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Obersteiner, Andreas; Reiss, Kristina; Ufer, Stefan; Luwel, Koen; Verschaffel, Lieven – Cognition and Instruction, 2014
External number representations are commonly used throughout the first years of instruction. The twenty-frame is a grid that contains two rows of 10 dots each, and within each row, dots are organized in two groups of five. The assumption is that children can make use of these structures for enumerating the dots, rather than relying on one-by-one…
Descriptors: Grade 1, Elementary School Students, Numbers, Number Concepts
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Van Dooren, Wim; De Bock, Dirk; Verschaffel, Lieven – Cognition and Instruction, 2010
This study builds on two lines of research that have so far developed largely separately: the use of additive methods to solve proportional word problems and the use of proportional methods to solve additive word problems. We investigated the development with age of both kinds of erroneous solution methods. We gave a test containing missing-value…
Descriptors: Numbers, Word Problems (Mathematics), Mathematical Logic, Problem Solving
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Verschaffel, Lieven; Reybrouck, Mark; Jans, Christine; Van Dooren, Wim – Cognition and Instruction, 2010
This study investigates children's metarepresentational competence with regard to listening to and making sense of simple sonic stimuli. Using diSessa's (2003) work on metarepresentational competence in mathematics and sciences as theoretical and empirical background, it aims to assess children's criteria for representational adequacy of graphical…
Descriptors: Auditory Perception, Auditory Stimuli, Music Education, Criteria
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Torbeyns, Joke; Verschaffel, Lieven; Ghesquiere, Pol – Cognition and Instruction, 2006
The aim of the study was to analyze the development of children's adaptive expertise in computing sums and differences up to 100. We defined the adaptive nature of children's strategy choices on the basis of problem (addition, subtraction), achievement, and strategy performance (accuracy, speed). Sixty-nine 2nd graders of high, above-average, or…
Descriptors: Children, Computation, Arithmetic, Problem Solving
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Torbeyns, Joke; Verschaffel, Lieven; Ghesquiere, Pol – Cognition and Instruction, 2005
In this study, we investigated the fluency with which first graders of different mathematical achievement levels applied multiple, school-taught strategies for finding arithmetic sums over 10. We characterized children's strategies with the 4 parameters of Lemaire and Siegler's (1995) model of strategy change (strategy repertoire, distribution,…
Descriptors: Grade 1, Mathematics Achievement, Thinking Skills, Teaching Methods
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Van Dooren, Wim; De Bock, Dirk; Hessels, An; Janssens, Dirk; Verschaffel, Lieven – Cognition and Instruction, 2005
Previous research (e.g., De Bock, 2002) has shown that--due to the extensive attention paid to proportional reasoning in elementary and secondary mathematics education--many students tend to overrely on proportional methods in diverse domains of mathematics (e.g., geometry, probability). We investigated the development of misapplication of…
Descriptors: Age Differences, Mathematics Education, Arithmetic, Mathematical Concepts