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http://dx.doi.org/10.7468/jksmed.2011.15.4.357

Analyzing Errors Made by Eighth-Grade Students in Solving Geometrical Problems  

Huang, Xingfeng (Department of Mathematics, Changshu Institute of Technology)
Cheng, Longhai (Faculty of Science, Ningbo University)
Publication Information
Research in Mathematical Education / v.15, no.4, 2011 , pp. 357-371 More about this Journal
Abstract
In mathematical problem solving, students may make various errors. In order to draw useful lessons from the errors, and then correct them, we surveyed 24 eighth-grade students' performances in geometrical problem solving according to Casey's hierarchy of errors. It was found that: 1. Students' effect can lead to errors at the stage of "comprehension", "strategy selection", and "skills manipulation"; and 2. Students' geometric schemas also influenced their strategy selection".
Keywords
geometrical problem solving; motivation; beliefs; schemas;
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1 Ames, C. & Ames, R. (1984). Systems of student and teacher motivation: Toward a qualitative definition. Journal of Educational Psychology 76 (4), 535-558. EJ306048   DOI
2 Berlyne, D. E. (1966). Curiosity and the quest for information. Voprosy Psikhologill 3, 54-61.
3 Bregman, N, J. & McAllister, H. A. (1982). Motivation and skin temperature biofeedback: Yerkes-Dodson revisited. Psychophysiology 19(3), 282-285.   DOI   ScienceOn
4 Buchanan, N. K. (1987). Factors contributing to mathematical problem-solving performance: An exploratory study. Educ. Stud. Math. 18(3), 399-415. ME 1988x.00083   DOI
5 Chinnappan, M. (1998). Schemas and mental models in geometry problem. Educ. Stud. Math. 36(3), 201-217. ME1999c.01417 ERIC EJ590267   DOI   ScienceOn
6 Casey, D. P. (1978). Failing students: A strategy of error analysis. In: P. Costello (Ed.), Aspects of motivation (pp. 295-306). Melbourne: Mathematical Association of Victoria.
7 Clarkson, P. C. (1991). Language comprehension errors: A further investigation. Mathematics Education Research Journal 3(2), 24-33. ME 1994c.00942 ERIC EJ464661   DOI
8 Clements, M. A. (1980). Analyzing children's errors on written mathematical tasks. Educational studies in mathematics 11(1), 1-21. ME 1980x.01238 ERIC EJ228646   DOI   ScienceOn
9 Clements, M. A. (1982). Careless errors made by sixth-grade children written mathematical tasks. Journal for Research in Mathematics education 13(2), 136-144. ME 1982x.00317 ERIC EJ260453   DOI   ScienceOn
10 Cobb, P. (1985). Two Children's Anticipations, Beliefs, and Motivations. Educ. Stud. Math. 16(2), 111-126. ME 1985k.03813 ERIC EJ320288   DOI
11 Cox, L. S. (1975). Systematic errors in the four vertical algorithms in normal and handicapped populations. Journal for Research in Mathematics education 6(4), 202-222. ERIC EJ128414   DOI   ScienceOn
12 Dai, Z. (1996). Mathematical problems of theory (In Chinese: 数学习题理论). Shanghai: Shang-hai Education Press.
13 De Bock, D.; Van Dooren, W.; Janssens, D. & Verschaffel, L. (2002). Improper use of linear reasoning: An in-depth srudy of the nature and the irresistibility of secondary school students' errors. Educational studies in mathematics 50(3), 311-334. ME 2003b.01467 ERIC EJ661873   DOI   ScienceOn
14 Lannin, J. K.; Barker, D. D. & Townsend, B. E. (2007). How students view the general nature of their errors. Educational studies in mathematics 66(1), 43-59. ME 2008a.00097 ERIC EJ772644   DOI   ScienceOn
15 Fiori, C. F. & Zuccheri, L. (2005). An experimental research on errors patterns in written substrac-tion. Educational studies in mathematics 60, 323-331. ME 2006a.00407   DOI   ScienceOn
16 Huang, Xing-feng & Cheng, Long-hai (2003). Analyzing errors in geometrical problem solving (In Chinese). J. Math. Educ. 12(3), 74-76. ME 2003f.04798
17 Knifong, J. D. & Holtan, B. (1976). An analysis of children's written solutions to word problems. Journal for Research in Mathematics education 7(2), 106-112. ERIC EJ135129   DOI   ScienceOn
18 Nesher, P. & Hershkovitz, S. (1994). The role of schemas in two-step problems: Analysis and research findings. Educational studies in mathematics 26, 1-13.   DOI   ScienceOn
19 Newman, M. A. (1977). An analysis of sixth-grade pupils' errors on written mathematical tasks. In: M. A. Clements & J. Foyster (Ed.), Research mathematics education in Australia (pp. 239-258). Melbourne: Swinburne College Press.
20 Pan, J. & Wu, Y. (2008). Suzhou Grade 7 and 8 students' mathematics comprehension: Current state and error Analysis (In Chinese: 关于苏州市初一和初二学生数学阅读理解水平的现状调查和困难分析). Journal of Mathematics Education 17(3), 58-61. ME 2009a.00209
21 Schoenfeld, A. H. (1985). Mathmatical problem solving. New York: Academic.
22 Schoenfeld, A. H. (1988). When good teaching leads to bad results: The disasters of "well taught" mathematics classes. Educational Psychologist 23, 145-166.   DOI   ScienceOn
23 Schoenfeld, A. H. (1989). Explorations of students' mathematical beliefs and behavior. Journal for Research in Mathematics education 20(4), 338-355. ME 1990b.00597 ERIC EJ397035   DOI   ScienceOn
24 Sweller, J. (1989). Cognitive technology: Some procedures for facilitating learning, problem solving in mathematics and science. Journal of Educational Psychology 81(4), 457-466. ME 1991a.02174   DOI
25 Yerkes, R. M. & Dodsor, J. D. (1908). The relation of strength of stimulus to rapidity of habit-information. Journal of Comparative and Neurological Psychology 18, 459-482.   DOI
26 Watson, I. (1980). Investigating errors of beginning mathematicians. Educational studies in mathematics 11, 319-329. ERIC EJ230952   DOI   ScienceOn