Arithmetic problems at school: When there is an apparent contradiction between the situation model and the problem model

Coquin-Viennot, Danièle; Moreau, Stéphanie

doi:10.1348/000709905x79121

Cited by 14 publications

(10 citation statements)

References 17 publications

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“…If the solver constructs a mental model of the text to answer this problem, the situation model evoked by the text could have implications for math performance. Indeed, situation models that contradict readers' expectations about the mathematical operation needed to complete a problem can impair problem solving (Coquin-Viennot & Moreau, 2007). Here, we show that situation models do not have to mislead a reader to hurt performance.…”

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confidence: 69%

Situating math word problems: The story matters

Mattarella-Micke

Beilock

2010

Psychonomic Bulletin & Review

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In two experiments, we explored how the situation model of a math story problem impacts math problem performance. Participants completed multiplication story problems in which a set of objects was associated with or dissociated from a protagonist, making them more or less accessible in memory during answer retrieval. On the basis of previous findings that the sum of two numbers interferes with retrieval of their product, the number of objects in the math problem was either highly interfering ("9" for 4 x 5) or less interfering ("8" for 4 x 5) for multiplication retrieval in the problem. Participants made more errors in problem solving when highly interfering numerical content was associated with the protagonist and, thus, foregrounded. Moreover, the lower one's working memory, the bigger this effect. In sum, small changes in the situation model of a math story problem can harm performance. These changes shift the balance of factors that influence math performance away from math knowledge and toward individual differences in general cognitive capacity.

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confidence: 69%

Situating math word problems: The story matters

Mattarella-Micke

Beilock

2010

Psychonomic Bulletin & Review

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“…In general, while comprehension is commonly defined as the construction of mental representations, the nature of these representations is explained differently according to various authors, based on their theoretical positions. In the context of this study, we focus on the development of two different but complementary levels of mental representation, namely situation models and problem models (Coquin-Viennot and Moreau 2007;Moreau and Coquin-Viennot 2003;Nathan et al 1992;Reusser 1990;Staub and Reusser 1995;Thevenot and Oakhill 2005;Thevenot et al 2007;Voyer 2006). Several authors highlighted the importance of a non-mathematical representation 2 in the initial phase of the problem solving process, that is a more qualitative representation in which the problem is presented, which refers to what many call the "situation model" (Kintsch 1998;Moreau 2001;Nathan et al 1992;Porcheron 1998;Reusser 1990;Staub and Reusser 1995;Verschaffel et al 2000;Coquin-Viennot and Moreau 2007;Voyer 2006).…”

Section: Comprehensionmentioning

confidence: 99%

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

Goulet-Lyle¹,

Voyer

Verschaffel

2019

ZDM Mathematics Education

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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 problemsolving 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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“…More recently, Coquin-Viennot & Moreau (2007) demonstrated that the age of pupils (elementary grade 3 vs. grade 4) influenced the role of the situation model in the resolution of word problems. Authors then analysed whether the situation model played an equal role for students with stronger or weaker problem solving skills, without being able to provide a definitive answer to the question.…”

Section: Information Included In the Problem Statementmentioning

confidence: 99%

Performance in Mathematical Problem Solving as a Function of Comprehension and Arithmetic Skills

Voyer

2010

Int J of Sci and Math Educ

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Many factors influence a student's performance in word (or textbook) problem solving in class. Among them is the comprehension process the pupils construct during their attempt to solve the problem. The comprehension process may include some less formal representations, based on pupils' real-world knowledge, which support the construction of a 'situation model'. In this study, we examine some factors related to the pupil or to the word problem itself, which may influence the comprehension process, and we assess the effects of the situation model on pupils' problem solving performance. The sample is composed of 750 pupils of grade 6 elementary school. They were selected from 35 classes in 17 Francophone schools located in the province of Quebec, Canada. For this study, 3 arithmetic problems were developed. Each problem was written in 4 different versions, to allow the manipulation of the type of information included in the problem statement. Each pupil was asked to solve 3 problems of the same version and to complete a task that allowed us to evaluate the construction of a situation model. Our results show that pupils with weaker arithmetic skills construct different representations, based on the information presented in the problem. Also, pupils who give greater importance to situational information in a problem have greater success in solving the problem. The situation model influences pupils' problem solving performance, but this influence depends on the type of information included in the problem statement, as well as on the arithmetic skills of each individual pupil.

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Arithmetic problems at school: When there is an apparent contradiction between the situation model and the problem model

Abstract: It is in situations where the problem schema is not automatically activated (younger subjects or compare problems) that the QSM plays its role of intermediate representation and causes performances to deteriorate if it does not correspond to the PM.

Cited by 14 publications

References 17 publications

Situating math word problems: The story matters

Situating math word problems: The story matters

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

Performance in Mathematical Problem Solving as a Function of Comprehension and Arithmetic Skills

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