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Representing quantity beyond whole numbers: some, none, and part.

E Bialystok¹, J Codd

¹Department of Psychology, York University, Toronto, Ontario. ellenb@yorku.ca

Canadian Journal of Experimental Psychology = Revue Canadienne De Psychologie Experimentale

|July 6, 2000

Summary

Children aged 3-7 develop number notation skills, moving towards conventional symbols. While understanding whole numbers and zeros, their grasp of fractions remains limited.

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Area of Science:

Cognitive Development
Numerical Cognition
Educational Psychology

Background:

Children's development of notational systems for quantities follows a progression from idiosyncratic to analogical to conventional numerical notations.
Prior research highlights a developmental shift in how children represent numerical information.

Purpose of the Study:

To investigate the development of children's ability to produce and interpret notations for whole numbers, zeros, and fractions.
To examine the influence of age and quantity type on children's notational choices and comprehension.

Main Methods:

Children aged 3 to 7 years created notations for quantities in a game-like setting.
Notations for whole numbers, zeros, and fractions were assessed for production and later interpretation by the children.
Children's notational choices were analyzed in relation to their age and the quantity type.

Main Results:

A developmental trend towards increased use of conventional notations was observed across all quantity types.
Interpretability of notations varied: highest for conventional numbers, lower for analogical, and poor for idiosyncratic representations.
Age was the primary factor influencing notation choice, not the specific quantity (whole number, zero, or fraction).

Conclusions:

Children demonstrate a developmental progression in using conventional numerical notations, with age being a key driver.
Comprehension of notations is strongly linked to their conventionality, with significant limitations in understanding fractions.
Early numerical development shows robust understanding of whole numbers and zeros, but requires further development for fractional concepts.