Based on his book “How I Wish I’d Taught Maths”, Craig Barton started a new website about problems that are identical on the surface but have different underlying mathematical structures. He calls them SSDDs (same surface, different deep structure).
His motivation for calling attention to SSDDs:
By always presenting students with a series of problems that are set in different contexts (i.e. have a different surface structure), but which are all from the same topic (i.e. have the same deep structure), we are robbing students of the opportunity to develop the ability to identify the problem’s deep structure and hence identify the strategy needed to solve the problem.
I love the idea, and the website has taken off in a short period of time. Having explored it, I can’t help but ask myself: can the idea of presenting identical images be used to promote problem posing?
I’ve been gaining an increasing interest in problem posing over the past year. Problem posing means shifting control over the problem-generating process from authority figures (me, textbooks, even MTBoS) to students. The few times I’ve tried it, I’ve seen that it puts the math we’ve been doing in a sharper light for them. Sometimes a dish tastes better when you’ve cooked it yourself.
Craig Burton’s website gave me the idea to give my students what is essentially a blank SSDD and ask them to create a different question for each image. I tried creating some images on my own for Algebra 1, and here’s the result:
I haven’t yet given this task to my students but I hope to do so in the near future. My plan will be to pair them up so they can take advantage of one another’s strengths. It wouldn’t be too shocking to discover that students were stronger at some topics over others. I’ll also ask them to answer their own questions. Maybe it’ll give them a sense of self-efficacy and the realization that they can answer a wide range of their own scholarly questions. Now that I’m writing this, I realize it’s like Dan Meyer’s Act Ones, except there’s a greater emphasis on comparing and contrasting structures.
Maybe this problem posing version of SSDD can also serve as a type of formative assessment. Ideally, it’ll root out misconceptions. But more than that, it’ll show me what topics spring to mind and what topics they only remember through heavier prompting. Too often assessment is about “do you know” vs. “do you not know”. Having them craft their own questions might help me (and them) see what they’ve truly attended to.