

The Innumeracy of Educators, or Mark Twain Was Right - tokenadult
http://scienceblogs.com/principles/2011/12/the_innumeracy_of_educators_or.php

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droithomme
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...](http://fcat.fldoe.org/pdf/releasepdf/06/FL06_Rel_G10M_TB_Cwf001.pdf)

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.

~~~
chunky1994
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
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.

~~~
tokenadult
_I would assume that Mr. Roach's degrees are in non-technical subjects_

Mr. Roach's degrees are now known to be in education.

<http://news.ycombinator.com/item?id=3326293>

"Roach, the father of five children and grandfather of two, was a teacher,
counselor and coach in Orange County for 14 years. He was first elected to the
board in 1998 and has been reelected three times. A resident of Orange County
for three decades, he has a bachelor of science degree in education and two
masters degrees: in education and educational psychology. He has trained over
18,000 educators in classroom management and course delivery skills in six
eastern states over the last 25 years."

I will note for the record that a proper, accredited degree program in
educational psychology ought to have a statistics for psychology class
included that would provide a mathematics refresher to postgraduate students
who don't test out of that course. If not, the degree program was appallingly
bad.

~~~
hessenwolf
Yes - but it's reaallllyyy hard to teach a bunch of non-mathematicians
statistics in a couple of terms. The problem is that it is an assorted mish-
mash of hard and easy maths, the basis of which is too difficult for them to
understand, and the brain-bending proper interpretation of a p-value.

------
VonLipwig
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
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
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.

------
tallanvor
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.

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CWuestefeld
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.

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DanBC
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?)

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scotty79
First two questions can easily be answered without doing any sort of
calculations. Just by eliminating stupid answers.

------
stouset
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
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
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.

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jessriedel
> 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.

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evolve2k
Ouch

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brudgers
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].

