When given an open-ended PBL type problem like “You own a zoo; how much should you charge for admission?”, students will flail about and come up with some things. To the proponents of PBL, what they come up with is great. “Look, they researched types of animals that are at a zoo, cost of capturing the animals, transporting them, caring for them, how many employees to hire, how much to pay…” and on and on.The exercise doesn’t teach about math so much as it does about the various aspects of zoos, employment and so forth. As such, the problem solving skills in such an exercise are fairly small and barely transferable.
This article at Fordham nicely articulates the down sides of PBL.
“When PBL is deployed, knowledge acquisition is driven by the demands of a given project. The object may be “deeper learning,” but the outcome is definitely narrower, potentially excluding other critical knowledge and skills. This should be solvable, yet the PBL instructional models make no specific reference to mastery. In other words, students can complete a project without mastering the skills in that project or the knowledge underlying its successful completion. ”
A friend of mine adds this observation about the article:
“They are tripping over themselves to address some of the problems they are now seeing while still ignoring the others we’ve been warning about. I suppose in a few years they’ll admit that the focus on skills and dispositions translated into political agendas and dumbed down 21st century skills.”
And another observation from someone:
“I recently attended a seminar where the inquiry method was being taught. A picture of a cell phone battery (like you see on your screen) charged at 21% and a time was shown. The question was “How long will it take to charge this cell phone?” I was very frustrated. There was not enough information to answer the question. After some fruitless guesses a second picture was shown. The phone had been put on a charger and 20 minutes later it was at 47%. Same question. Me still frustrated, not enough information. I believe the charge to time graph is not a straight line (because it is not) and many things make a difference. Which charger, which battery, is it being charged in a house or in a car, has the software been updated (actually makes a difference). We solved for a linear relationship. Showed us another picture. The relationship was linear… until the battery was about 70% charged, then it became a curve with diminishing returns. No-one got the right time after a half dozen reveals. I got a head ache and the impression that the person asking the question really did not understand the variables affecting the outcome…”
traditional math 
“barely transferable”
It illustrates the importance of breadth and depth of content knowledge for problem solving. This can’t be properly learned on an as-needed (just-in-time, as Barry says) basis, especially for math. Learning formal techniques of problem solving in math requires the development of content knowledge and mastery of the tools of math from the bottom up: drawing pictures, defining variables and equations, finding or creating missing equations or variables that can be fixed, and then turning the crank to solve for the answer. This can be done without the added complexity of unknown content knowledge and solving skills. It’s not that problems like these (requiring more assumptions or creation of equations) can’t be useful. They just have to be defined better than the silly too-many-step, top-down, guess and struggle, problems created by educational pedagogues. Just look in any proper math textbook an you will find plenty – all properly scaffolded.
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Reblogged this on The Echo Chamber.
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