New Insights and Their Implications

So far in this math class I have learned a lot of new ideas. The idea that has made the biggest impact on me is the use of problem solving to teach math. This method of teaching is entirely new to me. However, it makes a lot of sense, even though right now it is hard to learn because I have never been subjected to it. All the research findings in countries all over the world have shown what an impact teaching using problem solving has on students; it surprises me that the United States hasn't adopted more of the techniques of other countries and is still using most of the old methods of teaching. Also, I had never thought about how, in math classes, the teachers try to cover everything. It makes sense to me now why I struggled so much with math: I barely had time to learn the material before the teacher switched to another topic. I have forgotten so much from my math classes because we never spent enough time on any one subject. By using problem solving to teach mathematics to students, students will be so much more likely to understand the material and remember it, in part because they were involved with the material and had a chance to make connections with it. In math, depth is more important than breadth.