New Insights and Their Implications

This course has already helped me to gain a deeper understanding of what a successful math curriculum should look like. I have learned new knowledge from my peers, the instructor, and the readings in the book. From my peers, I have learned that there are a number of ways to comprehend and solve a problem. I have learned new strategies for which I can use to answer a problem. Through the group work in I have learned that everyone begins the solving of a math problem in a different way. In other words, there is not a right or wrong way to understanding and solving a problem. Math has multiple routes for which students can take and also multiple solutions. From the instructor I have learned that there are four types of methods for solving a math problem which include: George Polya's four steps to problem solving, drawing a diagram, solving a simpler problem, managing your point of view, constructing a table or chart, and the process for mathematical inquiry. In order for our students to be successful problem solvers, we must show and discuss with them these multiple routes for which they can chose from when working to solve a problem. They need to develop a sense of confidence in their math skills. If we are unable to help them develop the confidence at a young age, math will only become more difficult for them. I have learned from the class that teachers in the United States need to try a different approach to their instruction of math. Teachers should not just give students the answer right away. They should give students time to reflect and work with others around them before simply giving them the correct answer. Students need to develop stronger critical thinking skills not just for math purposes but for all subject areas. I believe that the process of specialization is a key building block for helping students understand math. Specialization is simply starting with a random problems and moving to more organized problems or in other words systematically changing the problem to make it more complex. Students again need to gain confidence in their math skills. We should allow them with the opportunity to get up and front of their peers and work out a problem and congratulate them even if they do not get the right answer. We should first discuss what they were doing right before criticizing what they are doing wrong. Overall, I believe this class will help me to be a stronger and more confident teacher of math.