Understanding of mathematics begins in the elementary schools where teachers generally have taught in a way that advocates rote memorization of disconnected facts and formulas. Mathematics should be taught as a cognitive process where the emphasis is on concept understanding. Teaching mathematics to increase mathematical understanding should include creating tasks that are relevant to the students' lives, encouraging discourse which sets the stage for what is important in mathematics, creating a safe environment for expressing mathematical knowledge, and analyzing the tasks, discourse, and environment. What aspects of these did I see in the classroom? If what was noted in my observations is representative of elementary schools in general, assigned tasks are not necessarily relevant, discourse is not encouraged, and environments are not always safe. Also, teachers are not apparently engaging in meaningful evaluation or ways of teaching mathematics would have changed. Teachers need to become conscious of the ways they teach mathematics and begin to focus on how they can help their students become mathematical thinkers.
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