The Standards for Mathematical Practice require students to think conceptually, sort out difficulties, and go on through critical thinking. Furthermore, critical thinking is important to mathematics, and teachers should provide students with regular opportunities to practice it. Regardless of its established relevance, critical thinking is difficult to define experientially. Over the last 60 years, scientific teachers have defined numerical critical thinking as a heuristic cycle, a rationale-based program, a technique for inductive and deductive disclosure, a framework for objectively organized dynamic, methods with various elements, a norm, and a model-evoking action. Every contextualization of numerical critical thinking impacts one's perception of what motivates it. Understanding critical thinking as revelation, for example, is epistemologically and educationally distinct from seeing critical thinking as a cycle.
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