Ann stated, “If you roll two dice (number cubes) and the numbers are 1 and 2, saying that 1 and 2 and 2 and 1 are different things, that is not true. It is like saying 8 + 9 and 9 + 8 have different outcomes.”


Edited by Julie Amador,, University of Idaho, Coeur d'Alene; Grace Parisi,, Long Beach Middle School, Lido Beach, New York; and Darrell Earnest,, University of Massachusetts Amherst.

Contributor Notes

J. Jeremy Winters,

Dovie L. Kimmins,, are colleagues at Middle Tennessee State University in Murfreesboro, Tennessee. They enjoy working with preservice and in-service mathematics teachers at all levels. Through these relationships, they have the opportunity to work with lots of K–8 students to investigate student thinking and student understanding.

(Corresponding author is author is Kimmins
Mathematics Teaching in the Middle School


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