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Misusing Math

We do a crappy job of teaching mathematics in this country.

How else do you explain the proliferation of lotteries and casinos offering worse than lousy odds or the complete lack of understanding, by both the media and the general public, of anything involving probability and statistics?

Even worse, according to a mathematician in a call to speak out directed at his colleagues, is the misuse of math when it comes to making public policy.

But the most common misuse of mathematics is simpler, more pervasive, and (alas) more insidious: mathematics employed as a rhetorical weapon–an intellectual credential to convince the public that an idea or a process is “objective” and hence better than other competing ideas or processes. This is mathematical intimidation. It is especially persuasive because so many people are awed by mathematics and yet do not understand it–a dangerous combination.

He goes on to explain that one of the more recent and egregious examples of this “mathematical intimidation” shows up in the debate over the “value-add” concept of teacher evaluation.

Value-added modeling pops up everywhere today, from newspapers to television to political campaigns. VAM is heavily promoted with unbridled and uncritical enthusiasm by the press, by politicians, and even by (some) educational experts, and it is touted as the modern, “scientific” way to measure educational success in everything from charter schools to individual teachers.

Yet most of those promoting value-added modeling are ill-equipped to judge either its effectiveness or its limitations. Some of those who are equipped make extravagant claims without much detail, reassuring us that someone has checked into our concerns and we shouldn’t worry. Value-added modeling is promoted because it has the right pedigree – because it is based on “sophisticated mathematics.” As a consequence, mathematics that ought to be used to illuminate ends up being used to intimidate. When that happens, mathematicians have a responsibility to speak out.

At the top of the list of many problems with this concept, mathematical and otherwise, is the fact that the value-added model is based on changes in test scores, which themselves are unreliable predictors of student learning and subject to many factors other than the quality of teaching.

There is much more to the article and it’s worth taking the time to read (dredge up some memories from that stats class you took once upon a time :-).

Especially since this value-added scheme is not going away, with the LA Times going back for seconds on publishing “value” ratings on teachers in their elementary schools, and my own state of Virginia pushing a new teacher evaluation system based in part on how their students score on the state SOL tests.

All of this educational malpractice by politicians and other “experts” put mathematics in the same league with evolutionary biology, climate science, and physics when it comes to making public policy.

If you don’t understand the science, just make up your own facts to fit what you already believe.

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5 Comments

  1. I agree, one of the surest sign that mathematics education is in dire straits are the seemingly endless supply of casinos and lottery tickets everywhere. The next best sign there is a problem is the misuse and abuse of statistics all over our society.

    4 out of 5 dentists agree, our mathematics education is in need of improvement.

  2. This is incredibly well stated.

  3. I agree with you. The question for me is “Why?”

    Don’t you think that’s partly because very few people (I’m especially including math teachers here) does a good job explaining why math skills are important? My friend’s daughter asked her math teacher, “Why is math important?” and the best he could come up with is “Well, if you become a math teacher…” [As if she had plans to be a math teacher.]

  4. Tim

    Ruth: IMHO, bad math instruction starts in elementary school where the focus these days is on lots of drills to get students to pass the spring tests. I also think that most elementary teachers don’t like math, don’t fully understand the subject, and are more interested in teaching reading, socialization, and almost anything else.

    When it comes to middle and high school (which is where I taught math), the curriculum is locked into teaching kids to follow algorithms with very little about why and how math is applied. For me, teaching applications was both more fun and more interesting. It’s also difficult (for both kids and teachers) and rather messy since real life rarely has one right answer or one method of getting there.

  5. Dr. Matthias H. Fröhlich

    I do fully agree to almost all of the arguments given here. However I would like to add some caveat.

    Lotteries and casino do surely offer lousy odds (well roulette isn’t *that* bad after all, is it? ;-) However, there are two things here, that I would like to point out:

    1.) What would be a “non-lousy” odd? 1:1? 2:1? :-))

    2.) There seems to be a “need” in a *lot* of people for some sort of playing, gambling, whatsoever. IMHO there is absolutely *nothing* wrong about that. Same reasoning may apply to some other “bad” habits. It only becomes questionable, when some addiction might result that could ultimately lead to self-destructing behaviours. However, we do still honor the “right of self-determination” – for good reasons, I would like to add – and thus do, e.g. *not* forbid smoking or else.

    So, the important thing to me is, to enable people to make *educated* decisions about the way to lead their lives. I would expect, that less people would be prone to the lure of gambling, casinos, smoking, etc. if the ability for making educated decisions would better be taught in school. At least for the schools in Germany, where I used to be a teacher only for two years – put a pupil for 13(!).

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