## Abstract

Some years ago Greer (1993) and Verschaffel, De Corte and Lasure (1994) provided evidence that after several years of traditional mathematics instruction children have developed a tendency to reduce mathematical modeling to selecting the correct formal-arithmetic operation with the numbers given in the problem, without seriously taking into account their common-sense knowledge and realistic considerations about the problem context. This evidence was obtained by means of a series of especially designed word problems with problematic modeling assumptions from a realistic point of view, administered in the context of a mathematical lesson. After having summarized these two initial studies, we briefly review a series of replication studies executed in different countries showing the omnipresence of this tendency among pupils. Then two related but different lines of follow-up studies are presented. While the first line of research investigated the effects of different forms of scaffolds added to the testing setting aimed at enhancing the mindfulness of students’ approach when solving these problematic items, the second one looked at the effectiveness of attempts to increase the authenticity of the testing setting. After having discussed these empirical studies, the results are interpreted against the background of schooling in general, and the mathematics classroom in particular. The notion of ‘the game of word problems’ is introduced to refer to the ‘hidden’ rules and assumptions that need to be known and respected in order to make the game of word problems function efficiently. In this respect a study is reported which reveals that the strong tendency toward non-realistic mathematical modeling is found among (student-)teachers too. Afterwards two studies aimed at changing students’ perceptions of word problem solving by taking a radical modeling perspective, are reported. The chapter ends with some theoretical, methodological and instructional implications of the work reviewed.

### Keywords

- Student Teacher
- Word Problem
- Problem Context
- Everyday Knowledge
- Didactical Contract

*These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.*

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## References

Burkhardt, H. (1994). Mathematical applications in school curriculum. In T. Husén and T. N. Postlethwaite (Eds.),

*The international encyclopedia of education*( 2nd ed. ). Oxford/New York: Pergamon Press, pp. 3621–3624.Caldwell, L. (1995).

*Contextual considerations in the solution of children’s multiplication and division word problems_*Unpublished undergraduate thesis, Queen’s University, Belfast, Northern Ireland.Carpenter, T.P., M.M. Lindquist, W. Matthews and E.A. Silver. (1983). Results of the third NAEP mathematics assessment: Secondary school.

*Mathematics Teacher*, 76, pp. 652–659.Clarke, D. and W.M. Stephens (1996). The Ripple Effect: The instructional impact of the systemic introduction of performance assessment in mathematics. In M. Birembaum and F. Dochy (Eds.),

*Alternatives in assessment of achievements*,*learning processes and prior knowledge*. Dordrecht, The Netherlands: Kluwer, pp. 63–92.Cobb, P., T. Wood and E. Yackel (1993). Discourse, mathematical thinking, and classroom practice. In E. Forman, N. Minick and A. Stone (Eds.),

*Contexts for learning: Social cultural dynamics in children’s development*. New York: Springer, pp. 117–148.Cognition and Technology Group at Vanderbilt. (1997).

*The Jasper project: Lessons in curriculum, instruction, assessment, and professional development*. Mahwah, NJ: Lawrence Erlbaum Associates.Cooper, B. (1994). Authentic testing in mathematics? The boundary between everyday and mathematical knowledge in National Curriculum testing in English schools.

*Assessment in Education*,*1*, pp. 143166.Davis, R.B. (1989). The culture of mathematics and the culture of schools.

*Journal of Mathematical Behavior*,*8*, pp. 143–160.De Corte, E. and L. Verschaffel (1985). Beginning first graders’ initial representation of arithmetic word problems.

*Journal of Mathematical Behavior*, 4, pp. 3–21.DeFranco, T. C. and F.R. Curcio (1997). A division problem with a remainder embedded across two contexts: Children’s solutions in restrictive versus real-world settings.

*Focus on Learning Problems in Mathematics*,*19(2)*, pp. 58–72.Freudenthal, H. (1991).

*Revisiting mathematics education*. Dordrecht, The Netherlands: Kluwer.Gerofsky, S. (1996). A linguistic and narrative view of word problems in mathematics education.

*For the Learning of Mathematics*,*16(2)*, pp. 36–45.Gravemeijer, K. (1997). Solving word problems: A case of modelling?

*Learning and Instruction*,*7*, pp. 389–397.Greer, B. (1993). The modeling perspective on wor(l)d problems.

*Journal of Mathematical Behavior*,*12*, pp. 239–250.Greer, B. (1997). Modelling reality in mathematics classrooms: The case of word problems.

*Learning and Instruction*, 7, pp. 293–307.Heuvel-Panhuizen, M. van den (1996).

*Assessment and realistic mathematics education*. Utrecht, The Netherlands: University of Utrecht.Hidalgo, M. C. (1997

*). L’activation des connaissances à propos du monde réel dans la résolution de problèmes verbaux en arithmétique*. Unpublished doctoral dissertation, Université Laval, Québec, Canada.Institut de Recherche sur l’Enseignement des Mathématiques (IREM) de Grenoble (1980).

*Bulletin del’ Association des professeurs de Mathématique de l’ Enseignement Public*, no 323, pp. 235–243.Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A.H. Schoenfeld (Ed.),

*Cognitive science and mathematics education*. Hillsdale, NJ: Lawrence Erlbaum Associates, pp. 123147.Lave, J. (1992). Word problems: A microcosm of theories of learning. In P. Light and G. Butterworth (Eds.),

*Context and cognition: Ways of learning and knowing*. New York: Harvester Wheatsheaf, pp. 74–92.Lehrer, R. and L. Schauble. (in press). Modeling in mathematics and science. In R. Glaser (Ed.),

*Advances in instructional psychology*(Vol. 5). Mahwah, NJ: Lawrence Erlbaum Associates.Lesh, R.,

*and*S. Lamon (1992). Assessing authentic mathematical performance. In R. Lesh and S. Lamon (Eds.),*Assessment of authentic performance in school mathematics*. Washington, DC: American Association for the Advancement of Science, pp. 17–62.Lieshout, E.C.D.M. van, A. Verdwaald and J. van Herk ( 1997, August).

*Suppression of real-world knowledge and demand characteristics in word problem solving*, Paper presented at the Seventh European Conference on Learning and Instruction, Athens, Greece.Nesher, P. (1980). The stereotyped nature of school word problems.

*For the Learning of Mathematics*, 1 (1), pp. 41–48.Polya, G. (1957).

*How to solve it*, Princeton, NJ: Princeton University Press.Renkl, A. ( 1999, August).

*The gap between school and everyday knowledge in mathematics*. Paper presented at the Eighth European Conference for Research on Learning and Instruction, Göteborg, Sweden.Reusser, K. (1988). Problem solving beyond the logic of things: Contextual effects on understanding and solving word problems.

*Instructional Science*,*17*, pp. 309–338.Retisser, K. and R. Stebler (1997a). Every word problem has a solution: The suspension of reality and sense-making in the culture of school mathematics.

*Learning and Instruction*, 7, pp. 309–328.Reusser, K., and R. Stebler ( 1997b, August).

*Realistic mathematical modeling through the solving of performance tasks*. Paper presented at the Seventh European Conference on Learning and Instruction, Athens, Greece.Schoenfeld, A.H. (1991). On mathematics as sense-making: An informal attack on the unfortunate divorce of formal and informal mathematics. In J.F. Voss, D.N. Perkins and J.W. Segal (Eds.),

*Informal reasoning and education*. Hillsdale, NJ: Lawrence Erlbaum Associates, pp. 311 343.Verschaffel, L. and E. De Corte (1997a). Word problems: A vehicle for authentic mathematical understanding and problem solving in the primary school? In T. Nunes and P. Bryant (Eds.),

*Learning and teaching mathematics: An international perspective*. Hove, England: Psychology Press, pp. 6998.Verschaffel, L.

*and*E. De Corte (1997b). Teaching realistic mathematical modeling and problem solving in the elementary school: A teaching experiment with fifth graders.*Journal for Research in Mathematics Education*,*28*, pp. 577–601.Verschaffel, L., E. De Corte and L. Borghart (1997). Pre-service teachers’ conceptions and beliefs about the role of real-world knowledge in mathematical modelling of school word problems.

*Learning and Instruction*,*4*, pp. 339–359.Verschaffel, L., E. De Corte

*and*S. Lasure (1994). Realistic considerations in mathematical modelling of school arithmetic word problems.*Learning and Instruction*,*4*, pp. 273–294.Verschaffel, L., E. De Corte and S. Lasure (1999). Children’s conceptions about the role of real-world knowledge in mathematical modeling of school word problems. In W. Schnotz, S. Vosniadou and M. Carretero (Eds.),

*New perspectives on conceptual change*. Oxford: Elsevier, pp 175–189.Verschaffel, L., E. De Corte, S. Lasure, G. van Vaerenbergh, H. Bogaerts and E. Ratinckx (1999). Design and evaluation of a learning environment for mathematical modeling and problem solving in upper elementary school children.

*Mathematical Thinking and Learning*,*1*, pp. 195 229.Verschaffel, L., B. Greer and E. De Corte (2000).

*Making sense of word problems*. Lisse, The Netherlands: Swets and Zeitlinger.Wyndhamn, J. and R. Säljö (1997). Word problems and mathematical reasoning: A study of children’s mastery of reference and meaning in textual realities.

*Learning and Instruction*, 7, pp. 361–382.Yoshida, H., L. Verschaffel and E. De Corte (1997). Realistic considerations in solving problematic word problems: Do Japanese and Belgian children have the same difficulties?

*Learning and Instruction*,*7*, pp. 329–338.

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Verschaffel, L., Greer, B., de Corte, E. (2002). Everyday Knowledge and Mathematical Modeling of School Word Problems. In: Gravemeijer, K., Lehrer, R., Van Oers, B., Verschaffel, L. (eds) Symbolizing, Modeling and Tool Use in Mathematics Education. Mathematics Education Library, vol 30. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3194-2_16

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DOI: https://doi.org/10.1007/978-94-017-3194-2_16

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