Understanding and making connections is at the heart of flexible mathematical thinking. Flexible thinking is generally observed in students' ability and willingness to work with multiple representations, but it can also be seen in their facility in adapting problem-solving strategies when faced with novel situations, reversing thought processes, viewing notation as a process as well as an object, interpreting others' ideas, and posing problems. Although teachers may characterize flexible mathematical thinking differently according to context, we can probably all agree that providing students with opportunities to engage in flexible mathematical thinking is vital for fostering the kind of mathematical understanding that we want them to have

The Mathematics Teacher
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