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The Simple Solution For All Math Problems

In his column this week, Jay Mathews considers some suggested revisions to the California Mathematics Framework. The changes, similar to those being proposed in Virginia, will attempt to develop a K12 program that better prepares all students to understand the math they will need as adults.

Mathews, of course, knows a better way to accomplish the same goal: Advanced Placement. Which is no surprise since his solution for pretty much every educational issue involves AP. Or charter schools. Or both.

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Blah, Blah, Blah… AP

I wish I understood why The Washington Post continues to provide print space for Jay Mathews.

Mathews was a long-time education reporter for The Washington Post and is now a weekly columnist. But then as now, his focus is extremely narrow. Most of his writing involves cheerleading for the Advanced Placement program1 and making excuses for charter schools.

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Time To Change The High School Menu

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Freakonomics sounds like it should be the study of strange business practices. But the books, radio show, live shows, and podcast that makes up that franchise tends to wander all over the place looking at problems in various parts of society. Which is probably a big reason why I like what they do.

A recent edition of the podcast took an odd-even-for-them detour titled “America’s Math Curriculum Doesn’t Add Up“. Although the program got stuck in a few of the usual cliches, including assuming that assessment was going to come in the form of a standardized test, I have to admit they did a pretty good job.

The math curriculum that most high students in the US are subjected to was created early in the previous century and is about as out of touch with the real world as anything in American education. Jo Boaler – author, Stanford professor, and math education reform leader – explains.

The curriculum that we teach in maths1 classrooms was really designed in days that are long past. It was a long time ago that somebody in the U.S. decided to teach what I think of as the geometry sandwich — a course of algebra for a whole year, followed by a course of geometry for a whole year, and then another course of algebra. I don’t know any other country that does that, and it’s part of the problem. So, I would change the curriculum to really reflect real mathematics, and I would also change it to reflect the 21st century, because maths still looks in classrooms pretty much as it did in Victorian days.

Geometry sandwich. Love it.

In the interview with Boaler, the host says that it’s “pretty obvious that we need a radical transformation in the math curriculum” (even if his program hasn’t made it “obvious” at that point) and asks her what students are missing.

When we look at the world out there and the jobs students are going to have, many students will be working with big data sets. So, we haven’t adapted to help students in the most important job many people will do, which is to work with data sets in different ways. So, statistics is really important, as a course, but is under-played. This is a fifth of the curriculum in England and has been for decades. But here in the U.S., it’s sort of a poor cousin to calculus.

Very few people will ever need or use Calculus.2 But the math sequence followed by the vast majority of high school students is focused on that one target.

On the other hand, even those adults who don’t work with big data sets will still need a good understanding of how big data sets work. How that data is collected, organized, analyzed, and presented. Or, very often these days, how it is obtained without the targets’ knowledge or consent, manipulated, and misused.

However, rather than simply add another course to the math curriculum, the program suggests that students should be studying the use of big data sets in subjects where they are actually used, like Biology and Government. Even better, that suggestion comes from the CEO of the College Board, purveyor of the Advanced Placement program and the SAT.

He was asked if the College Board had ever considered creating an AP data science course.

We have, but the more profound thing we’ve done, in candor, and I’ll explain why, is to include data science in the core exams we give like biology, like AP Government, is to make data analysis something you encounter over and over again.

I want to again push back slightly against the most powerful picture of data science as isolating it as a discipline all by itself. It often comes alive in its actual application to situations, and I would just be careful of that. And the reason why I’d be careful of making an AP data-science course is not because we don’t love it and think it’s valuable, but we find our courses spread much more quickly for all kids when they’re not an elective or a special course. That is, if I weave data analysis into AP biology that’s widely given, or if we weave it into AP Government and Politics, which 400,000 kids take, that will touch kids in public schools in all levels of our society. If I create an elective data-science course, that might only be taken by a few who choose to take it.

All of which addresses another problem with the high school curriculum, the ridged isolation of the subjects students study. Silos exist even within the broader topics. I’ve known many who thought of themselves as “Geometry teachers” or “government teachers” and would vigorously resist the suggestion to take another course in their department.

Anyway, there’s much more. And if you teach high school math, the whole podcast is worth an hour of your time. It might be even more relevant if you are simply someone who knows a teenager on whom that Geometry sandwich is being inflicted.

It’s time to radically change the high school math menu, and the ideas in this podcast would be a great place to start.


That math book pictured above was the one I used in high school. It was also the one I used in my first teaching assignment ten years later. It was still a fixture in math education when I left the classroom twenty years after that.

1. She’s British. She gets to use the term maths. I wish it was acceptable in the US since mathematics is not one thing. It is a wide and wonderful collection of many topics.

2. According to a study cited in the podcast, “About 2 percent said that they use calculus on a daily basis, and almost 80 percent say they never use it.”. I’ve read of others with similar results.

The AP Love Affair

Exam

You would be hard pressed to find a bigger cheerleader for Advanced Placement than Jay Mathews. Except possibly for the people at The College Board who run the extremely profitable program.1

For anyone who has not read the Post regularly over the past couple of decades, Mathews is well-known around here for writing full-throated, uncritical columns championing the AP program. Last month alone, three of his five columns centered on that topic.

The fall Education Edition of the Post Sunday Magazine published in October also featured an eight-page spread by Mathews that was ostensibly a profile of the director of the AP program. It was a sloppy wet kiss that a casual reader might have mistaken as nothing more than an “advertorial” paid for by the College Board, mixed in with the other ads for private schools, tutoring services, and military boarding academies.

And, of course, Mathews also is responsible for the farce known as the Challenge Index, an annual ranking that is embraced by schools and news media as a benchmark of high school quality. A measure that is based solely on the number of AP tests taken.2

In all of this promotional work (including at least three related books), Mathews rarely does much to address critics of the AP program. Mostly it consists of setting up very flimsy straw men and quickly knocking them down with a very dismissive attitude. Anyone who doesn’t agree that AP should be the foundation of a high school academic program is misguided at best.

Toward the end of the Sunday Magazine article, he mentions in one paragraph two rather prominent critics of the AP program, and then allows the subject of his piece to dismiss them with a couple of quotes containing no real rebuttal.

One of those critics is the 2009 documentary “Race to Nowhere”. In the film, produces look at how students are under increasing pressure to “succeed” in school, including by being pushed into taking more AP classes.

The other is a 2012 article from The Atlantic with the provocative title “AP Classes Are a Scam”.

Although I wouldn’t go so far to call the program a scam, the author, a former government professor at Boston College, makes some excellent points that deserve to be part of the debate. His last bullet point is one of my favorites.

To me, the most serious count against Advanced Placement courses is that the AP curriculum leads to rigid stultification — a kind of mindless genuflection to a prescribed plan of study that squelches creativity and free inquiry. The courses cover too much material and do so too quickly and superficially. In short, AP courses are a forced march through a preordained subject, leaving no time for a high-school teacher to take her or his students down some path of mutual interest. The AP classroom is where intellectual curiosity goes to die.

Which relates directly to some of my primary criticisms of the AP program, and especially the huge emphasis the classes receive in most high schools in this area.

For one, the whole AP program drives an assumption that the goal of every student should be attending a four-year college. Indeed, the entire curriculum is dictated by university officials who benefit from the stream of new customers. Too often, kids are given the impression that anything other than a brand name college represents failure.

Looking at the bigger picture, the AP structure reinforces the idea that a pure academic approach is the only way to understand any subject. That subjects can only be studied within their silo, a segmented approach to learning that was already an entrenched attitude in most of the high schools I’ve worked with over the years and now extending down into the lower grades.

That intellectual curiosity the professor spoke of is difficult, if not impossible, in a rigidly designed curriculum that leaves little room for exploration outside of the silo.

Anyway, after all that ranting, I wouldn’t advocate for high schools to drop AP classes entirely (as some schools are doing). I’ve both taken and taught AP courses, as well as spending a few summers scoring them and there is some value in the concept (if not the current execution).

Schools should be providing students with the option to participate. With the emphasis on option.

We need to help students understand and explore ALL their options during their time in K12 classrooms. Structuring high school entirely around a college-level program, which Jay Mathews appears to be pushing with his AP love affair, slams the door shut to those choices.


Image: Exam by Alberto G. Posted to Flickr and used under a Creative Commons license.

1. They also own the equally profitable, and questionable, SAT and other related testing programs. You can find more data on the finances of the College Board and other “non-profit” testing groups at Americans for Educational Testing Reform.

2. If you want to torture yourself with it, I’ve written far too much about that crap in this space.

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