The fact is, most elementary teachers do know how to do the math problems their students are learning to do. But not all of them can do the following:
- Explain the underlying concept—why, precisely, "does" 12 × 7 equal 84? There is a good reason for this.
- Prepare the student for what comes next—for example 3½ equals 7/2...but what is the purpose? How is this fact going to be used going forward?
- Show the relevance of the mathematics to everyday life—not only the cute story problems about numbers of apples and making change from a $20, but also problems not found in a textbook [it troubles me to think how few times teachers, and not only in math, don't even bother to try to come up with outside-the-book questions for students; this should be common].
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