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Symbolic arithmetic knowledge without instruction.

Camilla K Gilmore1, Shannon E McCarthy, Elizabeth S Spelke

  • 1Learning Sciences Research Institute, University of Nottingham, Wollaton Road, Nottingham NG8 1BB, UK. camilla.gilmore@nottingham.ac.uk

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|June 1, 2007
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Summary

Young children can use their innate approximate number system to perform symbolic addition and subtraction. This finding suggests new ways to improve early math education and overcome learning difficulties.

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Area of Science:

  • Cognitive Science
  • Developmental Psychology
  • Mathematics Education

Background:

  • Symbolic arithmetic is crucial but difficult for children to acquire.
  • Adults use approximate number representations for mental arithmetic.
  • Nonsymbolic number systems support approximate calculations in various age groups.

Purpose of the Study:

  • To investigate if young children can perform symbolic arithmetic using their nonsymbolic number system.
  • To explore the potential of nonsymbolic representations in early symbolic arithmetic acquisition.

Main Methods:

  • Children nearing arithmetic instruction age were tested on symbolic addition and subtraction problems.
  • Problems involved approximate calculations with large numbers.
  • Testing occurred in both laboratory and school settings.

Main Results:

  • Children successfully solved symbolic addition and subtraction problems.
  • Performance was observed across diverse socio-economic backgrounds.
  • Children leveraged their nonsymbolic number system for symbolic tasks.

Conclusions:

  • Symbolic arithmetic skills are accessible to children before formal algorithmic instruction.
  • Nonsymbolic number representations are a foundation for early symbolic arithmetic.
  • Findings offer insights into children's arithmetic learning challenges and potential interventions.