The relationship between different kinds of students’ errors and the knowledge required to solve mathematics word problems
Tipo de documento
Autores
Lista de autores
Haghverdi, Majid, Shahvarani, Ahmad y Seifi, Mohammad
Resumen
The main objective of this research is to examine the relationship between different kinds of errors and the knowledge required to solve word problems in Arithmetic, Algebra and Geometry. Kinfong’s and Holtan’s framework supports the analysis of the errors, and Mayer’s theory was implemented to understand the necessary knowledge for solving math word problems. The research methodology follows a semi-experimental method. Research tools comprise both a descriptive math test and a directed interview. The research findings revealed that students’ errors when solving arithmetic word problems result from the lack of linguistic, semantic, structural and communicational knowledge; when solving the geometric word problems, the lack of semantic, intuition and structural knowledge were the cause of the students’ errors. Regarding algebra word problems, miscalculation was the reason for the higher error rate. Results show that the highest deficiency is mainly related to the lack of semantic, structural and communicational knowledge.
Fecha
2012
Tipo de fecha
Estado publicación
Términos clave
Conocimiento | Cuasi-experimental | Errores | Resolución de problemas
Enfoque
Nivel educativo
Idioma
Revisado por pares
Formato del archivo
Volumen
26
Número
42b
Rango páginas (artículo)
649-665
ISSN
19804415
Referencias
BURTON, L. Why is intuition so important to mathematicians but missing from mathematics education? For The Learning of Mathematics, Montreal, Canada, CA, v. 19, n. 3, p. 27 - 32, 1999. CALDWELL, J. H.,GOLDING, G. A. Variable affecting word problem difficulty in secondary school. Journal for Research in Mathematics Education, Reston, Va., US, v. 18, n. 3, p. 187 - 196, 1987. CARPENTER, T. P. et al. Result of the third NAEP mathematics assessment:secondary school. Mathematics Teacher, Syracuse, NY, US, v. 76, n. 9, p. 52 - 659, dec. 1983. CASEY. D. P. Failing students: A strategy of error analysis. In: COSTELLO (Ed).Aspects of motivation, Melbourne: Mathematical Association of Victoria. 1978. p. 295 - 30. CLEMENTS, M. A. Analyzing children’s errors on written mathematical tasks. Educational studies in mathematics, Dordrecht, Holanda, NL, v. 11, n. 10, p. 1 - 21, 1982. COCKCOFT, W. H. Mathematics counts: Report of the committee of inquiry into the teaching of mathematics in schools. London: HMSO, 1982. CUMMINS, D. D. et al. The role of understanding in solving word problem. Cognitive Psychology, New York, US, n. 4, v. 20, p. 405 - 438, 1988. DE CORTE, E.; VERSHAFFEL, L.; DE WIN, L; Teaching word problem in the primary school. What research has to say to the teacher? In: B. Greer & G. Mulhern (Eds.), New Development in Teaching Mathematics, London: Routledge. 1989, p. 85 - 106. FISCHBEIN, E. Intuitions and schemata in mathematical reasoning. Educational Studies in Mathematics, Dordrecht, Holanda, v. 38. p. 11-50, 1999. GREENO, J. Understanding and solving word arithmetic problems. Psychological Review, Washington, US, v. 92, n. 1, p. 109 - 129, 1985. HERSHLOVITZ, S.; NESHER, P. The role of schemes in solving word problems. The Mathematics Educator, v. 7, n. 2, p. 1 - 34, 2003. KAUR, B. Difficulties with problem solving in mathematics. The Mathematical Educator. V. 2, n. 1, p. 93-112, 1997. KINFONG, D.; HOLTAN, B. An analysis of children’s written soloution to word problems. Journal of Research in Mathematics Education, Reston, Va., US, v. 7, n. 2, p. 106 - 121, 1976. LESTER, F.; GAROFALO, J. (Eds). Mathematical problem solving: Issues in Research. Philadelphia: Franklin institute Press, 1982. MAYER, R. E.; HEGARTY, M. The process of understanding mathematical problems. In: STEMBERG, R. J.; BEN-ZEEV, T. (Eds.), the nature of mathematics thinking, Mahwah, NJ: Lawrence Elrbaum, 1996, p. 29 - 53. MAYER, R., Thinking, Problem solving, Cognition. 2. ed. New York: Freeman, 1992. NCTM. NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS. An agenda foraction: recommendation for school mathematics of the 1980s. Reston, VA, 1980. NCTM. NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS. Principles andStandard for School Mathematics. Reston, VA, 2000. NEWMAN, M. A. An analysis of sixth-grade pupils’ errors on written mathematical tasks. Victorian Institute for Educational Research Bulletin, Columbus, Ohio, US, v. 39, n. n/c, p. 31 - 43, 1977. RUMELHART, D.; NORMAN, D. A. Representation of knowledge. In: AITKENHEAD,A. M.; SLACK, J. M. (Eds) Issues in cognitive modeling, Lawrence Erlbaum Associates. 1985. SCHOENFELD, A. Mathematical Problem Solving. San Diego, CA: Academic Press, 1985. VERSCHAFFEL, L.; GREER, B.; DE CORTE, E. Making sense of word problems. The Netherlands: Swets & Zeithinger, 2000. WONG, W. K.. et al. Learner-initiating instruction model based on cognitive knowledge for geometry word problem comprehension. Computer & Education, Manchester, v. 48, p. 582 - 601, 2007.