Summary & Synthesis

During the past few weeks of class, I have come to realize that I need take a step back and re-evaluate how I am going to teach math within my future classroom. All I have ever known about ways to teach math is what I observed in elementary school and high school. The same approaches were used class after class and year after year: the teacher provides step-by-step examples and then assisgns an abundance of similar problems for students to practice. However, after the short time spent in this course, I now understand the importance of teaching students how to problem solve rather than just practice the steps that were shown to them. By doing so, students are able to make their own interpretations and use their own approaches and background knowledge when solving problems. As we discussed in class, when teaching problem solving skills, we, as teachers, need to have several goals in mind: we need to help students recognize when various strategies are appropriate and when to use them, and we need to help students become capable of inventing their own strategies and adapting existing strategies. In simplest terms, this means that we need to provide students with the skills they need to come up with their own ways to solve problems rather than telling them how they 'should' be solving the problems.