This chapter describes instances of play within a teaching episode on integer addition and subtraction. Specifically, this chapter makes the theoretical distinction between integer play and playing with integers. Describing instances of integer play and playing with integers is important for facilitating this type of intellectual play in the future. The playful curiosities arising out of integer addition and subtraction tended to be concepts that we think of prerequisite knowledge (e.g., magnitude or order, sign of zero) or knowledge that is more nuanced for integer addition and subtraction (e.g., how negative and positive integers can “balance” each other). Instances of integer play and playing with integers are connected to the work of mathematicians, highlighting the importance of play in school mathematics.
Wessman-Enzinger, Nicole M., "Integer Play and Playing with Integers (Chapter Two of Exploring the Integer Addition and Subtraction Landscape: Perspectives on Integer Thinking)" (2018). Faculty Publications - College of Education. 250.