Children’s understanding of the arithmetic concepts of inversion and associativity
| Autor: | Katherine M. Robinson, Jerilyn E. Ninowski, Melissa L. Gray |
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| Rok vydání: | 2006 |
| Předmět: |
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Adolescent Concept Formation Transfer Psychology Age Factors Subtraction Association Learning Inverse Experimental and Cognitive Psychology Of the form Conceptual development Type (model theory) Inversion (discrete mathematics) Child Preschool Concept learning Developmental and Educational Psychology Humans Female Arithmetic Child Comprehension Psychology Mathematics Problem Solving Associative property |
| Zdroj: | Journal of Experimental Child Psychology. 94:349-362 |
| ISSN: | 0022-0965 |
| DOI: | 10.1016/j.jecp.2006.03.004 |
| Popis: | Previous studies have shown that even preschoolers can solve inversion problems of the form a + b − b by using the knowledge that addition and subtraction are inverse operations. In this study, a new type of inversion problem of the form d × e ÷ e was also examined. Grade 6 and 8 students solved inversion problems of both types as well as standard problems of the form a + b − c and d × e ÷ f. Students in both grades used the inversion concept on both types of inversion problems, although older students used inversion more frequently and inversion was used most frequently on the addition/subtraction problems. No transfer effects were found from one type of inversion problem to the other. Students who used the concept of associativity on the addition/subtraction standard problems (e.g., a + b − c = [b − c] + a) were more likely to use the concept of inversion on the inversion problems, although overall implementation of the associativity concept was infrequent. The findings suggest that further study of inversion and associativity is important for understanding conceptual development in arithmetic. |
| Databáze: | OpenAIRE |
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