The Innumeracy of Educators, or Mark Twain Was Right

http://scienceblogs.com/principles/2011/12/the_innumeracy_of_educators_or.php

by tokenadult • 15 years ago

85 35 15 years ago

droithomme2• 15 years ago

I'm glad to see the article has a link to an actual 10th grade standardized math test from Florida since I was wondering about this after reading that the school board member scored 10 out of 60 and didn't confidently know how to answer any of them, and upon later study concluded that the math in the test was irrelevant to real life. This made me wonder what sorts of questions the test asked.

http://fcat.fldoe.org/pdf/releasepdf/06/FL06_Rel_G10M_TB_Cwf...

The test proves mostly to be multiple choice with four possible responses. But there are a few questions with a scantron array of numbers for filling in numerical answers.

Calculators are allowed, but do not seem to be necessary.

The test covers at its most advanced basic algebra and simple geometry (no proofs). There is no trigonometry or calculus. There are also topics much simpler than algebra such as calculating percentages, areas, and fractions.

I did about the first half just now and didn't run into any problems. It does not seem conceivable to me that someone who can't answer any questions at all is adequately qualified to evaluate scientific data such as one might need to do when voting on matters of public importance.

It would be a very reasonable idea for all legislators and public servants who work in a decision making capacity to take a test similar to this and be required to post the results. Just for informational purposes of course.

waitwhat2• 15 years ago

I was shocked what a weak effort had been to make the questions appear relevant to real life.

The entire test reads as if the math problem was written first (20+2n=30+1.5n; n=?), then a story concocted to fit, with a few names awkwardly sprinkled on top.

DanBC2• 15 years ago

Please could you give an example? And your new version of a question to test the same concept?

Inufu• 15 years ago

That doesn't change the fact that they are _very_ easy. European student here - apparently our schools teach way more math.

chunky1994• 15 years ago

I'm an Indian, and a smart 8th grade kid could probably get a perfect score on this test. How on earth did Mr. Roach pass out of high school, let alone earn two degrees?

dubya• 15 years ago

This is at least partly a matter of retention. There was a study on giving algebra tests to adults, and one of the best predictors of performance was how much math the person had taken. So someone who had taken math through calculus did pretty well on the algebra test, regardless of age, while someone who had only taken through algebra had basically exponential decay from when they had taken it. (I can't think of where I saw this -- does anyone else know?) So I would assume that Mr. Roach's degrees are in non-technical subjects, and that he likely didn't take anything higher than pre-calc.

yummyfajitas• 15 years ago

He probably graduated before we had standardized tests.

This is actually a good argument in favor of standardized tests - make sure morons like Roach don't get to put things like "High School Graduate" on their resume.

evolve2k• 15 years ago

Ouch

DanBC2• 15 years ago

The reaction from some people - "math is pointless and it's fine to not know some really simple concepts" - is profoundly depressing.

In England we have, every year, complaints that the exams are getting easier and easier. There may be some truth in that, but I'd love to see anyone complaining about how easy the exams are actually sitting one of them, and releasing their answer sheet.

(I'd be fascinated to compare GCE / CSE math exams from the 60s, 70s and 80s with GCSE math exams from the late 80s, 90s, and 00s Are any full papers available?)

VonLipwig• 15 years ago

The problem is that if you do not practice you forget or get rusty.

I calculate percentages every day. Turns out yesterday the guy in charge of the company I worked for asked me the formula to work out the % difference between 2 numbers. He didn't ask because he is stupid or has no capacity to do Math. He asked because it has literally been years since he has been required to do it.

Similarly, if you ask me what an onomatopoeia is. I learned it in school and I know the word exists but I haven't been asked to define its meaning for so long that I have forgotten. Now I come to think of it, it might be a word that sounds like another word? Anyway, the point is if you do not practice or recap these things you forget.

4 years ago I passed the Cisco CCNA. I haven't touched a router or switch since. If you asked me anything about networking I would look at you with a blank expression and then answer it with 'Google it?'

Now.. failing a 10th grade Math exam then saying that the tests are too hard or not relevant to daily life is ridiculous. Some of this stuff may not be relevant to your daily life but in general a lot of jobs and general task's in day to day life touch on the key Math skills you learned in school.

School should provide you with a firm foundation in key subjects. If 5 years later you have forgotten 70% of what you learned in science because your job doesn't involve this knowledge and you have no interest in reading / keeping up with science in general it doesn't matter. The chances are you will have remembered 90% of what you learned in English and 80% of what you learned in Math because these you depend on to complete your work.

It doesn't matter that a board member completely flunked a Math exam. It doesn't make him stupid. What is worrying is the attitude the educator takes to his failure. The best response is 'wow compared to these kids I am really rusty at Math.' The worst response is 'my math skills are OK, this test is irrelevant to day to day life.' It undermines teachers and tells kids it is OK to be terrible Math. (If the kid has aspirations to be a school board member this may be true but for a million other jobs and situations it certainly isn't.)

shasta• 15 years ago

It might not prove him stupid (though my guess is you could find adjectives that are less fitting), but it does prove that he never understood the math. A concurrent post mentioned forgetting whether slope is rise/run or run/rise. That kind of thing is what you can forget. If you're "forgetting" the basic rules of algebra and can't recover them with a few moments of thought, then you're doing it wrong.

ebrenes• 15 years ago

I'm willing to accept someone was careless if they mix up rise/run or run/rise. But you can readily summon the correct expression if you understand what slope means algebraically/geometrically.

So barring a sloppy mistake, which we all have, it's just as indicative of lacking proper geometric understanding. For example, a basic linear equation y = m*x would readily yield that m being the slope is m = y/x, so it's rise over run. That's one of the things I always treasured about math, that you could work out the formulas if you didn't care to memorize them.

scotty79• 15 years ago

First two questions can easily be answered without doing any sort of calculations. Just by eliminating stupid answers.

tallanvor• 15 years ago

I looked over one of the example tests, and spent about 10 minutes going over 6 of the questions. I missed one because I had flipped the fraction on a question regarding the slope of a line - not having had to worry about slopes for a good 10 years or more, I'm not too upset about having missed that one. Similarly, I saw a simple geometry questions that I probably would have had to make an educated guess at because it's been even longer since I've worried about the definition of a rhombus.

So I think it's ok to expect that you may not be able to answer all of the questions that a high school student should be able to answer, but for an "educated" person to claim that he was only able to answer 10 of 60 questions, and those 10 were answered by guessing is stupid. There's no excuse for not being able to answer the basic algebra questions or the questions regarding finding areas of shapes when the equations for finding areas are given to you.

brudgers• 15 years ago

Mr. Roach is a politician, not an educator.

The title of the article is misleading linkbait both in regard to the innumeracy of actual educators and the nature of Mr. Twain's quote.

Generally speaking, most elementary school teachers in Florida have mastery of the FCAT - they spend much of the year teaching to it because the degree to which their students improve plays a significant role in merit pay and contract renewal [disclosure: my sister is a public school teacher in Orange County].

CWuestefeld• 15 years ago

The kind of math tested here is specifically what is necessary for a school board member. He needs to be able to answer questions like:

* Last year's budget was $X, and this year we're proposing $Y. What is the percentage increase?

* The teachers' union is asking for raises of 4% /year over three years. What will our final salary expense be at the end of that time?

* If the government cuts our funding by $X this year, and I we want to distribute that fairly over each school in the district, how do we make the cuts proportional to the size of each school?

But I especially appreciated the end of the article. The author discusses the fact that one can be an "intellectual" by completing completely ignorant of practical skills like basic mathematics. Yet we as a society seem to revere such intellectuals, and look to them for leadership.

stouset2• 15 years ago

The school board member claimed that he "managed to guess ten out of the 60 correctly"

Perhaps if he wasn't utterly innumerate, he could have realized that 10 out of 60 is one and a half standard deviations worse the expected value of selecting answers by chance. His understanding of math is so bad, he performed worse than he likely would have had he just answered questions randomly.

blahedo• 15 years ago

I thought the same thing, but it turns out the test is not all multiple choice---in the 2006 exam, 28 out of 58 problems were open answer, and the rest were 4-option multiple choice. So the expected value of a totally random selection would be 7.5 questions out of 58---meaning this guy was at least not doing worse than chance.

transphenomenal• 15 years ago

Getting 10 questions right may not be statistically more significant than just answering randomly. I would calculate this myself, but I'm going to bed, however, just eyeballing it makes me think this is quite possible.

stouset2• 15 years ago

Good catch. Thanks.

jessriedel• 15 years ago

> Where in a sane world, complaining that this sort of math is hopelessly impractical and not the sort of thing we should be testing would lead educated people to point at Mr. Roach and laugh (as I'm doing above), In this world, alas, it gets him the central role in sympathetic blog articles hosted by one of the nation's premier newspapers.

I have no interest in getting into a general debate about school reform, but I think it's important to note that this kind of work at the Washington Post is happening for one reason: because it supports the politically-motivated criticism of extensive standardized testing. Now, there's a lot to criticize when it come to high-stakes testing, but let's be clear that this sort of sloppy reasoning isn't caused by anti-intellectualism. It's caused by politics.

The Innumeracy of Educators, or Mark Twain Was Right

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