When I was a math teacher, I spent a lot of time doing what I thought was, well, ‘teaching.’ In my first few months on the job, I focused on the logic behind the mathematics, not the formulas or other shortcuts. Students constantly complained about this, and they were failing tests, so, after higher-level discussions, I started going over the easy way to do things: the formulas.
I was rather surprised when students started doing really well on tests – but when I verbally assessed their understanding of the logic, I was still greatly disappointed.
Furthermore, they completely fell f [...]
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