The trimester schedule that our school uses has many benefits, including 68 minute periods. This seems to be the perfect amount of time for me as a math teacher to give the right amount of weight to each part of a lesson. One major drawback, however, is that sometimes I’m not ready to let them go. Maybe it is an overall resistance to change, but more likely I feel that after 13 weeks, my classes are starting to make some major progress down the persistent problem solving path. And then I have to let them go. There are very few students that end up in my class more than once per trimester since the majority of what I teach is College Algebra and Probability and Statistics (both one trimester courses).
In my college algebra course, I’ve seen the progression and improvement in their problem solving abilities, but I wanted to see what they would say if I asked how they thought they had progressed.
So, as the last question on their final exam, I asked them what skills developed in this course they felt were most valuable. (Oddly enough, none of them said factoring a quadratic equation.) But they did say some things that helped solidify my approach to this class. Most frequently, students mentioned that they have improved their problem solving skills. I’m confident that they are referencing problem solving skills in relation to rich problems, since that is a majority of what we did in this class. Another common comment had to do with multiple approaches to solving problems. Many students mentioned that they didn’t realize how many different ways there are to approach a problem until these varieties were laid out by other students. I, too, improved my ability to look for and appreciate the diversity in problem solving strategies.
My favorite comment overall was from a girl who works very hard but who hesitates to share her ideas with the class. She states, “I can problem solve without a set procedure and now I feel like I can solve anything.” Bingo. I hope that I can help build that confidence as I work to improve some of the methods I used in this next trimester.
Number Loving Beagle 
It is so true that self-reflection is one of the keys to gaining knowledge. I give my students a Blue Book at the beginning of the term. Once a week, I make time (about 10 minutes) in class for students to reflect on the math they have learned, what they are struggling with, and what they are curious about. I used to try to read and comment on these math journals every week – but that was too much. I have found encouraging students to reflect on their mathematics learning really helps them see the progress they are making. It also is one of the best ways I have found to encourage students to be advocates for their own learning.
I think every math teacher at every level should be helping students experience multiple strategies and multiple solutions.
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