What gave me a deep impression is Michael's group's point that they used a mathematical way (drawing a function image) to represent the fact that a very small number of students in the class would pursue the goal of relational understanding, a very small number of students would purse instrumental understanding, and the majority of students would be the ones who probably could have built on their instrumental understanding and wanted to try to pursue relational understanding. I am skeptical of this view, although I think that the majority of the class will probably be composed in this way, the teacher needs to consider how to design the teaching methodology by putting themselves in the shoes of the students in the class and the distribution of their abilities.
Thanks!
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