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.