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Are You Better At Math Than a 4th (or 10th) Grader?
New submitter newslash.formatb points to this Washington Post blog post, which "discusses the National Assessment of Educational Progress test (specifically, the math part). One of the school board members took it and was unable to answer any of the 60 math questions, though he guessed correctly on 10 of them. He then goes on to claim that the math isn't relevant to many people. P.S. — if you want to feel like Einstein, check out some sample questions." Maybe this is mostly about the kind of life skills that are sufficient to succeed in management.
That a reasonably intelligent person cannot answer the following question: 1. (47 x 75) ÷ 25 = ... You can use a calculator.
After reading this article, having someone as influential as a school board member take this test and fail it is putting education on a very dangerous course. It normally wouldn't be too bad but this guy's ego is so big that instead of admitting that he just isn't knowledgeable on the subject, he goes on a rant about how irrelevant this stuff is to life and how unnecessary this subject matter is to evaluating a student's college career. I mean sure, it might not be relevant to him for his job duties, but any science/engineering discipline should be well versed in simple math like this. I really hope he doesn't make a push to dumb down these tests to make the math easier.
This is an apparently intelligent, certainly successful person - who cannot do basic math. He asks a number of questions - thinking that the answers are rhetorical, but they aren't. BTW, for those who don't RFTA, the guy was lousy on the reading-comprehension as well.
For example: if people can be successful (he has three degrees) and yet unable to answer these math questions, it must obviously be the case that the math is unnecessary or unrealistic. But there are other possible explanations:
- He would be even more successful if he actually had these basic academic skills.
- His success is due to other factors. Maybe he has people skills (i.e., a salesman type). Maybe he knows the right people. Maybe he's just lucky.
- Maybe his academic degrees are actually worthless (he doesn't say what fields they are in).
The thing that is most striking about the sample math questions is that you are allowed to use a calculator, even though they are nothing especially complex. At worst, you have to multiply by numbers like 29. These are the kinds of skills someone needs to balance their checkbook, to plan their annual finances, to do their taxes.
So RTFA, and then: what conclusions do you draw?
Enjoy life! This is not a dress rehearsal.
The guy's quite right. He shouldn't have a bachelor, let alone two masters and 15 credit hours towards a doctorate.
Unfortunately, too many students are in a similar position. Universities have been turned into for pay degree mills, and the qualifications the higher education industry produces are generally not worth the paper they are printed on.
The test that the school board person took was for tenth graders. The sample questions linked are from two entirely different tests. The first three are for fourth graders and the second three are for eighth graders.
Don't act surprised. We're talking about the country where some dumb fucks managed to make creationism part of the school curriculum.
It's like putting people in a motorized wheelchair so they never learn to walk. In theory it's not a bad idea - a wheelchair with a powerful motor would give us the ability to drive around faster than we can walk or run, and carry lots of luggage around etc. In practice it's a stupid idea, obviously.
What you should have done in that one problem was not used a calculator, but looked at the sizes of the numbers given in the multiple choices, and then picked the choice where the magnitude was in the correct ballpark.
Well, if you thought you couldn't use a calculator, it means you failed a comprehension test (the text clearly stated you could use one). Maybe that was the real test?
Exactly - this guy is so bad at maths that his educated guesses are actually worse than sheer random chance.
Impressive.
You can never know everything, and part of what you do know will always be wrong. Perhaps even the most important part.
My partner got crap grades at GCSE maths and wanted to re-take it (originally taken at 16 in the UK, this was ~15 years later).
Now I got an A the first time around for GCSE, and then at 18 I pretty much completely screwed up my 'pure' maths part and was only partially rescued by the statistical part. Trying to explain stuff to her made me suddenly realize that the parts I was good at, were the parts that I could visualize.
More than that, it wasn't that I had some mental block on some topics - it was just that I'd never learnt them (or been taught them) properly in the first place. If I spent a bit of time looking at the type of question, rather than the specific question, stuff 'clicks'. I came away with 2 thoughts:
1) If my knowledge is supposed to grow 'like a tree', a whole load of branches got lopped off a long time ago - just felt a little bit sad that I'd spent so long no even noticing that I'd given up. This led to a pub conversation around differentiation/integration - I knew what to do, I knew what the inputs and outputs meant (i.e. I could do the questions) but I'd never understood WHY. I'd always been very sniffy about those who could say only multiply if they'd learnt their times table by rote, but I was doing exactly the same thing, just on a topic a little bit more advanced.
2) Other thing I realized was that I was already doing some operations mentally in exactly the same way as some new technique in her book, that I'd never been taught. I'm unsure that everybody thinks in the same way and other techniques vary, but surely I'd have saved time if I'd been taught it - but then maybe it's the fact that my brain decided to solve them this way, that's made it stick for me.
Take for example the first test (47 x 75) ÷ 25
You can either know that you do the thing in the brackets first, then the thing outside - as you've learnt your rules. But stepping back and looking at it as a whole, it becomes trivial.
47 is a bit of a odd number, I'll leave that for now
I'm multiplying something by 75 and then dividing it by 25. So I'll throw those away and multiply by 3. Leaving me with 47 * 3
ah, 47 again. Well it's close enough to 50. So I'll do 50*3 giving me 150.
Finally time for the correction to my not knowing my 47 times table. I knocked off 3*3 to give me the easy 150, so just need to take the 9 off to give the 141.
I genuinely wonder if everybody else worked that out the same way, but it's now just the way my head works. Bit that annoyed me is that whenever I was taught anything, we were told "how to do it" - maybe education would be better if every teacher has to be able to explain 3 ways of approaching any problem. Better yet, rather than testing the student with the question and just getting a boolean pass/fail - the teacher should ask the pupil around their thought processes when they look at the problem - "talk me through it".
The chances of every coming across that particular question in the real world are practically nil. So the purpose of the question is to test whether the process is present in the pupil - yet maths papers NEVER seem to ask for this. From memory there was the 'show working' marks, but they just tended to dry up after the first mistake was made - and aren't particularly conducive to how I personally think (mental white-board and processing explained verbally).
It was a different test. The one he took was the 10th grade version. The one in the summary is 3 sample questions from each of the 4th and 8th grade tests
What you should have done in that one problem was not used a calculator, but looked at the sizes of the numbers given in the multiple choices, and then picked the choice where the magnitude was in the correct ballpark.
Uh, no. If a test question says I can use a calculator, I'm using a calculator. For some of these tests, there's too many questions not to. Obviously, this one was trivial, but you catch my drift. In *most* cases, a calculator is more efficient (yes, you can find some edge cases where realizing the "trick" is faster than typing the equation)
Tests from 2005 to 2007 are available at http://fcat.fldoe.org/fcatrelease.asp
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There is inferior bacteria on the interior of your posterior.
I considered the 50*3 approach for an instant, but decided that 40*3 + 7*3 was easier because I do addition faster than subtraction.
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Assuming all questions had four options and the answers were uniformly distributed, then yes, the "expected value" is 15. But, surely you recall that the standard deviation of the binomial distribution is sqrt(60*(1/4)*(3/4)) = sqrt(11.25) = approx 3.35. So to get 10 puts you less than 1.5 stdev from the mean. For normally distributed data (which I would expect the scores for such a test with random answer selection), 68% of the results are within 1 stdev, and 95% are within 2.
So, a score of 10 doesn't seem out of place at all. (And this is all high-school level stats, mind you, sticking to the Probability 101 theme here.)
Program Intellivision!
First, they cite the wrong exam. This school board member was not complaining about the National Assessment of Educational Progress test, but rather the Florida Comprehensive Assessment Test, or FCAT. (The NAEP test adjusts the skill level of its questions on the fly as you're taking the exam, and returns a score that is percentile-based. I'd actually like to see what this board member scores on the NAEP...it's a very good metric that can be used to measure one's skill level, and is not biased or corrupted by political influence.)
Second, the sample questions are misleading. Not only are they "4th grade" & "8th grade" leveled questions (not the 10th grade exam that this board member was complaining about), but even those questions are not as difficult as you will commonly find on a state exam. If you want to see the types of questions on the FCAT, you can look at the item sampler here.
I work in Education up in Minnesota. As you can see on page 13 of this report, there is a downward trend across grade levels in "percent proficiency." While the average joe might conclude that most 3rd grade teachers are fantastic while most 11th grade math teachers need to be fired, the skeptic while (rightfully) question the validity of the test. For example, on that table, you'll see that all the 2011 results are about 10-12% lower than their previous years (except the 11th grade). That's because, in 3rd - 8th grade that year, the state moved to a newer, more difficult exam which emphasizes heavier Algebraic understanding (with completion of Algebra I by 8th grade). Because the standards became more difficult, scores dropped. But the uninformed Joe would just conclude that teachers are getting lazier and use these results as a way to blame schools for not doing their job. (These changes to the standards have not affected the 11th grade yet, but will in two more years.)
I personally coached students for and administered the 11th grade exam last year at my school. The questions on the exam are not simple. Rather than throw traditional skill-based questions at you, the questions are worded in a very complex manner, requiring a deep level of understanding of the skills required to solve the problem in order to recognize which skills are required to solve the problem, much like that FCAT exam I linked to above. This test is not a valid metric of what students know or don't know; I saw one student personally who had no problems with the worksheets I provided him during our coaching sessions, but bombed the exam, not because he was stupid, but because he gets severe test anxiety. Other students told me that they just didn't understand what many of the questions were asking them to calculate.
The upper-level state exams are engineered to fail students, so that schools can be labeled failures. Particular politicians want schools to appear as though they are not doing a good job, to validate the privatization of our educational system. While you hear the expression "raising the bar," what they are really doing is increasing the failure rate. It's absurd what kids are being asked to accomplish; cognitive science has shown that what kindergartners and 1st grade students really should be doing is playing and reading, and we're trying to sit them down and teach them Algebra skills. (If you don't believe me, ask a 1st grade teacher in the state of Minnesota...even 1st grade standards now are engineered to incorporate "Algebraic thinking".) It's downright ludicrous, and it's all a political game.
I totally destroyed those 4th graders.
That was just the ego boost I needed for the day.
"You should always go to other people's funerals; otherwise, they won't come to yours." -- Yogi Berra
Second of two points inspired by parent post:
If a school board member is incapable of passing the NAEP tests, how the hell can he function as a school board member? Would that not be like having a driver education instructor who cannot pass the drivers license examination? Yeah, lame, but at least it is a car analogy
Perhaps candidates for school board positions should be required to demonstrate a minimum level of competence in the subjects that high school graduates are supposed to have mastered.
Will