New Insights and Thier Implications

From class, I have learned how much different it is to truly learn math. I feel that I have missed out on a lot of much needed information and as a result I don’t have a concrete understanding of reasoning’s in mathematics. As a result of only knowing how a procedure is done and not ‘why’, it is making this class a little more difficult to grasp these understanding. While it is stressful trying to understand the ‘why’ of the question, when I do get to that point in the understanding I feel as though I am in fact learning it for the first time and the right way. I have learned from my peers, that everyone does learn in a different way and it is critical as a teacher to be aware of that. Also, I have learned how useful the right manipulative is while teaching a lesson. Manipulative are able to help further the knowledge by allowing students to visually see and touch the objects. Through these interactions, students are able to learn math in a much greater, better way.

New Insights and Their Implications

In class I have learned that is best to give students problems and let them struggle and manipulate them to solve them. The students may work with partners or on their own to figure out the problems, and give them an adequate amount of time to work on the problems. I am doing my internship in Newcastle, NE at the junior high level. Wednesday I taught my first lesson to 8th grade algebra, and I taught them how to graph linear inequalities. First I explained what they were and how they were similar to graphing linear equalities, which they did the day before. I then showed a few examples on the board while explaining the material and getting their input from previous knowledge. They did great as a class on the board, but when I gave them problems to manipulate at their desk with graph paper I got a lot of blank looks even working with partners more than half of the class was lose. I had one of the groups of girls come up to the board to share their answer (which was correct) and explain to the class how they got it. The boys were still confused. I went over the steps and process again and they seemed to understand or were just pretending. I applied all the knowledge I have learned about the learning process and still feel that my lesson was unsuccessful to fifty percent of the class.

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.

Summary and Synthesis

When we came to class the first day, I was honestly scared about this class. I was to figure out how to find the answers without being told how to find them, was a scary concept after being told what to do to find the answer for so many years. I have actually enjoyed class a lot, I like being challenged, and being able to find those answers on my own or within the group work we do. I like that we are learning many different approaches to the same problem or question given to us. I am excited to be a part of this new way of teaching, because I think it is the right direction in helping students understand what they are doing. I have already shared some of the concepts with my oldest daughter, and cannot wait to teach my future students in a way that is easier to understand and realize why they are doing what they are doing.