Piaget's Concept of Number Development: Its Relevance to Mathematics Learning

Favreau, Mireille; Lemoyne, Gisèle

doi:10.2307/748927

Cited by 5 publications

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“…Findings tend to indicate, however, that exact sequences and concurrences may need to be reanalyzed and the operational model reassessed. For example, consistent with recent research, the acquisition of neither class inclusion nor conservation, whether through development or learning, appears to be an absolute prerequisite to the learning of many number skills (Fuson, 1982;Hiebert et al, 1982;Lemoyne & Favreau, 1981;Pennington et al, 1980;Saxe, 1979;Souviney, 1980). More importantly, the number skills treatment evidenced a greater transfer effect.…”

Section: Discussionsupporting

confidence: 64%

“…Attainment of at least some cognitive operations shows a moderate to high positive correlation with achievement in mathematics (Carpenter, 1980;Souviney, 1980). These operations do not appear to be absolute prerequisites for learning some number skills and concepts, although developmentally advanced children use more sophisticated strategies, and specific operations may be necessary to learn to apply more advanced processes (Fuson, 1982;Hiebert, Carpenter, & Moser, 1982;Lemoyne & Favreau, 1981;Saxe, 1979). However, correlational evidence affords a weak test of the premise.…”

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confidence: 99%

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Training effects on the development and generalization of Piagetian logical operations and knowledge of number.

Clements¹

1984

Journal of Educational Psychology

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Investigated the effects of 2 training sequences on the development of logical operations and number in 45 middle-class preschool children (mean age 4 yrs 6 mo). Ss were randomly assigned and trained for 8 wks in 1 of 3 conditions: logical foundations (classification and seriation), number skills (counting), and control. Each of the experimental treatments was based on either of 2 broad perspectives: the logical foundations model of Piagetian theorists or a skills integration model. Instruments measuring number abilities and logical operations were designed as pre- and posttest measures. Findings show that (a) both experimental groups significantly outperformed the control group on both tests, (b) the number skills group significantly outperformed the logical foundations group on the number test, and (c) there was no significant difference between the experimental groups on the logical operations test.

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Section: Discussionsupporting

confidence: 64%

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confidence: 99%

Training effects on the development and generalization of Piagetian logical operations and knowledge of number.

Clements¹

1984

Journal of Educational Psychology

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“…These are often ignored by general theories. Thus, it is not a surprise that grasping Piagetian concepts, such as conservation of number, is not related to learning and doing arithmetic (Hiebert, Carpenter, & Moser, 1982;Lemoyne & Favreau, 1981;Pennington, Wallach, & Wallach, 1980). Also, these theories underestimated the complexity of development.…”

Section: Capitalizing On Developmental Theoriesmentioning

confidence: 99%

Bridging Educational Priorities with Developmental Priorities: Towards a Developmental Theory of Instruction

Δημητρίου¹,

Greiff²,

Makris³

et al. 2020

Preprint

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This paper summarizes a theory of cognitive development and discusses its educational implications. The paper first outlines a set of principles that might allow tuning developmental priorities with educational priorities. It postulates, in contrast to several classic developmental theories, that developmental priorities change with development. It outlines the cognitive profile of four successive developmental cycles and presents evidence showing that developmental priorities change from interaction control in infancy to representational control in preschool to inferential control in primary school to logical truth control in adolescence. Studies are then summarized showing that the cognitive priorities of each cycle are the best predictors of school achievement in this or later cycles. Finally, we outline developmental changes in general problem-solving skills and show that learning in different domains, such as language and mathematics, depends on an interaction between the general cognitive processes dominating in each cycle and the state of the symbol systems associated with this domain. If command of any of these systems is deficient, specific learning deficiencies may emerge, as in dyslexia and dyscalculia. Principles for ameliorating these conditions are outlined.3 4 Bridging Educational Priorities with Developmental Priorities: Towards a Developmental Theory of Instruction delays in grasping and consolidating the concepts and skills of interest (Demetriou & Spanoudis, 2018). We focus on general problem-solving processes and learning and problem solving in two domains, language and mathematics. Table 1 summarizes developmental priorities, educational priorities, and learning goals across age periods and domains, Education has looked for direction and teaching practices in psychological theories since the early 20 th century. The interaction between education and psychology met with both successes and failures. Here, we will not discuss or evaluate in detail psychological theories, which have been important for education in the past. However, we attempt a brief overview of the main ideas drawn from them and evaluate their contribution to the development of education of our time. We will then present a comprehensive model drawing on the successes and failures of the past and capitalizing on recent research.

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“…Piaget's seminal studies of children's numerical development have generated a large range of related studies. Gelman and Gallistel (1978: 3) for example, criticised Piaget's theory of number development as characterising children's knowledge in terms of what they could not do rather than what they could do, while others have investigated (e.g., Steffe, Hirstein & Spikes 1976;Lemoyne & Favreau 1981;Hiebert, Carpenter & Moser 1982) the relationships between Piagetian abilities such as quantitative comparisons and class inclusion, and children's learning of arithmetic topics such as addition and subtraction. Studies such as these have provided a foundation for the development of theories of number learning that are more content-specific (e.g., Steffe et al 1983;Steffe & Cobb 1988) than those that resulted from the pioneering work of Piaget.…”

Section: Radical Constructivism and Information Processing Wdifferentmentioning

confidence: 99%

An application of the epistemology of radical constructivism to the study of learning

Wright¹

1991

Aust. Educ. Res.

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Piaget's Concept of Number Development: Its Relevance to Mathematics Learning

Cited by 5 publications

References 0 publications

Training effects on the development and generalization of Piagetian logical operations and knowledge of number.

Training effects on the development and generalization of Piagetian logical operations and knowledge of number.

Bridging Educational Priorities with Developmental Priorities: Towards a Developmental Theory of Instruction

An application of the epistemology of radical constructivism to the study of learning

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