In the last few years I’ve taken a variety of online aptitude tests, more for amusement than anything else, and I’ve been puzzled by the results. While I tend to score high in all of the various categories, I consistently score highest in mathematical aptitude. For example, on one recent test I scored in the “100th percentile” in “quantitative ability”, which this test defined as “an ability to solve numerical problems easily”. This score is fairly consistent with scores I’ve achieved on professionally administered aptitude tests, such as those administered by the local college’s admissions department. Indeed, I find that I can quickly solve a lot of practical math problems in my head. I don’t know how I do it - I just do.
But back when I was in school, I completely sucked at math. I dreaded math. I hated math. I finished high school with the absolute minimum math classes required to graduate, and rarely got better than a C grade in those classes. Part of the reason for those grades had to do with not completing homework assignments - I’d get frustrated and give up.
I don’t understand this at all. According to all these aptitude tests, I should have been a math whiz in school. Why wasn’t I? The only explanation I can come up with is that the methods for teaching math when I was in school (1972-1984) were an extremely poor fit for the way my brain learned new things. I can clearly remember listening to teachers explain mathematical concepts over and over, and reading it over and over in the textbooks, and just not getting it. And that’s the puzzle. If I have such high aptitude for math, why the heck could I never grasp what my teachers were teaching?
Conversely, I always performed well in reading and writing — “English” classes. I get higher-than-average scores in that area on the aptitude tests that test it, but not nearly as high as I score in math aptitude.
Well, for one thing, you’re comparing your current performance with your past performance.
Edit: I look back a questions I asked in middle school science and math, and they are reasonable questions. They were answered poorly, or not at all. It wasn’t until after college that I was able to get some of them answered, and it turns out that the answer isn’t “they don’t know” or “it doesn’t matter.” So yeah, teaching plays a role in it, too.
I’ve done a lot of math, and tutored a lot of math.
I’ve found mathematical ability may be easily hidden by hostility to math resulting from either poor instruction, negative experiences, or- most commonly in my experience- from incomplete instruction that is out-of-context.
So, when did you become hostile to math as a child? Something not explained well? Your teacher taught you something incorrect and you rejected the subject instead of rejecting their incorrect insistence (many elementary school teachers were not, shall we say, the top of their math class)?
I had to take a written exam last year to demonstrate analytical ability, and that test involved a LOT of math. I did very well on it, which surprised me since I was not known for my outstanding mathematical ability.
I think that a large part of the problem (at least for me) is that math is taught in the abstract, and students don’t understand why what they’re learning is important. For example, I don’t need to add up parts in a circle that doesn’t represent anything. I do need to add fractions (which, after all, are parts of a circle) if I’m cooking and I need to scale a recipe up or down.
As we get older, we see how these concepts apply to the real world. We understand how grids can be used to read a map. We know that systems of equations are great for figuring out how many of x were sold and how many of y were sold when the till has z dollars. That stuff was hard for me until someone put it into terms that made sense to me.
“Math” on an aptitude test or in your head is often just simple arithmetic and basic algebra on the order of “solve for x given x = 12a + 7b, a= 9, & b = 2.5.”
Being fluent at that is a very different thing from understanding “math” taught as concepts, or from being able to reason in mathematical terms, create simple proofs, understand basc trig, etc.
IOW, the tests aren’t testing what you weren’t good at. They’re testing something much lower level, which you were/are good at.
The tests and the specific math you took may be different parts of math. Being good at mental arithmethic doesn’t make you good at calculus, trig or algebra.
In math exams, often you need to show your process. There’s geometry problems I can solve through geometric reasoning but don’t ask me to do it through differential equations, my brain just doesn’t see the point.
Sometimes the same exam will get graded differently by different teachers.
I had one math teacher who counted “how many” errors you had and “how serious”; another one who counted “how many right lines.”
A problem where you copied a sign wrong from the previous line in the second line would get, say 8/10 from the first teacher and 1/10 from the second. A problem where you made the same exact mistake in the very last line, 8/10 and 9/10.
Which brings us to, it isn’t just the subject matter, but how it’s taught, graded, whether you had any reinforcement you needed, etc. I’m 39yo, studied Set Theory every single year from 6th to 11th grade, plus again in my first year of college - but it wasn’t until last year here at the Dope that someone’s explanations made me understand what it was about! (basically it was taught upside-down)
Good answers here. My WAG is that it’s all of the above, or at least some of the above:
An antipathy or hatred of math as a youngster (it was very cool when I was growing up to hate math; girls were told outright either that math was hard for girls or that we’d be good at algebra or geometry, but not both) and you’ve gotten over that since it’s not been in your face all the time.
It’s not an “aptitude” test once you’ve learned the material. Aptitude tests work by asking you some questions that a) people below your supposed level must know, b) some that people at your supposed level should know, and c) some that people at your supposed level probably don’t know. If you get all of a) right, but none of b) or c), then you’re “below” your supposed level. If you get a) and b) right, you’re “at” level and if you get a), b) and most of c) right, you’re “above” level. (This is all incredibly simplified, but it should suffice for these purposes.) But right now, you’re not supposed to be at any level - the aptitude test is useless. To get a meaningful result, you’d have to take a second one, based on the results of the first one - we have to find your “level” before we can test whether you have the capability to achieve further than it. If you’re taking an aptitude test for 5th graders as an adult, it won’t tell you anything useful.
Lots of online aptitude and IQ tests are totally bogus. They are easier than their school based counterparts, so that you feel good about yourself and sign up for more emails and quizzes from the website. Sad, but true; I probably don’t have the 180 IQ that the online IQ test would have me believe. (My IQ is high, but not THAT high!)
Even if it’s not bogus, it’s a lot different to sit relaxed at your computer and take a test no one but you cares about than it is to sit in a strange room on an uncomfortable seat and take a test which might determine the course of future events. I’d expect you to do a lot better with a home test than a standardized test.
Except that, as I [sort of] stated, my test results have been fairly consistent regardless of when I took the test. I’m almost 42 now, but I got similar results on tests at age 19, fresh out of high school. The highest-level math class I took in high school was “Algebra I” (first-year algebra), which was the minimum I could get away with and still graduate.
If I had to pin it down, I would say 5th grade (10-11 years old). I utterly despised my 5th grade teacher (looking back, I have to say she was an abusive bitch who hated children - I’ll explain if anybody’s interested), and frankly don’t remember learning anything from her. I remember she read “The Hobbit” aloud to us, but that’s about it.
All I can recall of her math “instruction” was a shelf full of boxes that contained large cards with math problems on them. We were supposed to progress through these cards by solving the problems, and once we had correctly solved all the problems on a card we would then progress to the next card. As best as I can remember, it was some sort of self-instruction. The first batch of cards reviewed what we had supposedly learned in 4th grade, and then progressed from there. I honestly do not remember getting any in-class math instruction from this teacher, unless my subconscious has blocked it out. I can remember these cards getting into long division, which was utterly unfamiliar to me. Apparently my 4th grade teacher hadn’t covered it in-depth. I recall a classmate trying to show me how to do it, but I just didn’t get it. I think that’s when I simply gave up on math. It wasn’t until 8th or 9th grade that I finally grasped long division.
My 6th grade teacher wasn’t much better.
This makes a lot of sense. At some point in adulthood, I realized that most of what I was doing in my head was algebra, even though I would be hopelessly lost if you asked me to express what’d I’d done as a written formula or equation. And that, I think, is why I struggled so much with it in school. As long as the problems involved actual numbers, I could often look at it and see the answer. But math teachers always had this irritating little requirement to “show your work”, and I unfortunately could not demonstrate how I arrived at the correct answer.
On the other side of the “abstract vs. practical” issue is higher education. I’ve made three separate, but short-lived and unsuccessful attempts at “college” - once at a state university at age 18 (lasted one semester) and twice at the local community college, at age 23 (lasted two quarters) and again at age 31(one quarter). Conversely, at age 20 I enrolled in a vocational (business) school, where I was twice elected to the student council (something I never even considered in high school) and ultimately graduated on the Dean’s List with a 3.7 GPA (compare that to my 2.95 high school GPA). What that tells me is that I have no patience for sitting around talking about things — I need to be, and learn best by doing things. My experience in the 2+ decades since bears this out.
But … but … I’m a BOY!
As far as the online IQ test I took, the site made it clear that their percentile rankings were done in comparison with everybody else who had taken the same test (in that case, more than 5 million people had taken the test). Their overall results showed the same bell curve as any similar test, and regardless of whether it was “easier” or not, I still scored in the 96th percentile of people who took the same test. And for what it’s worth, the online test takers are a self-selecting group, so will already be smarter on average than the general population - I doubt there are many genuine morons, imbeciles, and idiots deciding on their own to take an online IQ test. Regardless, my score on that test at age 40 was only 14 points higher than the score I achieved on a professionally-administered test taken at age 11 or 12 - a difference that is satisfactorily explained by improved reasoning ability and experience.
Similarly, my online aptitude test results are consistent with my professionally-administered test results. And for the purpose of comparing my own aptitude in one area to my own aptitude in another area, the actual score isn’t that important - it’s the difference in scores between one area and another that are important.
Riiiiight. They’re better today, but when I was a kid, they really were those stupid, “At 10:00 AM, Train A leaves Cleveland traveling southwest at 65 MPH and at 10:30 Train B leaves St. Louis heading northeast at 73 MPH. What time should the plucky reporter and her crew be on the scene to film the firey rubble of their collision in Plainfield?”
Or something like that. I’m a girl, so I was always bad at math.
You were bored in school because the material was too easy.
Just because you’re good at something doesn’t mean you have to like it.
Those two points logical conclusion is that you didn’t like it, you were bored with it, so you didn’t do your homework, and didn’t pass.
While working on my undergrad, I didn’t really see the point in doing upteen math problems every night, so I didn’t do them. Especially if they didn’t directly relate to something tangible. My math GPA in college was a 1.8, while my engineering GPA was closer to 3.8 or 3.9. Go figure.
Those were my favorite kinds of problem! I could do those in my head, and was never given credit because I didn’t show my work. Lame. I think Robyn’s point is extremely valid, at least in my case.
That is almost a full standard deviation–not by any means satisfactorily explained by any change in age. IQ tests are normed to fall in line with others in your age rangeand IQ scores past age six don’t change much (cite). I think a more likely explanation is someone is trying to sell you something and they’re more likely to succeed if they can get you to buy a package specially detailing just how smart you are.
You’re also guilty of claiming the two tests are separate by pointing out the two scores were scaled to their own participants but trying to prop up the online test by pointing out its reliability in terms of how your IQ “jumped” 14 points–jumped from where? I thought they were separate.
IMHO, all of that talk about how honest the test makers are is you trying to justify accepting the validity of a non-scientific test over an empirically tested scientific one because the online test re-affirms your positive self image.
I want to emphasize that I don’t think you’re unintelligent or less intelligent than me in any way. I don’t know you well enough to make that call and it would be pretty rude of me to insinuate other wise. My talk of re-affirming your positive self-image has nothing to do with intelligence but is instead a basic fact of human thinking we’re all guilty of, well supported by psychological research.
I think that goes back to my point that the abstract isn’t linked well to the concrete. When you’re used to having an abstract equation set up for you, and you’re taught that there’s one and only one way to set the equation up, finding the correct information and putting the variables and/or the solution in the correct places is a bloody bitch. So instead of using word problems to teach students how to use the information in the word problems to set up a different form of the equation, teachers tend to use them as a cop-out. “You know the equation, so solve the word problem!” Now these same problems are stupid easy for me, I can take all that information and solve the problem quickly.
I understand that there is a lot of math that is abstract by definition and that these branches don’t have real-world applications. I’m not talking about higher, college-level math. I’m talking about garden-variety high school math.
This is the first clue that this particular test (or at least the scoring of it) is bogus. You cannot be in the 100th percentile. Percentile, roughly speaking, means the percentage of people who score lower than you. You cannot score better than 100% of the test-takers because you’d be scoring higher than yourself.
The ability to do something well does not always correspond to enjoying it, with the result that one does not develop the ability. My younger daughter picked up simple arithmetic well before she started kindergarten. Anecdote: She was riding in the child seat in the supermarket cart. We passed the shelves of eggs and she asked “What is a dozen?” Yes, she could read then, too. I explained that it meant 12 of something; there were 12 eggs in each box. “Oh,” she responded. “Then two boxes would have 24 eggs.” Yep. “And three boxes would have 36.” She kept on going, adding in her head until she got into triple digits. Later on, she liked to pick up the discarded number tickets at the deli counter and add them together. In her head. For fun. I had visions of a lucrative career of some sort. However, well before she reached junior high school she began to hate math, arithmetic, and all related subjects. She majored in theater and makes a good living now as a bartender.
Also, as others have said, what’s tested on any particular “aptitude” test is not always what they say it is.
I understand that. I assume that what my score actually meant was that I correctly answered every question that measured this particular area of aptitude, and the printed response was limited by the wording of the template into which the numbers are plugged. Similar to how when you first sign up for MySpace and Tom is your only friend, it says, “You have 1 friends”.
While the above was based on an aptitude test, I just checked the full report on my IQ test results from the same site, and it appears that this site may be using a slightly different definition of “percentile”. Here’s what it says about my “Mathematical Intelligence”:
“You scored in the 100th percentile on the mathematical intelligence scale. This means that you scored higher than 90% - 100% of people who took the test and that 0% - 10% scored higher than you did.”
In other words, I scored in the top 10%. It appears they limited the individual section rankings by grouping percentiles by multiples of 10 - so people were in the 100th, 90th, 80th, 70th, etc. percentiles. They only got more specific with the total overall score (in my case, the 96th percentile).
In any case, if their bell curve is honest then a comparable number of test takers scored in the 4th percentile, so I don’t think they’re just handing me a bucket of eyewash.
Online tests are worthless and lack any scientific validity. They are, as you admitted, “just for fun” and have no demonstrable correlation with ability. Any discrepancy between your achievement and your placement on an online test is most likely attributable to a flaw in the test.
“a man hears what he wants to hear and disregards the rest” --Simon & Garfunkle
