New Insights & Implications

The most prominent new insight for me would have to be the fact that many mathematics problems can be solved using many different routes. In my previous math classes, we were taught formulas and specific ways of solving problems. However, this is not the best way to teach since every student thinks in a different way. Teaching this way merely forces students to use numbers in a certain way every time, go through the motions, and never really understand what they are doing or why they are doing it. When teaching, I now believe that the students should be allowed to come up with their own method of solving a problem by using the knowledge and understanding of certain concepts that they will hopefully gain through the teacher's guidance and activities. It will be a difficult task for me, since I was never forced to think deeply about mathematics before. I feel like I am starting over, but the more I am forced to think in this way in this math methods course, the more practice I will have, and eventually I will constantly be thinking in this way. When I start teaching, I will be learning right along with the students. But if I am learning mathematics in a different way with deeper understanding, I will know that my students should be as well.