The following is an adaptation of the workshop I planned for the Scholarship of Teaching and Learning (SoTL) Academy. It represents an activity I do with teachers that helps them to make their thinking visible as they are problem solving. The activity is intended to prepare the way for the problem solvers to write metacognitive memoirs (which I wrote about here).
Metacognitive Memoirs: Making Thinking Visible
Schema Activation: Making Your Thinking Visible [10 minutes]
Why are you here? What do you hope to get out of this presentation (blog post)? Please write your thinking down in order to make it public and permanent.
Schoenfeld found that one of the major issues novice problem solvers face when they encounter non-routine problems is an inability to monitor, and therefore regulate, their thinking. It’s what I call flat-lining. Einstein called it insanity.
Not surprisingly, the National Resource Council (2005) wrote in How Students Learn that one of the primary principles associated with learning is The Importance of Self Monitoring. They write:
“Meta” is a prefix that can mean after, along with, or beyond. In the psychological literature, “metacognition” is used to refer to people’s knowledge about themselves as information processors. This includes knowledge about what we need to do in order to learn and remember information (e.g., most adults know that they need to rehearse an unfamiliar phone number to keep it active in short-term memory while they walk across the room to dial the phone). And it includes the ability to monitor our current understanding to make sure we understand. Other examples include monitoring the degree to which we have been helpful to a group working on a project. (p. 10)
The focus of this workshop is to help us to be intentional about our thinking so that we can examine it, share it, and improve it.
Actions: Sowing Seeds [30 minutes]
As you work through this problem, try to be aware of your thinking as you make decisions about how to proceed. You will want to write as much of your thinking down as you can so that it will be available later as you work on your memoir. Also, keep track of choices you decided against and why. Were these possible pitfalls you avoided or just different approaches? What would have happened if you followed these paths instead?
This is a lot to keep track of, which means you probably will not arrive at a solution in the time provided. That is to be expected. In fact, if you can complete a task quickly, it was probably not a problem but an exercise. Only the problems found on sitcoms get rapped up in under twenty minutes.
After about ten minutes stop and on a separate piece of paper write a reasoning recount. What steps have you taken so far, and why did you take them? Don’t forget to include things you chose not to do and the rationale behind those decisions.
Reflection: Where did you ...? [15 minutes]
As you review your reasoning recount, try to identify where you are:
- Assessing (gathering data about your thinking and your progress);
- Analyzing (evaluating what was working and what was not);
- Adjusting (changing course because what you were doing was not making sufficient progress toward your goal); and
- Acting (putting your plan into action).
Thus far, most of the memoirs have been written as narratives. A few problem solvers layer their thinking on using sticky notes or the comment function of Word. We have also been experimenting with using two columns – putting the thinking in the left-hand side in order to recognize its importance in the process. Recently, some problem solvers have been using technology to record their thinking as they solve problems (a la this post).
So what are your thoughts about this approach to making thinking visible?
Love this. I need to wallow in it more to reflect thoughtfully, but I wanted to offer another alternative viewpoint about the inability of some problem-solvers to monitor their own thinking process. For myself, I have learned that this is intimately connected with the fight-flight-freeze response that kicks in whenever I am faced with a non-routine problem to work on. I literally freeze — as in, I go all deer in the headlights, even to the point of unconsciously holding my breath — out of panic at the seemingly imminent moment of shame and humiliation I anticipate will accompany my inability to get started.ReplyDelete
I've spent a long part of my life as a meditator and meditation teacher learning how to notice this moment happening in a wide range of situations, but that doesn't mean the conditioned habit of fight-flight-freeze ever goes away. It does mean, though, that I have developed a different relationship to it — a relationship of unconditional friendliness or maitri toward it. And that has helped to loosen its grip on my mathematical problem-solving mind.
Anyway, just some initial amuses bouches for thought.
- Elizabeth (@cheesemonkeysf)
As always, I appreciate your thoughts. I certainly agree with your perspective regarding our relationship with non-routine problems. We've experienced "math" as something you do quickly (if you're good at it) and not at all (if you're not). When I encounter a math "problem" that takes me more than a couple of minutes to "solve" I experience frustration and anxiety because I've been trained to think I was good/fast at math.
The interesting thing about this activity is that there is no problem - that's what makes it non-routine. Participants have to decide for themselves what would constitute a problem for them. In the most recent workshop where I used this, several university professor who professed to being bad at math (sigh) came up with a problem they could solve and talked through their process of solving it. By focusing on their thinking, not a solution, they can develop better capacity and agency around problem solving. At least, that's the hope.
Yes, it's a "non problem." That's where I stopped; it was clearly just some tidbits of information. The directions said I wouldn't arrive at a solution "in time" -- but the wording of the problem didn't ask for a solution. Therefore, I concluded that the task wasn't likely to make sense. I mean, if you tell me to solve something but there's nothing to solve, what else will you have written that really wasn't what you meant to write?ReplyDelete
(This is, I'm afraid, a direct result of people publishing things with fundamental errors so often that i learned not to assume things made any sense.)