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Showing 1 to 15 of 43 results Save | Export
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Hußmann, Stephan; Schacht, Florian; Schindler, Maike – Mathematics Education Research Journal, 2019
The purpose of this article is to show how the philosophical theory of inferentialism can be used to understand students' conceptual development in the field of mathematics. Based on the works of philosophers such as Robert Brandom, an epistemological theory in mathematics education is presented that offers the opportunity to trace students'…
Descriptors: Inferences, Epistemology, Mathematics Skills, Mathematical Logic
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Chandler, Cynthia C.; Kamii, Constance – Journal for Research in Mathematics Education, 2009
The purpose of this study was to investigate children's construction of 10s out of the 1s they have already constructed. It was found that, for many younger children, a dime was something different from 10 pennies even though they could say with confidence that a dime was worth 10 cents. As the children grew older, their performance improved.…
Descriptors: Problem Solving, Arithmetic, Number Concepts, Children
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Rousselle, Laurence; Noel, Marie-Pascale – Cognition, 2007
Forty-five children with mathematics learning disabilities, with and without comorbid reading disabilities, were compared to 45 normally achieving peers in tasks assessing basic numerical skills. Children with mathematics disabilities were only impaired when comparing Arabic digits (i.e., symbolic number magnitude) but not when comparing…
Descriptors: Symbols (Mathematics), Reading Difficulties, Mathematics Education, Learning Disabilities
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Pillay, Hitendra; Wilss, Lynn; Boulton-Lewis, Gillian – Mathematics Education Research Journal, 1998
Examines arithmetic and algebra knowledge from a cognitive perspective in an effort to determine what constitutes a pre-algebraic level of understanding. Presents results of a longitudinal study designed to investigate students' readiness for algebra. Proposes a model for the transition from arithmetic to pre-algebra to algebra. Contains 29…
Descriptors: Algebra, Arithmetic, Cognitive Development, Elementary Secondary Education
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Nesher, P.; And Others – Educational Studies in Mathematics, 1982
Research conducted in several countries has shown consistent patterns of performance on "change,""combine," and "compare" word problems involving addition and subtraction. These findings are interpreted within a theoretical framework which emphasizes development of levels of word problem-solving ability related to…
Descriptors: Addition, Arithmetic, Cognitive Development, Computation
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Baroody, Arthur J.; Gatzke, Mary R. – Journal for Research in Mathematics Education, 1991
Explored is young children's ability to estimate set sizes and use reference points such as 10. Results indicated that many children could accurately place sets somewhat smaller than a reference point but had difficulty placing sets somewhat larger than a reference point. (CW)
Descriptors: Arithmetic, Cognitive Development, Cognitive Structures, Elementary School Mathematics
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Thornton, Carol A. – Educational Studies in Mathematics, 1990
In two parallel one-year studies, solution strategies for subtraction number facts and achievement patterns of matched groups of first graders in two different instructional programs were examined. Significant differences between groups were found favoring the strategy approach. (Author/CW)
Descriptors: Arithmetic, Cognitive Development, Cognitive Structures, Elementary Education
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Treffers, A. – Educational Studies in Mathematics, 1987
Describes the characteristics of progressive schematization with regard to column multiplication and column division. Contrasts this with column arithmetic based on progressive complexity. Presents a summary of research data concerning column arithmetic. (TW)
Descriptors: Arithmetic, Cognitive Development, Cognitive Structures, Division
Gray, Eddie; Howat, Hazel; Pitta-Pantazi, Demetra – 2002
This paper considers whether or not curriculum initiatives within England are in fact leading to qualitatively improved levels of thinking among children identified as lower achievers in arithmetic. Revisiting data from two earlier studies and introducing current data, the paper draws comparisons in the strategies that 8-year-old children use to…
Descriptors: Addition, Arithmetic, Cognitive Development, Curriculum Development
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Okazaki, Masakazu; Koyama, Masataka – Educational Studies in Mathematics, 2005
When we consider the gap between mathematics at elementary and secondary levels, and given the logical nature of mathematics at the latter level, it can be seen as important that the aspects of children's logical development in the upper grades in elementary school be clarified. In this study we focus on the teaching and learning of "division with…
Descriptors: Grade 5, Misconceptions, Mathematics Instruction, Arithmetic
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Watson, Ivan – Educational Studies in Mathematics, 1980
Diagnostic interviews were conducted with third graders to determine why they made mistakes on sixteen arithmetical tasks. A modified version of the Newman method of analyzing errors is discussed and applied to these interviews. (MP)
Descriptors: Arithmetic, Cognitive Development, Computation, Elementary Education
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Schliemann, Analucia D.; Araujo, Claudia; Cassunde, Maria Angela; Macedo, Suzana; Niceas, Lenice – Journal for Research in Mathematics Education, 1998
Analyzes the use of the commutative property for solving multiplication problems by children who learn about multiplication in schools and by street vendors who solve multiplication problem through repeated addition. Concludes that the use of commutativity to solve multiplication problems is closely related to the use of multiplication. Contains…
Descriptors: Arithmetic, Cognitive Development, Cross Cultural Studies, Elementary Secondary Education
Kieren, Thomas E., Ed. – 1980
Presented are materials related to the work of the Number and Measure and Rational Numbers working group of the Georgia Center for the Study of the Learning and Teaching of Mathematics. Much of the content reports on attempts to bring constructs from developmental psychology and mathematics to bear in understanding children's ideas of number and…
Descriptors: Arithmetic, Cognitive Development, Cognitive Processes, Developmental Psychology
Reeve, W. D., Ed. – 1935
In the first chapter Brownell critically examines the psychological bases of the three most common theories of arithmetic instruction: drill, incidental learning, and meaning. In chapter 2 the results of a nation-wide survey of actual teaching practices are reported. Chapter 3 presents a contrast between "informational arithmetic" and…
Descriptors: Arithmetic, Cognitive Development, Computation, Elementary School Mathematics
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Davis, Robert B. – Arithmetic Teacher, 1991
Examined is the situation in which pupils invent mathematics on their own and teachers' reactions to this situation. The assimilation of students' original ideas into correct mathematical concepts is discussed. (CW)
Descriptors: Arithmetic, Cognitive Development, Cognitive Structures, Computation
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