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Catherine Thevenot - One of the best experts on this subject based on the ideXlab platform.
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Arithmetic Word Problems describing discrete quantities: E.E.G evidence for the construction of a situation model
Acta psychologica, 2018Co-Authors: Jeanne Bagnoud, Jane Oakhill, Nicolas Burra, Caroline Castel, Catherine ThevenotAbstract:In this research, university students were asked to solve Arithmetic Word Problems constructed either with discrete quantities, such as apples or marbles, or continuous quantities such as meters of rope or grams of sand. An analysis of their brain activity showed different alpha levels between the two types of Problems with, in particular, a lower alpha power in the parieto-occipital area for Problems describing discrete quantities. This suggests that processing discrete quantities during Problem solving prompts more mental imagery than processing continuous quantities. These results are difficult to reconcile with the schema theory, according to which Arithmetic Problem solving depends on the activation of ready-made mental frames stored in long-term memory and triggered by the mathematical expression used in the texts. Within the schema framework, the nature of the objects described in the text should be quickly abstracted during Problem solving because it cannot impact the semantic structure of the Problem. On the contrary, our results support the situation model theory, which places greater emphasis on the Problem context in order to account for individuals' behaviour. On a more methodological point of view, this study constitutes the first attempt to infer the characteristics of individual's mental representations of Arithmetic text Problems from EEG recordings. This opens the door for the application of brain activity measures in the field of Arithmetic Word Problem.
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Arithmetic Word Problem solving the role of prior knowledge
Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts, 2017Co-Authors: Catherine ThevenotAbstract:Abstract In this chapter, I will present empirical evidence about the crucial role of prior knowledge on Arithmetic Word Problem solving processes. First, I show that daily life experiences can either facilitate or hinder the construction of the adequate mental representations of the Problems. Second, Problem schemata, corresponding to ready-made Problem frames stored in long-term memory, can also negatively or positively influence the way students understand Word Arithmetic Problems. I will also present the main theoretical frameworks accounting for the influence of prior knowledge on Problem solving. Finally, I will describe several education programs designed to help students to successfully solve Arithmetic Word Problems.
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Mathematical Cognition and Learning Vol 3 : Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts - Arithmetic Word Problem Solving: The Role of Prior Knowledge
Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts, 2017Co-Authors: Catherine ThevenotAbstract:Abstract In this chapter, I will present empirical evidence about the crucial role of prior knowledge on Arithmetic Word Problem solving processes. First, I show that daily life experiences can either facilitate or hinder the construction of the adequate mental representations of the Problems. Second, Problem schemata, corresponding to ready-made Problem frames stored in long-term memory, can also negatively or positively influence the way students understand Word Arithmetic Problems. I will also present the main theoretical frameworks accounting for the influence of prior knowledge on Problem solving. Finally, I will describe several education programs designed to help students to successfully solve Arithmetic Word Problems.
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Arithmetic Word Problem Solving and Mental Representations
Oxford Handbooks Online, 2014Co-Authors: Catherine Thevenot, Pierre BarrouilletAbstract:Arithmetic Word Problem solving is considered as a testing ground of mathematical achievement, but remains the area of mathematics in which students experience the greatest difficulties. In this chapter, we review recent theoretical and empirical work that could shed light on these difficulties. We first describe the most frequently used classifications of Word Problems and assess their psychological relevance. Then, we present the main hypotheses concerning the nature of the representations involved in Word Problems. Some theories assume that Problem solving relies on the instantiation of schemas abstracted from recurrently encountered Problems of the same relational structure, whereas other theories propose that ad hoc transient mental representations are constructed for each Problem encountered. A third part is devoted to the impact of individual differences in calculation, reading comprehension, and more general factors, such as working memory capacity. Finally, we address the issue of enhancing performance in Word Problem solving.
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Arithmetic Word Problem solving: evidence for the construction of a mental model.
Acta psychologica, 2009Co-Authors: Catherine ThevenotAbstract:In the first experiment reported here, adults were given an unexpected task of Problem recognition after a resolution task. During the recognition task, participants were presented with the original Problems, inconsistent Problems that had never been solved, and paraphrases, which respected the relational structure of the original Problems but not their exact Wording. More precisely, paraphrases were constructed by inversing the terms and the linguistic expressions in the original Problems. Whereas the literal form of paraphrastic Problems bore the least resemblance to original Problems, paraphrastic Problems were associated to higher recognition rates than inconsistent Problems. A second experiment ruled out the interpretation that this result was due to a mere remembering of the exact values used in the Problem text. Taken together, these results provide evidence that a non-propositional representation is built by individuals to solve Arithmetic Word Problems and suggest that a mental model is constructed (Johnson-Laird, 1983).
Emmanuel Sander - One of the best experts on this subject based on the ideXlab platform.
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When masters of abstraction run into a concrete wall: Experts failing Arithmetic Word Problems
Psychonomic bulletin & review, 2019Co-Authors: Hippolyte Gros, Emmanuel Sander, Jean-pierre ThibautAbstract:Can our knowledge about apples, cars, or smurfs hinder our ability to solve mathematical Problems involving these entities? We argue that such daily-life knowledge interferes with Arithmetic Word Problem solving, to the extent that experts can be led to failure in Problems involving trivial mathematical notions. We created Problems evoking different aspects of our non-mathematical, general knowledge. They were solvable by one single subtraction involving small quantities, such as 14 – 2 = 12. A first experiment studied how university-educated adults dealt with seemingly simple Arithmetic Problems evoking knowledge that was either congruent or incongruent with the Problems’ solving procedure. Results showed that in the latter case, the proportion of participants incorrectly deeming the Problems “unsolvable” increased significantly, as did response times for correct answers. A second experiment showed that expert mathematicians were also subject to this bias. These results demonstrate that irrelevant non-mathematical knowledge interferes with the identification of basic, single-step solutions to Arithmetic Word Problems, even among experts who have supposedly mastered abstract, context-independent reasoning.
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When intuitive conceptions overshadow pedagogical content knowledge: Teachers’ conceptions of students’ Arithmetic Word Problem solving strategies
Educational Studies in Mathematics, 2018Co-Authors: Katarina Gvozdic, Emmanuel SanderAbstract:Intuitive conceptions in mathematics guide the interpretation of mathematical concepts. We investigated if they bias teachers’ conceptions of student Arithmetic Word Problem solving strategies, which should be part of their pedagogical content knowledge (PCK). In individual interviews, teachers and non-teaching adults were asked to describe students’ strategies in situational contexts within or outside the scope of the intuitive conception. The results revealed that teachers relied on their PCK and identified student strategies; however, in the presence of the intuitive conception, their PCK was overshadowed and they ceased to differ significantly from non-teachers. This brings the attention to certain biases that can have a strong impact on teachers’ efficient use of PCK.
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When outstanding mathematicians cannot figure out that 14 – 2 = 12
2018Co-Authors: Hippolyte Gros, Emmanuel Sander, Jean-pierre ThibautAbstract:We investigated what happens when non-mathematical knowledge interferes with mathematical knowledge in Arithmetic Word Problem solving. Adults and expert mathematicians had to evaluate the solutions of basic additive Problems. The non-mathematical knowledge evoked by the Problems hindered both populations’ success rates and response times when incongruent with the solving algorithm.
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Arithmetic Word Problem solving: a Situation Strategy First framework.
Developmental science, 2010Co-Authors: Rémi Brissiaud, Emmanuel SanderAbstract:Before instruction, children solve many Arithmetic Word Problems with informal strategies based on the situation described in the Problem. A Situation Strategy First framework is introduced that posits that initial representation of the Problem activates a situation-based strategy even after instruction: only when it is not efficient for providing the numerical solution is the representation of the Problem modified so that the relevant Arithmetic knowledge might be used. Three experiments were conducted with Year 3 and Year 4 children. Subtraction, multiplication and division Problems were created in two versions involving the same Wording but different numerical values. The first version could be mentally solved with a Situation strategy (Si version) and the second with a Mental Arithmetic strategy (MA version). Results show that Si-Problems are easier than MA-Problems even after instruction, and, when children were asked to report their strategy by writing a number sentence, equations that directly model the situation were predominant for Si-Problems but not for MA ones. Implications of the Situation Strategy First framework regarding the relation between conceptual and procedural knowledge and the development of Arithmetic knowledge are discussed.
Michel Fayol - One of the best experts on this subject based on the ideXlab platform.
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Why does placing the question before an Arithmetic Word Problem improve performance? A situation model account:
Quarterly journal of experimental psychology (2006), 2007Co-Authors: Catherine Thevenot, Pierre Barrouillet, Michel Devidal, Michel FayolAbstract:The aim of this paper is to investigate the controversial issue of the nature of the representation constructed by individuals to solve Arithmetic Word Problems. More precisely, we consider the relevance of two different theories: the situation or mental model theory (Johnson-Laird, 1983; Reusser, 1989) and the schema theory (Kintsch & Greeno, 1985; Riley, Greeno, & Heller, 1983). Fourth-graders who differed in their mathematical skills were presented with Problems that varied in difficulty and with the question either before or after the text. We obtained the classic effect of the position of the question, with better performance when the question was presented prior to the text. In addition, this effect was more marked in the case of children who had poorer mathematical skills and in the case of more difficult Problems. We argue that this pattern of results is compatible only with the situation or mental model theory, and not with the schema theory.
Jean-pierre Thibaut - One of the best experts on this subject based on the ideXlab platform.
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When masters of abstraction run into a concrete wall: Experts failing Arithmetic Word Problems
Psychonomic bulletin & review, 2019Co-Authors: Hippolyte Gros, Emmanuel Sander, Jean-pierre ThibautAbstract:Can our knowledge about apples, cars, or smurfs hinder our ability to solve mathematical Problems involving these entities? We argue that such daily-life knowledge interferes with Arithmetic Word Problem solving, to the extent that experts can be led to failure in Problems involving trivial mathematical notions. We created Problems evoking different aspects of our non-mathematical, general knowledge. They were solvable by one single subtraction involving small quantities, such as 14 – 2 = 12. A first experiment studied how university-educated adults dealt with seemingly simple Arithmetic Problems evoking knowledge that was either congruent or incongruent with the Problems’ solving procedure. Results showed that in the latter case, the proportion of participants incorrectly deeming the Problems “unsolvable” increased significantly, as did response times for correct answers. A second experiment showed that expert mathematicians were also subject to this bias. These results demonstrate that irrelevant non-mathematical knowledge interferes with the identification of basic, single-step solutions to Arithmetic Word Problems, even among experts who have supposedly mastered abstract, context-independent reasoning.
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When outstanding mathematicians cannot figure out that 14 – 2 = 12
2018Co-Authors: Hippolyte Gros, Emmanuel Sander, Jean-pierre ThibautAbstract:We investigated what happens when non-mathematical knowledge interferes with mathematical knowledge in Arithmetic Word Problem solving. Adults and expert mathematicians had to evaluate the solutions of basic additive Problems. The non-mathematical knowledge evoked by the Problems hindered both populations’ success rates and response times when incongruent with the solving algorithm.
Sylvia Weberrussell - One of the best experts on this subject based on the ideXlab platform.
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text integration and mathematical connections a computer model of Arithmetic Word Problem solving
Cognitive Science, 1996Co-Authors: Mark D Leblanc, Sylvia WeberrussellAbstract:Understanding Arithmetic Word Problems involves a complex interaction of text comprehension and mathematical processes. This article presents a computer simulation designed to capture the working memory demands required in “bottomup” comprehension of Arithmetic Word Problems. The simulation's sentence-level parser and text integration component reflect the importance of processing the Problem from its original natural language presentation. Children's probability of solution was analyzed in exploratory regression analyses as a function of the simulation's sentence-level and text integration processes. Working memory variables measuring the combined effects of concepts to remember and text integration inferences account for a significant proportion of variance in children's solution probabilities across the first four grade levels (K-3). Consistent with previous results from others, which highlighted the significance of small changes in Problem Wording, the simulation offers a process-oriented perspective as to why natural language presentation constrains the comprehension of mathematical relationships.