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The Acquisition of Addition and Subtraction Concepts in Grades One through Three
Abstract
Children's solutions to simple addition and subtraction word problems were studied in a 3-year longitudinal study that followed 88 children from Grades 1 through 3. The children were able to solve the problems using a variety of modeling and counting strategies even before they received formal instruction in arithmetic. The invented strategies continued to be used after several years of formal instruction. Four levels of problem-solving ability were found. At the first level, children could solve problems only by externally modeling them with physical objects. Modeling strategies were gradually replaced with more sophisticated counting strategies. The results of the study are at variance with important aspects of models of children's performance proposed by Briars and Larkin and by Riley, Greeno, and Heller.
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Citations
Cited by
Mathematics and Learning Disabilities
Geary, D. C. (2004) · Journal of Learning Disabilities · doi:10.1177/00222194040370010201 · Cited by 1,245
Using Knowledge of Children's Mathematics Thinking in Classroom Teaching: An Experimental Study
Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C.-P., & Loef, M. (1989) · American Educational Research Journal · doi:10.2307/1162862 · Cited by 1,015
Self-citationNi, Y., & Zhou, Y.-D. (2005) · Educational Psychologist · doi:10.1207/s15326985ep4001_3 · Cited by 666
The Prevention, Identification, and Cognitive Determinants of Math Difficulty.
Fuchs, L. S., Compton, D. L., Fuchs, D., Paulsen, K., Bryant, J. D., & Hamlett, C. L. (2005) · Journal of Educational Psychology · doi:10.1037/0022-0663.97.3.493 · Cited by 593
Children's mathematical development: Research and practical applications.
Geary, D. C. (1994) · doi:10.1037/10163-000 · Cited by 565
Metadata
- Authors
- Carpenter, T. P., & Moser, J. M.
- Venue
- Journal for Research in Mathematics Education
- Published
- 1984-05
- Volume
- 15
- Issue
- 3
- Pages
- 179-202
- ISSN
- 0021-8251 (ISSN-L)
- 1945-2306
- OpenAlex
- W4241305772
- Cited by
- 434
- References
- 0
- FWCI
- 6.55
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: The Acquisition of Addition and Subtraction Concepts in Grades One through Three. https://app.cochat.ai/papers/10.5951/jresematheduc.15.3.0179
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- Carpenter, T. P., & Moser, J. M. (1984). The Acquisition of Addition and Subtraction Concepts in Grades One through Three. Journal for Research in Mathematics Education. https://doi.org/10.5951/jresematheduc.15.3.0179
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
