I’m fascinated with the charm of student work. There’s something really inviting that my students’ feel about being asked to analyze and discuss someone else’s mathematical thinking. For whatever the reason, there’s a lure to it. If I project some anonymous kid’s work as they walk in the room, for example, it captivates them from the moment they glance at the board. It’s so bad that many won’t even put their bag down at their desk before they begin thinking about the work. Whether the work has errors or not, it almost never fails to pique their interest.
Other than generating student engagement and learning, the class discussion around the work often helps me better understand the student’s line of thinking, too. I regularly struggle to figure out my students’ thinking. By pitching the work back to them (anonymously, of course), they help me figure out what’s going on in the work in ways that I would not have been able to otherwise.
As a teacher, this is gold. But deep down I can’t help but wonder why they get so into it. Maybe it’s because I’m not asking them to actually do any computation? Maybe they’re trying to figure out if they did the problem correctly themselves? Maybe it’s the specific samples of student work that I’ve selected that are just nuanced enough? There has to be an interesting psychological aspect to this that I’m unaware of. I think the human element that comes with using a person’s written work to learn math may be at play here. It’s not neatly constructed on MathType or Latex or Google Docs. No, it’s human thought presented in one of it’s purest forms. Let me stop, I’m getting too deep. I’ll save that research for another post.
Because of all this, I’ve been hoarding student work. For the last two years, I’ve been collecting everything that I can get my hands on. Quizzes, exams, journals, you name it. I’ve been scanning, studying, and filing it all away.
But how? Scanning individual papers can take forever. Well, I’ve found student work to be so useful that it has forced me to rethink my assessments for the sole purpose of being able to scan them more easily. The idea is that I use scanned student work (and not just the overall results of the assessment) intentionally to further student learning. As long as it doesn’t take forever, or even more than 30 seconds for an entire class for that matter, why give an assessment if I can’t collect and leverage students’ written thoughts?
The most obvious example of how I’ve adjusted assessments to help me easily scan written work is exams. I never make them more than a single page (front and back). When I first started doing this a couple years ago, it had nothing to do with scanning student work and had everything to do with being lazy. I refused to take more than a day to get the exams back to the kids and knew that I wouldn’t be able to live up to this expectation if the exam was three pages of problems. I rarely give multiple choice problems and, if I do, I still require work.
Despite my laziness, over time I saw the real value in my one-page exams as being able to scan my kids exams quickly. Given the multifunction copier at my school, my exams serve an important purpose: they eliminate the need for stapling. Without a staple, each students’ thinking is contained in a single piece of paper — and this makes them dump-easy to scan. Before I mark the exams, I simply place them in the document feeder, hit scan, and they zip through one-by-one. Voilá, 15 seconds later, I have a PDF in my inbox of every students’ exam. Done. The same works for quizzes, too.
As I mark the exams, I take note of interesting examples of student thinking and grab a screenshot from the PDF. These samples usually become the focus of the opener for our post-exam reflections the following day, but also become features of future problems. I’ve framed the student work in different ways, mainly based on what I’ve seen other teachers do.
There’s the classic, What do you notice? What do you wonder?
There’s also the clever debate prompt, Who has a better error?
There’s even Algebra by Example tasks that use an example (often an incorrect one) to elicit a Why…? and extend student thinking.
Although I fail to ask Why? about any step of the example, here’s one of mine:
Another is the simple question, What do you think? Here’s one I projected last Thursday, the day following their exam.
Generally, restructuring exams so that all student thinking fits on one page is not trivial. It requires that I include less content on the exams and can affect how bunches of concepts, and big ideas, are taught and assessed. But this also means that, since I’m grading less per exam, I can test more frequently in smaller pieces. The exams arrive in smaller, bite-sized chunks rather than in all-encompassing behemoths. This is better for everyone. The kids like having less stuff on exams get more immediate feedback. I’m grading less per exam. And on top of the benefit of scanning and producing a goldmine of student work, I love it because I can be more precise and granular about which concepts I assess and how I assess them.
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