The good teacher knows if the learner learns through the ears, the eyes, or the hands just like the good spotter knows where the lifter wants support – at the wrists or under the elbows or on the bar. The good spotter is unhelpful; the good spotter doesn’t intervene at the first sign of struggle but realizes that the struggle is essential, that the struggle is the entire reason they are there, and waits as long as possible before intervening.

The good teacher puts weight on the student’s intellectual bar and lets her struggle under that weight as long as possible, asking questions to help her cut through the confusion, just like the spotter shouts encouragement at the lifter.

Mostly I envy the spotter. The job is so (comparatively) easy. The spotter steps in just as the lifter begins to collapse and not a moment before. That moment is nowhere near as obvious in teaching where what the learner says she needs and what the learner actually needs often are not the same thing, where it isn’t visually obvious that the learner is too perplexed or not perplexed enough.

And, my word: we’re spotting thirty people at once.

[Photo credit]

Rhett Allain kills me. Here you have him writing several hundreds words (with LaTeXing and diagrams) taking down the dubious physics of Ruff Ruffman, animated host of the children’s show FETCH! with Ruff Ruffman:

Ruff, if this is indeed the definition you used – I am not sure if it fits in this case. Maybe you meant momentum, although I think that is not quite right either. How about I solve this problem?

This is why God made blogs.

Robert Manwaring:

To put this in some perspective, if my prediction is accurate more California teachers will be given layoff notices than the entire state teaching force in 17 different states.

Manwaring guesses at 25,000 layoffs, which frames my own layoff with a wider lens, certainly.

February 7, 2008:

I bought my car new on January 15, 2006. Today, February 7, 2008, it has 37,846 miles on it. On what date will I need my 120,000-mile tune up?

February 20, 2009:

On what date will my car need its 120,000-mile tune up?

In 2008, my students proceeded admirably through a challenging problem, successfully navigating proportional reasoning, but let’s not pretend I did anything for their ability to see the world through a mathematical framework.

In 2009, my students had to ask themselves, “what do I need to know in order to answer this question?” a line of inquiry thoroughly absent in 2008, a line of inquiry thoroughly absent in my textbook, which supplies only relevant information and, in some cases, “helpfully” suggests a route to the solution.

As my (patient) readership has no doubt realized, the impotency of our textbooks to do anything but teach procedure has recently whacked me over the head. Part of this, I realize, is fundamental to the print medium, which doesn’t permit a layered application of mathematical structures, but part of this is the inexcusable lack of imagination of publishing houses, whose bundled supplements are both costly and unhelpful, who don’t understand that they need to help students less:

Dan bought his car new on January 15, 2006. It’s a four-door sedan with 16-inch wheels. Today, February 7, 2008, the car has 37,846 miles on it. He lives 24 miles from his job and drives, on average, 48 miles per hour. The weather in his hometown ranged from 23° to 107°. On what date will he need his 120,000-mile tune up?