I often hook illustrative anecdotes into essays making a larger point. But this anecdote has so many applications that I’m just going to put it out there in its pure form.

A colleague who I’ll call Chuck is pushing the math department to set a department goal. Chuck is in the process of upgrading our algebra 1 classes, and his efforts were really improving outcomes for mid to high ability levels, although the failure rates were a tad terrifying. He has been worried for a while that the successful algebra kids would be let down by subsequent math teachers who would hold his kids to lower standards.

“If we set ourselves the goal of getting one kid from freshman algebra all the way through to **pass** AP Calculus, we’ll improve instruction for everyone.” (Note: while the usual school year doesn’t allow enough time, our “4×4 full-metal block” schedule makes it possible for a dedicated kid to take a double year of math if he chooses).

Chuck isn’t pushing this goal for the sake of that one kid, as he pointed out in a recent meeting. “If we are all thinking about the kid who might make it to calculus, we’ll all be focused on keeping standards high, on making sure that we are teaching the class that will prepare that kid–if he exists–to pass AP Calculus.”

I debated internally, then spoke up. “I think the best way to evaluate your proposal is by considering a second, incompatible objective. Instead of trying to prepare every kid who starts out behind as if he can get to calculus, we could try to improve the math outcomes for the maximum number of students.”

“What do you mean?”

“We could look at our historical math completion patterns for entering freshmen algebra students, and try to improve on those outcomes. Suppose that a quarter of our freshmen take algebra. Of those students, 10% make it to pre-calc or higher. 30% make it to trigonometry, 50% make it to algebra 2, and the other 10% make it to geometry or less. And we set ourselves the goal of reducing the percentages of students who get no further than geometry or even, ideally, algebra 2, while increasing the percentages of kids who make it into trigonometry and pre-calc by senior year.”

“That’s what will happen with my proposal, too.”

“No. You want us to set standards higher, to ensure that kids getting through each course are only those qualified enough to go to Calculus and pass the AP test. That’s a small group anyway, and while you’re more sanguine than I am about the efficacy of instruction on academic outcomes, I think you’ll agree that a large chunk of kids simply won’t be the right combination of interested and capable to go all the way through.”

“Yes, exactly. But we can teach our classes as if they are.”

“Which means we’ll lose a whole bunch of kids who might be convinced to try harder to pass advanced math classes that weren’t taught as if the only objective was to pass calculus. Thus those kids won’t try, and our overall failure rate will increase. This will lower math completion outcomes.”

Chuck waved this away. “I don’t think you understand what I’m saying. There’s nothing incompatible about increasing math completion and setting standards high enough to get kids from algebra to calculus. We can do both.”

I opened my mouth…and decided against further discussion. I’d made my point. Half the department probably agreed with me. So I decided not to argue. No, really. It was, like, a miracle.

Chuck asked us all to think about committing to this instruction model.

Later that day, I ran into Chuck in the copyroom, and lo, a second miracle took place.

“Hey,” he said. “I just realized you were right. We can’t have both. If we get the lowest ability kids motivated just to try, we have to have a C to offer them, and that lowers the standard for a C, which ripples on up. We can’t keep kids working for the highest quality of A if we lower the standards for failure.”

Both copiers were working. That’s three.

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I do not discuss my colleagues to trash them, and if this story in any way reflects negatively on Chuck it’s not intentional. Quite the contrary, in fact. Chuck took less than a day to grasp my point and realized his goal was impossible. We couldn’t enforce higher standards in advanced math without dooming far more kids to failure, which would never be tolerated.

Thus the two of us collapsed a typical reform cycle to six hours from the ten years our country normally takes to abandon a well-meant but impossible chimera.

Many of my readers will understand the larger point implicitly. For those wondering why I chose to tell this story now, I offer up Marc Tucker, whose two–part epic on American education’s purported failures illustrates everything that’s wrong with educational thinking today. I would have normally gone into greater detail enumerating the flaws in reasoning, facts, and ambition but that’s a lot of work and this is a damn good anecdote.

Some other work of mine that strikes me as related:

- Education: No Iron Triangle
- Why Higher Standards are Impossible (one of the first pieces I wrote for this blog, and it still mostly works.)
- On Graduation Rates and Standards

I think I’ve written about my suggested solution somewhere, but where…(rummages)….oh, yes. Here it is: Philip Dick, Preschool and Schrödinger’s Cat–the last few paragraphs.

*“Reality is that which, when you stop believing in it, doesn’t go away.” *

When everyone finally accepts reality, we can start crafting an educational policy that will actually improve on our current system, which does a much better job than most people understand.

But that’s a miracle for another day.