Edutopia has advice for those math teachers who believe that Problem (Project) Based Learning (PBL) actually has something of value to offer.
I offer a brief commentary on their suggestions.
Address math myths: “Some teachers worry that PBL will take away time needed to practice math skills. Others insist that they need to “front-load” concepts before students can apply them, or worry about students encountering concepts out of the order outlined in their math curriculum.”
Those are my concerns as well. What the author calls “front-loading” concepts is what the rest of us call teaching. Many of us teach using direct and explicit instruction with worked examples and pratice problems. We do this so that students can then put to use what they learn–with guidance. The alternative is what I call “just in time teaching”. This is similar to throwing a kid in the deep end of the pool and instructing him/her to swim to the other side. The belief is that he/she will be ready to absorb the instructions the teacher is shouting from the side of the pool on how to swim.
Fancher and Norfar rely on research from the National Council of Teachers of Mathematics (NCTM), among other sources, to overcome common concerns about PBL.
That’s their first mistake.
For example, developing what NCTM calls procedural fluency does not require having students labor over worksheets. Fancher explains, “It’s better to have students do four or five rich problems and explain how they solved them.”
Rich problems: What are they? Generally, they are very wordy, tedious one-off type problems that do not generalize. Often they are open-ended and ill-posed (like, the area of a rectangle is 48 sq ft; what are its dimensions?) and require students to learn procedures on a “just in time” basis.
Explain how they solved them: Back to the kid who was tossed in the deep end of the pool. If by some miracle the kid makes it to the other side without drowning, he/she will likely say: “I don’t know how I did it, but I never want to do that again.”
“Don’t stop doing PBL if your project doesn’t go the way you dreamed,” Norfar cautions. Instead, reflect on what worked well and what didn’t, and consider how you can improve the project next time around. “PBL isn’t a cure-all,” she adds, “but it’s too powerful to give up on.”
My advice: Don’t waste your time, but if you do, your reflection should be on how you could have instead provided direct instruction on mathematical procedures. This could have been coupled with providing adequate practice with scaffolded problems. Finally, you could have provided instruction (and practice) on how to solve specific types of word problems. I believe that such tried and true methods are the ones too powerful to give up on. They are also the ones the education industry has discarded and from which the tutoring industry has greatly benefited.