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How does imposing a step-by-step solution method impact students’ approach to mathematical word problem solving?

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Abstract

This paper presents the second phase of a larger research program with the purpose of exploring the possible consequences of a gap between what is done in the classroom regarding mathematical word problem solving and what research shows to be effective in this particular field of study. Data from the first phase of our study on teachers’ self-proclaimed practices showed that one-third of elementary teachers from the region of Quebec require their students to follow a specific sequential problem-solving method, known as the ‘what I know, what I look for’ method. These results led us to hypothesize that the observed gap may have an impact on students’ comprehension of mathematical word problems. The use of this particular method was the foundation for us to study, in the second phase, the effect of the imposition of this sequential method on students’ literal and inferential understanding of word problems. A total of 278 fourth graders (9–10 years old) solved mathematical word problems followed by a test to assess their understanding of the word problems they had just solved. The results suggest that the use of this problem solving method does not seem to improve or impair students’ understanding. From a more fundamental point of view, our study led us to the conclusion that the way word problem solving is addressed in the mathematics classroom, through sequential and inflexible methods, does not help students develop their word problem solving competence.

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Notes

  1. People living in the province of Quebec in Canada.

  2. A non-mathematical representation is an episodic model of the situation described in the problem statement, allowing the solver to have a richer understanding of the story (who the characters are, what their actions and feelings are, where the story takes place, etc.), without directly contributing to solving the problem.

  3. This first phase was conducted after a smaller exploratory stage in which we interviewed ten teachers with the main goal of identifying different profiles regarding teaching practices related to mathematical problem solving methods.

  4. The other two-thirds of teachers do not oblige their students to follow the different steps in a specific order.

  5. When the answer to a question is “semantically equivalent to a part of the text or synonymous to a part of the text” (Giasson 2003, p. 266), then it is a question of a literal understanding.

  6. For example, using the ‘what I know, what I look for’ method can be a problem for some students who do not remember ‘what goes in what section’.

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Goulet-Lyle, MP., Voyer, D. & Verschaffel, L. How does imposing a step-by-step solution method impact students’ approach to mathematical word problem solving?. ZDM Mathematics Education 52, 139–149 (2020). https://doi.org/10.1007/s11858-019-01098-w

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