This seems germane to our (roiling) discussion of Khan Academy.
2011 June 6. Sam Critchlow, in the comments:
Lets not forget the contrapositives, which must also be false:
- If they’ve learned it, it’s because I’ve explained it well.
- If they haven’t learned it, then I just must not have explained it well.
A curious moment from Salman Khan’s interview on The Colbert Report on Thursday:
What we’re seeing in classrooms [with Khan Academy videos] is it’s kind of liberating teachers. So instead of giving one-size-fits-all lectures to a bunch of students – some of them lost, some of them bored – now they can assign this as homework and kids can come into the class and actually do homework there and actually interact and actually take advantage of the fact that there’s actually people in the room there that you can get help from.
Don’t give one-size-fits-all lectures to students. Instead, send them all home with the same ten-minute video.
Someone needs to tighten up that message.
2011 Jun 05: Comments closed.
Bowen Kerins documents a high-leverage practice:
The concept of guess-check-generalize starts by changing the nature of the problem. The question to start with changes from “What is the correct bar height?” to “Is 100 the correct bar height?”
Later, he notes that guess-check-generalize can reduce the difficulty level of word problems “by 2 or 3 grade levels immediately.” Of course, once you reach the point of generalization, the problem is just as challenging as it was before. The difference is how many more students you help reach that point.
The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill.
Victor’s Scrubbing Calculator offers an elegant solution to certain kinds of mathematical problems. But does it help students formulate them? (Like Victor did, turning this into this?) Maybe I’m just whining that it won’t poach an egg or iron the drapes, but if students struggle to formulate problems, is the Scrubbing Calculator any use to them?
With Interactive Exploration of a Dynamical System earlier this month and today’s Scrubbing Calculator, Bret Victor is doing some of the most provocative work in math education right now. As much as I’m curious how STEM educators perceive his work, I admit I’m much more interested in the perceptions of educators in the humanities and of people who, at one point or another, were totally put off by the abstract symbology of mathematics.
I’m also strongly inclined toward P.J. Karafiol’s critique:
If our goal is to empower students to do more and more interesting mathematics, we can’t just hand them simulators and tell them to go play: we need to teach them how to create those simulators. Doing that requires a lot of math and a lot of programming. So Victor’s “simulation” model of doing math ultimately requires teaching kids a lot of traditional mathematics.
Of course, replace “simulators” with “calculators” and we have another familiar argument. Obviously, I’m of two very different minds about this.
