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.
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.
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?
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.
"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.
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.
I believe the study you're thinking of is "Lifetime maintenance of high-school mathematics content" (Journal of Experimental Psychology). I read about it in Why Don't Children Like School, perhaps you did too?
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.
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.
I went to school in the US and the test represents what I personally had been taught and was competent in by the end of 7th grade (age 13), not 10th grade (age 16). That was some years ago. It wasn't in Florida but I have no reason to believe their schools are substantially different.
It might be that the test doesn't match actual 10th grade curriculum and is a minimum competency test. Then again, based on math skills of typical high school and college graduates, I am not completely surprised that school board members with a masters in education can't do basic math. It's not just math that is a problem, there are also many high school graduates now who are functionally illiterate (meaning they may have basic reading skills but can't understand anything they read that is more than very simple). This is not to say the schools are incompetent since obviously many very skilled and talented people make it through the same system.
Also, it has been established that Masters of Education students have the lowest GRE and SAT scores of any major.
"Research over the years has indicated that education majors, who enter college with the lowest average SAT scores, leave with the highest grades. Some of academic evidence documenting easy A's for future teachers goes back more than 50 years.
Furthermore, the most intelligent and competent education students are the most likely to rapidly leave the field (see Progress Through the Teacher Pipeline; Henke, Chen, & Geis, 2000; http://nces.ed.gov/pubs2000/2000152.pdf)
There's tons of papers and research about this issue, sometimes discussed as the "teacher quality" problem, though that may be a misnomer. More than I can reasonable cite but once you know about the issue, and some of the above citations as starting points can lead you down a pretty deep rabbit hole once you start researching.
That's a required test for 10 graders, so most of our students would pass it as well.
Math retention is another thing all together. Almost everyone could pass that test when they were in 10th grade, give it to a 100 random 50 year olds anywhere in the world, and see what happens.
Abdul plans schedules for several biologists who are researching the manatee. One biologist must travel from Newport to Russell Key. Later the biologist has a meeting in Islamorada. Abdul must use the map below to find the distance from Russell Key to Islamorada to determine how much time the biologist can spend on Russell Key. [diagram of a right-angled triangle, three points labelled "Russell Key", "Newport" and "Islamorada", one side labelled "13.2 mi.", the other "15.5 mi."] What is the distance in miles (mi.) from Russell Key to Islamorada?
The whole manatee/biologists/Abdul story is irrelevant and distracting, relies on an incredibly unlikely coincidence (the right-angle), assumes that Abdul is bright enough to get a map out and measure distances but not bright enough to measure the distance he actually cares about, and confusingly sets the reader up to expect a question about time rather than distance.
My version: "[diagram]. How far is it from Russell Key to Islamorada?" or skip the place names entirely and "[diagram] What is the length of the third side of this triangle?"
(edited to remove a comment about Islamorada -- turns out that it is a real place. It also turns out that the map seems to be using real place names, but not real distances, which can only serve to confuse people who know the area.)
I think that's the whole point of these types of problems: the first step is always to parse the question, find out what's the actual problem and which data is relevant. You know, just like in real life. (Granted, those particular examples may be especially contrived, but that's a different problem...)
Indeed. The entire purpose of word problems is to see if you can apply math to real life, to see if you can come up with formulas to fit the situation at hand. You aren't given formulas in real life.
If I save a certain percent, P, of my monthly income, N, and I want to save an amount, X, to buy something, and I want to know how long in months, M, I'm going to have to save. The formula M = X / (P * N) [or P / 100 depending on how we're expressing the percent] isn't going to magically appear in front of me. Whether I can solve it or not won't matter if I can't come up with it.
That's a trivial example, but I hope the point is clear. Word problems are supposed to test your ability to convert life to math, not just your ability to do simple algebra. Which is why it's especially concerning that in many of the word problems they actually give the formula. It defeats the whole purpose of making it a word problem.
Yes - there is nothing as sexy as being given a big chunky real-world problem with no predefined mathematical representation and getting to pick and choose your own. I live for these moments.
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.
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.
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?)
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.)
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.
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.
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.
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.
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.
> 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 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].
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.