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題名：數學障礙學生數學概念理解、數學推理能力與數學解題表現之關係分析研究
書刊名：特殊教育與復健學報
作者：趙旼冠／楊憲明 引用關係
作者(外文)：Chao, Min-kuan／Yang, Hsien-ming
出版日期：2006
卷期：16
頁次：頁73-97
主題關鍵詞：數學障礙；數學概念理解；數學推理；數學解題；Mathematical disabilities；Mathematical-concept understanding；Mathematical reasoning；Mathematical problem solving
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  • 被引用次數被引用次數:期刊(3) 博士論文(0) 專書(0) 專書論文(0)
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  • 共同引用共同引用:34
  • 點閱點閱:54
本研究的主要目的在於探討影響數學障礙學生數學概念理解、數學推理能力及數學解題表現之因素。 本研究以高雄市五所國小一年級學生為篩選對象，篩選出非閱讀缺陷／數學障礙學生27人，閱讀缺陷／數學障礙學生27人及一般學生29人，共計83名受試者。所有受試者均接受數學概念理解測驗、數學推理測驗、數學解題測驗及國民小學一二年級閱讀理解測驗等四項測驗。所得之測驗結果以描述統計及多元迴歸分析等統計方法加以分析考驗。 研究結果顯示： 一、閱讀理解能力是數學概念理解能力發展的主要影響因素。 二、不同數學成就學生之數學推理能力，分別受智力、閱讀理解能力和數學概念理解能力的影響。 三、不同數學成就學生之數學解題表現，分別受閱讀理解能力、數學概念理解能力和數學推理能力的影響。 根據以上研究結果，本研究提出：閱讀理解能力、數學概念理解能力和數學推理能力，對於不同亞型數學障礙學生的解題能力有不同的影響力。因此，建議教師在提升閱讀缺陷／數學障礙學生的解題能力時，應優先注意其閱讀理解能力；非閱讀缺陷／數學障礙學生則需注意其數學概念理解能力；一般學生則需注意其數學推理能力。
The purpose of this study was to explore the factors which influence the performance of students with mathematical disabilities (MD) in mathematical-concept understanding, mathematical reasoning, and mathematical problem solving. The eighty three subjects were selected from first graders in five elementary schools in Kaohsiung City, composed of twenty seven students with disabilities in mathematics only (MD-only), twenty seven students with disabilities both in mathematics and reading (MD/RD), and twenty nine normal students (NS). All students took four tests tapped on mathematical-concept understanding, mathematical reasoning, mathematical problem solving, and reading comprehension for first and second grade students. The results were obtained with the multiple regression analysis and path analysis. The main findings were summarized as follows: 1. The ability of reading comprehension is the main factor influencing the development of mathematical-concept understanding. 2. The performance of mathematical reasoning of students with different level of mathematical achievement is affected by intelligence, reading comprehension, and mathematical-concept understanding. 3. The performance of mathematical problem solving of students with different level of mathematical achievement is affected by the abilities of reading comprehension, mathematical-concept understanding, and mathematical reasoning. The results of the study suggested that reading comprehension, mathematical-concept understanding, and mathematical reasoning are contributed differentially to the performance of different subtypes of mathematical disabled students. It was implied for mathematical teaching that reading comprehension, mathematical-concept understanding, and mathematical reasoning should be emphasized to improve respectively for students with ME-RD, students with MD only, and for normal students during mathematical instruction.
Other
1.Ginsburg, H. P.(1997)。Mathematics learning disabilities: A view from developmental psychology。  new window
期刊論文
1.Geary, D. C.(2004)。Mathematics and Learning Disabilities。Journal of Learning Disabilities，37(1)，4-15。  new window
2.Hanich, L. B.、Jordan, N. C.、Kaplan, D.、Dick, J.(2001)。Performance across different areas of mathematical cognition in children with learning difficulties。Journal of Educational Psychology，93(3)，615-626。  new window
3.Wilson, K. M.、Swanson, H. L.(2001)。Are mathematics disabilities due to a domain-general or a domain-specific working memory deficit?。Journal of Learning Disabilities，34(2)，237-248。  new window
4.Doerr, H. M.、English, L. D.(2003)。A Modeling perspective on students’ mathematical reasoning about data。Journal of Research in Mathematics Education，34(2)，110-136。  new window
5.Montague, M.、Applegate, B.(1993)。Middle school students' mathematical problem solving: An analysis of think-loud protocols。Learning Disability Quarterly，16(1)，19-30。  new window
6.Robinson, C. S.、Menchetti, B. M.、Torgesen, J. K.(2002)。Toward a two-factor theory of one type of mathematics disabilities。Learning Disabilities Research and Practice，17(2)，81-89。  new window
7.Bull, R.、Johnston, R. S.(1997)。Children's arithmetical difficulties: Contributions from processing speed, item identification, and short-term memory。Journal of Experimental Child Psychology，65，1-24。  new window
8.Passolunghi, M. C.、Siegel, L. S.(2001)。Short term memory, working memory and inhibitory control in children with difficulties in arithmetic problem solving。Journal of Experimental Child Psychology，80，44-57。  new window
9.Mercer, C. D.、Miller, S. P.(1992)。Teaching students with learning problems in math to acquire, understand, and apply basic math facts。Remedial and Special Education，13(3)，19-35+61。  new window
10.朱經明、蔡玉瑟(20000600)。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，18，173-189。new window  延伸查詢new window
11.Geary, D. C.、Hoard, M. K.、Hamson, C. O.(1999)。Numerical and arithmetical cognition: Patterns of functions and deficits in children at risk for a mathematical disability。Journal of Experimental Child Psychology，74，213-239。  new window
12.Jordan, N. C.、Hanich, L. B.(2000)。Mathematical thinking in second-grade children with different forms of LD。Journal of Learning Disabilities，33(6)，567-578。  new window
13.Jordan, N. C.、Montani, T. O.(1997)。Cognitive arithmetic and problem solving: A comparison of children with specific and general mathematics difficulties。Journal of Learning Disabilities，30(6)，624-634。  new window
14.秦麗花(19950600)。國小數學學障兒童數學解題錯誤類型分析。特殊教育季刊，55，33-38。new window  延伸查詢new window
15.Siegel, Linda S.、Ryan, E. B.(1989)。The Development of Working Memory in Normally Achieving and Subtypes of Learning Disabled Children。Child Development，60(4)，973-980。  new window
16.Montague, M.(1997)。Cognitive strategy instruction in mathematics for students with learning disabilities。Journal of Learning Disabilities，30(2)，164-177。  new window
學位論文
1.陳標松(2003)。國小六年級數學學習困難學生因數倍數問題解題之研究(碩士論文)。彰化師範大學。  延伸查詢new window
2.蔣大偉(2001)。由工作記憶角度探討數學障礙兒童的表現(碩士論文)。國立中正大學，嘉義縣。  延伸查詢new window
3.張宗育(2003)。國小六年級數學學習困難學生時間化聚問題解題之研究(碩士論文)。國立彰化師範大學。  延伸查詢new window
4.林淑玲(1999)。國小數學學習障礙學生對比較類加減應用題解題表徵之研究(碩士論文)。國立臺灣師範大學。  延伸查詢new window
5.黃淑君(2003)。國小學童聽覺理解能力與閱讀理解能力之相關研究(碩士論文)。臺中師範學院，臺中市。  延伸查詢new window
6.林秀柔(1989)。國小數學學習障礙兒童鑑定方式之研究(碩士論文)。國立彰化師範大學。  延伸查詢new window
7.秦麗花(1994)。國小數學學習障礙兒童數學解題補救教學實施成效之比較研究(碩士論文)。國立台南師範學院。  延伸查詢new window
8.邱佳寧(2001)。國小數學學習障礙學生解題策略之研究(碩士論文)。國立彰化師範大學。  延伸查詢new window
圖書
1.教育部(2003)。國民中學九年一貫課程綱要--數學學習領域。臺北市：教育部。  延伸查詢new window
2.Polya, G.(1981)。Mathematical discovery: on understanding, learning, and teaching problem solving。New York：John Wiley & Sons。  new window
3.Van de Walle, John A.、張英傑、周菊美(2005)。中小學數學科教材教法。五南圖書出版股份有限公司。  延伸查詢new window
4.Polya, G.(1985)。How to solve it: A new aspect of mathematical method。Princeton, NJ：Princeton University Press。  new window
5.Lerner, J. W.(2003)。Learning disabilities: Theories, diagnosis, and teaching strategies。New York：Houghton Mifflin Company。  new window
6.Skemp, Richard R.、陳澤民(1995)。數學學習心理學。臺北市：九章。  延伸查詢new window
7.Polya, G.(1968)。Mathematics and plausible reasoning。Princeton, NJ：Princeton University Press。  new window
其他
1.孔繁鐘(2002)。精神疾病的診斷與統計。  延伸查詢new window
2.王瑋樺(2001)。國小三年級數學學習障礙學生加法文字題解題歷程與補救教學之研究。  延伸查詢new window
3.林穎義(2002)。從資源班教師觀點進行數學學障生教育診斷之研究。  延伸查詢new window
4.俞筱鈞(1995)。瑞文氏圖形推理測驗系列指導手冊。  延伸查詢new window
5.陳瓊瑜(2002)。國小三年級數學學習困難學生乘法應用問題解題歷程之研究。  延伸查詢new window
6.喻平(2002)。論數學解題教學的現代理論基礎。  延伸查詢new window
7.甯自強(1992)。正整數概念的啟蒙。  延伸查詢new window
8.趙振威(2001)。怎樣學好數學。  延伸查詢new window
9.Badian, N. A.(1983)。Dyscalculia and nonverbal disorders of learning。  new window
10.Englert, C. S., Culatta, B. E., & Horn, D. G.(1987)。Influence of irrelevant information in addition word problems on problem solving。  new window
11.Feagans, L., & McKinney, J. D.(1981)。The pattern of exceptionality across domains in learning disabled children。  new window
12.Fleischner, J. E., & Frank, B.(1979)。Visual-spatial ability and mathematics achievement in learning disabled and normal boys。  new window
13.Geary, D. C.(1993)。Mathematical disabilities: Cognitive, neuropsychological and genetic components。  new window
14.Geary, D. C. & Brown, S. C.(1991)。Cognitive addition: strategy choice and speed-of-processing difference in gifted, normal, and mathematically disabled children。  new window
15.Goldman, S.(1989)。Strategy instruction in mathematics。  new window
16.Gordon, N.(1992)。Children with developmental dyscalculia。  new window
17.Gross, J.(1993)。Special education needs in the primary school: Apractical guide。  new window
18.Hitch, G. J., & McAuley, E.(1991)。Working memory in children with specifc arithmetical learning difficulties。  new window
19.Holzman, T. G., Pellegrino, J. W., & Glaser, R.(1982)。Cognitive dimensions of numerical rule induction。  new window
20.Hulme, C., & Rooden rys, S.(1995)。Verbal working memory development and its disorders。  new window
21.Johan, L.(2000)。Mathematical reasoning in task solving。  new window
22.Kosc, L.(1974)。Developmental dyscalculia。  new window
23.Kosc, L.(1981)。Neuropsychological implications of diagnosis and treatment of mathematical learning disabilities。  new window
24.Linda, P.(1999)。Supporting mathematical development in the early years。  new window
25.Little, T. D., & Widaman, K. F.(1995)。A production task evaluation of individual differences in the development of mental addition skills: Internal and external validation of chronometric models。  new window
26.McLean, J. F., & Hitch, G. J.(1999)。Working memory impairments in children with specific arithmetic learning difficulties。  new window
27.Montis, K. K.(2000)。Language development and concept flexibility in dyscalculia: a case study。  new window
28.Norman, C. A., & Zigmond, N.(1980)。Characteristics of children labeled and served as learning disabled in school systems affiliated with child service demonstration centers。  new window
29.Parmar, R. S., Cawley, J. F., & Frazita, R. R.(1996)。Word problem-solving by students with and without mild disabilities。  new window
30.Silver, C. H., Pennett, Deborah-Lynne H., Black, J. L., Fair, G. W., & Balise, R. R.(1999)。Stability of arithmetic disability subtypes。  new window
31.Swanson, H. L.(1993)。Working memory in learning disability subgroups。  new window
圖書論文
1.Riley, M. S.、Greeno, J. G.、Heller, J. I.(1983)。Development of children's problem-solving ability in arithmetic。The development of mathematical thinking。Academic Press。  new window
 
 
 
 
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