If we want students to become better problem solvers, not only must we provide situations where they can practice their problem solving skills, but we also need to make sure they are thinking meta-cognitively about the problem solving skills they are developing. One way to do that is to use a rubric with students.
Sandra Cushway, another teacher in my district, and I are presently in our 5th year of an action research project concerning teaching the whole curriculum through problem solving. As part of that project we developed a problem-solving rubric modeled somewhat after the rubrics developed by the BC Ministry of Education. Thus we chose to evaluate the same 4 aspects of mathematical thinking as those of the Ministry’s rubrics (namely, Concepts & Applications; Strategies and Approaches; Accuracy; and Representation & Communication), but we wrote the descriptors as “I statements” so students could self-assess. (Download our rubric here.)
The ministry’s rubrics were developed for specific grade levels (link here to see those) but Sandra and I and chose to make one rubric that was applicable to many grades.
For instance, if a student might choose this statement in the Strategies & Approaches aspect: “I chose a strategy that worked. It allowed me to get an answer but it took a long time, and was confusing in places.” That statement can apply to a primary student using strategies for double-digit addition as well as for a high school student looking to solve trig problems.
If you are new at using rubrics, may I suggest this: it is much better to begin the self-assessment process with a single aspect. In other words, choose one line from the rubric like “Strategies and Approaches” and only use that “strip” across the page with students. Talk about what the different levels mean and show samples of problem-solving work at each of the four levels. Have students work together to assess some work so they can get a feel for evaluating what good (and poor) strategies look like.
Let me know how the rubric works for you and your students! I know it can make a difference in the quality of work they do.