Are You Better At Math Than a 4th (or 10th) Grader? 845
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.
RTFA - really, it's interesting! (Score:5, Interesting)
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?
Or you never visualized them in the first place. (Score:5, Interesting)
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).
Re:Meh ... (Score:4, Interesting)
I have less problems with the creationists and theocrats: I don't want them running the country, but at least they don't even pretend to have science on their side. Much worse are people who try to use tidbits of science to push political agendas without having the slightest idea of what they are talking about.
Re:This is dangerous... (Score:4, Interesting)
Exactly. I rarely see the answers presorted for me into four possibilities of which I know one must be correct.
Re:Or you never visualized them in the first place (Score:5, Interesting)
oops, left off the bit I clicked reply for. (Score:4, Interesting)
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.
Re:Or you never visualized them in the first place (Score:4, Interesting)
Re:No inteligent information to draw conclusions. (Score:5, Interesting)
Actually that was one of his complaints: it's almost impossible for any responsible adult to see or evaluate the tests. He had to pull strings to be allowed to take it, and he's a school board member.
I don't know whether he's right about the contents of the test, but he's absolutely correct that that degree of secrecy is not healthy - especially when students are being denied diplomas based on the test.
Re:Or you never visualized them in the first place (Score:5, Interesting)
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 [alfiekohn.org]
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. ....
Re:Summary is a little misleading (Score:5, Interesting)
Re:Or you never visualized them in the first place (Score:5, Interesting)
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.
Second point (Score:5, Interesting)
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.
Re:Or you never visualized them in the first place (Score:3, Interesting)
"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. :-)