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The Role of Implicit Models in Solving Verbal Problems in Multiplication and Division
Abstract
Arithmetical operations were assumed to remain attached to primitive behavioral models that influence tacitly the choice of an operation even after the learner has had solid formal-algorithmic training. The model for multiplication was conjectured to be repeated addition, and two primitive models (partitive and quotative) were seen as linked to division. A total of 623 pupils enrolled in 13 Italian schools (Grades 5, 7, and 9) were asked to choose the operation needed to solve 26 multiplication and division word problems. Violations by the numerical data of the constraints imposed by the assumed tacit models (for instance, when the operator was a decimal number) constituted particular sources of difficulty at all three grade levels. The findings seemed to confirm the impact of the repeated addition model on multiplication and of the partitive model on division. The quotative division model influenced the pupils' choices only at the ninth-grade level.
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Cites
Mathematics as an Educational Task
Freudenthal, H. (1972) · doi:10.1007/978-94-010-2903-2 · Cited by 1,336
Cited by
Learning and Teaching With Understanding
Hiebert, J., & Carpenter, T. P. (2006) · Handbook of Research on Mathematics Teaching and Learning · doi:10.1108/978-1-60752-874-620251006 · Cited by 964
Rational Number, Ratio, and Proportion
Behr, M. J., Harel, G., Post, T., & Lesh, R. (2006) · Handbook of Research on Mathematics Teaching and Learning · doi:10.1108/978-1-60752-874-620251018 · Cited by 403
Prospective Elementary Teachers' Knowledge of Division
Simon, M. A. (1993) · Journal for Research in Mathematics Education · doi:10.2307/749346 · Cited by 273
Representational systems, learning, and problem solving in mathematics
Goldin, G. A. (1998) · The Journal of Mathematical Behavior · doi:10.1016/s0364-0213(99)80056-1 · Cited by 268
Why is learning fraction and decimal arithmetic so difficult?
Lortie-Forgues, H., Tian, J., & Siegler, R. S. (2015) · Developmental Review · doi:10.1016/j.dr.2015.07.008 · Cited by 266
Metadata
- Authors
- Fischbein, E., Deri, M., Nello, M. S., & Marino, M. S.
- Venue
- Journal for Research in Mathematics Education
- Published
- 1985-01
- Volume
- 16
- Issue
- 1
- Pages
- 3
- ISSN
- 0021-8251 (ISSN-L)
- OpenAlex
- W2101922032
- Cited by
- 471
- References
- 1
- FWCI
- 5.35
- Type
- journal article
- Language
- en
- Open access
- closed
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- Fischbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The Role of Implicit Models in Solving Verbal Problems in Multiplication and Division. Journal for Research in Mathematics Education. https://doi.org/10.2307/748969
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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