Many of us embrace the order and beauty in mathematics. The order of operations is an iconic mathematics topic that seems untouchable by time, reform, or mathematical discoveries. Yet, think for a moment about a commonly heard statement in teaching the order of operations: “You work from left to right.” At another point in the curriculum, when working on properties of the operations, we say, “You can add numbers in any order” (commutative property). How can both of these statements be true? Preparing students to do mathematics means that they have an integrated understanding of rules and properties in mathematics.
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