Schoenfelds article

After reading Schoenfelds article it has opened my eyes to some things that may be going wrong in a math classroom. There are many times when I have taken courses myself where I was told or shown how to go about a certain question. It was not explained to me why we were carrying out the procedure we were but only guided through the steps. I had to go beyond the workings myself to find the understanding or go to the teacher on my own time.
In some math courses, especially the public courses students reach in grade 12 there are many objectives to cover. There is a pressure put on teachers to get the material covered on time for that big 50% exam. As stated by Schoenfeld(1988) the textbook does not often help. "Most textbooks present problems that can be solved without thinking about the underlying mathematics.."(p16) I often did feel this way as a student. I would open the textbook, begin practicing following the procedures that were presented by my teacher. I always try to explain things to my students during a class. I make them understand and I attempt to relate it to the real world.
I found it interesting when the example of division was shown, where the same number was added together and divided by the number of those same values there were. The fact that some students would add it all up and divide, not realizing this was not necessary. I can see some of my students doing that, but I see many of them picking up on what was going on because they do understand. We have encountered problems where they can solve a problem my merely taking the square root of each side. There are others who end up carrying out the quadratic formula to solve for x. This lets me know who the students are that actually do understand when we discuss operations and those who cannot grasp it but only follow a procedure.

Textbook chapter 1 to 3

As I began to read the text I started to think about my own teaching methods. At Amber Hill it is obvious that they are following the more traditional approach where there is an obvious barrier separating students from teachers and definitely the principal. There was not a whole lot of interaction between either.According to Palinscar(1998), "interactions such as those achieved through classroom discussion are thought to provide mechanisms for higher order thinking". At Amber Hill the lack of communication that was occurring within the classroom will hinder such development.


Phoenix Park on the other hand did foster more communication. The principal along with the teachers were constantly interacting with the students. This type of interaction will allow for higher order thinking.

I try to use a balance of both schools. Due to the high percent of students marks being based on the paper pencil test as well as the vast number of objectives that have to be covered by June it would be hard to use the project inquiry discussion all year but in no way is it useful for me to get up at the board doing a chalk and talk all class. I do present objectives and examples but I also give the students time to explore ideas on their own using the investigation approach. I also get students up to the board to lead discussions. I think that for now my balance is working. I would like it if there was not such an emphasis on the paper and pencil testing.

Palinscar, A. (1998). Social constructivist perspectives on teaching and learning. Annual Review            

                      Of Psychology, 49, 345-375.

Reading 2 thoughts

As mentioned before I had the belief growing up that math is concrete and there is always a right answer. After reading the article involving Hersh I start to think about the nature of mathematics myself. The laws that I learned, growing up and the objects we found the surface area for, well where did all these come from? Who decided a square was a square or a circle a circle? When you really sit down and think about anything in this life, well where did anything come from? After I read this article I start to think and reflect and growing up believing in something, such as math is concrete, then reading an article which questions this is difficult.
In terms of teaching I am going to try to push harder for independance for my students. They do enjoy it when I am at the board doing examples, but I refuse to do that in my class all the time. The students are responsible for becoming part of the class, for contributing and figuring things out on their own. I will get them up to the board more often then I am already doing and I will make them work harder to learn for themselves, not because they must just get good grades.