In the summer of 2001, Suzanne and Annie took over the conference room at the Math Forum and sat down to distill their thinking about the elements that go into crafting a great PoW submission. What did they look for when they chose student work to highlight on the Sample Solution page?
After covering every whiteboard in the room with their thinking, they boiled down what they were looking for into two big categories, each of which had three sub-categories:
After determining those rows, Suzanne and Annie turned their attention to the ratings, or columns. Since Suzanne values problem solving as a process to improve upon, she felt that communicating where students stood on a spectrum of mastery would be better than numerical scores, so they came up with the levels of progress: Novice, Apprentice, Practitioner, Expert. Also, not having numerical scores helped each rubric category stand separately. Rather than averaging the scores together to tell students “you got a 15 out of 24 on the problem” the rubric communicates “You’re still a novice at writing your steps completely and I couldn’t tell if your strategy was sound, so you’re a strategy apprentice. But you’re a practitioner at interpreting problems, calculating accurately, and writing clearly. You’re a novice at reflection.”
Each current FunPoW, PreAlgPoW, AlgPoW, and GeoPoW comes with a problem-specific rubric that the teacher can use to understand more about what it takes to be a practitioner on this PoW (and which teachers sometimes share with students after they solve the problem). In addition, teachers and students can view generic Math Forum rubrics that use student-friendly language to explain each rubric category. We offer generic rubrics for every service, from Primary up through Trig/Calc!
Many PoW teachers report that they start with one category at a time. Some focus on Problem-Solving, starting with Interpretation or Strategy, while others just want the students to get used to writing their thoughts, and so focus at first on Completeness. A simple way to achieve that focus when mentoring online is to click the check-box for “Hide the Rubric from Students” then simply type their score on the focal category in the mentoring response. Teachers can also check “Choose Not to Score this Submission” and leave the rubric blank.
Rubrics are a great way to communicate a lot of information about student progress very compactly. We hope the PoW rubric is useful to you, and that you enjoyed learning a little more about the history and philosophy of the rubric!