The Child's Conception of Number

By J. Piaget. 1953

Subfields: Cognitive Science & Psychology

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Learning to Reason Deductively: Math Word Problem Solving as Complex Relation Extraction (2022, background): “Solving math problems generally requires deductive reasoning, which is also regarded as one of the important abilities in children’s cognitive development (Piaget, 1952).”
Why Does Gender Matter? Counteracting Stereotypes with Young Children. (2011, background): “His thinking was influenced by Piaget, who portrayed children as active learners who use interactions with their environment to construct an understanding of the world around them (Piaget, 1961).”
Natural Number and Natural Geometry (2011, background): “Although the development of natural number has been subjected to intense investigation since the pioneering studies of Piaget [94] and Gelman and Gallistel [95], the development of Euclidean geometry has received less attention.”
Understanding Primes: The Role of Representation. (2004, background): “In this approach, the property of primality is added as a yes/no property assigned to the object of a natural number that has been constructed by learners at earlier stages as an outcome of generalization of equivalence and seriation (Piaget, 1965).”
A Learning Trajectory in 6-Year-Olds' Thinking about Generalizing Functional Relationships. (2015, background): “For us, this is reminiscent of Sfard’s (1991) account of how a child with an operational conception of number would respond to the question “How many objects are there?” by repeating a procedure of counting rather than stating the total number of objects (see also Piaget, 1952).”
Fostering At-Risk Preschoolers' Number Sense (2009, background): “One is the belief—still held by some early childhood educators (see, e.g., Balfanz, 1999; Copley, 2004)—that mathematics instruction in general is not developmentally appropriate for preschoolers (e.g., Piaget, 1965; Thorndike, 1922).”
Executive Functions (2012, unknown): “For example, in Piaget’s famous test of conservation of liquid volume (Piaget 1952/1941), the same amount of liquid is poured into a short, fat beaker and a tall, thin beaker.”
Mathematical Play and Playful Mathematics: A Guide for Early Education (2006, background): “Also, despite strong critiques (e. g., Donaldson, 1978), we should not forget the substantial body of Piaget's research (e. g., Piaget, 1952a; Piaget & Inhelder, 1967) showing that children do indeed have clear cognitive limitations.”
Gender Identity and Stereotyping in Early and Middle Childhood (2010, background): “Gender constancy is related to children’s cognitive-developmental task of learning constancy and conservation in general (Piaget, 1965).”
On “Understanding” Children's Developing Use of Inversion (2009, background): “Understanding relations among operations that conform to principles such as commutativity, associativity, inversion, and compensation is critical for understanding arithmetic as a coherent mathematical system (Bryant, Christie, & Rendu, 1999; Piaget, 1952; Starkey & Gelman, 1982).”
Objects, actions, and images: a perspective on early number development (2000, background): “JMB: in press (1999) 3 INTRODUCTION The notion that numerical concepts are formed from actions with physical objects underpins the conceived cognitive development of simple arithmetic (see, for example, Piaget, 1965; Steffe, Glaserfeld, Richards, & Cobb, 1983; Kamii, 1985; Gray & Tall, 1994).”