I was struck recently when reading Robert Kaplinsky’s post, Why Are You Using That Problem?. In this piece, he articulates 3 different reasons that we might choose to use a particular problem: to introduce a concept, for productive struggle, or for problem completion – each of which has its own value. Kaplinsky convincingly argues that we should be purposeful not just in which problems we choose, but in why we choose a particular problem. I have been considering his thoughts in reference to productive struggle, and specifically in how to best to support students when we choose a problem with this as our goal.
I have always talked about encouraging and nurturing a classroom culture in which it is safe to take risks, and to experiment. When I introduce a novel problem, I tell students that my expectation is that they try – that making an attempt is what I value. My marking scheme always always includes credit for getting started, and for each step of a problem. But in some ways, my marking scheme has been generally geared toward a sequence of steps leading toward a correct answer. In awarding credit for specific answers, I have been communicating to students that I value those answers. If I want students to put value on productive struggle, I need to demonstrate that that is what I value – and by extension, that is how they can earn marks. (For now, I’ll leave the question of whether earning marks in general is productive at all…)
I worked with Dr. Andreas(@), my excellent colleague in the chemistry department, to create a set of guidelines and a rubric to support students in becoming independent and confident problem solvers. In our guidelines, we tried to give students some explicit ideas to try when they are presented with a novel situation, and in our rubric, we tried to express criteria that values the process more than the answer. We want students to make valid arguments, to justify their reasoning, to persevere in problem-solving, and to feel that they can take risks, including taking a path that might not lead to a correct solution. I hope that our guidelines and materials communicate these values. I want to be explicit and transparent with students about this. We’ll need to set aside time where we are not focused on learning specific content, but instead are focused on becoming strong and reflective problem solvers who know that they can earn respect and grades with this focus. I want to put my marks where my mouth is.
Here are the rubric and problem-solving guidelines, based on Polya’s four steps. I’ve included both Word and PDF versions, and a blank version, which is intended for students to use as an organizer for their work. These are written with 10th grade students in mind, but I plan to create simplified versions of these for middle and elementary school students. Please let me know if you can use these, and if you have any suggestions for improvement.