If all students could learn by having us just tell them how to do it, we would not have any of the problems that we have in mathematics education today. For over one hundred years the dominant pedagogy was teaching through telling. If that had worked, then all students would have been in our highest streams, and all students would have gotten the highest marks. But that has not been the result. Student difficulty with mathematics has been a pervasive and systemic problem since the advent of public education—not because students can’t learn mathematics, but because, by and large, students can’t
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