In order for teachers to increase their effectiveness, it's helpful to explore how problem solving relates to developing a deeper understanding of mathematical concepts in their own work. It's likely that our own experience includes a substantial amount of problems for drill and review. And this may be the first notion about problem solving that comes to mind -- that it is mostly associated with drill and practice in the classroom context. In this section, we'd like to expand the idea of problem solving and offer a task that invites a chance to be self-reflective about what we do as teachers when we solve problems on our own.
As you solve this problem, think about the steps and strategies you follow. How do you set up the problem? How do you record your work? Do you self-monitor? What is your response to error? How long does it take you? Why do you try or reject specific strategies? The more experiences you have in solving problems and reflecting on your own approaches, the more effective you will become in implementing the standard as a foundation of mathematics teaching and learning in your classroom.
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