Philosophy of Teaching – Bora Bosna
Philosophy of Teaching
Graduate Teaching Associate
Department of Mathematics
Winner of the 2012 Graduate Associate Teaching Award
Since coming here from Turkey in June 2006, I had been struggling to understand the consensus here that students in America are worse at math and sciences than students in other countries. I observed that they could not get over algebra mistakes and years of miseducation for the concepts to make sense, hence lacked confidence in themselves. At first I just wanted them to do well so I developed a very direct, “catering” style to teach the procedures without necessarily understanding them. I learned how to break down problems into baby steps at a very good pace. I learned to get in the students’ head and think like them, to spoon-feed them solutions to exercises that covers just the points they would have trouble with by anticipating their mistakes. Office hours were similar, I catered without making them do the work. It was very teacher oriented. They became dependent on me and asked fewer questions. They were very happy. They got good grades and I got good SEIs. What changed me was when everyone in my Winter 2008 class passed with a C- or better (a miracle) and I got 5.0 overalls on all my SEIs. In 1.25 years I had found a formula to work the system. I felt like a sell-out. Was it okay with me that students got good grades, moved on and never cared for what they learned?
I was still struggling with the differences between students in America and students in other countries. It must be a conflict between math and the culture, I thought. At the time I was reading humanistic psychoanalyst Erich Fromm. His idea of “social character,” that a society’s particular way of living strongly influenced individuals’ characters, matched my observations: impatience, anxiety, dependence on calculators and being deprived of human faculties as a result. The “American character” seemed incompatible with math. Math was the antithesis of American lifestyle, the opposite of instant gratification. I was also unhappy with the lifestyle of my own teachers, peers and the math culture. When we were students we did not go to class, studied just the night before, and aced our classes. We pass this on. There is a culture of taking no attendance in math classes, an over self-reliance and overemphasis of “smartness.” We lived disembodies lives lost in thought, as “intellectual cognition machines.” Awkwardness, bad posture, weak muscles, personal difficulties and stuckness abound among us. Everything I say here applied to me. So my development as a teacher went parallel to my development as a human being as I became healthier in body and mind with yoga, dance and theater
My goal as a math teacher then is the cultivation of a fully human person, to reinstate confidence in and reclaim human powers, in a more student-oriented way a la Carl Rogers. Math makes a great human being who can marvel at achievements of the human mind, is able to take joy in complex endeavors for its own sake, care for the human adventure rather than grades.
We teach procedures rather than a discipline with a history full of success and failures. Do we tell our students of mathematicians such as Galois, who died at 21 in a duel? Or of Alan Turing, the father of computers, who was prosecuted for being gay and took his own life with a poison apple? So it must be taught “with a human face” rather than a vacuum of belief and history in which it is taught. This much was clear to me. Then I discovered the Humanistic Mathematics movement in the States. They’ve been saying the same things for a while! To cultivate fully human persons, another goal of mine is to give the body its due in mathematical activity. During years of working one on one with students I observed that most of the students’ mistakes come from impatience and anxiety. I noticed they’re hyperventilating and their hands are shaking, that most algebra mistakes (as I watch them do it) come from tense hand and arm muscles firing wrong, bad handwriting and organization habits. If the body is not relaxed and breathing deep, their mind is confused. I noticed that when a student understood something he had been struggling with for a while, it elicited a bodily response like a relieving “ooohhh,” his shoulders relaxed and his breathing settled with a deep exhalation. Something “shifts” in the body. I was convinced that “the mind is a muscle” and math is done with the muscles. I found confidence in this when I read Eugene Gendlin (a student of Carl Rogers) who had empirical evidence for a therapy style that focused on bodily responses.
These goals are hard to achieve. Textbooks have side notes on mathematicians but at best it is lip service. There is no time for appreciation of history. And I can’t ask students to change their bodily habits. I had to focus on things that could be done. I decided to present myself as the “face” and “body” of the math I wanted to see in the world, as the example of a person who loves math, is playful in a healthy body, enjoys mental challenges and embodies the good human values curiosity, independence, inquiry. I observed that slowly it rubs off on students. I want to erase the stereotypical idea of math and a mathematician. I want to cultivate good human beings so I’m looking for qualitative results, but I also want them to keep doing well by understanding the material, not by proceduring. I want them to understand that mathematical writing is aesthetic very much like writing literature, you write it for an audience, not to get grades.
My approach changed from “catering” to “maximum independence and responsibility for the student.” I ask and demand far more questions now, I am far more Socratic, indirect, and put more emphasis on the whys rather than the procedures. I make historical anecdotes, tell math stories, make jokes and “dance my math”: I run, move and point excitedly around the board; make use of the vertical space as well as the horizontal to break the “fourth wall” that is so common to math classes; use my body to demonstrate graphs and movement so much so that it really looks like I’m dancing. Though students find me a bit “strange” first, at the end of the quarter some tell me I successfully put a face and body on math. I’m now more student-oriented. I still pick examples that are best representative of the material, but now I ask students what they want to learn, and in case nobody has questions I present my pick. In office hours I switched to a “busy bee model,” where I keep hovering from one person to another having everyone work by themselves and never “cater” to them as passive receivers. This is certainly helping students. Grades and SEIs are still as high even though the last few years I focused on upper level (more difficult) classes, and I noticed a shift in students’ attitude in general. They ask me more “outside the procedures” questions, about where theorems come from, their curiosity (a most important human value!) is aroused. They want to learn and understand beside just getting good grades. They care.
The humanistic journey showed me the most important element in teaching: to care to go the extra mile. So I prepare extra practice material, have extra office hours on weekends, and I got out of my comfort zone to seek further development as a teacher. For the last two summers I was a senior TA in our TA training program for new PhD arrivals, training new grads in teaching. I also sought exposure to more diverse students and courses so I worked for SASSO, tutoring athletes in courses I usually do not get to teach. I went through SASSO’s tutor training program, which helped me articulate teaching concepts I was intuitively doing right but did not know the words for, such as Socratic method, direct vs. indirect teaching, global, local, kinesthetic, visual, auditory learners etc. This way I could articulate them better to my students so they can come up with the best learning strategies for themselves. I helped organize the Young Mathematicians Conference at OSU. I also became a yoga teacher; teaching something very different than math showed me my strengths and weaknesses. There is still so much I can improve in teaching, I think. Teaching is far deeper than we think. The human cultivation capacity it holds is limitless. As I keep growing I am looking forward to the future for even greater developments.