kitchen table math, the sequel: teaching math facts: equivalent sums or iterative grouping?

## Tuesday, September 4, 2012

### teaching math facts: equivalent sums or iterative grouping?

ABSTRACT

This experiment tested the hypothesis that organizing arithmetic fact practice by equivalent values facilitates children's understanding of math equivalence. Children (M age = 8 years 6 months, N = 104) were randomly assigned to 1 of 3 practice conditions: (a) equivalent values, in which problems were grouped by equivalent sums (e.g., 3 + 4 = 7, 2 + 5 = 7, etc.), (b) iterative, in which problems were grouped iteratively by shared addend (e.g., 3 + 1 = 4, 3 + 2 = 5, etc.), or (c) no extra practice, in which children did not receive any practice over and above what they ordinarily receive at school and home. Children then completed measures to assess their understanding of math equivalence. Children who practiced facts organized by equivalent values demonstrated a better understanding of math equivalence than children in the other 2 conditions. Results suggest that organizing arithmetic facts into conceptually related groupings may help children improve their understanding of math equivalence.
It Pays to be Organized: Organizing Arithmetic Practice Around Equivalent Values Facilitates Understanding of Math Equivalence.[Article]
McNeil, Nicole M. 1; Chesney, Dana L. 1; Matthews, Percival G. 1; Fyfe, Emily R. 1; Petersen, Lori A. 1; Dunwiddie, April E. 1; Wheeler, Mary C. 1
Journal of Educational PsychologY | Publish Ahead of Print, POST AUTHOR CORRECTIONS, 25 June 2012

Anonymous said...

"Results suggest that organizing arithmetic facts into conceptually related groupings may help children improve their understanding of math equivalence."

It's hardly surprising that teaching and practicing a concept makes it more likely that kids understand that concept. I would have been more interested if they had tested for something other then "understanding of math equivalence", like speed of recall or ability to subtract.

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Allison said...

This is the reason that Singapore's primary mathematics series is excellent at teaching arithmetic and beyond. The focus on number bonds as a way to understand quantities, so that e.g. students grasp sevenness, and learn all of the equivalent ways of expressing seven as a whole made of two parts, teaches a concept that gets to the heart of number sense. Addition and subtraction then follow naturally from the concept, because addition and subtraction are just variations in how to express the same core concept.

It's not enough to explore number bonds though, they must be taught to mastery. Primary math does this in the first 6 weeks or so of 1a.