I am a college instructor with a Master of Arts in Mathematics who is currently working on a Specialist in Math Education. I am concerned with improving my skills as a math teacher. My students often tell me that I am the best math teacher they ever had and I made math easy for them to understand, but my main concern is for those students who just "don't get it." I feel it has a lot to do with their problem solving skills and their ability to reason mathematically. I get a number of students who have a poor Algebra background, but those who posses the appropriate problem solving skills can quickly catch up and move on. Those who don't are usually "lost in the shuffle."
I applaud the NCTM for their concern with integrating mathematical reasoning and problem solving throughout the curriculum. I'm sure that after reading the discussion draft, teachers feel they already incorporate some problem solving within their curriculum and didn't know it. This is where my concern comes in. There are a number of teachers who do not really understand what problem solving is or when it takes place. Since a lot of teachers feel that they already incorporate problem solving in their classrooms, they will not give this standard the attention it needs. In all, I feel that the NCTM community should put a stronger emphasis on this standard over all others. If they have a strong mathematical reasoning background, students should be able to conquer all areas of mathematics with confidence and success.