One of the useful things I've learned at Stanford is what, precisely, I object to about progressive education. I knew the behaviors I didn't like, of course, but I didn't know what to name the precise tenets. I now know three of the biggies, which makes life much easier. Instead of saying "I am ideologically opposed to the crap they teach at ed school", I can say firmly "I am not overly thrilled with complex instruction, student centered classrooms, and discovery-based learning." I speaketh the jargon. (Of course, progressive describe me a tad differently: "Committed to maintaining white privilege; supports both testing and tracking.")

However, Sequoia has raised another interesting question in my mind. I'd noticed that many of the students at College Track have abysmal GPAs. Many of them are taking Algebra I as juniors. Before Sequoia, I had assumed that they had just been deemed unready for Algebra and had taken two years of pre-Algebra, or some such.

Nope. Many of these students have failed Algebra II/Trig at least once. Some have flunked twice. Worse, many of them failed almost exclusively because they didn't do homework.

So you get situations like this pretty often:

The students are using their graphing calculators to find approximate values. Say, for example, that Joe's Fonda Afford¹ costs $25,000 at the time of purchase, and depreciates 4% every year. At what point will his car be worth half of its original price?

So they create the function, plug it into a graph, and use the table to find the two years sandwiching $12,500.

As they began the task, my CT said "Now, some of you know another way of solving this problem, but that's not the method to use today. Just use your calculator to find the approximate value."

I thought that was such an odd thing to say. What kid who knew logs would end up flunking Algebra II?²

And then I was working with a group and one boy snorts derisively, "Why can't we use logs? It's so stupid doing it this way."

I did a double take and he grinned. "I learned it last year."

I recovered. "You want to talk stupid? Stupid is flunking when you know how to do the math. Stupid squared is getting a low grade the second time through when you remembered what you learned last year."

This young man had the grace to blush. "Well, I just don't like to do homework."

"I don't care what you like. Here's what I don't like: I don't like giving bad grades to kids who know how to do the work. SO GET THAT HOMEWORK DONE."

I've been looking for research on the failure rate in heterogeneous classes, but even if there were such a thing, I'd need something more specific.

The tracking debate matters only in schools that have underperforming minority students and high income achievers. You can find these schools in many suburban areas, and you can usually predict whether or not they track based on the percentage of whites and Asians.

Schools in this cateogry that track run essentially two programs in the same campus (the high schools in Palo Alto and Menlo Atherton are classic examples). Their white and Asian students comprise a majority (or near that) of their students; however, the campuses are located near low income areas that provide a hefty segment of low income Hispanics and (to a lesser degree) African Americans.

Schools with these highly diverse populations and don't track have more under-represented minorities than wealthy or middle class whites and Asians combined. They are usually detracking for ideological reasons, but they know full well that the whites and Asians will leave if educational quality is compromised, and there goes their tax base and a lot of money.

So how to thread the needle of quality and access? I was drawn to Sequoia because I thought they'd done exactly that. And in a way, they have. Many of the kids who have flunked this class once or twice have solid to better math scores. Sequoia is teaching their students very well. But colleges value GPAs over test scores these days. How are they helping students if the cost of their heterogeneity is GPAs in the low 1s?

If I'm right, both the rigor and the inclusion of the strongest students hurt in different ways. Many students who failed the first time because they genuinely didn't get the material and are struggling with it again this year. But we can't slow the course down to help them out.

Then you've got students who just won't do their homework. They don't care enough. But they'd skate through an easier course in a heartbeat, because their grades would be the highest in the class, as opposed to solid Bs or the occasional C when compared against the strongest students. Their failure to do homework would drag their A test average down, yes, but only to a B or at the worse a C.

As I said, I can't find any research on this. You'd need something like number of times taking the class, grade, and a standardized test score.

Then, I'd need some comparative data from a school that tracks. What if the heterogeneous students had the same or higher test scores as students in the non-honors math courses who passed their less rigorous course with As and Bs? What does that mean?

(Note: I wrote this in October or November, after my site went password protected. My experience at Sequoia confirmed a lot of what I wrote here. I also wrote an email to a pro-tracking researcher whose name I can't remember, and asked if there was any research. We had an interesting discussion.

It turns out, by the way, that I'm really good at working in heterogeneous classrooms, probably because of my skills at motivating less engaged students. I am teaching in heterogeneous classrooms in my first job, and I'm happy to be doing so--even though I haven't changed my opinion about tracking.)

**********************************************************************************

¹Isn't there some obvious synergy here? Honda pays for product placement, textbooks are cheaper, and the kids don't snigger at the name changes.

²For the non-math people, logarithms (logs) are the inverse of exponents. So if your $25,000 car depreciates 4% every year, its new value is always 96% of the previous year. You can set up an exponential function like this:

where x is the number of years you've had the car.

So at what point does the car have half its value? Without a logarithm, you have to guess and check. With a logarithm, you can find the exact amount.

But logs are covered in the second half of Algebra II, so you wouldn't normally expect a student to know about this option.