Multiplication always makes bigger? A case of learning with conceptual change in mathematics

Manuscript (ελληνικά)
Published: Jul 21, 2022
DOI: https://doi.org/10.12681/psyhps.30685
Keywords:
Νatural number bias number concept conceptual change multiplication makes bigger misconception
Konstantinos P. Christou
Department of Early Childhood Education, University of Western Macedonia
Abstract

Ιn this paper, the conceptual change theoretical framework is used to test students’ difficulties with rational numbers, and more specifically to test their misconceptions about the results of the operations between given and missing numbers (e.g., 14:_=5). The main hypothesis of the study was that the natural number bias - which is the tendency to apply the initial, intuitive conception for numbers which is organized in a number concept that share the same properties with natural numbers- in situations that involve reasoning with non-natural numbers, have a dual effect on operations between given and missing numbers: a) it affects students to connect each operation with certain size of results, regardless of the numbers involved in the operation (e.g., that multiplication always makes bigger, and division always makes numbers smaller), and b) it affects their tendency to think that the missing numbers could only be natural numbers. Generalized estimated equations model (GEE) applied to the answers of a unified sample of 300 5th and 6th grade students, from two previous studies which tested the same hypothesis. Participants were given tasks that were either inline or counter-line with their intuitive beliefs about the properties of numbers in operations. The results supported the hypothesis of the study. The students showed statistically significant higher accuracy rates in those tasks that were in-line with their intuitive beliefs about the size of the results of each operation, and also about the missing numbers being natural numbers, than in the tasks that falsified these beliefs.

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