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Teaching the Subject vs.Teaching the Student
When I took my education degree, there was a lot of talk about StudentCentered teaching versus SubjectCentered teaching versus TeacherCentered teaching. I was very young and fresh out of my physics / math degree (where the "real learning" took place); I felt that all this talk on "Teaching" was mumbojumbo. I really didn't care about whether I taught the subject, or whether I taught the students. I just wanted to get my certificate so that I could teach math and science in the high schools. The education degree itself was, for me (the young me) a huge waste of time.
Now, after many years of teaching, I find myself going back to those "wasted" two years of my life and reflecting back on certain themes / topics we touched upon. I find that the many years I taught have influenced me and my opinions of good teaching  and what it means. (Also writing a blog once in a while on my teaching experiences also gets me thinking and thus I find that I become a more thoughtful teacher.) And only now I realize that what I thought back then a "waste of time" are useful contemplations of the teaching profession.
One of these teaching "ideas" came back to me when I read a comment on my previous blog:
...In the text the teacher decides to "quit teaching reading, writing and arithmetic" and decides to teach children instead. As I analyze that sentence, I observe the difference in teaching the subject to the students oppose to teaching the students "the subject". The students have to be understood as well as on task, in order to teach the students the subject.
When I read this comment, the discussion/debate we had in one of our education classes came back to me as if it was yesterday: Teaching the Subject versus Teaching the Students.
I, of course, was a pure mathematician back then, and felt that math in itself, if presented properly, would be enough to inspire kids to learn it / understand it. From my experiences as a student, math was so beautiful, that the teacher really didn't need to understand me to teach me the subject. In my Math/Physics university classes I was one of many many students, and it didn't matter that the teacher didn't even know who I was, what my name was, etc. The subject in itself gave way. Of course, I had better and worse teachers. Depending on the teacher, I found that I understood a subject more or less, but this, I figured, was due to their presentation, their ability to convey information. Back in teaching school, I was totally and unequivocally a "SubjectCentered" teacher  I believed in teaching the subject.
Other students in my education class believed in the "StudentCentered" philosophy, where the teaching revolves around the student, and not the subject. For instance, a teacher should first realize what the student knows, how the student learns, their background, their likes and dislikes, etc. before trying to "teach" them anything. For me this was so silly. What do I care if a student likes the color green as opposed to the color pink when I teach them how to do fractions? How can I absolutely know all of my students and adjust my teaching to all their different needs/wants/learning styles/etc when I am teaching math. Of course this is a bit of an oversimplification, but that was the jist of my thought process.
There was a third possibility in teaching philosophies: "TeacherCentered". This is more a totalitarian way of teaching, where the most important thing in the class is the teacher (not the subject nor the student). Whether or not the subject is delivered properly, and whether or not the students understand or care to understand, the teaching is done through the teacher, their methods: they are at the center of the teaching. I somehow knew that I couldn't be this type of teacher. I had teachers like this before, and I didn't learn much in that kind of environment. In fact, this past year I met the purist TeacherCentered teacher. His classes were very quiet, all the students were terrified of him. He did he not care about his students, if they liked him or not, if they learned anything or not, if they understood what he was saying. I think he absolutely despised them. One time, in the teacher prep room, he told me: "Teaching is great, until you have to teach, and see their faces staring back at you." But the funny thing was, that he didn't even enjoy the subject. In fact he was teaching the subject incorrectly, and he marked the students wrong even when they did the questions right, because he didn't know how to do the problems himself. I couldn't believe it... not only did he not like to teach students, but he didn't even like the subject he taught! WOW, how can such a teacher exist.
But I digress, back to the topic at hand. What's better  presenting the subject, and letting the students absorb what they can/need (SubjectCentered), or first thinking of the student, and then adjusting the teaching method according to the student (StudentCentered).
After many years of teaching and tutoring, I find that I am switching over to the other side of the debate, and I realize that the student is a huge (if not the most important) part in my teaching. Even though I love to present a subject in its pure form, I still take into account who I am talking to. I know for instance, that if I go too slow when I'm teaching a really bright set of students, that I will lose their attention very quickly. In this case I need to speed up or ask really indepth/complex questions in order to keep their attention. On the other hand, if the students are slower at math/science, it is important for me not to lose them. Thus I need to show them how easy the concept is, with the simplest examples, or how useful a concept is, with a really appropriate or funny application. These are trivial examples of my adjustments to the varied students, however, I wanted to show that even with the smallest of differences in students, I must change even my basic ways of teaching.
Knowing the audience is key. I have totally switched sides. I'm no longer the hard nosed pure mathematician. I realize now that if I don't center my teaching around the student, I will not, absolutely will not deliver my message  the beautiful message of mathematics, and thus I would fail as a teacher and as a mathematician.
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