As a graduation requirement, I had the privilege of designing a forty-hour experiential learning project. I decided the best setting for my growth as a future educator would be in the college's tutoring center. Below is a journal entry documenting what I learned from this valuable journey.
October 10, 2018
Today I was working with a student on factoring. The student was confused about how to factor it when there were extra variables. I had him notice that even though there were x’s and y’s they were symmetrical in the same way that a normal second degree polynomial was. I advised him that the best way to do it was to treat it like he would a normal second degree, and factor it whatever way he was used to. There are hundreds of ways to factor, and a lot of them are really specific to one teacher or another. The way that I do it now was taught to me by a success student that I tutored a couple of years ago, and I haven’t done any of the other ways in a long time. As soon as he started I could tell that he was going with another method that I had forgotten. When he got stuck I wasn’t sure exactly how to help him because I didn’t know the procedure he was using. I was immediately really tempted to convert him to my way, and even tried to for a second, but I quickly righted myself. I eventually caught on to what he was doing an was able to help him along his own cognitive process. It’ so important for teachers not to impose one way of thinking on their students. My nightmare is to be the kind of teacher who squashes alternative methods just because they are unfamiliar, different, or seem more difficult to me. Real learning happens when we allow the student to develop their own mental representations of mathematical process and then strengthen (or adjust if necessary) those unique representations. We need to utilize the representations they already have rather than try to overwrite them!
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