特教，18，28-34。
56. 王雪瑜, Hsueh-Yu(2006)。國小數學學障兒童數學解題錯誤類型分析之探討。特殊教育現在與未來，臺中=Taichung, Taiwan:
57. 王瓊珠（編）, C. C.(ed.),陳淑麗（編）, S. L.(ed.)(2010).突破閱讀困難：理念與實務.臺北=Taipei, Taiwan:心理=Psychological.
58. 王瓊珠, Chiung-Chu(2018).學習障礙：理念與實務.臺北=Taipei, Taiwan:心理=Psychological.
59. 王瓊珠, Chiung-Chu(2005)。閱讀障礙學生識字教學研究回顧與問題探究。突破學習困難——評量與因應之探討，臺北=Taipei, Taiwan:
60. 朱淳琦, Chun-Chi(2011)。電腦化圖示策略在數學學習障礙學生數學解題教學上的運用。特殊教育現在與未來，臺中=Taichung, Taiwan:
61. 朱經明, Jing-Ming(2006)。行政院國家科學委員會專題研究計畫成果報告行政院國家科學委員會專題研究計畫成果報告,Taichung, Taiwan:Asia University, Department of Psychology。
62. 朱經明, Jing-Ming(2000)。行政院國家科學委員會專題研究計畫成果報告行政院國家科學委員會專題研究計畫成果報告,Taichung, Taiwan:Taichung Teachers College, Department of Special Education。
63. 朱經明, Jing-Ming(2011)。行政院國家科學委員會專題研究計畫成果報告行政院國家科學委員會專題研究計畫成果報告,Taichung, Taiwan:Asia University, Department of Early Childhood Education。
64. 朱經明, Jing-Ming(2005)。行政院國家科學委員會專題研究計畫成果報告行政院國家科學委員會專題研究計畫成果報告,Taichung, Taiwan:Taichung Healthcare and Management University, Department of Psychology。
65. 朱經明, Jing-Ming,蔡玉瑟, Yu-Ser(2000)。動態評量在診斷國小五年級數學障礙學生錯誤類型之應用成效。特殊教育研究學刊，18，173-188。
66. 何東墀, Dong-Chyr(1995)。行政院國家科學委員會專題研究計畫成果報告行政院國家科學委員會專題研究計畫成果報告,Changhua, Taiwan:National Changhua University of Education, Department of Special Education.。
67. 吳嫻, Hsien(2009)。行政院國家科學委員會專題研究計畫成果報告行政院國家科學委員會專題研究計畫成果報告,Toayuan, Taiwan:National Central University, Institute of Cognitive Neuroscience。
68. 呂佩真, Pei-Chen,黃秋霞, Chiu-Hsia,詹士宜, Shi-Yi(2015)。錨式情境教學對學習障礙學生的數學文字題解題的學習成效。中華民國特殊教育學會年刊，2015，135-156。
69. 李秀妃, Hsiu-Fei(2010)。學習障礙學童的數學學習困難～時間篇。台東特教，31，38-42。
70. 李佳穎, Chia-Ying(2009)。中文識字的認知與神經基礎。基礎教育學報，18(2)，63-85。
71. 李俊仁, Jun-Ren(2009)。行政院國家科學委員會專題研究計畫成果報告行政院國家科學委員會專題研究計畫成果報告,Taipei, Taiwan:National Taiwan Normal University, Department of Educational Psychology and Counseling。
72. 李俊仁, Jun-Ren(2017)。數學計算障礙的認知分析。突破數學學習困難：理論與實務，臺北=Taipei, Taiwan:
73. 李源順, Yuan-Shun(2012)。行政院國家科學委員會專題研究計畫成果報告行政院國家科學委員會專題研究計畫成果報告,Taipei, Taiwan:University of Taipei, Department of Mathematics and Computer Science Education。
74. 周台傑, Tair-Jye(1997)。行政院國家科學委員會專題研究計畫成果報告行政院國家科學委員會專題研究計畫成果報告,Changhua, Taiwan:National Changhua University of Education, Department of Special Education.。
75. 周台傑, Tair-Jye,詹士宜, Shi-Yi(1993)。國中智能不足學生數學應用問題解題歷程研究。特殊教育與復健學報，3，179-215。
76. 周台傑, Tair-Jye,蔡宗玫, Chung-Mei(1997)。國小數學學習障礙學生應用問題解題之研究。特殊教育學報，12，233-262。
77. 孟令夫, Ling-Fu(2009)。行政院國家科學委員會專題研究計畫成果報告行政院國家科學委員會專題研究計畫成果報告,Taoyuan, Taiwan:Chang Gung University, Department of Occupational Therapy。
78. 孟瑛如, Ying-Ru,吳東光, Tung-Kuang(1999)。數學學習障礙與多媒體教材之發展應用。特殊教育季刊，72，13-18。
79. 林玉華, Yu-Hwa(1995)。淺談數學學習障礙兒童之診斷與輔導。中縣文教，22，50-53。
80. 洪儷瑜, Li-Yu(2011)。行政院國家科學委員會專題研究計畫成果報告行政院國家科學委員會專題研究計畫成果報告,Taipei, Taiwan:National Taiwan Normal University, Department of Special Education。
81. 洪儷瑜, Li-Yu(2006)。學障教育在台灣的第一個三十年——回顧與展望。特殊教育季刊，100，3-15。
82. 洪儷瑜, Li-Yu(2009)。行政院國家科學委員會專題研究計畫成果報告行政院國家科學委員會專題研究計畫成果報告,Taipei, Taiwan:National Taiwan Normal University, Department of Special Education。
83. 洪儷瑜, Li-Yu(2014)。行政院國家科學委員會專題研究計畫成果報告行政院國家科學委員會專題研究計畫成果報告,Taipei, Taiwan:National Taiwan Normal University, Department of Special Education。
84. 洪儷瑜, Li-Yu,連文宏, Wen-Hung(2017)。數學學習障礙學生的鑑定。突破數學學習困難：理論與實務，臺北=Taipei, Taiwan:
85. 胡永崇, Yeong-Chrong(2007)。學習障礙學生的時間與日期之教學。屏師特殊教育，15，27-34。
86. 秦麗花, Li-Hua(2006)。從數學閱讀特殊技能看兒童數學閱讀的困難與突破。特殊教育季刊，99，1-12。
87. 張羚羚, Ling-Lin,林惠秋, Hui-Chiu(2011)。問題中心雙環教學模式在國中數學學習障礙教學之應用。桃竹區特殊教育，18，15-27。
88. 梁瑞真, Ruei-Chen(2004)。讓學生學好應用問題─數學學習障礙兒童的補救教學。特教通訊，32，65-69。
89. 連文宏, Wen-Hung(2018)。臺北市=Taipei, Taiwan，國立臺灣師範大學=National Taiwan Normal University。
90. 郭靜姿, Ching-Chigh,許慧如, Hui-Ju,劉貞宜, Chen-Y,張馨仁, Hsin-Jen,范成芳, Chen-Fang(2001)。數學學習障礙之鑑定工具發展與應用研究。特殊教育研究學刊，21，135-163。
91. 陳映雯, Ying-Wen(2007)。數學學習障礙學生時間化聚解題與教學策略。屏師特殊教育，14，1-9。
92. 黃秋霞, Chiu-Hsia,方美珍, Mei-Chen(2007)。圖示表徵解題策略對國小學習障礙學生數學文字題學習成效之研究。中華民國特殊教育學會年刊，2007，257-278。
93. 黃慈愛, Tzu-Ai(1997)。閱讀障礙兒童與數學學障兒童在數字記憶廣度數學心算能力上與普通兒童之比較。特殊教育學報，12，293-319。
94. 黃瑋苓, Wei-Ling(2006)。淺談數學學習障礙。台東特教，23，48-53。
95. 楊憲明, Hsien-Ming(2002)。行政院國家科學委員會專題研究計畫成果報告行政院國家科學委員會專題研究計畫成果報告,Tainan, Taiwan:National Tainan Teachers College, Department of Special Education.。
96. 楊憲明, Hsien-Ming(2000)。行政院國家科學委員會專題研究計畫成果報告行政院國家科學委員會專題研究計畫成果報告,Tainan, Taiwan:National Tainan Teachers College, Department of Special Education.。
97. 臺灣精神醫學會（譯）,American Psychiatric Association(2014).DSM-5精神疾病診斷準則手冊.新北=New Taipei, Taiwan:合記=Ho-Chi.
98. 蔡翠華, Tsui-Hua(1996)。國小數學學習障礙學生的學習型態與學習策略之相關研究。特殊教育研究學刊，14，157-177。
99. 蕭美玲, Mei-Ling,陳香吟, Hsiang-Yin(2005)。淺談數學學習障礙學生的數學解題。屏師特殊教育，11，20-30。

1. 彭慧雯,佘永吉(2021)。互動式電子白板融入國小學習障礙學生數學教學與直接教學法之成效比較。特殊教育季刊，160，15-26。
2. 楊哲宇,王瓊珠(2021)。替換式數學對增進國小數學學習困難學生在除法計算與文字解題之成效。特殊教育學報，53，1-29。
3. (2023)。數學學習困難學生與非數學學習困難學生分數數值比較能力之差異與具體－表徵－抽象策略之教學成效。特殊教育學報，58，33-84。