Throughout this first unit of the Quantway MLCS course, Heather and I have both had lots of moments of questioning whether or not students were benefiting from the approach. They like most of the lessons and are engaged but still have that somewhat skeptical reaction to the course approach. It's just so different from what they are used to that the adjustment is real.
But yesterday, something wonderful happened. We graded the first set of open-ended problems they were asked to solve as a group.
Part of our idea in approaching this course is that we want to develop real problem solving skills as well as critical thinking. As anyone who's held a job knows, problems don't come boiled down, well organized, or well defined. Part of the problem with problems is just figuring out where to start. Plus, you have to figure out what you know, what you don't, what's relevant, and what's extraneous.
Traditional developmental math word problems are very nicely presented to students. They're short usually, 1-3 sentences, and full of key words. Often, they follow a "type" that students can recognize. Once they know how to deal with that type, they can solve the problem.
This sounds like the problems are easy. But anyone who has taught word problems knows that even with all these nice facets, students often seize up when presented with one and have little success with them.
One perk to this course is that like a statistics course, every problem is presented in a word problem format. The catch is they don't look like it. So students get used to reading the scenario presented and are willing to attempt them. They're not always successful but at least the willingness level is higher.
Every lesson is filled with problems to solve based on a scenario. But nearly all the problems have a unique solution. This is so we're not so out of the box that students resist entirely. They like solving a problem and checking their answers. The problems are realistic and difficult but they can find out if they're right or not.
That's all well and good but we do want them to see what real problems look like. Enter our once per unit open-ended problem.
On day 1 of the unit, students are presented with a large paragraph that explains the scenario and problem. Students have 3 weeks to work with a group to solve it. We intentionally help them through this by having regular revisits to the problem, each time with specific tasks for the group to complete. The first time through, we have them identify what they know, what they don't, what terminology they need help with, etc. The second time around, we have them develop a list of tasks for the group members as well as a timeline for completing them. They're also challenged with starting their rough draft. The third time has them looking at the rough draft with the group, refining it and making a plan for the final solution. They submit, we grade, and we debrief the whole thing the fourth time in class. We show them a strong solution, talk about the problem, and make notes for the next one so that they can do better when facing another problem at this level.
It's an interesting approach and we had our fingers crossed the whole time hoping they could do it. Every time they worked together, they went into the typical mode students do when they're confused. "We're lost. We don't get it. Can you help us?" Usually we swoop in as teachers and hold their hand. Heather and I both made an agreement: we will not do that or else they will never be able to do these problems. Instead, we ask questions and answer questions with questions in an attempt to get them talking. This helps them from getting too frustrated, but also keeps them in charge of figuring out their solution.
When they submitted the solutions, more than one student said they had done some research on their own, talking to people who might have been in the situation in the problem. They were talking and thinking about math outside of class and not just in the "what's the answer?" way they usually do. We were very pleasantly surprised.
Grading them, we were even more surprised and pleased. In short, they rose to the occasion. The grades were much better than we ever expected, some C's but mostly A's and B's. No perfect papers but that was to be expected. They followed the expectations, and we could see that they finally got to the other side with the problem. In class, so often they were struggling to get started but at some point, they dug in and solved it. We had them do an individual assessment of their work and the group's after submitting their solution. Repeatedly, we read that students liked working with the group and enjoyed the process. We didn't ask them "do you like your group? Do you like this approach?" We just asked them to give a percentage to the level of work each person did and comment on anything if they wanted to. If someone wasn't pulling their weight, this was a private chance to tell us. What they volunteered was unexpected yet great to read.
All in all, it was a very positive way to close out the unit. Monday is the first test. My fingers are going to cramp from all the crossing but I do hope they can do well and rise to our expectations again. We've prepared them; the ball's in their court now.
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