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…”
Elizabeth Green, of Chalkbeat has a new piece out on teaching fractions. She is the one who wrote the piece “Why Americans Stink at Math” which appeared in the NY Times Magazine and was riddled with errors and assumptions that the cognescenti and punditry were totally unaware of and just assumed she was right. And when people pointed out her errors, (see, for example here and here) the errors continued to go unnoticed.
Now she writes about a “Math Lab” experience in NY:
“The Math Lab’s emphasis on learning math by talking and thinking about it is clear almost as soon as the students enter the room. A list of the class’ “math community agreements,” posted on a board, reminds students to “add onto each other’s thinking” and “analyze and observe each other’s work.”
“To help students internalize that philosophy, Van Duzer led an activity called “convincing a skeptic,” where students were asked to fold pieces of green paper into squares one quarter the size of the original and then convince their partner that the new shape was, in fact, one-fourth of the original.”
Sorry; that’s about as far as I got. (I recognize the “convince me” gambit from Steve Leinwand’s promotion of the technique). Being able to explain and convince rather than be instructed in the basics and given scaffolded problems to help reinforce procedures and understanding is off the table. Such techniques in the worldview of reformers is apparently too procedural and rote-like.
Then there’s this:
“As teachers reflected on Tuesday’s lesson, a debate of their own emerged. They began wondering about how Cipparone handled what the group would begin calling “Kris’ problem” — the moment that morning when Kris misplaced five-thirds on the number line and Cipparone had to make a split-second decision about whether to correct him before the students left for the day. Deirdre Flood, a teacher at Brooklyn’s P.S. 11, said it could make sense to end the lesson ambiguously if “every single [student] made a decision before they left, so they were thinking about it on their way out.” ”
Because ambiguity and not teaching students what they need to know (particularly when they need to know it) has just worked out great for the last 25+ years, now hasn’t it?
Just call me unconvinced.
Scores on the Common Core-aligned tests in NY state actually went up this year. But some things have to be taken into account:
“This year, for example, students had more time to answer fewer test questions, so the modest gains may simply reflect that students had an easier time taking the exams, not that they learned more.”
Not to mention that perhaps even the cut-scores were lowered, though I have no evidence of that. (Parenthetical digression: I once received criticism that I didn’t know anything about statistics or percentiles if I thought that lowering the cut scores meant anything. For example, if getting 30% of the questions right puts you in the 80th percentile, then a cut score based on percentiles is appropriate. Somehow I don’t agree, but then again, my critiquer is correct; I’m not a statistician, so don’t listen to me!)
Because of the confusion with what test scores actually mean, there’s this solution being offered:
“Leaders here have become accustomed to navigating the ever-changing targets that often come with the state accountability system, and for many of those schools that come with consequences, including possibly facing an outside takeover. Now, rather than focus on the tests, they are turning their attention to classroom practices.
“If the focus on improving classroom instruction is clear and intentional, students will thrive,” said Will Keresztes, chief of intergovernmental affairs, planning, and community engagement for the Buffalo district. “Speculating on testing changes is not a strategy for improving student outcomes.” ”
I can only imagine what they feel are appropriate classroom practices. Let’s stick with the test scores, flawed as they may be, and let the teachers work around the many hurdles placed in their way.