When intuitive conceptions overshadow pedagogical content knowledge: Teachers’ conceptions of students’ arithmetic word problem solving strategies

Gvozdic, Katarina; Sander, Emmanuel

doi:10.1007/s10649-018-9806-7

Cited by 17 publications

(10 citation statements)

References 33 publications

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“…This proposal has been defined in the expert blind spot, where advanced subject-matter knowledge of a scholarly discipline can lead educators to overlook the difficulties certain content can pose for students. On the other hand, findings revealed that when problems are congruent with the intuitive conception, teachers consider them to be easier for children, just like non-teachers do, even when this is not in line with student performance (Gvozdic & Sander, 2018). These findings highlighted that in a parallel way as described by the expert blind spot, teachers' PCK was overridden when the intuitive conception was involvedby their intuitive blind spot.…”

Section: Discussionmentioning

confidence: 86%

How robust are intuitive conceptions? Insights from production tasks regarding arithmetic operations.

Gvozdic¹,

Naud²,

Sander³

2022

Preprint

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Intuitive conceptions are known to be prevalent among young learners and can impose constraints to knowledge acquisition. Data even suggest that instruction does not eradicate them, but the phenomenon has rarely been quantified. In this study we raise the question of how robust intuitive conceptions are. Moreover, we look at how persistent they are long after instruction of the studied notions. Production tasks concerning the four elementary arithmetic operations were used for measuring the degree to which they prevail and impose constraints among adults, 131 bachelor students as well as 168 high-school and 57 mathematics teachers. The findings revealed that in most cases (88.93%) participants evoked examples that are congruent with an intuitive conception. This was observed for all the arithmetic operations and population involved in the study. Even when explicitly prompted to find incongruent cases, they failed on two thirds of the cases. The educational entailments of these findings are discussed.

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Section: Discussionmentioning

confidence: 86%

How robust are intuitive conceptions? Insights from production tasks regarding arithmetic operations.

Gvozdic¹,

Naud²,

Sander³

2022

Preprint

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“…In their study, Clément and Richard (1997) found that participants sometimes miscategorized a specific solving step as "impossible" due to their prior knowledge, and thus required more time to overcome this self-imposed constraint. Likewise, in simple arithmetic problems, overcoming the common misconception that subtraction always involves removing part of a whole can be a very difficult task for children (Brissiaud & Sander, 2010) and can even limit teachers' understanding of students' strategies (Gvozdic & Sander, 2018). Hofstadter and Sander (2013) propose that to achieve a more accurate understanding of subtraction as "the distance between two numerical values", a form of conceptual flexibility is needed, which depends on the ability to flexibly categorize the concept of subtraction itself.…”

Section: Flexible Categorization In Problem Solvingmentioning

confidence: 99%

Leveraging cognitive flexibility through flexible categorization training

IACONO,

Clément,

Guerrien

et al. 2024

Preprint

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Being cognitively flexible is crucial for academic success, especially in disciplines requiringproblem-solving and abstract reasoning, such as mathematics. Therefore, investigating whetherthe expression of cognitive flexibility can be trained in specific areas of knowledge is a majorchallenge for mathematics education. The current study examines the efficiency of a trainingprogram designed to improve flexibility in solving proportional word problems. 147 fifth gradestudents from high priority educational schools in the Paris region participated in thisexperiment. Ten classes, from five schools, were divided into experimental and control groups;both groups took part in eight learning sessions focused on solving proportionality problems.The experimental group received specific training on flexible categorization and problemcomparison, while the control group followed a more conventional teaching on proportionalityproblems. Students’ ability to categorize and solve the problems was evaluated pre-and postintervention.Results showed a significant effect of the intervention program on children’sability to categorize and solve proportional word problems. These findings highlight the roleof flexible categorization training in promoting arithmetic word problem solving. Theimplications for pedagogical design are discussed.

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“…Des résultats similaires ont même été obtenus auprès d'enseignants en biologie (Goldberg & Thompson-Schill, 2009), démontrant la robustesse de l'influence des conceptions intuitives. Il en est de même pour les conceptions de notions arithmétiques (Gros, Sander, & Thibaut, 2019 ;Gros, Thibaut & Sander, 2021 ;Gvozdic & Sander, 2018 ;Sander, 2018) personnelle et sociale. Cet enseignement articule des valeurs, des savoirs et des pratiques (pp.5-6).…”

Section: Esprit Critique Flexibilité Cognitive Catégorisation Multipl...unclassified

Caractère résilient des conceptions intuitives des notions de justice et de liberté : résultats d'une étude au collège dans le cours d'enseignement moral et civique

Sander¹,

Marcoux²,

Wyss³

et al. 2021

Preprint

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Depuis, et avec l’impulsion de, l’esprit des Lumières, le développement de la pensée critique en tant que compétence transversale est devenu un enjeu éducatif en France et dans de nombreux pays francophones (Crahay & Marcoux, 2011). Plus encore, aujourd’hui et suite aux derniers faits divers scolaires, il semble crucial de préparer les élèves, en tant que membres déjà actifs de la société et citoyens de demain, à porter un regard critique, au sens d'avoir une opinion éclairée, sur les valeurs proposées par la société dans laquelle ils sont insérés. Pour cela, une proposition est, comme le formule la Charte du Conseil de l'Europe sur l'éducation à la citoyenneté démocratique et l'éducation aux droits de l'Homme (2010), de donner aux élèves les moyens de s'informer et de participer à la vie politique et sociale. Ce lien de l'éducation à la citoyenneté avec l'enjeu pédagogique du développement de la pensée critique a déjà été mis en évidence par de nombreux chercheurs donnant naissance à la notion d'éducation à la citoyenneté critique (Johnson & Morris, 2010 ; voir aussi Leenders, Veugelers, & De Kat, 2008 ; Veugelers, 2007). En France, même si Feyfant (2014) a montré que l’enseignement de la morale n’allait pas de soi et que Kahn (2015) s’est interrogée tant sur sa valeur universelle que sur sa transmission possible, il existe, depuis 2015, un programme d’enseignement moral et civique qui a pour ambition de servir ces deux objectifs. Cependant, il apparaît également de plus en plus clairement que les idées préconçues peuvent entraver les conceptions des questions de société et donc influencer les attitudes et les décisions. Dans ce cadre, améliorer ses connaissances de notions essentielles en éducation citoyenne telles que la justice et la liberté permettrait d’aller au-delà de ses idées préconçues et de faire évoluer sa perspective, favorisant ainsi le développement de l’esprit critique. Sur le plan scolaire, il semble fécond d’accompagner les élèves dans l’enrichissement de leurs conceptions de ces notions afin qu’ils soient en mesure de participer aux débats de manière mieux informée.

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When intuitive conceptions overshadow pedagogical content knowledge: Teachers’ conceptions of students’ arithmetic word problem solving strategies

Cited by 17 publications

References 33 publications

How robust are intuitive conceptions? Insights from production tasks regarding arithmetic operations.

How robust are intuitive conceptions? Insights from production tasks regarding arithmetic operations.

Leveraging cognitive flexibility through flexible categorization training

Caractère résilient des conceptions intuitives des notions de justice et de liberté : résultats d'une étude au collège dans le cours d'enseignement moral et civique

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