## The Two Lies Of Teaching

According to Tom Sallee:

1. If I say it then they will learn it.
2. If I don't say it then they won't learn it.

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:

1. If they’ve learned it, it’s because I’ve explained it well.
2. If they haven’t learned it, then I just must not have explained it well.

## Salman Khan Isn’t A Fan Of One-Size-Fits-All Lectures

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.

## Guess-Check-Generalize

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.

## Albert Einstein On Bret Victor’s Kill Math Project

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?

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