I have found that “thinking mathematically” a very power tool of teaching and learning mathematics.
As a good and effective math teacher, one needs not only be able to solve the mathematical problems and explain to students but also needs be able to teach students to use a good problem solving strategy. As a pre-service math teacher, I often overlook the importance of good and systematic problem solving strategy. Each of the three phases -entry, attack, and review is an independent, crucial, and indispensible stage, but there are also connect to other phases, complement to one and another. However, the most important part of problem strategy is not give up when we got stuck. The students’ problem solving abilities will improve over the time if they can pick up some new mathematics insight when they got stuck.
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