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Related Experiment Video

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Quantifying Learning in Young Infants: Tracking Leg Actions During a Discovery-learning Task

Quantifying Learning in Young Infants: Tracking Leg Actions During a Discovery-learning Task

Published on: June 1, 2015

Why set-comparison is vital in early number learning.

Kevin Muldoon¹, Charlie Lewis, Norman Freeman

¹School of Life Sciences, Heriot Watt University, Edinburgh, EH14 4AS, UK. k.muldoon@hw.ac.uk

Trends in Cognitive Sciences

|April 21, 2009

Summary

Cardinal numbers have two key roles: quantity and set equivalence. Current models focus on quantity, but we explore how children learn to link counting to comparing sets for equivalence.

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Area of Science:

Cognitive Science
Developmental Psychology
Mathematics Education

Background:

Cardinal numbers serve dual functions: quantifying elements within a set and determining set equivalence.
Existing numerical models primarily address the 'how many' aspect of counting.
These models are insufficient for understanding the 'set equivalence' function of cardinal numbers.

Purpose of the Study:

To investigate the cognitive processes linking counting to set comparison.
To explore the developmental trajectory of understanding number for equivalence.
To identify how numerical understanding shifts to encompass set equivalence.

Main Methods:

Conceptual analysis of numerical representation and its functions.
Exploration of developmental stages in numeracy acquisition.
Examination of the transition from quantity representation to equivalence understanding.

Main Results:

Numerical representations sufficient for quantity are insufficient for equivalence.
A developmental shift is necessary to link counting to set comparison.
Understanding equivalence requires a more abstract numerical representation.

Conclusions:

Current models of counting need to incorporate the equivalence function.
Further research is needed on the formative years of numeracy development.
Developing an understanding of set equivalence is a crucial step in mathematical cognition.