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Fostering Formal Commutativity Knowledge with Approximate Arithmetic.

Sonja Maria Hansen1, Hilde Haider1, Alexandra Eichler1

  • 1University of Cologne, Department of Psychology, Cologne, Germany.

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|November 13, 2015
PubMed
Summary
This summary is machine-generated.

Approximate calculation with symbolic quantities can improve elementary students' use of mathematical shortcuts. However, this procedural improvement doesn't always translate to deeper conceptual understanding of principles like commutativity.

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Area of Science:

  • Cognitive Psychology
  • Mathematics Education
  • Developmental Psychology

Background:

  • Nonsymbolic number estimation is known to enhance exact number processing and arithmetic skills in children.
  • The potential of approximate calculation with symbolic quantities to improve understanding of abstract mathematical principles remains less explored.

Purpose of the Study:

  • To investigate whether approximate calculation with symbolic quantities can influence procedural and conceptual knowledge of the commutativity principle in elementary school students.
  • To examine the relationship between procedural proficiency and conceptual understanding of commutativity.

Main Methods:

  • Three experiments were conducted with first and third graders.
  • Participants engaged in approximate calculation with symbolic quantities.
  • Performance on formal arithmetic tasks assessing the use of commutativity-based shortcuts and conceptual knowledge was analyzed.

Main Results:

  • Approximate calculation with symbolic quantities positively impacted the spontaneous use of commutativity-based shortcuts in arithmetic problems across different grade levels.
  • No comparable positive effect was observed on the application of conceptual knowledge of the commutativity principle.
  • Procedural proficiency in applying commutativity did not consistently correlate with conceptual understanding.

Conclusions:

  • Approximation strategies can enhance the procedural application of specific arithmetic principles, such as commutativity, in elementary education.
  • Conceptual understanding of mathematical principles may lag behind procedural skill development during elementary school years.
  • Findings highlight a potential dissociation between performing mathematical procedures and grasping their underlying concepts.