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<p>I agree. Some will figure out but most will not. However, getting the students to observe and discuss is a good idea as long as the discussion is not allowed to drag out while it is clear that the students are not figuring out the concept on their own. It is important for the teacher to underscore what the students have learned on their own.
My S taught math to young children and this was a key thing that he was told to do. Even when most if not all of the class “got it,” it was important for him to go over the problem and spell out the procedure and solution in order to clarify, and inscribe it, so to speak, in the students’ mind.</p>
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<p>Probably, but too often, the teacher is just parroting what s/he has read in the text and is not actually explaining the concept, why it works and when it should be applied. So that when a student goes astray, the teacher is not able to bring the student back onto the proper path to a solution. It’s not as if the traditional method has been so successful. If it had, there would not be all these attempts at improving math teaching!</p>