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I am so aware of how much I take for granted. I think I could ask my middle schoolers some of these questions, and it would be a new way of thinking for them. Even realizing that a number line is a jump from a number path helps me understand why, when we introduce coordinate graphing, some kids always want to count spaces instead of lines, or place the points on the spaces instead of at the intersection of lines.
I’m taking this course because I am very aware that I am not a trained math teacher and often do not know (as in the example above) why a student is making the mistake he is making or thinking the way she is thinking. I really want to strengthen my own awareness of the steps kids take in their reasoning. Thanks!