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Kainulainen, Mikko; McMullen, Jake; Lehtinen, Erno – Cognition and Instruction, 2017
Difficulties with rational numbers have been explained by a natural number bias, where concepts of natural numbers are inappropriately applied to rational numbers. Overcoming this difficulty may require a radical restructuring of previous knowledge. In order to capture this development, we examined third- to fifth-grade students' understanding of…
Descriptors: Numbers, Foreign Countries, Grade 3, Grade 4
Do First Graders Make Efficient Use of External Number Representations? The Case of the Twenty-Frame
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
Sfard, Anna; Lavie, Irit – Cognition and Instruction, 2005
Based on close observations of two 4-year-old children responding to their parents' requests for quantitative comparisons, we offer a "participationist" account of the origins and development of numerical thinking, one that portrays numbers as a product rather than a pregiven object of human communication. In parallel, we propose a…
Descriptors: Cognitive Development, Number Concepts, Mathematics Instruction