It’s been a while since I’ve revisited the Taxonomy of Problems I threw together a while back, but I think it’ll be helpful to spend some time there when considering the following Most-Wanted question around Problem-Based Learning:
At what point after allowing the students to work on a problem do I scaffold the content knowledge?
It’s probably important to identify exactly what type of problem you’re implementing before deciding this.
One of the reasons I wanted to think about this as a potential framework is to address scaffolding (I’ve already addressed assessment). It might not be perfect or precise, but here’s what I basically envisioned.
Unintentionally, this kind of mirrors the ideal progression of both a PrBL Unit as well a classroom and high school experience.
So once you’ve figured out where you are on the taxonomy, where you are in the unit, you can think about your scaffolding.
What & When
I’ll toss out a couple broad-brush rules that oughtn’t be universally applied.
When you’re at the left end of the spectrum – the Content Learning Problems, I’d suggest the following.
If the need for the content is germane to the problem, intervene relatively quickly and with the entire class.
If the need us for an ancillary concept or “side-topic”, consider holding back and/or offering small, differentiated workshops.
For example, I threw Dan’s Taco Cart task into my unit on Linear Equations.
However, use of the Pythagorean Theroem is required to develop your linear equations to model. There will no doubt be a need for some – probably not all – students to revisit or relearn the Pythagorean Theorem. That is ancillary content knowledge: essential, but not the targeted content knowledge skill. Consider holding off on scaffolding that – another groupmate might be the better vessel to explain the concept. Or, if you deem yourself the ideal vessel, consider jigsawing that concept or holding a small pullout workshop with one groupmember per group (the groups’ “student-teacher liaison” as it were).
If the knowledge is germane and is the targeted content knowledge of the task, the scaffolding might need to be more prescriptive, more whole-group. You certainly could lecture (Grant Wiggins has an exceptional post on that), but you could also offer one of these scaffolding tasks. I’m a huge fan of manipulatives and students evaluating student work samples.
Ah, but when do you offer that scaffolding? How much productive struggle should we allow students before intervening? This is where teaching is more of an art than a science. Although if it is truly germane to the problem and it’s a Content Learning problem, I’d err on the side of quick-intervention. Twenty minutes after a problem is launched, perhaps? Thirty?
More important than a time demarcation for instruction is probably some classroom behavioral evidence. Here’s a short list of things to look for to initiate INSTRUCTION MODE:
- Over half the groups or students asking the same or similar thing
- Loss of cognitive demand in the attempted solutions
- Attempted solutions going totally off the rails
What have I missed? What are some indicators that it’s time for you to intervene with scaffolding? Or do you have a particular system or time-frame when considering when to cease the productive struggle time?
If
If your problem is more to the right on that arrow above – Exploratory or Conceptual Understanding problems – the question might not be “what and when” to scaffold but “if”. There is inherent value in an unscaffolded, nonroutine, “ill-structured” problem with a lugubrious associated standard. For these problems consider restricting yourself solely to small workshops devoted to ancillary content knowledge. Or perhaps follow up the problem with a standalone scaffolding task – perhaps, again, a manipulative or evaluation of work samples. Scaffolding for Assessment problems should focus on revision and peer-editing.
The tension between inquiry and instruction shifts from day-to-day, problem-to-problem, so I wouldn’t hold anyone to a hard-and-fast rule. I hope you’ve appreciated my self-indulgence as I continue to try to figure this out and establish a few basic tenets of solid PrBL practice. As always, feedback and commentary is appreciated.
emergent math 