Cognitive Development: Construction of Number

Vocabulary flashcards covering the cognitive and developmental foundations of number acquisition, counting, subitizing, and early mathematical concepts.

Insight (Gestalt theory)

A sudden conscious realization of one's own mental functioning and problem-solving process, closely related to metacognition.

Constructivism (Piaget)

A developmental theory stating that knowledge is constructed through the child's active interaction with the material environment, where cognitive structures emerge from action rather than innate faculties alone.

Innatism (Chomsky)

A theoretical approach asserting that fundamental cognitive and linguistic faculties are innate and present from birth, developing independently of environmental construction.

Kinesthetic approach to number construction (Brissiaud)

A psychological theory positing that mental imagery and bodily actions—particularly finger and hand gestures—support the internal representation of numerical quantities without explicit counting.

Mental imagery

The internal, concrete visual representation of objects in the mind, characterized by substantial inter-individual differences.

Bi-univocal correspondence

A strict one-to-one mapping between a physical or symbolic representation (such as a clay ball in ancient Mesopotamia) and each individual represented entity (such as an animal).

Psychoanalytic approach to dyscalculia (S. Baruk)

A perspective that attributes emotional and affective origins to numerical difficulties or dyscalculia, linking them to family dynamics such as the birth of a sibling or birth order.

Conservation (Piaget)

The cognitive understanding that a quantity or physical entity remains unchanged despite alterations in perceptual appearance; considered an a priori functional requirement for operational thought.

Object permanence

The earliest form of conservation according to Piaget, describing the awareness that an object continues to exist even when it is out of sight.

Rabbit window experiment (Melher, 1990)

An experimental demonstration that 5-month-old infants expect tall rabbits to appear in an elevated window opening and show surprise when they do not, proving that infants perceive objects as dense physical entities and challenging pure empiricist accounts.

Empiricism (Associationism)

A theoretical stance claiming that knowledge develops entirely through stimulus-response associations and feedback, arguing that infants cannot reason about situations they have not previously experienced.

Proto-concept non-permanence (Wynn & Houdé)

The developmental hypothesis that early competencies (such as 5-month-olds detecting arithmetic violations like $1 + 1 = 3$) may temporarily disappear around ages 2–3 due to perceptual interference before re-emerging around ages 4–5.

Quantity discrimination (Estimation)

An approximate, fast, non-symbolic, and non-conscious process used to compare relative magnitudes or set sizes without counting, independent of language and experience.

Habituation paradigm (Xu and Spelke)

An experimental procedure where infants are repeatedly presented with visual arrays containing a fixed number of dots until gaze duration decreases; recovery of attention when the dot count is doubled proves sensitivity to a $1:2$ ratio.

Subitizing

The rapid, non-counting ability to instantly assign a cardinal value to small sets of items, processed in parallel by visual short-term memory.

Chunking (in subitizing)

The mental grouping of items into conventional, recognizable spatial arrangements (e.g., dice patterns or 10 dots split into 5 and 5) that enables rapid quantity apprehension.

Enumeration (Dénombrement)

A quantitative process that abstracts from visual surface properties (such as size and spacing) to determine the exact decomposition and cardinal value of a set.

Pseudo-counting (Pseudo-dénombrement)

A child's verbal recitation of the number word sequence (e.g., chanting "1, 2, 3, 4") while pointing, without understanding that the final recited word designates the total cardinality of the set.

Cognitive inhibition (in numerical tasks)

The executive process required to suppress salient visual dimensions (such as physical item size, line length, or spatial spacing) in order to judge sets purely by numerical quantity.

Cardinal use of number

The mathematical application of a number to represent the total quantity or size of a collection of items.

Ordinal use of number

The mathematical application of a number to designate rank, sequence, or position in an ordered set (e.g., building floors, hopscotch squares).

Number-word association task (Karen Wynn)

An experiment showing that 2.5-year-old children succeed at identifying a card with 1 object versus multiple objects, but require an additional year to reliably discriminate cards depicting 2, 3, or 4 objects.