New Insights and their Implications

There are many things I have learned from my peers, the instructor, and the readings about elementary school students and the teaching and learning of mathematics. From my peers, I have learned some different ways students may think about problem solving other than the ways I thought they would. Through small group and whole group discussion, I have learned other ways, routes, and strategies to problem solving that elementary students are going to use. I have also learned that I will not always be able to know or guess what routes students are going to take to solve problems since there is no direct route to problem solving. Students are going to use their own experiences and past knowledge to find a strategy that works best for them. As a teacher, I need to be flexible and let them explore these strategies. Through discovery, students will be able to build on their own schema's and become better problem solvers over time. From the instructor I have learned that it is best to have students explore and justify their answers through using multiple strategies. Mathematics is not about teaching students the way to arrive at the answer through a set of processes but rather have the students discover for themselves how to arrive at an answer. Mathematics teaching has changed dramatically this way since I was in elementary school. Teaching mathematics today is about facilitating students on how to develop problem solving skills and have students use their metacognition to think about what they are thinking about. Problems should be open ended in that they should have more than one solution, they should draw on the student's mathematical knowledge, they should address Common Core Standards, and they should be presented in realistic/authentic context. From the reading, I have learned that teachers are lacking focus and coherence while students are lacking reasoning and sense making. As future teachers, we must instill that students are able to draw conclusions on the basis of evidence and have the ability to develop understanding by connecting it with prior knowledge. I have also learned the many tools that can be used such as George Polya's steps to problem solving, ten problem solving strategies, and processes of mathematical inquiry. By learning these new strategies, as a future teacher I plan to implement them into my classroom so my students can feel better about approaching and solving mathematical problems.