Children’s Understanding of Equality: A Foundation for Algebra. Research by K. Falkner, L. Levi, and T. Carpenter. The Problem. Teachers were asked to share the following problem with their classes: 8 + 4 = + 5
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Research by K. Falkner, L. Levi,
and T. Carpenter
Answers given to 8 + 4 = + 5
About 3/4ths of them were in second and third grade
Falkner (who taught the mixed 1st and 2nd grade class) chose to help her students understand by using true and false number sentences, such as the following:
4 + 5 = 9 12 – 5 = 9
7 = 3 + 4 8 + 2 = 10 + 4
7 + 4 = 15 – 4 8 = 8
The children used manipulatives (Unifix cubes and other materials) to help make models of the situation
7 + __ = 6 + 4 etc
More students understood the concept. By springtime, she was integrating discussions about equality with discussions about other algebraic concepts
For example, she asked the class to look at the sentence: a = b + 2.
She asked them: which is larger…a or b?
For children (or anyone) who struggles with the concept of equality, this problem would prove daunting…so how did a class of 1st and 2nd graders handle it? (read page 236)