The Importance of Mathematical Thinking

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According to Susan Jo Russell (1999), both what children learn and how children learn determine that “mathematical reasoning must stand at the center of mathematics learning” (1).

Mathematics is a discipline that deals with abstract entities, and reasoning is the tool for understanding abstraction. From the very beginning, children encounter the abstraction of mathematics—not only five fingers or five rabbits but the idea of “fiveness,” not just that circular clock or this circular penny but the idea of a circle. Reasoning is what we use to think about the properties of these mathematical objects and develop generalizations that apply to whole classes of objects—numbers, operations, geometric objects, or sets of data.

(Russell 1999, 1)

Thinking and reasoning mathematically are integral to children’s construction of mathematical knowledge. As children collect, organize, interpret, apply, and evaluate information in problem-solving activities, they are developing pathways and memory structures. As they extend, extrapolate, identify patterns, and make connections, they integrate and reinforce their knowledge. As they conjecture and test, not only do they learn how to confirm or reject trains of thought, but they also develop inquiry skills and the “habits” of questioning and justifying. “Reasoning mathematically is a habit of mind,” write the authors of NCTM’s Principles and Standards for School Mathematics, “and like all habits, it must be developed through consistent use in many contexts” (NCTM 2000, 56).