ERIC Number: EJ1177107
Record Type: Journal
Publication Date: 2018-Apr
Abstractor: As Provided
Open Word Problems: Taking the Additive or the Multiplicative Road?
Degrande, Tine; Van Hoof, Jo; Verschaffel, Lieven; Van Dooren, Wim
ZDM: The International Journal on Mathematics Education, v50 n1-2 p91-102 Apr 2018
Previous studies have repeatedly shown that children often incorrectly use an additive model for multiplicative word problems, and a multiplicative model for additive word problems. The present study aimed to investigate which model upper primary school children tend to choose in word problems that are open to "both" ways of reasoning. In particular, a non-symbolic variant of the snake task of Lamon ("Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers," Taylor & Francis Group, New York, NY, 2008) was administered to 279 children in fifth and sixth grade of primary education. Children were asked to indicate which of two snakes had grown the most, and to verbally explain the reasoning behind their answer. Results revealed that additive reasoning (i.e., absolute growth) was more frequently used than multiplicative reasoning (i.e., relative growth), although it appeared to be harder to verbalize. Second, both trends were more prominent for fifth than sixth graders. Third, contrary to previous studies with younger children, we did not find any differences between answers on discrete and continuous variants of the task. Nevertheless, children's answers were more often explicitly verbalized in discrete than continuous items. Theoretical, methodological, and educational implications for solving word problems, and more generally for modelling in the domain of additive and multiplicative reasoning, are discussed.
Descriptors: Word Problems (Mathematics), Mathematics Instruction, Mathematical Models, Multiplication, Elementary School Students, Elementary School Mathematics, Mathematical Concepts, Grade 5, Grade 6, Mathematical Logic, Age Differences, Problem Solving
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Publication Type: Journal Articles; Reports - Research
Education Level: Elementary Education
Authoring Institution: N/A
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