This article is mostly about Andrew Hacker’s arguments about math education, but I’m not going to get into that. I want to focus on the usual arguments I see in almost every article about math ed that appears these days. I would like education writers to do a better job in writing about education in general, and math education in particular, which means asking questions of the people they’re interviewing, rather than taking on faith that traditionally taught math is the culprit. Let’s start with this paragraph:

*“Jonathan Farley, professor of mathematics at Morgan State University, agrees that standard ways of teaching the subject can miss the mark. “Math is often times taught in a way that makes it appear useless,” he says. Many instructors teach a concept and give practice problems to be worked ad nauseam without ever connecting to the practical application of said concept. If we were to put this into taxonomy terms, math is oft taught to only the knowledge and comprehension level.”*

Depends what grade level you’re talking about. Dr. Farley doesn’t identify those levels but talks in the typical vague style that most critics of math education do. The practical application of some aspects of math isn’t always seen unless you go into engineering or the sciences later, but it does provide the preparation for doing so. Requiring ALL students to take math up through calculus is another issue but I don’t think that’s what he’s talking about here.

*” ‘While the nature of the subject seems to be application based, it’s never fully fleshed out as such in a practical way. The problem is not the content,’ Farley says, ‘but in the inability to reveal the beauty of math. You don’t study math merely to learn how to build bridges; you study mathematics because it is the poetry of the universe.’ “*

Uh, I’m having trouble here. He says math should be taught to see how one applies it in a practical way. Then he says practical ways are immaterial since the real reason to study math is because of its poetry. Well, if he thinks math should be taught for math’s sake, then why is he making such a fuss about application?

The article goes on:

“While experts tend to disagree on the utility of abstract math, all seem to agree that the current way it’s taught doesn’t work.”

This sentence seems lifted from the “Big Book of News Stories About Math Education” that most education writers use. I run across it in many news stories. Is the writer talking about K-8? Because the way it’s been taught in lower grades the past 25+ years has been in a state of deterioration. I have made this point repeatedly and met with the same criticism of that statement: that constructivist/inquiry-based and student-centered approaches aren’t all that prevalent. Well, they are a LOT more prevalent than they were in previous eras when students entering algebra 1 in high school actually knew their math facts and how to operate with fractions, decimals and percents.

But if the statement is talking about high school math, I would say that algebra 1 and 2 and geometry have been watered down over the years. There is a dearth of good word problems; such problems (termed “real world applications”) are generally tedious and not very challenging. The word problems of the past (distance/rate, mixture, work, number, coin, etc) did provide structure for problem solving that the current cast of problems does not.

So if the current way of teaching doesn’t work, it isn’t because they’re teaching it like they did in previous eras when it actually did.

Thanks, BG, for your call to ed writers. I understand why these writers report as they do and that several things–including simultaneously writing to attract AND inform readers–are in play, but there is definitely a need to help them understand educational issues more totally. When they don’t (leading with ideas like ‘Approach X is just wrong, and has been for ages’ or ‘Aided by tech, students in ABC district are learning on their own terms’ or whatever), they reinforce for ed’s consumers and practitioners that ideas are ‘best practices’ when they’re still just ‘cool practices’–sexy and disruptive and all, but far from proven. To guard against over-corrective tendencies at ed’s practice level, I wonder sometimes if we should use more energy connecting with and educating ed writers/message distributors. Goodness knows engaging directly with the engines producing the unproductive ideas doesn’t get us very far.

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McCaslan writes

“While experts tend to disagree on the utility of abstract math, all seem to agree that the current way it’s taught doesn’t work.”

Statements like this lead me to sanity-threatening levels of eye rolling. “Experts … all seem to agree”? What’s she saying? Which experts? “Seem”? To whom? “The current way” … uh, what would that be? Perhaps she means the so-called “reform way” which has had an inexorable increase for some 30 or 40 years under continual flogging by writers such as her and folks like Dan Meyer. But if that’s so, then she would probably object, “No, no no! I mean the traditional way — which is still ‘the way’ people are teaching because reform hasn’t caught on”. Gee, maybe she should talk to millions of parents across our world who are tearing out their hair at the crazy attempts at innovation in the schools. Sorry, traditional (or what I call “conventional” because it is the natural and time-tested way to pass on mathematical knowledge) math education has been seriously diminished in our schools and has been now for a very long time.

But c’mon folks. The statement that “experts seem to all agree” is facile. It’s an unfalsifiable statement. I can say anything “seems” to be so to me and what would prove that wrong? Unless the experts are specified, of COURSE you can find experts that agree (with whatever proposition you’d like to support) — just deem anyone with whom you don’t agree to be a non-expert.

It’s a tautology that experts agree with you no matter who you are, as long as you reserve the prerogative (as she apparently does) of deciding who is, and isn’t, an “expert”.

In point of fact many people who hold relevant expertise do not agree with this statement at all, if what she’s knocking is conventional instruction in math (I qualify this by “if” because, as Barry points out the fellow she cites seems to be all over the map on this question…). And not only experts — the empirical data supporting that expertise, which I personally find far more compelling than a million references to unspecified “experts”

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The point of slamming conventional education always appears to be intended as an explicit or implicit “Yes, Minister” false syllogism in favour of some proposed variety of reform:

Something must be done!

This is something!

Therefore,

This must be done!

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