Natural number bias in arithmetic operations with missing numbers – A reaction time study
| Autor: | Wim Van Dooren, Jo Van Hoof, Konstantinos P. Christou, Courtney Pollack |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Rational number
lcsh:BF1-990 Experimental and Cognitive Psychology Natural number Operand 050105 experimental psychology Decimal 0501 psychology and cognitive sciences Arithmetic Mathematics Numerical Analysis natural number bias lcsh:Mathematics Applied Mathematics 05 social sciences 050301 education Division (mathematics) lcsh:QA1-939 Multiplication table rational numbers operation lcsh:Psychology multiplication makes bigger Product (mathematics) misconception Multiplication 0503 education |
| Zdroj: | Journal of Numerical Cognition, Vol 6, Iss 1, Pp 22-49 (2020) |
| ISSN: | 2363-8761 |
| DOI: | 10.5964/jnc.v6i1.228 |
| Popis: | When reasoning about numbers, students are susceptible to a natural number bias (NNB): When reasoning about non-natural numbers they use properties of natural numbers that do not apply. The present study examined the NNB when students are asked to evaluate the validity of algebraic equations involving multiplication and division, with an unknown, a given operand, and a given result; numbers were either small or large natural numbers, or decimal numbers (e.g., 3 × _ = 12, 6 × _ = 498, 6.1 × _ = 17.2). Equations varied on number congruency (unknown operands were either natural or rational numbers), and operation congruency (operations were either consistent – e.g., a product is larger than its operand – or inconsistent with natural number arithmetic). In a response-time paradigm, 77 adults viewed equations and determined whether a number could be found that would make the equation true. The results showed that the NNB affects evaluations in two main ways: a) the tendency to think that missing numbers are natural numbers; and b) the tendency to associate each operation with specific size of result, i.e., that multiplication makes bigger and division makes smaller. The effect was larger for items with small numbers, which is likely because these number combinations appear in the multiplication table, which is automatized through primary education. This suggests that students may count on the strategy of direct fact retrieval from memory when possible. Overall the findings suggest that the NNB led to decreased student performance on problems requiring rational number reasoning. ispartof: Journal of Numerical Cognition vol:6 issue:1 pages:22-49 status: published |
| Databáze: | OpenAIRE |
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