Using Arrays for Meaningful Multiplication

Author: Karl W. Kosko1
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  • 1 Kent State University, Kent, OH

Use Cuisenaire™ Rods to emphasize the column-and-row structure in arrays for meaningful multiplication.

Mathematics Teacher: Learning and Teaching PK-12
  • Barmby, Patrick, Tony Harries, Steve Higgins, and Jennifer Suggate. 2009. “The Array Representation and Primary Children’s Understanding and Reasoning in Multiplication.” Educational Studies in Mathematics 70, no. 3 (April): 21741.

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  • Davydov, Vasiliĭ Vasil'evich 1991. “A Psychological Analysis of the Operation of Multiplication.” In Psychological Abilities of Primary School Children in Learning Mathematics, edited by V. V. Davydov, pp. 985. Reston, VA: National Council of Teachers of Mathematics.

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  • Hackenberg, Amy J., and Eric S. Tillema. 2009. “Students’ Whole Number Multiplicative Concepts: A Critical Constructive Resource for Fraction Composition Schemes.” The Journal of Mathematical Behavior 28, no. 1 (March): 118.

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  • Kosko, Karl W. 2019. “Third Grade Teachers’ Self-Reported Use of Multiplication and Division Models.” School Science and Mathematics 119, no. 5 (May): 26274.

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  • Kosko, Karl W., and Rashmi Singh. 2018. “Third Grade Textbooks’ Models for Multiplication and Division.” In Proceedings of the 40th Annual Meeting of the North American Chapter for the Psychology of Mathematics Education, edited by T. E. Hodges, G. J. Roy, and A. M. Tyminski, pp. 11720. Greenville, SC: University of South Carolina and Clemson University.

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  • The University of Chicago School Mathematics Project (UCSMP). 2016. Everyday Mathematics: Grade 3. 4th ed. Columbus, OH: McGraw-Hill.

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