My fourth field experience took place over two months at Lower Canada College in Cote-des-Neiges, Montreal. I have learned a lot, worked hard and had a lot of fun with four classes from Grade 9 to Grade 12 at LCC. Below I have linked to my evaluations and written a reflection on the experience.
|FE4 Evaluations||A sample of the evaluations from my cooperating teacher and supervisor.|
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I have thought a few times during my fourth field experience, “if only I could only teach my Grade 10, 11 and 12 classes! How much easier my life would be!” While it indeed would have made my life easier to have taught three instead of four classes over my seven weeks at Lower Canada College, I would have completely missed out on the learning opportunity of teaching my Grade 9 class. In retrospect, the class played a central role in my development as a teacher through the internship and I wouldn’t trade that away. In reflecting on my experience of the F.E., in many ways I am reflecting on the experience of growing with my Grade 9s.
Don’t get the wrong idea—they aren’t a “bad” class, whatever that means. In fact, I see evidence of their intelligence and engagement every day. However, before this field experience the youngest students I had taught were Grade 10s, so I had adopted my teaching and classroom management strategies to the older age group. With my older groups I was (and continue to be) laid back, giving the students much of the responsibility for policing their own behaviour. My Grade 9 class overwhelmed me at first with their sheer energy, much of it undirected or at least not directed towards math. Whereas with older groups I could rely more on the focus mechanisms they had developed, I would need to work with this group to develop these strategies while we learned math together.
A large part of my efforts to adjust my teaching to the Grade 9 students has been learning to teach the mathematical material at the Grade 9 level, which in some cases feels like re-learning math myself! Take the example of inverses: I prepared a group investigative activity on linear inverses with a handout. A couple minutes in, the students were clamouring for my attention: “sir, what does it mean to find the function f”? I have had to re-teach myself what the inverse of a line is without using the word “function”, which isn’t covered until Grade 10.
My teaching trajectory in the Grade 9 class was perhaps predictable. We were covering analytic geometry, which at the Grade 9 level introduces the distance between points and the midpoint, and combines these with linear relations and linear systems which the class had already learned. I started off fine, leading the class through discovering the distance and midpoint formulae which engaged most of the students; then I stopped challenging the class and gave them simple distance and midpoint problems. A big group of boys, realizing that their attention no longer needed directing towards the math, directed it elsewhere and gave me a hard time behaviourally in class.
Realizing in discussion with other teachers in the math office that I was not challenging my class enough, I overcompensated. I brought in a few challenging problems that combined linear systems with the distance and midpoint and asked the class to do these without building up through intermediate-level challenges. This came to a head when I gave the students the equations of three lines which made a triangle, and asked them to find the perimeter of the triangle formed by the midpoints. It’s a great problem and I had shown them all the parts independently, but had not scaffolded the learning process enough and so only a few could put it together. The result was a difficult class where many students tuned out because they didn’t understand the challenge.
Finding the sweet spot in the middle—and differentiating this for each my students—is an ongoing process, but one where I have seen a good development. In the group activity on inverses I mentioned above, I explicitly practiced my goal of directing students at each others’ ideas by restricting my own involvement in the group process. While some groups immediately took to this style of learning through discussion, many others were somewhat distressed without the continual presence of the teacher to answer questions. One girl in class had an idea of how to interpret the inverse of a line which they had graphed, and told me as I was passing by their group to listen. “Why don’t you share this with your group?” I asked, but she didn’t seem to understand why she should do that, and repeated her question to me a couple times before I walked away. I can’t fault her too much, as her experience in school has likely been that discussions about course material (especially in mathematics) always go through the teacher.
I succeeded recently in finding a balance and differentiating to some extent with my analytic geometry assignment, where in a class work period I was able to work with some students on the basics, spending more time to make sure they understood clearly, and also able to give slight direction to other students on the more advanced problems. I was also able to step back at several points and admire that my intervention was not necessary, as the students were mainly productive.
Considering everything, I think I have now reached a comfortable place with the class, and I suspect this would only improve were I to continue teaching the class after this week. As well as finding a mathematical challenge appropriate to each student, part of this change has been classroom management. I gradually split up the large group of boys who distracted each other, with some moving to the back to work with the teacher-observer (who acted very effectively as a TA) and some moving toward the front. I have identified a few students of both genders who I have spoken with individually and have made deals with regarding their behavior. I feel now that if I were midway through the second month of school, I would be satisfied with the direction of the class.
Along with my reflections on teaching mathematics, I have reinforced a few broader lessons out of this field experience. The first is that issues—such as a class where I am struggling to find my way—necessitate a lot of positive, cheerful energy. Invariably when I entered a class pessimistic about the outcome and not prepared to put in the energy, the class would not go very well for me. The second, relatedly, is that energy management and life balance in general are SO important as a teacher. Teaching is not one of those things where I can wear myself down and still be effective.
Of course, while I have noticed these things with all my classes, the lessons are the most pronounced with my Grade 9s. It is not a coincidence that the night before my too-challenging triangle class, I had stayed up late to write a McGill assignment, or that before my successful class I went to bed early. Indeed, perhaps the closest I can get to describing the behaviour of my Grade 9s is that they have an amplifying effect on my mood and behaviour: if I am enthusiastic and ready to focus on math, they are there with me, but if I am distracted, tired and bored they will reflect this and place their attention elsewhere. It might not make my life easy, but the practice in energy management is well worth it and will pay me back over my teaching career.