The Innumeracy of Educators, or Mark Twain Was Right
scienceblogs.com
scienceblogs.com
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.
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.
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.)
It's in Florida, as are the students this test is aimed at (and the Manatees too for that matter).
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.
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.
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.
http://www.cbsnews.com/8301-505145_162-37245744/heres-the-na...
"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.
The referenced study on education major grade inflation: http://www.aei.org/article/education/k-12/grade-inflation-fo...
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.
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.
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 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.)
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.
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.
* 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.
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?)
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 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].