Throughout the semester, one assignment that we had was to create a problem solving log which contained 8 different mathematics problems that could be solved using multiple heuristics. This log was very useful in helping me understand the importance of different problem solving strategies in mathematics. In regards to being a good math teacher, this log demonstrates that good math teachers should find and teach problems in multiple ways to ensure that all students can learn about math. One thing that my mathematics methods course taught me was to allow the students to use their own way to solve a problem. Algorithms should be taught at a later time. By focusing on different heuristics students are not bound to the algorithm and can use multiple methods to solve a problem. This can decrease the amount of errors that students make because they are choosing their own methods. I have even seen this idea in my placement classroom. My cooperating teacher taught the students how to use the lattice method and the standard algorithm for multiplication. While she encouraged the students to learn the method, she did not tell the students which method to use. She told them to find a method that they liked and to use that method. This allows students to have freedom of choice when solving multiplication problems.

The documents below show a three of my eight problems that I taught to my fourth grade students in my placement classroom along with my problem solving critique. Throughout these lessons I learned that many students used the algorithm to solve the problem, which makes me believe that they have been constantly taught to focus on the algorithm. When I reviewed the problems, I tried to give multiple ways to solve the problems. I hope that when I am student teaching in the spring and when I have my own classroom that I can incorporate different heuristics into my lessons and problems to show students that it does not matter how a problem is solved as long as they find the correct answer.

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