Transfer of strategy use by semantic recoding in arithmetic problem solving

Gamo, Sylvie; Sander, Emmanuel; Richard, Jean-François

doi:10.1016/j.learninstruc.2009.04.001

Cited by 48 publications

(56 citation statements)

References 20 publications

(29 reference statements)

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“…Our materials were inspired by Gamo et al (2010), who showed that problems with the same formal mathematical structure are nevertheless preferentially solved with one of two available solving strategies, depending on the semantic content of the problem. Consider the weight problem in Table 1: this problem can be solved through two strategies.…”

Section: Methodsmentioning

confidence: 99%

“…The authors demonstrated that slight, mathematically-irrelevant changes in the semantic relations linking the objects mentioned in the cover stories (e.g., computers assigned to secretaries vs. secretaries assigned to computers) led to significant performance differences. Subsequent research has shown that non-mathematical semantic information related to the entities described in a problem influences lay solvers' performance (Bassok, Chase, & Martin, 1998;Gros, Sander, & Thibaut, 2016;Thevenot & Barrouillet, 2015;Verschaffel, De Corte, & Vierstraete, 1999;Vicente, Orrantia, & Verschaffel, 2007) as well as strategy choice (Gamo, Sander, & Richard, 2010;Gros, Thibaut, & Sander, 2017) and transfer (Gros, Thibaut, & Sander, 2015) on arithmetic word problems. Most of the available evidence regarding this issue has been collected with children and non-expert adults on problems that were not straightforward (e.g., complex permutation problems).…”

Section: Introductionmentioning

confidence: 99%

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When masters of abstraction run into a concrete wall: Experts failing arithmetic word problems

Gros

Sander

Thibaut³

2019

Psychon Bull Rev

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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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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

When masters of abstraction run into a concrete wall: Experts failing arithmetic word problems

Gros

Sander

Thibaut³

2019

Psychon Bull Rev

Self Cite

View full text Add to dashboard Cite

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“…Especially demanding is the "knowledge compilation" mechanism involved in transfer, which "operates like a translation device, interpreting prior declarative knowledge into a set of procedures or cognitive rules to perform a specific task… [and]…can cause performance errors because of the working memory limitations that constrain how much declarative information can be retrieved" (Nokes-Malach & Mestre, 2013, p. 187). Researchers infer transfer from scores in the transfer task in measures such as recall (O'Sullivan & Pressley, 1984), number of analogies produced (Brown & Kane, 1988), or number of problems solved (Gamo, Sander, & Richard, 2010). However, a more precise assessment of transfer requires measuring not only these performance scores but also the degree of transfer of the strategy (or rule, etc.).…”

Section: Transfer Of Cognitive Strategies In Childrenmentioning

confidence: 99%

Young children's transfer of strategies: Utilization deficiencies, executive function, and metacognition

Clerc

Miller

Cosnefroy

2014

Developmental Review

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The purpose of this review is to present a new perspective on children's development of transfer of learning. The focus is on transfer of the effectiveness of a skill (i.e., improved performance), rather than just the transfer of the skill (e.g., a strategy) itself. Specifically, we examined the role of strategy utilization deficiencies, along with cognitive capacity, in the transfer of a memory strategy and, especially, strategy effectiveness (increased recall). Executive functions, metacognition, and mindset were considered as mechanisms that can both facilitate and hinder transfer of strategy effectiveness. Implications for theorizing about both transfer and utilization deficiencies were discussed.

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“…Die Möglichkeit des Strategietransfers zwischen unterschiedlichen Aufgaben wurde in der Geometrie von Chinnappan und Lawson (1996) und für die Arithmetik von Gamo et al (2010) untersucht und bestätigt. In der genannten Studie zum Strategietransfer im Bereich Geometrie wurde anhand eines Kontrollgruppendesigns der Einfluss eines Strategietrainings, das aus den Elementen Wiederholendes Lesen, Planung und Kontrolle bestand, auf die Testleistungen von Schülern bei der Bearbeitung von mathematischen Aufgaben untersucht.…”

Section: Modellierungskompetenzunclassified

Selbstberichtete Strategienutzung und mathematische Modellierungskompetenz

Schukajlow

Leiß

2011

J Math Didakt

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ZusammenfassungIn der vorliegenden Untersuchung wurde die selbstberichtete Strategienutzung von Neuntklässlern beim Bearbeiten von Modellierungsaufgaben erfasst und im Zusammenhang mit ihren mathematischen Leistungen betrachtet. Dazu haben 86 Neuntklässler aus zwei Realschulklassen und acht Gymnasialklassen zunächst einen Modellierungstest bearbeitet. Anschließend wurden sie zu ihren allgemeinen und aufgabenbezogenen Lernstrategien beim Lösen von Modellierungsaufgaben befragt. Die Schüler gaben im Rahmen der allgemeinen Befragung an, deutlich seltener ihre Lösungsprozesse zu planen, als Kontroll-, Elaborations-, Wiederholungs-oder Organisationsstrategien zu benutzen. Die Ergebnisse der aufgabenbezogenen Befragung zeigen, dass die Strategien Zeichnen einer Skizze und Suchen einer Analogie häufiger beim Bearbeiten der Modellierungsaufgaben zum Inhaltsbereich Satz des Pythagoras als zum Bereich Lineare Funktionen berichtet werden. Bezüglich der selbstberichteten Strategienutzung und der mathematischen Modellierungsleistungen der Lernenden konnten keine signifikanten Korrelationen festgestellt werden, so dass sich hier die Frage der inhaltlichen Bedeutung von Lernstrategien bzw. des methodisch angemessenen Vorgehens stellt, welche in weiteren Studien zu validieren ist.Schlüsselwörter Modellieren · Strategien · Anwendungsbezogener Mathematikunterricht · Strategien S. Schukajlow ( ) FB10 Mathematics Subject Classification (2000)97C30 · 97C70 · 97D50 · 97D70 · 97M10 Self-reported use of strategies and mathematical modellingAbstract This article deals with a report by ninth graders on their use of learning strategies when solving modelling problems and to what extent the strategy use is related to modelling competency. 86 ninth graders from 2 German middle track classes (Realschule) and 8 upper track classes (Gymnasium) first took a modelling test. Afterwards they were asked about their use of general and task-specific learning strategies while solving the problems. The students reported that they used planning strategies more seldom than the control, elaboration, rehearsal and organisation ones. The analysis of the task-specific questionnaire shows that the strategies "make a drawing" and "search for analogy" were reported to be more frequently used while solving modelling problems about the "Pythagorean theorem", than about "linear functions". There were no significant correlations between the self-reported strategy use and the modelling competency. Therefore, both the role of learning strategies in performance and the method of measuring learning strategies and performance ought to be explored in further studies.

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Transfer of strategy use by semantic recoding in arithmetic problem solving

Cited by 48 publications

References 20 publications

When masters of abstraction run into a concrete wall: Experts failing arithmetic word problems

When masters of abstraction run into a concrete wall: Experts failing arithmetic word problems

Young children's transfer of strategies: Utilization deficiencies, executive function, and metacognition

Selbstberichtete Strategienutzung und mathematische Modellierungskompetenz

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