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Iterating between lessons on concepts and procedures can improve mathematics knowledge.

Bethany Rittle-Johnson1, Kenneth Koedinger

  • 1Department of Psychology and Human Development, Vanderbilt University, Nashville, Tennessee 37203, USA. bethany.rittle-johnson@vanderbilt.edu

The British Journal of Educational Psychology
|February 21, 2009
PubMed
Summary
This summary is machine-generated.

Iterating between concept and procedure lessons improved students' learning and transfer of decimal arithmetic procedures. This iterative approach supports knowledge development in both concepts and procedures.

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Area of Science:

  • Educational Psychology
  • Mathematics Education

Background:

  • Knowledge of concepts and procedures develops iteratively, with gains in one type fostering gains in the other.
  • Iterative learning sequences may enhance overall educational outcomes.

Purpose of the Study:

  • To compare the instructional benefits of iterative versus concepts-first lesson sequences.
  • To evaluate learning of decimal place-value concepts and arithmetic procedures.

Main Methods:

  • Two classroom experiments involving sixth-grade students (N=77 and 26).
  • Students used an intelligent-tutoring system for six decimal lessons.
  • Lessons were sequenced either iteratively (alternating concepts and procedures) or concepts-first.

Main Results:

  • Students in the iterative condition showed greater gains in procedural knowledge and transfer.
  • Conceptual knowledge gains were similar across both iterative and concepts-first conditions.
  • Pre-test knowledge in one domain predicted gains in the other, supporting an iterative model.

Conclusions:

  • Iterative lesson sequencing enhances learning and transfer, especially for mathematical procedures.
  • Findings support an iterative model for the development of conceptual and procedural knowledge.