Last week I was teaching in a Grade 8 math class and we experienced an interesting situation of different teaching techniques. I was working as a TOC (teacher-on-call, aka substitute teacher) and the class also happened to have a student teacher. The student teacher was an experienced math teacher from overseas, so I think it is fair to say that we both felt pretty comfortable in front of the class.
The lesson was on algebraic equations and solving for a variable. The kids were going through a worksheet with questions like:
$$2x = 6 + 4$$
Most kids didn’t have any problems with this. However, further down the worksheet kids were starting to have problems with questions such as:
$$4x + 2 = 12 - x$$
I was going through the classroom from student to student, having them work through the problems with some guidance. Usually I would end up taking the student up to the front whiteboard to go through a problem. I went through this process a few times when the student teacher grabbed everyone’s attention. She worked through a problem on the overhead projector, showing the kids how to move variables around. Makes sense, right?
But this is where the big difference lies. The student teacher depended upon transmission teaching: she told, the kids listen and learn. I try to avoid this method because I find that the students have it in themselves to figure the answer. However, if the student teacher hadn’t intervened, I would have quickly been swamped for help. So what would I have done differently? Most likely in another 10 minutes I would have gone up the overhead projector and done the same. I might have first tried to get the students to help each other first though. However, what I would have liked to do is whiteboarding. If this was my classroom I would have had a set of whiteboards and markers for the students. They would have been giving some initial guidance and instruction and then I would have the students work through the problem on their own whiteboard. I could then pick one or two groups with the best answers to demonstrate their ideas and whiteboards for their classmates.
Some people might think that just giving a short lesson is a lot more efficient, and in some cases maybe it is. On this day though, the consequence of superficial learning was very evident. After letting the students work on the problems for a while, I got in front of the class and presented them with the expression:
$$7n - 1n$$
I asked them what the answer was. Did the students think the answer is 6n or 7? The class was pretty much split 50/50 on this on. Clearly the procedural lesson moving variables around didn’t contain enough information for some deeper understandings.
I don’t really mean to be too critical of the student teacher’s method. Her participation was needed and useful. As well, with a bit more planning the lesson could have effectively addressed one or two common misconceptions with the topic. If nothing else though, the lesson further convinced me of the worth for whiteboarding in group work.