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.
traditional math 
Reblogged this on Nonpartisan Education Group.
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“Pointers for middle and high school math teachers who have concerns about incorporating project-based learning in their classes.”
“When the new school year began in Oklahoma City, Telannia Norfar’s math students realized right away that they were in for a different kind of learning experience. On day one, Norfar challenged them with a problem worth solving: Design the “ultimate classroom” that will meet the needs of all learners.”
As if these students have a clue to what the needs are for “all learners.” What if a student said that “all learners” should not be in the same classroom? What if a student says that PBL does not meet the needs of her learning style? Who gets to decide what’s “ultimate” – schools or students?
“Telannia Norfar is a mathematics teacher at a public high school in Oklahoma City, OK. She has taught all high school courses including AP Calculus AB since 2005. She has served as department chair and team lead for the 9th grade academy. She has used project-based learning as a core strategy in her classroom since she started teaching.”
I want to see her PBL examples for AP Calculus.
More is always more, but if you take class time for these projects, then the more is done by others. It just shifts the unit concepts and skill mastery work to the students at home. What proof does she have that PBL class time taken away from other work helps when students, parents, and tutors know what’s needed and fill in her gaps. Schools and teachers do whatever interesting stuff they want and their mastery asses are covered by others who won’t allow failure.
“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.”
So, not working “the way you dreamed” (whatever that means) could not be because PBL is just a bad use of time when you’ve pre-decided that “it’s too powerful to give up on.” It’s powerful (maybe) if others do your work at home or with tutors. We’ve been explaining the problems of PBL (etal) approaches for ages, but their problem solving approach does not allow them to question fundamental assumptions.
School bands and orchestras can do interesting stuff when they know that most of the students have been taking private lessons for years, paid for by parents. That’s apparently now the model desired by all teachers. Do the fun stuff in class and assume that engagement gets the rest of the job done. At least the music teachers know that’s wrong.
And this is all supposed to be about critical thinking and problem solving. The kids are the losers.
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