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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.
Havent taken a math test in a little while, was worried I was missing something after every question.
I wasnt.
That a reasonably intelligent person cannot answer the following question: 1. (47 x 75) ÷ 25 = ... You can use a calculator.
well... that's sad.
#
#\ @ ? Colonize Mars
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But I found those questions trivial without a calculator, how you'd manage to fail with a calculator is beyond me.
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.
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.
Wait.
Even a gorilla could have got 15/60. It's probability 101. (And a rather sensible assumption that all questions had 4 options)
Some apps are WYSIWYG. Some others are WYSIWTF.
Especially those of us that deal primarily in accounts, deal with budgets, and worry about statistics.
I think what it really does highlight is that there is always at least one moron in the public administration system that no one can fire, thus they keep getting promoted so they become 'someone else's problem'. Eventually they become everyone's problem.
Then again maybe it's just not the one moron in public administration...
Dan. -- So what if it's spelt wrong, nobody's perfect
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.
I read the first article and agreed with his conclusions - but he couldn't do any of the questions?
Ran through the test, and erm they were very easy. I can only assume it was a different test.
Reminded me of the RSA animation on education - http://www.youtube.com/watch?v=zDZFcDGpL4U
So my conclusion is... LOL
I imagine most slashdotters would barely slow down their reading before checking the correct answers for this test. I forget sometimes most people aren't like that.
But how bad he is at guessing. Everyone knows you always pick b.
If you mod me down the terrorists will have won
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.
We don't see the right questions i believe. Since he made a test for 10th graders but the questions that we see in the other link are for 4th and 8th graders. So where's the exam that he took? What degres does he got?
So maybe the exams are out of focus.. or maybe he got degres and became a specialist in another area outside maths and he doesn't need specifics math skill anymore and it's out of pratice. We don't know almost anything essencial with so many words written so far.
The article spends its entire space criticising the idea that the test is measuring something useful, and then the quiz link title is "How smart are you?".
The right hand needs to talk to the left hand over at the Post.
The article mentions the board member took (and failed) a 10th grade assessment test. But the linked sample questions are from a sub-article talking about a study of 8th grade tests? Surely the test discussed in the main article is different than the linked sample.
Can it be that anyone with a high school diploma (let alone the degrees the article claims) can not only fail a test with questions like these, but then come to the opinion that the test is at fault and not their radically inadequate math and problem solving abilities? After reading all this I have decided that the article must simply be wrong- the author has had a giant practical joke played on them, or the sample test questions were from the 4th grade version?
Quite frankly, if someone with 2 post-graduate degrees (even if his masters degrees were in basket-weaving and finger painting) could only hazard guesses at questions with this level of difficulty, they should simply resign from any job related to educating others. I'd also ask for a tuition refund from their university.
On the other hand, I would like to see all the test questions to form a proper opinion. I took the sample questions linked and scored 5/6 (possibly due to not having studied maths in English and not bothering to look up the word "vertex"). The first five questions are definitely things that everyone needs to know to get through life in any field. On the other hand, I do think we did a lot of "useless" maths in school that I don't remember now (20 years on) and have never needed. I don't quite see the point of forcing everyone to do that.
I'm surprised that students are allowed calculators to work out these problems, particularly the eighth grade students. I think mental arithmetic is a useful skill even in the age of calculators/computers/mobile phones with built in calculators.... the ability to estimate an approximate answer is sometimes more useful than the ability to provide a specific answer.
This article sounds like an arrogant person with a serious case of sour grapes: "Yeah I bombed that test, but look at me! I'm seriously successful and I don't need to use any of the stuff that's on that test anyway! Stupid test!"
I remember when I was a schoolkid other kids would whine things like "Why do I need to learn fractions? I'm never going to use them!"
Just a note:
That board member took a 10th grade test. The sample questions in the article are for 4th and 8th graders and might or might not be related at all.
This seems to have 10th grade tests from 2005 and 2006:
http://fcat.fldoe.org/fcatrelease.asp
A link at the bottom is named
"Quiz: How smart are you? Test yourself with some National Assessment of Education Progress questions."
That has little to do with how smart you are, rather how educated you are.
Honestly, but this is not "math" but "calculating".
And in this case the quoted person is wrong. If you cannot do this kind of calculation, you should not make decision that impact others. Perhaps you shouldn't even make decision for yourself.
CU, Martin
People can legitimately criticize multiple choice tests and a "test based culture": it doesn't make sense to determine people's futures based on minute differences in answering long lists of questions. But this test is so trivial that people who don't pass it really have no business in a white collar job or going to college. Every adult should be able to answer these questions in their head; they are necessary for basic participation in a modern economy.
I think a side remark at the beginning tells us why he is successful: he has "influential friends". It's the incompetent hiring the incompetent based on their social skills and connections. And now these people want to establish an idiocracy by eliminating even basic math from our curriculum. This kind of thing really doesn't bode well. We need more math in school, not less. Every college-bound high school student should know geometry, statistics, and basic calculus; without that, their decisions and reasoning about topics from microeconomics to climate change will just be based on hearsay, sympathies, and superstition.
I took the SAT in 8th grade as part of a university study and scored 1200. I took it again for real upon graduating high school and scored 1080. However, I created a successful IT career for myself ending in managing the networks for a multinational company prior to a medical retirement.
Very timely that I just finished watching "Gattaca" again...
I have something in common with Stephen Hawking...
What do you expect from the combination of crappy pay and horrible working conditions? People who are actually smart and could land any job wouldn't touch the teaching profession with a ten foot pole.
Pay teachers well and make sure their job description doesn't include "must have experience with taming wild animals" and you'll get better teachers and hence better education. For reference, see Finland.
We used to have a Bill of Rights. Now, with the rights gone, all we have left is the bill.
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).
$288 * 29/40
Good grief. I hope you're not designing anything important.
In a standardized test, you could even guess the answer since the number had to be a fraction, and it had to be basically 75% of $288.
YOU DIDN'T EVEN HAVE TO DO MATH TO GET THAT ANSWER RIGHT!!!!
I'm an old codger too. And you've demonstrated why I'm still a f*cking genius in every day life no matter what I do.
He guessed 10 right out of 60. In a multiple choice test with 4 possible answers each. Now, it's been a while since I was in statistics, but either that guy got REALLY unlucky with his guesswork or he's even too stupid to make an "informed guess".
We used to have a Bill of Rights. Now, with the rights gone, all we have left is the bill.
I am a recent import from Canada to the US, working near 'Intelligently Designed' Dover, PA.
The amount of willful ignorance here in the US is shocking, even this far North.
This whole article is a symptom of the 'dumbing down' of the the US, embracing style over substance, abandoning reason for the sake of conformity.
The math questions are relatively easy (even for a sleepy dyslexic), I only had to grab a pen and paper for the hourly wages one.
Yes, there are smart people in the US, but the majority are afraid to think for themselves.
They gravitate towards the loud pompous idiots, and will ignore facts and the reality around them.
Current and past GOP candidates are a very sad commentary of American leadership (Palin for education czar, Gingrich for morals minister?).
The US is a quickly fading empire, willing to blame anyone and everyone (immigrants) but itself for becoming non-competitive in the world market.
I can understand he might get some wrong and have forgotten others - but none?
My best guess is that he's pissed off with how the school board is being run, he's tried to get things changed and nobody is listening.
So he wants to go public. How does he get attention?
"Board member doesn't like tests"
"Board member didn't do as well on tests as he thought he would"
"Board member cannot do anything on test"
In his position I'd be selecting the headline, and then just filling in the test to ensure I got the one I wanted.
... didn't have a problem solving any of them, only using the calculator out for one (the 29/40 question) and that only out of laziness ... where's the problem there? ... best example: The Front-Runners of the US presidential candidates ... and the people supporting them ... obviously, how can you want people with the knowledge and the IQ of a peanut to be your representative?
OK, I do acknowledge the world's population is getting dumber by the day
Maybe he just doesn't believe in math You know, everyone is entitled to their opinion!
If you have a high school diploma and fail a test that is pretty much a part of the curriculum that you have to master to get that diploma, shouldn't you probably hand it back since you obviously showed that you don't deserve it?
And yes, I do expect to be able to repeat my university degree's required qualification tests right now and pass again. That's basically what that degree is supposed to tell someone: That you mastered the required courses, that you are able to understand the matters discussed there and that you have acquired the knowledge that you are supposed to have based on the courses the degree represents.
If it doesn't, then, hell, what's the degree good for? I don't give half a shit whether you knew it back when you got the degree, what good is it to me what you knew 10 years ago? What matters to me, as your employer, is what you know NOW. And if you do not know NOW what that degree claims you know, put the degree on your toilet, there it can still serve well in case of a paper shortage.
We used to have a Bill of Rights. Now, with the rights gone, all we have left is the bill.
FTA: "Last week, Maureen earned $288.00 (before taxes) for working 40 hours."
Setting their expectations low. (So that they won't go occupy something.)
thank god, i thought i was the only one that did math that way. (it feels sort of wrong, after learning to do it the 'traditional' way) disassembling the problem, rounding, cranking the generator, then fixing for the round. It works, its just makes your math teacher pull her hair out.
I've decided to Diversify my Holdings. I've divided my cash between my left and right pockets, instead of all in one.
There is an easier way to solve the first one than calculating 47 * 3.
(47 * 75) / 25 (50 * 100) / 10 = 500. The only answer that is less than 500 is 141
OK!!! Now we know why all of those people's homes were foreclosed. They could not do the math to figure out how much they could afford, and people took advantage of them. Remember, "Math is not relevant." I make $2,000 a month. My mortgage is $3,000 a month. I can afford this house!!!
Have a look here, it has 10th grade tests from 2005 and 2006:
http://fcat.fldoe.org/fcatrelease.asp
Guy gets into an undergrad program in education or something. Takes the very minimum to get his math requirement out of the way in his freshman year. Finishes his degree. Gets into grad school .... hold on a second here .... now, the GRE is required for just about every (Liberal Arts and Science) graduate program in the States and even if you're going for a grad degree in English Lit., you still have to take it and it does of a relatively intense math section - algebra, geometry and I think probability - it's been a long time.
I think this guy just forgot everything because he's just not using it in his professional and academic roles.
His conclusion though, I find completely incorrect. A child needs to at least have had the material for the future - I'm currently working in a shit menial job, and I have had to use most of the math on that test.
This article is more of a bitching session by educators over the testing of kids and the results being used to evaluate them.
How you did:
Great job! You got every question right.
Duh. And no calculator needed. TFA is again biased.
For what it's worth, my first step was also to simplify * 75/25 to *3 .
The second step was also 50 * 3.
However, my third step was to look at the answers. Only one answer (141) was in the right ballpark. All the others were off by so much that they couldn't be right.
The 'guestimation' strategy fails at question 5 that has two answers that are very close to each other ($203.00 and $208.80). However, my mathematical instincts tell me that 203.00 is an unlikely outcome when multiplying with 29. I used a calculator to confirm my guess (as allowed by the test).
Nope, same way i.did it in my head (and all the rest of the problems such as the getting paid $288 for 40 hours and now worked 29... how much did they get paid.
I didnt feel like flipping from my browser to the calculator and back on my phone, plus i figured it would be a good challenge considering i just woke up before taking it (and according to it i got all of them correct)
In a multiple choice test I go for logical reasoning spiced with a little bit fast and easy 101 calculating
1.) The brackets are there to seduce you
2.) 75 / 25 = 3
3.) 47 x 3 = less than 1000 because of the digits
I know it's cheating but it's multiple choice, you just have to choose the right cheat, you essentially not to know the right answer.
Hehehe, people always say I`m weird or complicated when I explain how I do my math. Nice to know there are others sharing this technique,
Bah.
2. Almost. I generally multiply large-components first, as everything else.. is just everything else.
47 * 3:
40 * 3 = 120
7 * 3 = 21
120 + 21 = 141.
I find it difficult to keep this straight in my head:
47 -> 50
50 * 3 = 150
50 - 47 = 3
*confusing the threes around and not realizing there are now two _different threes, I initially tried 150 - 3*47)
3*3 = 9
150 - 9 = 141.
Your way works, yes, and it was brought to my attention in high school, but I immediately dismissed it. After all, when you can multiply two four-digit numbers in a couple seconds, why do you need tricks?
8267 * 3233 = ?
well, 8 * 32 = 8 * 30 + 8 * 2 = 256
2 * 3233 = 6.
256 + 6 = 262. Add zeros (8 _000_ and 32_00_), yields 262 000 00.
Oh, I'm off? How much? 67 * crap? Well 67 is about 50, half of 100, so 3 * 100 / 2 = 300 / 2 = 150 (plus three zeros -- 3_000_ - 3_233_) is about 15000 00, right? Ok, 277 000 00, 27 700 000.
What's the actual answer? 26 727 211, an error of 3.6%. Not bad, for doing it in my head. Does that 3% matter? Not much. Three cents per dollar, ok, for being sure that it's 20$, I might be off by 68 cents.
Honestly I may've done something wrong, I'm usually much closer to the correct number (usually error 1%). The number seems high at the add half of crap plus a couple zeros.
I assure you, it doesn't make your math teacher pull her hair out. I was taught how to do math formally, then how to do it quickly in my head. The latter involved introducing small errors to make the calculation easier and then correcting for the error, exactly like the GP described it. This was considered "bonus material" that wasn't part of the curriculum. The problem was and is even more so today that there are parents who don't want their kids to learn these things, because "they can use a calculator, why should they learn how to do complicated calculations in their head".
As others have pointed out, these questions are for 4th and 8th graders. The Florida sample questions for 10th graders, i.e. the level of test that this guy flunked are here: http://fcat.fldoe.org/pdf/sample/0910/reading/FL517300_10_Rdg_TB_WT_r2g.pdf These still seem to be pretty straightforward for anyone with a BSc and double Masters...
The technique you describe is how my mother taught mental arithmetic to primary school children here in the UK.
http://science.slashdot.org/story/11/12/09/221233/you-really-are-what-you-know
He may have done better when he was actually in 10th grade.
Orange County Florida board of education member Rick Roach took the 10th grade FCAT test. His less than stunning results were narrated by Marion Brady in the Washington Post.
The informal quiz on the Washington Post's web page has example questions from 4th and 8th grade questions by the National Assessment of Educational Progress.
Visit the practice FCAT test page to download a practice FCAT math test and answer key. It's an entirely different kind of test than the one at the Washington Post's web site. Consider the very first question:
Believe it or not it is something I and many others do every. Sure we crank everything though spreadsheets and all sorts of other tools, but its always easy to place an extra zero, drop a zero or transpose number. At least if you have a ballpark figure you know if something is an order of magnitude off it can't possibly be right.
If it makes you feel any better, I work for a software company, and what you describe is exactly how I conduct interviews. I ask candidates to code, but I don't actually care that much if their program is bug-free. I care about how they go about doing it, and how they figure out solutions as I point out problems. I care more about the work they show than whether they happen to get this instance exactly right.
When I was growing up, my dad told me that none of the facts I learned all the way through high school mattered that much in the end, but what mattered is that going through it taught me HOW to learn.
Here in Germany math is used as a means for selection who is to get a university-entrance diploma.
cb
On 4th graders: My niece is in 4th grade & is a class leader in math. So, how do I know, for a fact, that I'm better @ it than she is (not that I am "proud" of it, but because it benefitted her during tutoring in math)?
Easy - I am a large part of the reason she's doing so well!
I had to know more, before she did, to teach her tricks about math!
(Which she fully mastered, like how to check subt w/ add (& vice-a-versa), div. w/ mult. (& vice-a-versa), & how add with carry works, later also with multi-digit multiplications how the 1's, 10's, 100's etc. columns really work & more...)
Yes, I know - not "huge accomplishments" but they mattered to teach her to be good @ it herself (fundamentals & principles for 'err checking' really).
I simply said to her while tutoring her specifically in math, this little speech (to make her feel that I am just a teacher, not a dictator & so she felt comfortable making mistakes @ first):
"To do well at math, you must do your homework. It's that simple. So, if you don't understand a way to do your work, just say so or ask questions, and we'll review it step by step until you do. You're never stupid asking a question when you don't know what you're doing after all..."
That, worked with her. I'd say it'd work with most kids in fact, as it removes fear of feeling "stupid" etc./et al...
(That was with everything from add/subtract - multiply/divide onwards into fractions/decimals work)
E.G.-> I took her ahead too, into sq. root divisions calculations even, she mastered them (way ahead of time)...
Plus, the last time that happened, is when I taught her division ahead of time, so she could double-check multiplication answers (& vice-a-versa too).
When division FINALLY came up later in class in being taught? Well - she knew INSTANTLY how to do division when it finally came up & said "Uncle Al, another boy and I knew how to do it right, and both of us had our uncle's show us how".
Was great to hear & better to see "A's" coming from her in school, especially in an essentially DRY area like math.
Her 1st tutor (another relative) did NOT do this & made her cry @ times, calling her stupid etc.!
THAT relative of mine got a stern "talking to" from myself in fact, for that bullshit!
(E.G.-> AND, I challenged them to do discrete math problems with me (they never even got NEAR that level of math in their day is why, I took them to where they were ignorant, just like how my niece felt, so they too were humbled (@ least they responded to reason on that account & felt bad for their "teaching methods")).
---
On 10th graders:
Well, all I can say, is this: I literally scored 95% on my NY State Regents Exam in High School on Geometry...
(During the year, I even showed my teacher a new way to do a proof, which took me 30% of the time in a test, & he marked me wrong: I took it up to he, we "step traced" the proof, & he said "Well, so it does work!" & gave me credit (it took the long way to China, but it worked (more steps than his answer proof had in statements & reasons)).
SO - that "all said & aside":
Well, IF 10th grade students nowadays can score better than that on the state final exam in Geometry (std. curriculum in 10th grade)?
My hat's off to them!
(Simply because then, & ONLY THEN, can they say they're better than I am in THEIR math, even though it's been 30++ yrs. since I took it!)
APK
P.S.=> Heh, that was some memories I actually have the records of to this day (on 10th grade math)... & the part on my niece in 4th grade is not "bragging" here (because by my age you had BETTER be better @ math than a 4th grader is), but more to show that teaching kids the right way, is what I felt I did (but to be a good teacher, you'd have to know your material, what it builds into next, & what its foundations are (because that's where the "tricks" are learned, by knowing fundamental mechanics of math, 1st!))
...apk
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.
I personally did the first part the same way (47*3) but then did the multiplication directly (47*3=120+21=141). I did use the round+add/subtract afterwards in the 29-hour-wage question though.
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".
Here in Czech republic, 7th or 8th graders do this in geometry. Part of the year is spent over writing down instructions how to construct given shapes (for example 30 degree angle using only compass and staightedge) or following such instructions in practice.
Everyone makes life changing decisions that involve maths - quite advanced math, at that - regularly. For instance, take this type of question:
Deadly disease X has a prevalence of 1 in 10,000. Consuming substance A reduces your risk by 80%. Deadly disease Y has a prevalence of 1 in 500. NOT consuming substance A reduces your risk by 20%. If this is all that is involved, should you or should you not consume substance A?
Many decisions we make involve things like this. If one lacks the ability to reduce the maths, how can one live?
Prediction for end of Universe #42: Fencepost error in Quantum_bogosort.cpp
People who are actually smart and could land any job wouldn't touch the teaching profession with a ten foot pole.
I can see someone hasn't watched "Stand and Deliver" lately...
This is why we probably need to teach proofs beginning in elementary school. I mean proofs, where you start from the axioms and work to the conclusion.
Maybe they should focus more on logic and problem-solving skills as opposed to "just getting the right answer", even if that means only covering half the material currently planned.
RTFA and link in TFA. The test he took was FCAT (The Florida Comprehensive Assessment Test®) for 10 graders and the sample math test can be found here http://fcat.fldoe.org/fcatitem.asp
It's not that hard but it's a lot harder then just summing some numbers.
Tests from 2005 to 2007 are available at http://fcat.fldoe.org/fcatrelease.asp
---------
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.
Quidnam Latine loqui modo coepi?
I do 47 * 3 like I would on paper: 7 * 3 + 4 * 3 * 10 (i.e. ((4 * 10) + 7) * 3)
But on the more complicated problem I used the following strategy:
28 / 4 = 7
8 / 4 = 2
so 288 / 40 = 7.2
7.2 * 29
is 7.2 * 30 - 7.2
is 72 * 3 - 7.2
is 216 - 8 + 0.8
is 208.8
I like doing problems like this in my head as I feel that it helps practise my short term memory.
I do math the same way.
This problem decomposition technique is now a standard method for arithmetic taught in UK schools. It's given the name "clustering".
However, while intuitive, seeing examples written down in textbooks baffles many parents, who simply don't "get" how to encourage their children to do it. The homework often asks the student to "solve (47 x 75) / 25 using clustering", show your working. For a parent who isn't familiar with the jargon, this could be a very frustrating experience, particularly as there are dozens of ways of getting to the answer.
... the math teachers were well-known for taking the final tests themselves and consistently getting maximum scores every year. They knew their math, alright. (Recalling how I did in class, needing private tutoring by another math teacher, their teaching skills perhaps could stand some improvement.) Then again now-a-days freshly minted teachers have more experience sharing their feelings in huggy-feely "class" than that they get their spelling or numbers right. And their teachers, in turn, have the same problem.
How this "highly successful" guy can fail every last one of the math questions besides having all sorts of "success" attached to his name? The obvious answer, to me, is that his degrees aren't worth much. And this is also an increasingly public secret. American College[tm] is far more about the sports and the brand, the connections and landing a job because of that bit of paper, than it is about learning something. That even so he is but one of the very few to even try, speaks volumes for the unjustified overconfidence of school boards. They really aren't up to snuff.
My credentials? Uh, busy with the Stanford online stuff (finals for one, catching up on the other two), yet I found the time to answer all those math questions by typing them into a calculator. Mine isn't graphing, no, so alright that was all but one, but flipping a single sign I still can do without help, thanks. In fact given a little more time and a bit of paper I would've done it without calculator, too, even though I obviously lack recent practice. Which I'm going to fix after these classes finish.
When're you going to brush up on skills you've gone too long without practicing?
I'm 35, so maybe it's all changed now, but first bit of rote mathematical learning was out 1..12 times tables. :)
Even then most people learnt them off by heart, and I was adding and substracting to get the answers from previously learnt tables (I think it was something like we learnt one a week in ascending order).
Not for one moment saying learning them isn't necessary - but always seemed they were missing a trick. 1..9 makes sense. When you get to 10 I think it went a bit wrong. I seem to remember this was the 'easy' week, as you just needed to add a zero. Then the 11 times was easy, as 11,22,33,44 etc all very easy - until you get to 11*10 (which you pulled back from your 10* table).. but then 11*11 it all sort of fell down and people had to learn these.
Unless, you were me - 11*11 = 11*10 + 1*11
Maybe the trick that's missed is that once you've learnt up to your 10*, 11* should be explained as 10* + 1*, 12* as 10* + 2* etc.
Again, I'm guessing that depending upon age and school, many people are probably taught this - but I wasn't and it makes me feel a bit pissy
Just feel that if we exposed children to this right from the beginning - i.e. there are multiple ways of looking at questions, then going forward everytime they saw a new problem/type of question, they'd automatically start considering what worked best for them (and lock those synapses in place for the rest of their life).
As someone with a masters in maths and PhD in physics, this is the same way I did the calculation. In fact, I suspect it's the way anyone who knows some more advanced maths would do it: What you've effectively done (in maths language) is:
1) Use the associative property of multiplication and its inverse: (AB)C=A(BC).
2) Rewrite the unknown product 47*3 in terms of two known products, by first rewriting 47=50-3, thus (50-3)*3.
3) Expand the bracket: 47*3=50*3-3*3.
Now this is much akin to the 'normal' method used to teach kids, except they always expand their brackets in terms of positive numbers broken up by powers of 10, ie 47=40+7, however from a mathematical standpoint there's no reason not to use any splitting you like, only the expedience of learning a limited number of multiplications.
The true gift of good mathematicians is not only being able to make these thought processes, but properly explain them so that others can too. Far too often maths as it is taught is just a voodoo recipe for performing calculations rather than a well explained, reasoned setup. This is fine for people who merely have to perform the function (much as you don't need to know the workings of an internal combustion engine to drive a car) but if you want to derive a deeper understanding of what's going on its woefully insufficient.
I'm pretty certain that the school board member in question could explain the difference between the 4th and 8th grade NAEP questions you looked at and 10th grade FCAT questions. Most commenters on this thread must sit around lazily all day, brains atrophying due to a lack of usage, because they're too dim to notice obvious and basic facts.
Yes, I did it the same way - though I then checked it with 3*40=120 + 3*7=21 to get 141.
Just remember, the sort of people who add 2+2 and get 22 are the same people who are using force to take 1/4th of your paycheck to ensure you have funds and medical care when you are retired.
i do the same thing for complicated calculations. 47x3 I did straight up though.
The Cloud - because you don't care if your apps and data are up in the air.
/for definitions of 'lazy' that involve doing some work.
In the future, I would want to not be isolated from my friends in the Space Station.
I think I'm pretty much the same speed on either, but I'm now trying to consider why.
I *think* it's because I'm again doing my maths visually.
I prefer 150-3*3...and I suspect I'm now going to lose people, but I'll try and explain
150 is a multiple of 10. In my head I've got a grid of 10*15 - well actually it's definitely (and always is) 10 wide and I'm vaguely aware it's 15 high, but I'm not focussing on this right now.
I take off 9 from 150, so I've done 10-9, to give me one left on my top row. I know I'm still on the top row, so I still have 140 as my 'foundation', and oh theres one 'thing' left over this, so I just add the one on to give me 141.
I'm getting strangely fascinated by all the different ways people are approaching the same very simple problem.
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.
On multiple choice tests, always read the answers first, and identify the key differences. Here, the options are:
141
1,175
3,525
4,700
And it should immediately jump out that one of these is an order of magnitude lower than the others. So, you know right away that either you can throw this one out or it's the right answer. As soon as you reduce he problem to 47 times 3, you know it has to be that one. Mark A and move on to a harder question. (You can check your work later if you have time.)
If the answer had a higher order of magnitude, the next thing to consider would be whether the answer is likely to be the nice, round 47 times 100 -- another easy-to-identify possibility.
I only realized afterwards, but I made my left hand into the axes (the thumb is the X, the 1st finger Y), held and 'drew' the point with my right and then moved it over to the other side.
Of course if I'd had some paper to hand (sorry) I'd have used it.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
This is pretty much what kicked off my original comment. I'd never heard of it before and was trying to decipher wtf it was going on about - then suddenly I twigged that it was the closest thing I'd seen on paper to how my head was actually working.
Hurrah for progress - I just worry that it shouldn't replace the 'traditional' method. Seem to be plenty of people who quite happily just say they multiple 47*3 as a single mental process. I'd then be really fascinated to know if the people who do this do better in an environment that teaches this way - I always felt I was almost cheating - and then when my little self-taught shortcuts left me high and dry on the next level of problem I was stumped until I developed my own way of looking at it.
Which led to my issue between GCSE and A-level when the syllabus was racing forwards faster than I could come up with my own ways of understanding.
Can't be bothered to look again, but wasn't there only one answer that ended in a 1?
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
And I don't like the excuse of "It's been awhile. I've been out of school for YEARS but some things you just don't forget. The fact that he couldn't answer a single one dumbfounds me; this isn't the CEO of a tire company, this is a person in a position to set educational curriculum. They need to be held responsible for not knowing anything about their "business", just as one -should- be held accountable if one ran a computer company without having any idea how they worked (which, unfortunately, is also probably much more common than it should be).
What really gets me is that these are math questions. Not English or Science. Management is business and business is money; if you have no real mathematical education and cannot even answer word problems, people should be SCARED that you are in a position of monetary control; that, even WITH a calculator, you cannot figure out what your company may or may not be bringing in or shelling out.
Then again, there's always the possibility he simply failed the test on purpose in order to push his agenda. Which apparently involves making himself look incompetent and mildly retarded, but, hey, if it gets the test changed in the way he wants, more power to him for gaming the system in an absolutely disgusting manner.
In multiple choice, I probably have a multi-step approach.
Run through it without looking at the answers using my own strange inner whiteboard/counters/whatever I can conjure up to help me. If that hits an answer I feel smug.
If I look down and don't see anything that matches, then I'll switch to something else - e.g. if all trailing digits in the question are unique, then just focus on working out what that should be. Then probably a quick check using the ^10s to just check that I've got a figure that's not an order of magnitude out.
For example on the salary question, I looked at it as a 40 hour week, followed by a 30 hours week and knowing the real answer would be a smidge less than the ballpark number I came up with.
I'd done fine at maths throughout school until mid-way through higher (roughly final year of highschool level) I was suddenly struggling. There were whole sections of the syllabus where I just couldn't see it. There'd be a question and I just couldn't grasp how to get from the info given to the solution required. I failed my mock exam, and not just marginally.
I was a "B maybe A" in all other classes. The teacher was pretty good and everything.
As luck would have it, my dad was friends with an engineer who offered some tutoring. First couple of sessions were straightforward and he said he didn't know what the problem was. He was giving me stuff that was as hard as it gets in the exam and I was able to solve them and explain it, not just following memorised procedures. Next session we came across something I just had no idea. He walked through solving it and one of the steps I was just what? I can't even remember what it was, some concept that once you have it you don't even think about it, like how you can multiply both sides of the equation to simplify. He'd barely started explaining it and I was like ooh - it just clicked.
We abandoned the sessions soon after that because I'd literally gone from being an D/E to a strong B student in but a moment of comprehension. I must have simply been off sick that day or something, and the specific weakness never picked up in marking - perhaps due to rather large class sizes. I suspect that's not the real root though. Mid-way through the year, the classes were shuffled and my desk partner was changed from a friend who I worked well with to someone I didn't know and pretty much didn't work with at all. It was probably about this time my grades began to fall and my friend's grades slipped as bad as mine (he was the other mock fail). But he wasn't as lucky as me, he didn't have a dad with an engineer friend, he failed the finals while I was a couple of points away from an A.
I figured it was roughly three quarters - getting down to two choices - and that 29/40ths of an only-just-round number of dollars would be unlikely to give another round number of dollars.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
100%. That was easy.
That explains a lot about 21st century America.
Frankly, I'm atrocious at maintaining numbers in visualization even if I do realize that (47*75) is half of 7500 minus three 75s. But, good god man, with a calculator? Maybe every kid should be required to use a slide rule to get a feel for the idea that this "weightiness" of a number times that "weightiness" of a number gives this approximate result because with those multiple choice options you really can just guess at the nearest answer.
I don't think any school before the college level does any real math, i.e. proving things within a formal system.
So yeah, I'm necessarily better than them at it, since they don't even know what it is.
If I'm trying to visualize it, it's always easier for me to start with the 150 and then add or subtract from it as required. 150 is a nice rectangular shape I can hold on my head without too much effort. If I was say trying to hold 141, it would be a rectangle of 140 with an annoying little extra thing I'd have to remember with it.
Aggh, not explaining this well, probably best I'm not a teacher.
I think it just boils down to the fact that I firstly try to break the question down (obviously), but break it down into things I can hold easily in my head - and this guides how I choose to break it down. It's not the operations I find hard, it's the variables.
150 fits easily as say 'one visual unit'
141 is harder as just considering that number, I'm mentally holding that not as 141, but (14*10)+1. Everytime time I need to recall that number, there's 3 f'in parts of it to juggle, so I'd like to push these 'hard' variables towards the end of my thought process, so I have to deal with them for the absolutely minimum length of time.
Thinking it through even more, I have 'emotions' towards numbers. If I was just asked which number do I prefer, I'd choose 150 over 141. 150 feels friendly, 141 is a pain in the arse and I wish to spend as little time as possible even thinking about it.
I am not suprised at the results. I've long sensed that we have idiots running the place.
And, it's getting worse. I taught a group of nursing students last summer, and there's a lot of dangerous nursing students out there. I taught the second semester of Anatomy and Physiology, and the students today want to learn facts, but they don't want to have to do any analytical thinking. For example, you could teach them A=B and B=C, but they couldn't come up with A=C.
Unfortunately, I'm 59, so I'll probably have to be taken care of by these idiots sometime in the next 10-20 years.
I took the sample exam and got 83%. The question I missed was the triangle question, and I was sure that I was correct, so I went back and looked at it, and the negative sign on the (-3,7) vertex of the triangle was crap on my wife's laptop screen. I sure as hell wouldn't have given the (3,7) answer if I'd correctly seen the vertex as (3,7)!
Seems to me that the school board member who was so candid about his performance in that test might have hailed from the wrong side of the "arts vs. sciences divide", where arts-focused people for some reason just don't "get" maths.
When I was in high school (back in the early 14th century, before we had calculators), I fell into this camp (bottom 20% of the school), but when I changed direction (long story) into engineering in the early '90s, I suddenly found I could romp through the maths with absolutely no difficulty. Maybe it's something to do with motivation.
But even so, I was a bit astounded when browsing through the NAEP questions tool to see this entry: "Convert temperature from Fahrenheit to Celsius (calculator available)" classified as "hard". With a calculator, it should be possible to arrive at a plausible result pretty damn quickly, even if you do have to make a few stabs at what to do with the factors of 5, 9 and 32.
That's why good multiple choice tests have ringer answers to short circuit this kind of logic. REALLY good multiple choice tests have the incorrect answers being the *right* answer for different mistakes. If there is an answer that's correct for (47 * 75) - 25, you know you need to get that kid glasses.
Great job! You got every question right.
What he demonstrated was that people who are charismatic and aggressive have a career track available to them that makes use of very few classroom-learned skills.
That comment alone says it all...
Twelve-and-three-quarter inches. Unyielding. This wand belonged to Bellatrix Lestrange.
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 agree! When all learning is memorization of "cuz I said so" except for one advanced geometry class sophomore year, you end up with people who will believe ANY convincing "cuz I said so".
Geometry (and AP Computer Science) were two of the most important classes I took in high school from a "how to think" perspective.
When I was in high school, calculators were only newly available and not permitted in examinations. We had to use books of tables (or slide rules, if you had one and knew how to use it). Either way, we got fairly proficient at establishing a correct order of magnitude in our calculations.
My impression is that most textbooks and curricula suck right now. Teach them how to arithmetic the right way, then teach them the order of operations, then teach them "clustering" as an easy way to do arithmetic using things they have already learned. It can't NOT make sense. Always, always demand mastery of the "right" way before teaching short-cuts.
but just considering 140 and 150 - 150 is a nicer number to me.
One is visualized as 10x14, the other as 10x15 - so yes, both rectangles.
140 I see as being composed of 2 other rectangles bolted together - 2 10x7's
150 is 3 10x5s, but also 2 10x10s, with the top square only half filled in. If there's one thing I find easier than a rectangle to visualize, it's squares.
I got the triangle one right, but carelessly clicked the wrong answer anyway. D'oh!
XML is like violence. If it doesn't solve your problem, you're not using enough of it. --AC
My first step was to laugh at the "you can use a calculator" instruction - what the heck? What are they testing with this question?
He continued, “It seems to me something is seriously wrong. I have a bachelor of science degree, two masters degrees, and 15 credit hours toward a doctorate.
Yeah, something is wrong. If he took a test with questions like the sample, how the hell did he manage to get a BS without the ability to figure even one of them out. "you can use a calculator"!!!!
I'd really, really, really like to review the original test now...
Can you be Even More Awesome?!
100%.
Look, my daughter is 2'nd grade. The math is now called everyday math. She is learning her multiplication in 2'nd, rather than in 4th when I did. From what I saw, this was right in line with what she has. More importantly, this math probably is exactly what kids need in later life. Do they really need the theory? Yes, at a later time. But at first, they need to get a decent understanding of how it is applied around the world. And for adults that can not do this kind of math, well, I would have to say that it reflects more on the adult, then the coursework.
I prefer the "u" in honour as it seems to be missing these days.
It's not easy to distinguish 202.13 and 208.17 "by magnitude" now is it?
Since the difference is in the 3rd sig figure, d'you think performing the calculation (actually a division) using a calculator is really that unreasonable?
Not that there aren't good tricks for doing division, like for example factoring small factors like 2 out of denominator/numerator quickly to eliminate them, but after a certain point it's just quicker to type (at 80wpm) the numbers into a Python shell and get an answer.
--PM
http://www.tampabay.com/opinion/columns/primary-purpose-of-education-learning-how-to-learn/1200122
I promise to be different...
Managers and bureaucrats don't need math.
What 'crappy pay'?
In Washington State yearly pay is is searchable online.for state employees, although it is 2 years old data.
State school employees are state employees, you do the math.
For extra credit; why are there more school employees than students?
No brain, no pain.
Bias up front: I am an ex academic (in engineering), bored early retiree who is now teaching senior Maths/Physics at high school (in Australia) - including 10th grade Maths. As well as being an academic, I worked in the private sector (including my own business), so I have some idea as to what I would expect of general clerical staff.
I am truly astonished that a "well educated" person could not solve the sort of problems referenced in the article. Simple Maths problems like these do not just show Mathematical capability, but also demonstrate logical reasoning skills - the sort of skills I would look for when hiring someone for a general clerical position.
That said, quite a few of my (middle to lower ability class) kids in 10th grade this year failed to meet this sort of standard, although with most of these it was lack of effort/application not innate ability that determined their outcome. Quite a few of these kids said they couldn't care less as "Maths was irrelevant" to their area of career interest (despite solid examples that demonstrated that idea to be incorrect).
I have the feeling that many kids regard Maths as hard and "you can do well without it" as a socially accepted truth. Yet we live in an increasingly technical (numerate, Mathematical) world, so I can't help but feel this widely accepted "truth" will (or quite probably already is going to) bite us in the bum: without logical, (mathematically literate) people to run our world, it will fall into a hole...
I saw the (...*75)/25 = (...*3) part, but I chose to do it modulo 10 - that is, work out only the unit's place digit. If I recall, only one answer ended in the requisite 47*3 = ??1, so that must be it.
Well, after a 30 year career in engineering, it is nice to know that I can still do 8th grade math (got all of the sample questions correct)! :-)
Especially once you realize that 3*7=21 and only one answer ended in 1.
That's why good multiple choice tests have ringer answers to short circuit this kind of logic. REALLY good multiple choice tests have the incorrect answers being the *right* answer for different mistakes. If there is an answer that's correct for (47 * 75) - 25, you know you need to get that kid glasses.
That's why making multiple choice tests (and grading them) is so frigging difficult to do very well. To do it completely perfectly you need to be able to predict all possible incorrect interpretations and be sure that none of your "wrong" answers are "right" in a way that you would want to give points for.
Of course, before you go through all that effort (or any formal evaluation for that matter) you should probably figure out exactly why you want to do the testing in the first place. If the point is to use the evaluation to assist in the learning then maybe time would be better spent by having the students create tests for each other and then go over them together in groups, or something "radical" like that. It is not clear that formal grades and exam scores out of 100 give any real benefit to the learning process.
Here is an old article by Alfie Kohn about reasons to question the whole process of formal grading:
http://www.alfiekohn.org/teaching/grading.htm
GRADING
The Issue Is Not How but Why
By Alfie Kohn
Why are we concerned with evaluating how well students are doing? The question of motive, as opposed to method, can lead us to rethink basic tenets of teaching and learning and to evaluate what students have done in a manner more consistent with our ultimate educational objectives. But not all approaches to the topic result in this sort of thoughtful reflection. ....
This article is full of FUD. It's like me telling you my friend failed his biology test, but if you can answer 1+1 correctly (hint: the answer is 2), it proves my friend is an idiot. Sure, my question has little to do with biology, but does that really matter? More impressive is the number of Slashdot readers that think these are questions from the test. My faith in Slashdot readers: falling fast.
Most Maths graduates can't do simple maths either.
Is it easier if you are referring to (47*75)/25 problem, to note that 75 is 3*25 and 47*3 is (50-3)*3 or 150-9? For the 4th and 8th grade samples on the link, you can tell that whoever developed the questions spent time designing them.
I don't thinks so.... Can't be bothered to double check, but I believe the answer is pancakes.
Margin of Error = 1/SQRT(1) = 100%
Time to ask Siri...
If you can't do the math without a calculator, you should not be doing it!
Fight Spammers!
I think there are two horrible things about the school board's member's reaction.
* Completely glossing over his poor reading score.
To me, this guy sounds like a Herman Cain -- good at motivating people, good at listening to people and good at letting a minion do the mental work.
* Implying that all professions don't need this level of math
“I have a wide circle of friends in various professions. Since taking the test, I’ve detailed its contents as best I can to many of them, particularly the math section, which does more than its share of shoving students in our system out of school and on to the street. Not a single one of them said that the math I described was necessary in their profession."
Looking at the Florida test example, there is no way that anyone at the working level of finance or STEM job would perform so poorly on this. Does this guy not want people working for him that understand amortization? I see this type of thinking from other managers and engineers. "I don't understand it / remember it therefore it is trivial." I think it comes from the ego and confidence required to move up. In some cases, the super star or entrepreneur has to be confident enough to leap into an "opportunity" that a more balanced thoughtful person would not.
The test questions grate on me. "You can use a calculator." Yes, I suppose I'm capable of using one. But am I allowed to? It's hard to take seriously the complaints that people are failing a test in one of the three Rs, when the test itself is failing another.
Anyone who tries to tell me that it's okay because language evolves is cordially invited to get off my lawn.
Chelloveck
I give up on debugging. From now on, SIGSEGV is a feature.
yay something on this site that doesn't make me feel dumb...
nice change of pace
. even if it is designed for 10th graders
Using only a scratch paper and no calculators, I go two wrong! On one I failed to read the answers completely/properly and chose an answer that I knew was not precise. I pondered why they would use an approximation, but still chose incorrectly. The triangle one, I had no clue whatsoever.
I'm scared. I scored 66% on a child's math test.
The test he took was the 10th grade one. The article says the example questions come from the 4th and 8th grade tests.
This school board member's (lack of) quantitative skills and his attitude towards them are now endemic in the U.S., and are emblematic of the decline of our culture and of our institutions. As a faculty member in a large public university I helped put in place a program to require students to pass a test of 8th-grade math (mostly arithmetic) before passing the university's gen-ed math class (the easiest offered). This test was modeled on state requirements for that grade level, and contained nothing students were not ostensibly required to know before receiving a high school diploma. They were given any amount of free tutoring they wanted, and could take the test as many times as they needed to pass. The reaction to this requirement from the students, their parents, and even some faculty was so ferocious that it had to be abandoned, which means the university continues to award bachelor's degrees to people who can't calculate a percentage, or who even know what that means. This situation indicates that the U.S. will not recover as a functioning democratic republic, because the ignorant cannot govern themselves.
The 'guestimation' strategy fails at question 5 that has two answers that are very close to each other ($203.00 and $208.80). However, my mathematical instincts tell me that 203.00 is an unlikely outcome when multiplying with 29. I used a calculator to confirm my guess (as allowed by the test).
I calculated the hourly rate and found out that the last digit is not zero.
It is what it is.
TFA lamenting the adult scoring poorly also pointed to black students scoring far below whites. I cannot imagine how a college grad running a large organization scored so poorly on the test unless he's a worthless schmoozer in a designer suit whose executive assistant does everything for him. Is this posturing to dumb down the tests so more students can pass? Make a case that the test is too hard because college grads cannot pass it? The sample questions were not that hard. I got all of them correct before morning coffee. It's easy enough that it would be fair to require every politician to pass the test before running for office.
Thank you, but no one cares. You are irrelevant.
This school board member's (lack of) quantitative skills and his attitude towards them are now endemic in the U.S., and are emblematic of the decline of our culture and of our institutions. As a faculty member in a large public university I helped put in place a program to require students to pass a test of 8th-grade math (mostly arithmetic) before passing the university's gen-ed math class (the easiest offered). This test was modeled on state requirements for that grade level, and contained nothing students were not ostensibly required to know before receiving a high school diploma. They were given any amount of free tutoring they wanted, and could take the test as many times as they needed to pass. The reaction to this requirement from the students, their parents, and even some faculty was so ferocious that it had to be abandoned, which means the university continues to award bachelor's degrees to people who can't calculate a percentage, or who even know what that means. This situation indicates that the U.S. will not recover as a functioning democratic republic, because the ignorant cannot govern themselves.
More like "I make $2000 a month and my mortgage is $1000 a month and I didn't understand the part about the interest rate changing from 1.9 to 6.9 five years from now."
Exactly how I did it.
I'm a mechanical engineer and used to tutor math. I try to teach people to think this way.
And as an engineer, I'm inclined to skip the 'subract 9' step now and then, if just to annoy mathematicians ;)
http://nces.ed.gov/nationsreportcard/itmrlsx/landing.aspx
"Not enough storage is available to complete this operation."
I genuinely wonder if everybody else worked that out the same way, but it's now just the way my head works.
Actually I appreciate the explanation. I hadn't considered multiplying 47 that way, but now in the future, I will.
"First they came for the slanderers and i said nothing."
That said, on an international scale, I don't thing the sample 10th grade tests are unreasonably difficult. Just a though (maybe I'm missing some point here), but perhaps the US needs an explicitly tiered school system, like in my home country, where we have 3 types of secondary schools for non-handicapped kids:
All three tiers are free by constitution. Students (or rather, their parents), are free to choose tiers, assisted by recommendations given at the end of primary school. Switching to a higher tier midway would be difficult, motivating parents to put their children as high as possible to start with. The biggest criticism of this system is that children who are placed too high by their parents and are forced to switch to a lower tier often end up wasting one or more years and getting demotivated.
But we're going a bit off-topic... I still find it outrageous that a school board member wouldn't be able to get 50% of the 10th grade questions right with confidence, leave alone "knowing the answers to none of them, and managing to guess ten out of the 60 correctly".
Actually once you figure out the hourly rate by dividing 288.0 by 40 to get 7.2, it's the only one that fits, since ?.2 * ?9 is going to be ??.8
You still don't need the calculator. The problem is (29 * 288) / 40. Reduce that to (29 * 72)/10, and you immediately see the last digit must be 8.
Not quite sure how it happened though - well I do. They were a startup and interviews were just nice little chats to see how we got on. Managed to staff ourselves with a wonderfully random selection of people (architects with doctorates in literature and all sorts).
Maybe the reason it worked is that it assumes that some people are curious and some aren't. As long as you're curious and have access to google, you can usually make a reasonable job of most things - and ENJOY the process.
I occasionally get drafted in to ask the technical questions on interviews. I feel like a fraud as I'm bluffing a bit on some of the questions - but then when the answers come back it's amazing how somebody who clearly knows their technologies/acronyms seems to completely screw up the answer. Really simple 'real world stuff' - "You have a dev team offshore, what steps would you take to ensure implementation is successful?"
No right answers, but half the interviewees seem to hear a different question and answer "I'll review every line of code that comes back" or "I'll ensure they are all certified on X". I much prefer somebody that considers that problems may start with them - "I'll give them my design to review and we'll all talk it through before anybody opens Eclipse."
My nice company got bought by evil-megacorp and it's slowly killing me. Now have an attitude that unless you're in the relevant department, certain areas are off-limits. Everybody now sits in their little silo and doesn't seem to care about anything they're not contractually responsible for and any (however polite) suggestion at how they could improve something is taken as a personal slight against them. Oh, and asking for help and advice is tantamount to admitting you're a cretin. My personal introduction to colleagues seems to consist of trying to drill into them "If the design looks bollocks, please tell me and we can talk it through, it's entirely likely I screwed up" and "Whilst sobbing over your PC to 4am to solve a problem might look great on your timesheet, wtf didn't you just ask me?"
I seem to have drifted completely off topic now, so I'll stop..
Am I the only person who sees the first question that has no correct answers?
It's been a long time since I've done any "maths" but last time I checked, when I divide 100 by 0.25 (1/4) I get an answer of 400.
(47 x 75) = 3,525
this answer divided by 1/4 (which is equal to 25%) = 14,100
As far as I know, there is no correct answer to the first question which gives me no confidence in that tests ability to determine the kids knowledge levels.
I always do this too. I taught my 5th grade teacher how to do it. She immediately knighted me "genius kid".
If I have to convert fahrenheit to celcius, if I don't just type it into Google, I derive the formulas knowing that one degree = 5/9th of the other, -40 is a fixed point of the conversion and 32F = 0C. For some reason if I go from memory I always garble it.
If you ask me 9*12, I'm still doing (10*12)-12
Nothing wrong with memorizing your 12-times table, just I can't see why you'd memorize that and not the 13-times.
My point (combined with that of another poster) is that if you teach up to 10x, the 11x and onwards seems a lovely point to break from rote learning and instead introduce long multiplication.
I'm not saying rote learning isn't important, it provides the foundations you need to build on. Additionally, as you perform mental arithmetic, you'll pretty much automatically memorize the 'sums' you use often. e.g. 25*3 I just know is 75. Doesn't mean I was ever told to learn 25*3 or 3*25 at primary school.
Then there's the ones you pick up later on, which are specific to what you do day to day. I know quite a few x*1024 multiples - but I'm not for one moment suggesting we formalize this for primary school children.
Oh, look. A school board member can count to frist.
I seemingly think in Russian
Is that last week I realized that simple calculus allows you to generate the function for the surface area of a sphere from the volume of sphere and why that is the case. I don't think many 10th graders would figure that one out. (Let alone realize that calc also lets you generate area of a circle from the circumference formula.)
Did you know 80 to 90% of the moderators on slashdot wouldn't recognize a troll even if one dragged them under a bridge.
The summary takes a cheap shot at the anonymous school board member, and a lot of comments mistakenly assume that the board member took, and failed, the 4th grade math test for which there were sample questions, rather than the 10th grade test. I think the school board member's criticisms are well founded, and many here are missing the point.
There's the often-referenced essay (in PDF format), A Mathematician's Lament, which argues that the method of teaching mathematics in the US is arbitrary, rigid, and fails to teach mathematics -- and that furthermore, not all students actually need or want to learn advanced mathematics, and the rigid math curriculum is a hindrance to those students who do need or want to learn it.
In practice, much of the way our education system works is not about teaching practical skills, providing the background knowledge for full participation in a democracy, or enabling a rich and rewarding life. It's about sorting out who goes in which social class. Tests are designed so that kids will fail -- and increasingly, so that teachers will be fired. If enough teachers and students rise to the challenge, and more students pass the tests, they'll just make the tests harder.
Honestly, how many people have studied calculus? How many people have sweated over integration with hyperbolic functions, and yet never have to cope with mathematics more complex than simple algebra in their daily lives? Certainly, mathematics is important, and certainly, it would be better if people knew more about such an important field of human endeavour -- but there are other things that are important to know as well.
... when folks don't especially respect intelligence or wisdom, when high schools are used as holding pens and not as institutions of learning, and when we don't value those who teach our young much.
Check your premises.
I've got a Masters degree with distinction in Applied Mathematics, and I've tutored 2nd year university students.
I'm not from the US, so I'm not sure how old 10th graders are, but I hope I'm better at maths than them! (Yes, I got all the questions in the linked article correct).
Parent post inspires me to raise a couple of points. Here is the first one:
He continued, “It seems to me something is seriously wrong. I have a bachelor of science degree, two masters degrees, and 15 credit hours toward a doctorate.
So the guy is highly educated. To which the following aphorism applies:
Education is what you have left after you have forgotten everything you learned. --anon.
Will
Did it exactly the same way without really even thinking about it.
How can you not know this as a grown up? Especially as a teacher. Honestly, everything except logarithms of decimal numbers isn't that hard once you figure out what's going on. Just requires some space in your memory and the ability to remember a number for a few iterations. On another note, this does say more about managers than about the difficulty of these tests.
Still easy, considering 280 = 7 times 40, so you have 8 divided by 4 resulting in two with a shift to right due to division by 10. :P
For this problem, once I had 7.2 x 29, I just multiplied the last digits of either number, knowing that the answer had to end in that. Only one of the choices ended in 8 - 208.8. So that had to be the right one.
For all you smug people, how about trying a sample for the real test (pdf)? They are all 10th grade level geometry and algebra. This surprised me a little, because even the GRE you take for graduate school has a few questions of the sort in the test the OP linked to.
This space intentionally left blank.
As a Ph.D. in physics you should have realized that there was only one answer which looked about right in magnitude :)
Everything else was way smaller or way larger.
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
Yeah, something is wrong. If he took a test with questions like the sample, how the hell did he manage to get a BS without the ability to figure even one of them out. "you can use a calculator"!!!!
It depends on what the BS was in. A little more digging reveals this:
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.
I'm not sure why the education undergrad degree was a BS, rather than a BA, but that, combined with the two master's degrees in education, explain a whole lot. He could probably have gone through all of those degrees, including the 15 hours towards a doctorate (by which he probably means an Ed.D., which is definitely not the same as a Ph.D.) without ever taking any math more advanced than basic algebra. Educational psychology might (and definitely should) have included basic statistics, but it might not have, and depending on the way the course was taught, might have been easy to skate through.
Also, being able to oversee a large budget tell me nothing about his math ability. It tells me he has basic Excel skills. If he thinks he doesn't need those math skills in his job, he probably doesn't realize how much more efficiently/accurately he could be doing his job if he did have and use them.
"Anyone who [rips a CD] is probably engaging in copyright infringement." - David O. Carson
True, I would normally just ballpark it, but I was pointing out that this is the way I do mental maths in general. How I do the undergrad exams as a test of their reasonableness - use pi=3, g=10 etc. Generally if I can't do all the questions in 1/10th the time of the exam, it's too hard.
But yeah, reversing the answers for reasonableness is the way to do multiple choice exams quickly, usually you can rule out all but 1 or 2 due to magnitudes (or physics equivalent dimensions).
Wow, that was overkill. You guys need a quick lesson in standardized testing: My thought process was
50*3
And pick the closest looking number. 3 of the four answers were not even close to this, so it simplified things tremendously. With standardized testing, 3 of the 4 answers are usually garbage answers, so getting close is good enough. Remember standardized tests are timed, so running out of time can be worse than getting a few wrong here and there. Accurate only counts so much, fast is a factor too.
-=Geoskd
I wish I had a good sig, but all the good ones are copyrighted
Exams aren't supposed to benefit the learning process, they are supposed to test that the learning actually took place. They can benefit the teaching process, because analyzing the answers helps the teacher improve their methods.
... and be sure that none of your "wrong" answers are "right" in a way that you would want to give points for.
I was in a science class in middle school, and sometimes I would get back an exam that had an answer marked wrong that I had simply interpreted the question wrongly.. or something like that. Anyways, I would bring it to the teacher, explain my logic, and reasoning, and usually got a corrected grade for that question... probably more so, because I could explain my argument logically and rationally than for anything else. (I was like 12-ish, give me a break, I don't remember details.)
Of course, in college, I had a TA mark a problem dealing with induction that I did as wrong. I brought it to the professor, and he noted that it was indeed correct, and he ended up scolding the TA for marking my test wrong. Oddly, it was kind of a fallacious argument that the professor made. Basically, like, "I know this student is good, and is likely going to have the right answer, and you're in the wrong for not recognizing that." But then, the TA marked me wrong because I didn't fit his happy rote-memory version of what was correct, rather than me actually being wrong... so in a way, the TA kind of did deserve the scolding because he was grading brainlessly...
I guess the point of my whole post is: students who can explain why they should be right should not be afraid to bring such concerns to the teacher. If a student is right just by dumb luck, they don't really deserve to be right at all, but a student who is actually thinking and reasoning deserves to be right even if his answer doesn't match the answer in the book. (That being said, (45 x 75) / 24 = 141, regardless of the explanation that the student gives...)
WARNING! This girl exceeds the MAXIMUM SAFE standards established by the FDA for BRATTINESS
One way to convert if you can't remember the scale is that 32 F = 0 C and that -40C = -40F. With those two points, you should be able to figure it out from there. Set the X value to be the degrees in F, Y to be degrees in C. So you have (32, 0) and (-40, -40). Slope is (Y1 - Y2) / (X1 - X2). Slope intercept form is y = mx + b, where B = y - mx.
So, we end up with m = 40 / 72. Let's pick (32, 0) to solve for b:
0 - 40/72 * (32) = -1280 / 72, which is roughly -17.7.
So we have now, Celsius = (40/72) Fahrenheit - (1280 / 72)
Plug in 212 (boiling point of water in F) and you get back 100. Easy check.
With a calculator, this is fairly trivial to solve, as many calculators will even give you this form of the equation if you just know those two points.
TI 83 you can go:
STAT
STAT Edit
Put the X values in L1, put Y values in L2
Hit STAT again, then go to CALC
Press 4
Hit ENTER and there you go, you now have the slope and intercept solved for you, you just need to know how to apply it.
SSC
is that this guy asked around and found nobody who considered math useful for their jobs. He certainly didn't ask any of my coworkers.
My guess is that since he's a manager, he asked other managers. He didn't ask anyone who actually had to design or implement anything real.
"That's why making multiple choice tests (and grading them) is so frigging difficult to do very well. To do it completely perfectly you need to be able to predict all possible incorrect interpretations and be sure that none of your "wrong" answers are "right" in a way that you would want to give points for."
Tests are better planned than you think. When you construct a (good) test, all of the answers are put there BECAUSE they tell you something specific about the person taking the test. That's why on four answer questions you'll usually see that one answer is right, one answer is absolutely wrong (i.e. the test taker was guessing wildly) and the other two are the answers that the test taker would arrive at if they didn't understand something.
This can be done for two reasons.
First, it allows test takers who understand the subject well enough to eliminate some of the answers a better chance of getting the right answer, which (indirectly) gives students partial credit for partial knowledge.
Second, test can be scored with different values for different 'wrong' answers. For example, 'right' might be worth 5 points, 'wrong' might be worth 0 points, and the 'close' answers might be worth 2 points, explicitly giving students partial credit for partial knowledge.
And if the testing system is really smart, it can analyze the right and wrong answers and give better guidance to the instructor so that they know to provide specific guidance to the student. For example, if someone repeatly subtracts instead dividing, perhaps they're confused about what the division symbol means, so they can get help with that specifically. Or, as someone else in the discussion pointed out, if they read the division symbol as "+" then perhaps they need glasses. Most scoring systems don't do this, but some do. :-)
Enable 3D printed prosthetics!
You also need to teach them how to grammar the right way.
No sig for the moment.
Exams aren't supposed to benefit the learning process, they are supposed to test that the learning actually took place. They can benefit the teaching process, because analyzing the answers helps the teacher improve their methods.
Of course they are supposed to benefit the learning process! That is the whole point of the schooling system. If they are providing no educational benefit then why waste the time and effort doing them?
We should be making politicians pass this test before they're allowed to run for office.
Tests are better planned than you think.
Rarely, unfortunately.
All of your ideas are perfectly valid, and tests CAN be made that way, but for the vast majority of testing done by individual instructors to their classes, they are not prepared so meticulously. Doing so requires a lot of research, field testing, and benchmarking. It is not simple work. Without all of that work, you can never be confident that what you think are the reasons people are picking those "wrong" answers (or even the "right" answers) are the actual reasons they are doing so.
REALLY good multiple choice tests have the incorrect answers being the *right* answer for different mistakes.
My first year university inorganic chemistry test was multiple choice. It was one of the hardest exams I have ever written, for exactly this reason.
Basic maths not useful in real world? Lets see - How much paint do I need to cover a wall? Gallon of paint says it covers X square feet, wall is LxH, so multiply and divide (then add a bit extra for spills). I guess he also has someone to help with his taxes, and help evaluate investments. And never makes use of any engineered products. Sigh.
Here's a link with some sample grade 10 questions: High school math
"Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe and not make messes in the house." -- R.A.H
It's better than just putting it into a calculator because it gives you a rough estimate of what the answer should be. Then if the two answers don't mesh you can assume one of them is wrong. Whenever I finish a physics problem (I'm taking AP right now) I ask myself if the answer makes sense, saves me from so many mistakes.
I know people that do Math that way. I do sometimes, but not always. My wife does it like that all the time.
I think Math would be the ONLY subject I could actually teach in the US public school system. I tutored my mom and step-dad in College Algebra, and my Step-Dad in Calculus. The way I taught was:
1) This is how the book says to do it.
2) This is why it works.
3) This is how you can do it differently and get the same answer.
4) This is why the different way works.
By showing them the way the book said FIRST, they could easily look back and see I'm not full of it. Then after they understand the book way, I showed why it works, so that I could then show them another way. Leading them through the steps to come up with often better and more efficient ways of working a problem type allowed them to come up with their own ideas in how to figure out a problem. My favorite saying about math is:
Math is a language. Learn the language and it's much easier.
It is quite sad how few people could do these simple ballpark estimates... I teach CS and half of my students do not know that 2^10 \approx 1000.
What you've effectively done (in programming language) is:
Problem solve.
Take a large complex problem, and break it down into smaller solvable problems.
this part of the article really hit home:
"By any reasonable measure, my friend is a success. His now-grown kids are well-educated. He has a big house in a good part of town. Paid-for condo in the Caribbean....."If I’d been required to take those two tests when I was a 10th grader, my life would almost certainly have been very different. I’d have been told I wasn’t ‘college material,’ would probably have believed it, and looked for work appropriate for the level of ability that the test said I had."
I took all those tests and blew them out of the water, according to the tests I should have several college degrees and done fantastic at life. But I have no degree, parents made just barely too much for me to receive financial aid and the govt wouldn't allow me to file on my own until I was 24. I still went but the money ran out before I could finish.
But I did fine. Went into real estate during the bubble and cleaned up. My house is paid off (real house, not on wheels) and I drive a recent porsche convertible and my 10 yr reunion was just a few years ago.
So where does that leave me? Tests said I'd do fine but college didn't work out, and still I'm doing better than most Americans my age.
my karma will be here long after I'm gone
..when you got a purdy mouth? It's the only qualification you need for a middle-management position.
Yeah, 2^10 ~ 10^3 is one of the standard ones, along with a few other things like sqrt(2) ~ 1.4 (1.5 at a pinch) sin(30)=1/2, sin(60) = sqrt(3)/2 ~ 0.85 normally is enough to get through an undergrad physics exam without ever using a calculator. Using (A+b)^n ~ A^n + n*A^(n-1)*b for small b/A gets you most powers quick enough that students will think you're the rain man... eg (2.1)^4 ~ 16 + 8*4*0.1 = 19. There's a ton of others, of course, and doing the mental maths is one of the only things that keeps me sane whilst teaching.
The school board member took a test for tenth graders. The sample questions are for fourth and eighth graders. The impression given by submitter and editor is not supported by the evidence presented.
It should be illegal to say that freedom of speech should be limited.
How you did:
Great job! You got every question right.
I would have worked the same way had there been various answers in the right ballpark. Since the only thing sensible was 141, the other answers were way too big, I clicked on 141 immediately after realizing it was 47*3. I guess as an engineer I try to size up orders of magnitude almost as a second nature, so the answers in the thousands were instinctively "off".
A successful API design takes a mixture of software design and pedagogy.
No, that's how you are supposed to do the math if you understand it. Teachers who demand rote following of the rules are idiots and I will say that without any reservations, to their face, and I will never ever apologize for there's no need to when stating facts. Feynman was completely right about that.
A successful API design takes a mixture of software design and pedagogy.
I couldn't see it right myself. I've made worse math errors due to eyesight during divorces. i don't have to compete with 4th graders on that one.
If you'd read the article more carefully, you would realize that you can take the actual assessment here:
http://nces.ed.gov/nationsreportcard/itmrlsx/landing.aspx
Clearly, the person has a LOT of paper credibility (the token diplomas and degrees), and he claims he can manage people and figures (and can make enough money doing this to have a large house and a vacation home in the Bahamas).
It makes one wonder why Managers get paid so much when they don't even have the math skills to manage, and yet they have the arrogance to claim that they can manage.
Personally, I stopped taking Math in grade 10 (I just couldn't handle it), and I got a perfect score on the sample questions. I've never had anything more than minimum wage jobs. Maybe if I was less competent I could become a respected elected official and highly paid manager as well.
I think your math teacher never realized that there is structure to numbers, and most math problems in general. When solving a problem, it's silly to ignore all the knowledge you may have that lets you infer certain things without grudgingly following some procedure that's useful for a computer perhaps. If your, perhaps informal, knowledge of number theory and basic algebra, lets you select results without doing any computation -- fine. Computation is just a rather long proof of a theorem, so if you can prove that theorem quicker/simpler, more power to you. It's this lack of understanding that computation is, in fact, proving a theorem (about the answer), using a very limited set of rules (the "rote" way), or some more advanced ones (you're skipping steps, as a dumb teacher would say), is irrelevant. As long as your reasoning is correct, you're fine.
A successful API design takes a mixture of software design and pedagogy.
That's how I got 141, but then I am a lazy sod and don't want to waste my time doing the sum if I can spot the answer using a quick and dirty cheat like that ;-)
This is, without a doubt, the single most stupid statement that I have ever read on Slashdot, and that's saying a lot.
That's how I was with complex numbers :)
A successful API design takes a mixture of software design and pedagogy.
Math totally isn't needed in everyday life. Nobody is in debt. Nobody is getting mortgages their finances can't support. Countries aren't on the brink of going bankrupt. Yep, math definitely isn't needed.
It happened to me only once, in an elasticity exam, where the grader (a grad student in that field) would grade my answer as incorrect. I was apparently an "outsider" and didn't do it the way "they" usually did it (that's my interpretation of what transpired). The professor of course corrected the grade, he is a great teacher.
A successful API design takes a mixture of software design and pedagogy.
No, you are not the only one...and it is not wrong since it is mathematically correct
It's multiple choice, friendo. Once you realize that it's 47*3, you realize that the answer has to end in 1. There's only one answer choice that fit that requirement. Bingo bango. The other question? 29 is about a quarter less than 40. So you think, well about 72 less so about 216. Just a little under this, eh, 208 will work.
A NYC lawyer blogs. http://www.chuangblog.com/
Because they are used to prove that the schooling system prior was meeting "the whole point." A student isn't expected be making new academic discoveries at the time of the test; that was supposed to already have happened and the test is the confirmation that it happened properly. (Though a smart kid may be able to infer some new academic principles during the test in lieu of rote preparation, if they're good/cocky enough.)
"You saved 1968." - Ms. Valerie Pringle to the crew of Apollo 8
I originally read the question as (47 X 75) + 25.
Due to some quirk of the font that was used, "%" was not visually distinct from "+".
There is always room for an honest misunderstanding.
Also, (45 x 75) / 24 = 140.625
http://xkcd.com/756//
Look, schools teach stuff that we don't use in everyday life. A large majority of us don't need to use the kind of math taught in schools. We forget more of what we learned in school then the math we use in real life. Without the practice of these skills then we don't recall how to apply them on a day to day basis.
Also, testing (and school) is an artificial gauge of intelligence. In real life we are not expected to do math without the use of reference tools or materials. Our lives are not dependent on the ability to recall how to solve math problems on the spot. If I needed to use some kind of calculus or geometry to solve a problem I have all the resources of Google and the Internet at my disposal. Because I had the past experience of learning those math skills I know how to quickly look up a reference to how to reuse those skills on demand. Intelligence is not about how to regurgitate facts quickly its about knowing when and how to retrieve those facts when required and apply them to solving problems. If I should use a calculator or computer to solve a problem, am I stupid? No, because I can solve it quickly and move on with the rest of my life. It might take 10 - 15 minutes for a grade 10 student to solve a single math problem, but I can look it up and solve it in a few minutes because most likely its a very small part of the problem I am trying to solve.
If someone asks me some grade 10 math question and I can't answer it on the spot but a student currently studying those skills can answer it right away, the only dumb person in the equation is the one assuming that I am not smart because I don't readily practice the same math skills taught in school.
Also, give me a few days to study for a test and I am sure I will do as well as, if not better then a grade 10 student as I have gained maturity, discipline, and patience and will treat studying far different then an immature child who doesn't want to be in school in the first place.
I haven't thought of anything clever to put here, but then again most of you haven't either.
Well, this is how I did it:
47*75 + 25 = 23*2*75+75+25 = 23*150+100 = 2300+1150+100 = 3550
Then I looked at the choices, was a little puzzled for a while and finally realized that they used some funny sign instead of slash to denote division.
Circular slide rules FTW! IMHO it's even easier to use than a linear one. Pass 1 to the right, multiply the result by 10. Pass 1 to the left, divide by 10. Can't do that on the linear slide rule.
A successful API design takes a mixture of software design and pedagogy.
Then perhaps it's not the answers that should be graded, but the worksheets students use to arrive at their answers.
Of course, the political hot button of budgets for public education and how to fund those budgets come into play because who wants to pay for the manhours to grade worksheets as opposed to feeding a bunch of score.cards through a machine.
Yep, especially that the interest is still most of the payment so early into a 30 year old mortgage. So, there are really only two ways you can get that: either you're told (and remember!) that little tidbit, or you can quickly figure it out for yourself, and are in the habit of figuring things out, mathematically. That's why knowing the "useless theory" is so damn important. Because even if you forget stuff, you can still figure it out, or at least know how to look up the "aprtial answers" (various theorems you could have forgotten the details of, too).
A successful API design takes a mixture of software design and pedagogy.
it's not even unlikely. 29 is prime, and the total was an integer (if i remember correctly).
I got them all correct without using Google.
There was an unknown error in the submission.
I'm guessing the school board member in question hasn't used anything more complicated than basic arithmetic for a few decades now. However, I've managed to use at least most of the high school math I've learned in one form or another over the years. If I wasn't using it, I was tutoring someone, so at least most of the information was kept fresh. What I couldn't recall off the top of my head I was able to look up, study it for 30 seconds, and crank it off like I had never forgotten it.
However, if you want me to speak or read French, I won't be able to do so, even though I was at least moderately ok at it once upon a time. And don't even begin to ask me about biology or history, even though I did pretty well in those subjects back when I took them. It's possible to maintain all of that information if you want to, but it takes time, and unless you want to be a professional student or teacher, there's not much point in doing so unless you find it enjoyable, and most people don't.
-Restil
Play with my webcams and lights here
Although, you almost certainly learned the rule that multiplication and division commute - so, just another rule to apply.
/.]
On this one I actually took advantage of the fact that there were only four answers and none were "none of the above" and noticed that all I needed was a very quick estimate - and noticed that 47/25 is about equal to 50/25=2 which makes the answer slightly less than 75*2 (i.e., 150) and there was only one candidate answer so I didn't bother to compute and subtract off my rounding error.
Back in the stone age, I was never taught how to take multiple choice tests -- which was an oversight because of, if nothing else, SAT tests! Rule number one: Read The Choices First, then read the question. This often allows you to eliminate all answers except one more quickly than figuring out "the exact answer" and looking for it among the choices. Also, often, if you're in the last minute or two of the available time, you can eliminate one or two of the answers VERY quickly and just guess among the remaining ones - a good strategy depending on how right/wrong answers are scored WRT to how many choices there were. Of course, this last tip probably doesn't work so well on computer directed "no going backward or forward" tests because it probably could drive you down a "dummies" branch of questions which offer less scoring value per question so guessing could screw you beyond the raw scoring on that one question [do any "insiders" know how this sort of tests are commonly scored/directed?]
I learned to do quick estimates not in school but on the job in server software development for a MPP system. I was sometimes called in on performance problems which my group's (or occasionally my) code was being blamed for or just because I could provide insight. There were many performance metrics across a time dimension and across nodes resulting in lots of raw data. I got very good at skimming a column with 100's of numbers and coming up with a pretty good average. Several times, someone looked at me as I did this and questioned that this was possible and would cut/paste the numbers into a spreadsheet or use awk to precisely average the values and realize my answer was damned close. I could do this not because I'm smart, I could do it because I'm lazy and inadvertently developed this skill as a result.
[posted AC so I can mod idiots into oblivion on this thread should I find such an idiot -- although I doubt the school board member in question reads
the teacher should ask the pupil around their thought processes when they look at the problem - "talk me through it".
That's why you are supposed to show your work and not just put 141. If a math(s) test is multiple choice, its not a real math(s) test.
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Hippie Logger Jock
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I just took the reading and math sample tests off of the FCAT site and scored 92% in the reading and 90% in the math. I have an English bachelors degree and have been out of school for over a decade. The tests are harder than the 4th/8th grade samples, but not orders of magnitude harder. The guy is dumb, and the fact that he has seniority in a large organization doesn't surprise me all that much.
I thought I was the only person who had to derive that every time I need it. But I can't even remember 5/9 but I know that the freezing point for H2O @ STP is 32F/0C and boiling is 212F/100C so I derive from there.
This reminds me of a thing I noticed in college. At least in my experience, most text books, when presenting you with a problem to solve for practice, will chose a selection of numbers that, when solved for the answer, will produce a number that does not seem abjectly strange (nothing like 6.531943 ohms per square library of congress). That way, when you do the problem, if the answer you get is truly bizarre, you know you've made a mistake.
However, in a course I took on electricity, part of the coursework involved a workbook that was created by some students at Texas Tech if I recall, and the math problems they created for the workbook (mainly things about resistance and whatnot) always had answers that where so strange, that it made it almost impossible to tell if you had it right or not. We where allowed to use a calculator, but several times, after running the problem through the calculator, I would look at the answer produced and go 'Huh.' and then work it out the long way on paper, just to be sure the machine was not bullshitting me.
I've decided to Diversify my Holdings. I've divided my cash between my left and right pockets, instead of all in one.
Honestly, when the judge asks OJ to try on the gloves do you think he's going to just pull them on and say 'Wow! They fit!' The school board member had a pre-meditated motivation to proof that the tests are worthless- do you really think he tried? I heard this story on NPR where he was claiming that none of his 'scientist friends' use the math you find on these tests, which is so untrue as to be absurd, unless of course all of his scientist friends are 'political' scientists.
FTR I am not a fan of standardized tests but the confirmation bias in this whole story makes it nothing more than crappy journalism.
So long, and thanks for all the Phish
This guy could have passed the test if he wanted to. He failed because that helps his agenda of not wanting to give the tests. He does not want his work to be evaluated objectively.
Or, you could realize that it's multiple choice and recognize that all the other answers are beyond the bound of reason. :p No reason to get those last digits of precision if they aren't needed.
Unfortunately, the vast majority of formal exams are terrible at demonstrating good student outcomes - really the only reason that they are so common in our educational system is that they are very easy to do (at least to do poorly), and they have the illusion of being an objective measurement of student achievements.
In any case, I highly agree with the overall thrust of the article in question - it is shameful that anyone who has graduated from a modern school system would perform poorly on this type of evaluation, and worse that they would state that the skills being tested (or at least trying to be tested) have little value in the "real world" encountered by most adults.
A set of choices might be something like (of course, only the best answer gets any credit):
The process of elimination just didn't work well :(
Same here, but instead I was nearly failed for "not showing my work and cheating off other students" although I was always the first student done w/ the test.
Don't blame me, I voted for Kodos
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.
Why is it that mathematics is taught the way it is? Well, either educators underestimate the ability of students to learn mathematical theory, or it's simply easier to teach mathematical theory after students have a working knowledge of mathematics.
Your approach is actually no better than simply doing the operations in order because it does little to explain WHY it works.
Why is it you can reduce the given expression to 47 * 3? Well division is simply the same as multiplication by the reciprocal of the divisor. So (47 * 75) ÷ 25 is the same as (47 * 75) * 1/25. Multiplication is associative so now the expression is 47 * (75 * 1/25) which reduces to 47 * 3.
Now enter the hidden algebra. Though the question only lists the expression (47 * 75) ÷ 25, the implied equation is (47 * 75) ÷ 25 = x and the question is asking you to solve for x. So now we have (47 * 75) ÷ 25 = 47 * 3 = x.
Equality has properties that given a = b, then a + c = b + c and a * c = b * c. (I forget if and what the properties are formally called.) So going back to the equation...
47 * 3 = x is equivalent to 47 * 3 * 1/3 = x * 1/3 is equivalent to 47 = x/3
47 = x/3 is equivalent to 47 + 3 = x/3 + 3 is equivalent to 50 = x/3 + 3
50 = x/3 + 3 is equivalent to 50 * 3 = (x/3 + 3) * 3 is equivalent 150 = x/3 * 3 + 3 * 3 (distributive property) is equivalent to 150 = x + 9
150 = x + 9 is equivalent to 150 - 9 = x + 9 - 9 is equivalent to 141 = x.
x = 141 (because of the property if a = b, then b = a)
Where solving an algebraic equation is somewhat of an art is in the selection of terms and factors that make the equation easier to solve, e.g. adding 3 to 47 to get 50. There are rules of thumb to use to help make a selection, but it's an intuition you develop over time.
So again, your methodology does little to show you have a firm grasp on the mathematical concepts involved. What it does show is a cognitive difference in the way your brain processes numbers because there are those who have no trouble multiplying 47 and 3 right away (some think 21, carry the 2, 12 + 2 while others think 120 + 21). It gets more interesting for people who are diagnosed with synesthesia who perceive numbers as having colors, shapes, sounds, or even personalities and are able to process numbers in hard to imagine ways, at least hard to imagine to those who are not synesthetes. It would be cool if students would not only be divided by aptitude, but also by how their brains are wired, and the lesson is optimized to the way the class thinks.
Congratulations! You get a double block of "reading comprehension" instruction assigned.
I object to power without constructive purpose. --Spock
For them to be a TA and not be able to see the correct but different answer is an embarrassment to the professor.
I object to power without constructive purpose. --Spock
I never seem to see the option of rounding up to 50. My first instinct is always to split it up to 40 and 7. Like you said, I can get to the same answer in the end, but it's often the hard way. I'm not sure how to get myself out of that habit...
Is 1563649 a prime number?
There was indeed only one answer ending in 1, which also happened to be the only answer in even remotely the right range, the others were all over 1,000!
Is 1563649 a prime number?
This is, without a doubt, the single most stupid statement that I have ever read on Slashdot, and that's saying a lot.
Why? Because you don't understand the meaning of "deserves"? It doesn't mean that they are right, it just means that the student who is actually thinking is doing what they're supposed to be doing, and the student filling in random bubbles is not.
WARNING! This girl exceeds the MAXIMUM SAFE standards established by the FDA for BRATTINESS
Also, (45 x 75) / 24 = 140.625
Damn ALL the typos!
WARNING! This girl exceeds the MAXIMUM SAFE standards established by the FDA for BRATTINESS
I was a TA in an fairly big (300+ students IIRC) required "intro to programming" class for engineers (this was back when we coded on 80 column wide stone tablets and very few students entering the program had ever written a program). For the midterms and final, it wasn't practical to do anything but multiple choice tests. We went to a lot of effort to build these tests. All the TAs and the professor submitted questions and then we all met for a few hours to winnow and refine them - particularly introducing good "plausible distractor" answers. Every test was "from scratch" because there were too many ways for students to get their hands on prior semesters' tests and, by having a different set of TAs every semester, the tests ended up with differing flavors each semester.
The Scantron cards were tallied and the professor ran a variety of statistical tests on the results. We then met to discuss the results.
In particular, we studied questions where one particular wrong answer was selected "too often" by students who had done very well on the rest of the questions -- especially where "ordinary" students hadn't picked this wrong answer as often. We looked very carefully at the particular wrong answer and tried to figure out why it was popular among smart students. Often, we discovered there was some possible ambiguity in the question or the "correct" answer and would eliminate the question. We were pretty willing to discard a question in this category if we could find a sniff of ambiguity leading to the popular wrong answer.
We also looked carefully at questions where, overall, a particular wrong answer was picked often. Usually this wrong answer was, in fact, a plausible distractor but occasionally we decided that there was something that was slightly ambiguous and would drop the question.
Then the tests were "rescored" without the discarded questions (usually around 5% IIRC) we eliminated.
This worked pretty well at eliminating arguments about ambiguous questions while still having fresh tests every time.
i looked at the real fcat, and while i think the test would have been pretty difficult for my 10th grade self, the idea that an "educated" person could not correctly answer any of the questions except by guessing is wildly implausible. i strongly suspect that mr. roach wasn't taking the test seriously, and if instead the circumstances were that his career was on the line, he would have scored far better.
as to the question of the politics of standardized tests, while i don't believe that school funding should be tied to standardized test results to the exclusion of all else, i don't think it's unreasonable to expect more of our children than was expected of us. remember that we are living in a world of increasing globalization, and our children face more competition from the rest of the world than we or our parents did. so, our power over the question of how much and what kind of education is "good enough" will be diminished in the face of globalization. further, if we get the answer wrong, the ability to legislate money to a program will also diminish as the money finds a home in another, more competitive nation.
First of all, I replied to a comment wondering about other people's calculation strategies, so I provided mine. Secondly, "I like doing problems like this in my head as I feel that it helps practise my short term memory". Thirdly, :), I haven't attended american school so I am not used to multiple choice.
The 'guestimation' strategy fails at question 5 that has two answers that are very close to each other ($203.00 and $208.80). However, my mathematical instincts tell me that 203.00 is an unlikely outcome when multiplying with 29. I used a calculator to confirm my guess (as allowed by the test).
Rely on your instincts not your calculator; there's actually a catch there. It's probably designed specifically for students who stop division at the decimal point . . . or engineers who miss setting the scale with bc!
$ bc -q
288/40*29
203 - hey that is one of the four possible answers!
scale=5
288/40*29
208.80000 - but not the *right* answer....
Tell you what, find a good pack of lead-weighted slide rules and we can go over to this education board and educate them on the value of knowing how to do sums.
Your method of solving it was good - and a method I've seen used by a lot of older people -- and computer programmers*. The alternative is to remember that a series of multiples and divides can be done in any order, so (47*75)%25=47*(75%25)=47*3
*Yes, using left/right shifts and add/subtracts, which is all you were doing, is not only very fast in the human brain but it's also very fast on a computer. Much more so than general multiplication/division.
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
Indeed. I have a bachelor of science degree in CS and It took me about a minute to answer all of those sample questions correctly, no calculator required. How can this guy have a bachelor of science degree and two masters degrees and yet be unable to answer even elementary math problems correctly? Perhaps he is yet another example of an increasing number of "students" who either cheated their way through school or received their degrees from for profit diploma mills or both. You know the type. They often received credit for "life experience" and other such BS. By the way that would be bull shit, not bachelor of science, although at some schools they're apparently not so dissimilar. This is what happens when we send everyone to college, it makes a mockery of what used to be a substantial achievement: a university degree.
30/40 = 3/4
Calculate that in your head using guesstimation and subtract the hourly rate. The rest is obvious and left as an exercise for the reader.
1 / .75 ^ 60 = 30 million to 1 against
A quick peak at the American age pyramid suggests that each teenage year represents about 2% of the American population, or about 6 million students at each teenage grade level.
If 1% play the game of zero-knowledge monkeys, you'll average about one student every 500 years achieving an unmotivated zero.
Far easier to achieve a zero if you have some knowledge, but installed the battery in reverse, or if you have a lot of knowledge and installed the battery in perverse.
The example grade 10 test I viewed was not exclusively multiple choice.
So you figured out what was going on and you didn't help your friend out?
Some friend you are...
I used to read Caltizzle. I was a lot cooler than you.
288 * 29 / 40 is 208.8, or in this case $208.80.
very good point (about the glasses). A close friend of mine who is/was training to be a fighter pilot thought all he was doing on a test was answering questions but in fact the test served two purposes, (the obvious one) and was also used to diagnose dyslexia (and who knows what else). So in his case they found out he had undiagnosed dyslexia and consequently will not be flying certain aircraft etc.
Pay teachers well and make sure their job description doesn't include "must have experience with taming wild animals" and you'll get better teachers and hence better education.
Not with pricks like this in charge of your school board you won't.
I think the trick is just practice - I tend to look at the first two digits. If the second digit is 0-3 I round down and add (23 becomes 20+3), if it's 4-6 I go for the nearest 5 (44 becomes 45-1) and 7-9 (87 becomes 90-3) I go above and subtract. One way to break the habit might be to try always going above and subtracting for a while and try to get used to it. You'll find 8s and 9s easy enough, but 2-3s harder so maybe your brain will learn the path of least resistance ;)
Or the answers were separated by order of magnitudes. Solving 50*3 is close enough to 47*3 to get you the correct order of magnitude.
I got them all right and I'm a bit older. I've been indulging my extreme nerd side lately and going through the whole Khan Academy exercise set:
http://www.khanacademy.org/exercisedashboard?k
It's more productive than playing video games but takes less motivation than programming.
When I got bad grades it was because I missed a class or wasn't paying attention to some important concept and was unable to figure out what it was, or I thought I found the correct concept until the exam where it was marked wrong.
100 x 75 is 7500, so the answer is about 3500/25, or 35x4 or about 100
looking at the possible anwers, only one or two (I forget) are close
you sir, the physicist, are an idiot
And hate to admit dropped out of college 10 years ago, I didn't miss a single one of the "practice questions" nor did I find them difficult. If the people "running" our day to day lives can't do these, I'm scared...
I'm teaching at the moment. One of my biggest struggles is setting an exam. I know my students pretty well. I know what questions they will get right and what questions they will get wrong. Why would I put questions on an exam that I know they will get wrong? I am instructed to set my exams so that there is a nice bell curve with the average at a certain place. That way they can sort the "good" students from the "bad" students. But, if the students can't answer a question I've taught them, isn't that my failure? And if I haven't taught them, what is the point?
So I set the level of the material to match my students abilities. I teach them the material and I make sure they know it for the exam. My expectation is that they will get 100%. Not all of them do, for a variety of reasons and it pisses me off. So I try to find what the problem is and fix it. Anything else seems like a betrayal.
But apart from verifying my understanding of their level (which I already need to do in class), I don't see the point of an exam -- especially one where the students are *expected* to answer the questions wrong.
That is how I did it.
Alternatively you can also stop at 50*3=150 and realize the answer must be less than 150 and only one answer was available.
I am going to be a little blunt here. Past a certain ability level of the testee, multiple choice does not test whatever the test creator intended, and instead is a contest between the test creator and the testee to see if the test creator can actually make you do the problem the test intended you to do. I usually win that game.
Laziness is the mother of invention
I give you the microwave oven and the TV dinner. And, I am sure many can name more.
Do not underestimate the power of the truly lazy.
A school board member who is fighting tooth and nail against standardized testing as a means of evaluating the quality of staff and schools fails the standardized test and holds that up as proof said test is invalid. Color me not surprised.
I took a statistics and probability course. All exams were multiple choice. Also, "none of the above" was a choice on every single question. I think it was a cruel joke. No marks for showing your work, and if you messed up one thing, you always go "none of the above". Add to this the fact that the professor constantly (almost ever class) started out by explaining the wrong way to solve the problem, and then correcting herself half way though the question, meant that quite a few people did quite bad in that class.
Anthropic principle: We see the universe the way it is because if it were different we would not be here to see it.
I had a firm grasp of the concepts involved? I think I was mainly just musing on how we all read the same question, write the same answer, but handle the processing in a completely different way.
I'm fine with (basic) algebra - but it's always something I'd write down. I've never, for example, mentally drawn and solved an equation in my head.
Even when I'm solving these on paper, there's still a visual element. I know that x=1 is the same as 3x=3 - but I'm still imaging a pair of objects, one on each side of a line, that were the same size and have now both got 3 times larger.
Just drilling down into this thought, I can't imagine '3' as a complete abstract. I can imagine the character or more usually it's 3 'things' - the things aren't specific, but there's definitely 3 of them. When I go from 3x=3 -> x=1, I'm separating the group of 3 things into 3 separate groups of 1 thing, or just imagining a thing of size 3, shinking down to 1/3 of its size.
I'm intrigued as to what happens inside your skull when you do the same. Does your 3 exist as a complete abstract?
I'm not for one moment suggesting that my process is 'good', it's not and scales horrifically - but it's how at the lowest level my mind copes.
Incidentally, it's not just maths. If I think of 'fast', if whilst not picturing something, I feel something moving 'fast'.
I further wonder if people can be taught to change - if somebody explained to me a better '3', would that have helped me?
Finally - I notice I seem to be obsessing on '3' - some people might have just been more general 'integer' or just 'number' - but even to write this post I needed an actual example I could visualize before I could talk about it.
(Incidentally, 3 this evening were 3 little Go stones (black ones - I have no idea why)).
Why is maths difficult for US students. Reason 1: The teachers have not understood the concepts and just write them on the board – just copying form the text book. Reason 2: They never understood that mathematics is about pattern recognition and pattern matching – from simple to complex. Reason 3: Deductive logic is used when teaching arithmetics and algebra. Inductive reasoning – hypothesis testing is used in spacial dimensions – geometry. Reason 4: Homogeneous discrete quantities can be added and multiplication is a short hand notation for successive addition, exponentiation is short-hand for self multiplication, factorial is short-hand for successive decreasing multiplication etc., so that complex relationships could be broken down to simple relationships – using divide and conquer approach and so on. Reason 5: Continuous quantities are subject to measurement errors, thus to reduce the error integration, differentiation etc., are used. Examples of continuous quantities involve flow of water, electricity, wind and motion etc. Reason 6: Mathematics allows to create a simpler model whose parts have either discrete or continuous quantification, thus the methods to solve them. Incrementally these models are improved until almost as close model as reality could allows. Reason 7: Mathematics is a language – very precise with a single meaning, thus learning the rules of the grammar of mathematics allows us to “think or visualize in space” approximated mathematical models. Have you ever seen any one teaching like that? Only a very few lucky mathematic teachers can make you understand these concepts. US has lost it's edge excepting producing most incompetent work force.
I simply observed that the answer had to be an integer multiple of 9 (in cents). So the answer had to be $208.80.
"Guesstimation" works in q5 easily enough.
288 / 4 = 72 (dividing 28 by 4 and 8 by 4 are trivial in your head tasks), so $7.20 per hour.
9 times 0.20 is 1.80, so our answer must end in 80 cents.
If course 72 + 72 + 72 - 7.20 is just as simple to just do.
None of those questions needed a calculator. I could understand a 4th grader making some mistakes by being careless or misunderstanding something, but for an adult to get them all wrong you'd have to be well into mentally disabled territory.
The point of grades is to have the stakeholders in a child's education informed of the child's progress so corrections to the child's behavior the the instruction can be made. Pre-federal funding of state education, the primary stakeholders were parents and local school teachers/administrators (Children are NOT the primary stakeholders. They are not independent of their parents and the parent's wishes re: education are primary unless and until the children come of age or are legally emancipated). Now that the Federal government provides a good chunk of money to the States that is used for education, the Federal government has become a stakeholder. Grades are a relatively standard way for parents and other stakeholders to assess a child's performance. As a parent, I would not give up my right as the primary stakeholder in my child's education to teachers or some level of government. Schools that don't use grades in their assessment AND share them with parents are short changing the involvement of the primary stakeholder (even over the child) in the child's education.
I frankly was a little baffled at (47 x 75) Ã 25, and stared at it for five minutes to make sure I wasn't missing something. I thought for a second it perhaps meant divided by 0.25, which is a good way to trip people up (Although not with a calculator)...but, no.
I mean, seriously. A useful test is the ability to do that with a piece of paper. People who can't do it with a calculator, which is done by literally punching it in exactly as shown (And it doesn't even need the parens!) need to have their high school diploma revoked or something.
And, yeah, I worked it that way in my head also. And then checked with a calculator, just in case.
The only question I missed was the flipping triangle thing, and that's probably because I've literally done no geometry in over a decade and couldn't remember what the heck a 'vertex' was. If they'd said 'angle' I would have figured it out, but I thought maybe the vertex was the point it flipped around.
If corporations are people, aren't stockholders guilty of slavery?
That is, in fact, the opposite of cheating.
If corporations are people, aren't stockholders guilty of slavery?
Well, I just did (47 * 75) : 25 = 47 * 3 = something that will end with a 1. So only 141 would be a valid option. No need to complete the calculation. Besides the point that 47 * 3, will also certainly never be above 1000 if you make an estimate, which also only leaves 141 as the only option.
As the board member took tests of 10th grade instead of 4th or 8th grade, it might be more helpful to look at the relevant website instead:
http://www.dpi.state.nc.us/accountability/policies/naep/naep
Here are sample questions of the 12th grade. Only 3 though: economics, science and reading. I'm the CEO of the second company I founded (after selling the first one to a NASDAQ listed corp), I drive a Porsche and a Volvo suv and have 3 houses. I'm considered to be (highly) intelligent. So I'm considered successful by most standards. And I'm happy too, btw :)
Yet I failed 2 out of 3: got the geology question right; and ok, I could have known the economics one but wasn't sure...
My conclusion: these questions are more like 'jeopardy!' than anything else. There must be something broken after the 8th grade test level. Most probably because that's about the level of intelligence where the test makers from the sixties where at, back then.
Tests are silly in any case: trying to fit into a one dimensional number the entire complexity of intelligence is plainly stupid.
I did neither the step 2 (except the rewriting part) nor 3.
I figured it is 47*3 and all the options except the first are larger than 1000! And 47*3 can't be > 1000.
Yeah, it takes a second or two more, If I do the multiplication. But knowing it from looking makes it easy.
At the same time, the 5th problem needed working on it (math).
The options had 208.80 and 203 in them, and they are close enough that a guesstimate could get it wrong.
For the first example, I did it in a similar manner : 47 is close to 50, and 75 is 3/4 of 100. 50 times 100 is 5000, three quarters of 5000 is 3750 (trivial because 4*1000+4*250 = 4000+1000), and since your dividing by more than 4, it can't be anything but the smallest answer. It's not as elegant, but if I'd re-written it in proper notation (with the divisor underneath), I'd have done it like you did. Again, how a question is written changes how you answer it.
I'm still flummoxed at how the person in the article has a friend who has two Master's degrees, is going towards a doctorate, and can't do basic maths like this... with a calculator.
"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". "
This is actually -partly- how it is done in France. During mandatory education, there are no standardized tests with multiple choice answers, and calculators were (I don't know if it's still the case) generally not allowed. Most tests consisted of 10 to 20 questions, of which a quarter or a third were obvious direct applications of what had been learnt "(47*75)/25=?", then most of the remaining part of the test involved putting these numbers in situation "Jane has 47 cows..." where the student had to determine what signs to use, as well as what information provided was relevant to solving the question. The last part of the test would be slightly more complex, asking students to build upon what they know and show understanding of more general rules "Jane wishes to know how many cows she should sell in order to make the most money...".
Each questions is not to be answered merely by a number, but the method of solving should be provided to the corrector/teacher. This can involve writing what the student is doing in mathematical notation or in plain writing. Part of the "credit" is for showing understanding of the method, although this is often only the case for the intermediary and advanced questions, whilst the basic questions are boolean right/wrong. This means that the teacher can point out where in the reasoning the student made a mistake, and judge if it was inattention or a mistake in understanding the question rather than in the actual mathematical process (i.e. a student who at one point mis-copies a 8 as a 9 can still be awarded full credit if the method used is correct, and had the copying error not occured, the correct answer provided).
However, I don't know if this has increased mathematical literacy in French youth compared to other countries.
I wasn't aware of it at the time and anyway I doubt he had the exact same issue. Maybe if we'd had free periods at the same times, or been BFF's or whatever, we might have been doing homework together or something, but that's not how it turned out.
That is exactly the I too work with numbers. Round of to the nearest multiple of 5 or 10, do the math and then do the fixing for the round up, or some times break it up, do the calculation and then add up again for example 47 = 40 + 7, multiplying them by 3 means 120 + 21 and so on. I teach my children too to do their math this way.
There's a very old book published by Dover Press "How to calculate quickly" that is a whole book of methods like this.
Third Career: Tree Farmer Second Career: Computer Geek First Career: Teacher, Outdoor Instructor, Photographer.
In math, you might not always be interested in testing that someone can calculate the right answer. Maybe you actually are interested in seeing if someone can spot that the other answers are all order-of-magnitude wrong.
An occasional question like that, which you *can* short-circuit (although, some students may still calculate it if they haven't learned basic algebraic rules, and approximation, well enough), is actually a good thing, in my book.
I think kids *should* learn to be able to learn how to do things quickly using approximation and order-of-magnitude analysis.
And if it didn't say "you can use a calculator", I probably would have done that. (Back "in the old days" when calculators were only used for trig and log and actual *difficult* maths, I certainly would have).
But in a test situation, if you're going to say "yes, you may use this device which will just *give* you the answer assuming you have basic data entry skills", I'm bloody going to turn off the brain and punch the numbers in. Remember, there's no "show your work" half marks here anymore, just right/wrong. Oh, and there's a time limit.
I wonder if the questions are anything like the questions asked at the sample test. If they are, I must ask this: Seriously? He couldn't get 1 right? Really? And America is supposed to be a world power?
...and that's why multiple choice tests are bad.
I hope it doesn't make your math teacher pull her hair out. If so, she isn't very good at algebra (or recognizing where simple algebraic manipulation is applicable).
SIGSEGV caught, terminating
wait... not that kind of sig.
And people wonder why we're losing the innovation race to China - this whole idea that people can become rich just by coming up with a great idea and without knowing anything about the science and math necessary to make that idea a reality is such a crock. How many people have "invented" the brilliant idea of a flying car? The fact that this clown managed to become an executive with so little evidence of any real skills aside from possibly schmoozing is just sad.
Reminds me that just last week (during scrum planning) when a small double digit integer multiplication came up, the project manager and I (both C.S. majors) each made the calculation in head agreeing down to the digit - a second later the business developer using the windows calculator, stated his answer which was off by 3 somehow. Scrum master calmly noted that 2 heads beat 1 calculator, and noone needed to confirm that.
Run with the lemmings, and you'll get your feet wet.
3 years of business school, would allow you to get it wrong as well - but I guess some might consider it the same thing.
Run with the lemmings, and you'll get your feet wet.
There's dozens of ways to solve the problem (47*75)/25. Breaking it up as a parent poster said 47*3 = (50-3)*3 = 150 - 9 is perfectly acceptable, just remember why it works. Personally I solved it as (40+7)*3 = 120 + 21, but you can break it up however you want.
I'll first say, if the entire test was like what was given by the article, then the entire test is horrible. I'm a graduate teaching assistant that teaches the very basic College Algebra and I have to say that multiple choice problems are horrible ways to test how a student is doing in mathematics. Honestly, when we test students, it's a lot less about the arithmetic (47*75 / 25) and more about the concepts and how to apply the concepts correctly. Generally we choose very small numbers or convenient numbers that won't require a calculator. Multiple choice is a poor way to test if someone understands the subject, because you're not subjecting them to come up with the answer on their own (which is more realistic if you want to test for real life application). When I took the few test questions they offered, I didn't have to make any calculations, I only had to make estimates and then I could guess them correctly. That's good, if all I need to do was have a ballpark figure, but to be accurate I would need to be tested on being able to come up with exact answer without being hinted at what the solution is.
I thought "47 times 3 should be something close to 150. Definitely not 1175, 3525 or 4700."
Being smart is better than being good at numbers.
Of course, you can be both.
My high school math teacher required us to show all our work in homework and on tests. Then he meticulously examined the work of every student on every problem. Get a sign wrong? Circle it and dock 1 point. Then keep working through with the mistake to see if the student did the rest of the solution correctly. In a class of 30 students, if there were 15 different answers to one of his questions, he would have worked every one through and noted for each student where they went wrong. Also, on a 20 question test, you didn't lose 5% for getting one wrong. You might lose only 1%, depending on how many and what type of mistakes you made.
That took kids who would have been 75% students with a C, and made them 86% students with a B+, a lot of confidence, and an explanation of exactly what they had done wrong. Instead of despairing about math and sinking into Cs and Ds, they built confidence and became A/B math students. And they were always eager to dig apart their own failures to see how to do better next time.
I had one college professor like that. He was willing to let you take a failure apart and see where it went wrong. My final exam went from an F to an A when I showed him the one liner that sank me, and how to fix it.
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.
I had the exact same thought process as you.
That is the same thing that happened to me. In eighth grade we started algebra. The teacher taught that you move a term to the other side of the equal sign and magically plus becomes minus and multiplication become division. ??? I was lost. For two years I struggled until someone showed me that you subtracted, divided, etc the term on both sides of the equation and that's how it disappeared from one side and changed function on the other side of the equal sign. I guess I was so frustrated with the procedure that I never noticed the mechanics of the operation. Suddenly algebra was fun and soon became my favorite subject. One bad teacher caused me to struggle for two years. I later taught at the University of Abidjan while I was a Peace Corps Volunteer and I always made it a practice to make sure my students understood the mechanics of what they were doing in my class.
Since when is "public safety" the root password to the Constitution?
The article was just a screed against standardized testing. Yes, using student testing outcomes has problems. It's a far more accurate way to determine teacher ability than any other method the teacher unions will accept though. It's really sad when you see someone decrying the concept of merit pay as a concept who expects to be paid more for having a masters degree.
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Yes I got them all right but really? This is 10th grade math? I sure hope not, these were more like 7th grade questions or even 6th.
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It's not "bonus material" for my 3rd graders, it's taught directly in the curriculum. They call it "estimating", and they started doing it with addition instead of multiplication, but it's the exact same concept.
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Bingo. I did the simplification to get 3 * 47, then looked in the ones place for likely results.
This is a sad commentary on our school system and proof that you really don't get what you pay for in the public education business. I'm wondering if the school board member can spell without using spell-check.
You're right - I was speaking about professionally constructed testing, which is all field tested, etc. Without that, you're certainly right that you can't be confident that you're measuring what you think you are. For instructor constructed tests, they usually try to do something along the lines of what I described, for the same reasons, but without the rigor.
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In fact, you cannot. You can get selected questions from the 4th, 8th, and 12th grade tests for a several years. The 10th grade questions are not on there. I tried some of the "HARD" 12th grade questions... I can see getting some of those wrong, even forgetting most of what you need to solve them, but 100% guessing on all levels? That's either incompetence or laziness masquerading as incompetence.
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I'm 31 and wad taught in Scottish then English schools and the way you describe working out the problem reducing to simplest numbers then estimation and rounding the kids being asked to do this paper should defiantly have been taught this technique from an early age. Oh and maths papers particularly at gcse or A-level were looking and awarding marks (most of them) for the working out par. Very little marks for the answer, something often criticised. Like the idea of lots of methods but given that that's made it in to canoe and kayak coaching I would think teachers have been exposed to it.
You're not very good at math. 1175 is about 8.3x more than 141, while 3525 is just three times 1175. More approximately (and more immediately, which is the point), the first answer is in the hundreds and the rest are in the thousands. It's easy to narrow down which of those the answer will be without resorting to calculation (much less a calculator).
But more importantly, you're not very good at tests. These answers weren't selected at random. They were selected by a human. Why were these particular numbers chosen? Reverse engineer that and you can get good odds on any multiple choice test, even if you know very little about the nominal subject.
My math teachers in schools were horrible, mostly. I had school in Maryland & Florida, USA. I moved from Maryland to Florida and started 4th grade without being taught fractions in the 3rd & the teacher wouldn't explain to me how to reduce a fraction with lowest common denominators. I was told in no uncertain terms that because I wasn't taught that in the 3rd grade, I would be failed and repeat the year and be taught then.
I was scarred by that, since it stayed in my records and every teacher since has treated me like a retard. I did algebraic & trig style equations at home for engine designs & metallurgy in my high school years, and I learned everything out of books. School has and always will be a waste of time for those that are ambitious, IMHO.
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I was in the math club in HS, and I took "number sense" tests where you're not permitted to use a calculator or write anything other than the answer (no scratch paper either), everything must be done in your head. Shortcuts such as the one you described are exactly how we worked out such problems. Number sense tests are also timed, so you have to do it in your head very quickly and accurately (all answers must be given accurate to 3 decimal places if decimals are necessary). There are many such shortcuts, and they're extremely handy in everyday life, much more so than formal, long-hand operations.
make imaginary.friends COUNT=100 VISIBLE=false
In the UK we had 12 pence in the old shilling up until early 197? - I dunno, before my time.
If you're still using inches&feet, then there's another reason to include 12x
The failure to switch over to a full metric system, imho, indicates that eejits are in charge of the place.