New Insights and their Implications

The first couple weeks of class, we had talked about a new aproach to teaching mathematics though problem solving. When asked my level of understanding and knowledge on problem solving on a scale from 1-5, I said I was about a 2. At the time I didn't feel very confident in my knowledge of what problem solving was and how to use the skills of problem solving. This is not a good thing, considering I will need to have a strong understanding of problem solving in order to teach my students mathematics. After reading the chapter on problem solving and discussing it in class, I feel like I have gained knowledge and a better understanding about problem solving.

I learned that problem solving is a "way of teaching." Althought there are many factors that influecne problem solving, there is no prescribed method for teaching problem solving skills. Problem solving is student-centered, rather than teaccher centered; it begins with and builds on student's understanding. From the senteo quiz, I learned that in order to meet the student with where they are at in their mathematical knowledge, is important for teachers, when selecting activities for problem solving task, to choose activities that have multiple "entry points." From class discussion we also formulated ideas for ways a teacher should teach problem solving. First and formost, is to be well produced in your own problem solving in order to teach students. It is important to spend time teaching students how to use different routues-which is done by giving them time and opportuinities to find and use these different strategies. Other ideas we came up with, that are important to consider are, encourage students to verbalize their thinking process to help make them aware of the strategy/process they are using. Lastly, it is important to teach the structure of the problem in order for students to apply it to other problems to see and understand how matehmatical problems are/can be realted. From the reading I also learned about the teachers purpose in a more specific way as far as what they do before, during and after the phases of a lesson on problem solving. During class, I was also learned about 3 different tools ( George Polya's Steps to Problem Solving, Ten Problem-Solving Strategies, Processess of Mathematical Inquiry) that I can consider and refer to when teaching my students mathematics through problem solving.

Through reading and class discussion I have gained a greater understanding of what problem solving is and ways in which I, as a teacher, can teach students mathematics through problem solving. I can now say that on a scale of 1-5, on how comofortable I am with problem solving, I would say I am about a 4.5 :)