I found Kohn's opinion on positive reinforcement to be incredibly interesting because I am not sure where I stand on this matter. Part of me immediately thinks, "that's common sense, because if we give positive reinforcement for sharing, then the gratification of sharing is replaced by the positive reinforcement from our parents/instructors". But then another part of me has a knee-jerk reaction in opposition which says, "we should give positive reinforcement when children do the correct thing, so that they know that society approves and encourages the behaviour and by extension, we discourage selfishness". I hope that this is a subject that we can discuss in class in more detail.
In contrast, I was very much in agreement with Boaler's opinion of multi-dimensional teaching. I can understand why some people like the traditional method of teaching the subject and then letting the students listen and practice it, as that is what they are familiar with. However, I think that that method would only work for people who either understand math easily or only know how to learn material in this manner. By incorporating multi-dimensional teaching, you can encourage students of all levels to play with it, share opinions, see more worldly uses of math, and become active learners. This would engage a wider variety of students and seems like a better method all around.
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