Summary and Synthesis

Since my last posting it has really hit home for me that it takes a commitment from the student to be willing to work through the process in order to truly construct their knowledge. This became very apparent to me during the work with fractions that the first group presented to the class. I knew that I could find the correct answer if I resorted to my existing knowledge of the steps needed to resolve the problem. I also knew that if I wanted to experience the learning the way that a student who wasn't taught the procredures but instead was provided with a conceptual way of learning that I would have to struggle with the math. Trying to stay away from the procedural steps and work with the concrete and semi concrete models in order to find the reason for the procedural steps I went back through the models and tried to evaluate what I was learning about the problem. Due to spending the time struggling I did come to an understanding of moving from the semi concrete model into the symbolic problem. Experiencing this process instead of reverting to the methods that I knew would give me the right answer was definitely beneficial to me. The willingness to be uncomfortable during the process is something that as a teacher I will be asking my students to do; I think that I need to be willing to experience it also. This really brought the message of constructing our knowledge about math to the forefront for me.