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Understanding arithmetic concepts: Does operation matter?

Katherine M Robinson1, Jill A B Price1, Brendan Demyen1

  • 1Department of Psychology, University of Regina, Regina, Saskatchewan S4S 0A2, Canada.

Journal of Experimental Child Psychology
|October 20, 2017
PubMed
Summary
This summary is machine-generated.

Children’s understanding of arithmetic concepts varies widely, with multiplicative concepts being harder than additive ones. Associativity proved most challenging for all students across grades 5-7.

Keywords:
AdditionArithmeticConceptual knowledgeDivisionMultiplicationSubtraction

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Area of Science:

  • Cognitive Development
  • Mathematics Education

Background:

  • Limited research on children's arithmetic concepts focuses on additive and single concepts.
  • Existing research may not fully capture the complexity of conceptual development in arithmetic.

Purpose of the Study:

  • Investigate additive and multiplicative versions of six arithmetic concepts (identity, negation, commutativity, equivalence, inversion, associativity) in students from Grades 5 to 7.
  • Examine grade-level differences and individual variability in understanding these concepts.

Main Methods:

  • Assessed understanding of additive and multiplicative arithmetic concepts in Grades 5, 6, and 7.
  • Employed cluster analysis to identify patterns in individual differences.
  • Analyzed problem-solving accuracy in relation to conceptual knowledge.

Main Results:

  • Multiplicative concepts were less understood than additive ones.
  • No significant grade-level differences in conceptual knowledge were found, but older students were more accurate problem solvers.
  • Children demonstrated varied understanding, with identity and negation being well-understood, while associativity was the most difficult concept for all.

Conclusions:

  • Children's conceptual knowledge of arithmetic exhibits significant individual variability.
  • Understanding of arithmetic concepts is complex and develops differently across students.
  • Associativity and multiplicative concepts present particular challenges in arithmetic learning.