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March 15[edit]

"Not good at mathematics"[edit]

What do people mean by "not good at mathematics"? Has there been studies on self preception of mathematical ability and actual ability? Do these people have any numeracy ability? Can they count money or figure out how many chickens and pigs are there based on the number of legs? 107.77.194.174 (talk) 16:52, 15 March 2017 (UTC)[reply]

For starters, those examples are arithmetic, although some might consider arithmetic to be the same as mathematics. ←Baseball Bugs ^{What's up, Doc?} carrots→ 17:01, 15 March 2017 (UTC)[reply]

Quote from our article: Arithmetic ... is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations between them—addition, subtraction, multiplication and division. -- Jack of Oz ^{[pleasantries]} 20:04, 15 March 2017 (UTC)[reply]

Yes, arithmetic is a part of mathematics. So if someone says they're not good at mathematics, do they really mean they're not good at arithmetic? Or do they mean they're fine with arithmetic but have a little trouble with stuff like differential equations? ←Baseball Bugs ^{What's up, Doc?} carrots→ 23:50, 15 March 2017 (UTC)[reply]

(edit conflict)It's often a declaration of social standing rather than a comment on any specific ability. In such a case it means "I think people who are mathematically competent are socially-inept geeks and weirdos, and I'm not one of them." Shock Brigade Harvester Boris (talk) 17:03, 15 March 2017 (UTC)[reply]

Yes, they can count money and figure out how many chickens based on the number of legs (unless they're also not good at zoology!). But they may make a lot of mistakes in trying to balance their checkbook, or they may have had a hard time in high school geometry or beginning algebra. Loraof (talk) 19:02, 15 March 2017 (UTC)[reply]

I believe we lose a lot of people when math goes beyond what can be pictured. That is, you can use marbles to show adding, subtracting, multiplication, and division (although if that gives you fractions you need to use something like pizzas). Negative numbers can be visualized as owing something. Even with very large numbers, the concepts are understandable as performing operations on physical objects. But when you get to things like interest compounded continuously, that's where you start to lose students, as that can't be visualized directly. StuRat (talk) 19:17, 15 March 2017 (UTC)[reply]

There's a lot of stuff on the role of self-perception in education (and especially math education); I don't have any sources at hand right now and can't remember the names of any of the famous experiments (argh!) but hopefully some kind soul can fill in the blank here. -165.234.252.11 (talk) 19:19, 15 March 2017 (UTC)[reply]

"Not good at mathematics" is language used to reduce expectations in the realm of mathematics. Even those who describe themselves this way retain some skills in the realm. Bus stop (talk) 19:50, 15 March 2017 (UTC)[reply]

Is this actually a difficult expression for you to parse? I am sure, at some point in your life, there has been something you did not feel proficient in. It is no different for math than it is for anything else. In some cases it's comparative: I am good at math compared to some, but very poor compared to others. Some people have difficulty with more abstract maths like calculus or trigonometry, while others cannot perform simple arithmetic (dyscalculia). General weakness in terms of numbers and math gets lumped into innumeracy. Matt Deres (talk) 02:47, 16 March 2017 (UTC)[reply]

In about the fourth grade, age 10 in the US, multiplication is taught. Students (and their teachers) go about it in two ways. Some are taught to draw figures of x rows and y columns, and count the results. Six rows and seven columns (or, commutatively, six columns and seven rows) will always produce a sum of 42 when counted out. This is a foolproof method, and allows the student to integrate a new principle he can build upon to learn division, fractions, powers, and so forth. If you forget 9 x 7, you can draw it and count the result.

Or the student is simply told to memorize by rote that six times seven is 42, without the physical demonstration. Math becomes an ever more increasingly mysterious and baseless matter of rote memorization, without actual comprehension. Long division is a nightmare, and algebra an impossibility. These are the students who are "not good at mathematics". It is like being pushed down hill in skates never having learned to ride a tricycle.

It's at about this age when the students who've been crippled by pedagogical incompetence start to resent the "nerds" who actually comprehend the basis for the STEM curriculum. μηδείς (talk) 03:57, 16 March 2017 (UTC)[reply]

It might be that these elementary school teachers don't understand it either. "Those who can't learn, teach." I recall how easy Trig was, for a vaguely similar reason. Cosine and sine might be mysterious, unless they're explained as the (x,y) coordinates on the unit circle. Easy as Pi. ←Baseball Bugs ^{What's up, Doc?} carrots→ 04:39, 16 March 2017 (UTC)[reply]

Yes, I specifically remember my 4th grade teacher telling us she was going to explain multiplication, and having us draw six rows of eight dots, then demonstrating that if you turned the paper the number of dots was still the same. Other students were taught "flash cards" which was okay for practice, but was otherwise just a form of magic if you never learned the rows and columns principle in the first place. These poor children had to learn over 100 combinations (up to 12 x 12) rather than just one single principle. The problem was the incompetence of the rote method, not the limitation of the average student. But once you get to where you start resenting math, it's hard to remediate. The same thing applied with phonics versus the "look and say" method. μηδείς (talk) 13:37, 16 March 2017 (UTC)[reply]

They need to teach both methods, because you can't stop to draw 8 rows of 6, and then count them, whenever you need to multiply. You could pull out a calculator, if you have time, but be prepared to be laughed at. Some memorization is helpful. StuRat (talk) 17:30, 16 March 2017 (UTC)[reply]

Of course, I thought that was quite clear; but the principle behind why it works must be taught first. Then memorization is both economical, and you can check your work if you are not sure. If you don't know why multiplication works, you'd have no basis upon which to deny that six times nine equals 42. μηδείς (talk) 18:36, 16 March 2017 (UTC)[reply]

That method also lays some groundwork for understanding some geometry basics, like squares and rectangles. ←Baseball Bugs ^{What's up, Doc?} carrots→ 22:12, 16 March 2017 (UTC)[reply]

I'll also agree with you, Bugs, that I found trigonometry entirely obscure until I saw the projection of a point on a circle rolled along a cartesian graph. Everything should ultimately be reducible to the perceptual level, so that complex concepts like monocot (which I taught to a copy-editor in about 15 minutes one day in Central Park) can ultimately be reduced to the evidence of the senses. Newton, Gallileo, Einstein, Georges Lemaître; all were visual thinkers. (Obviously this perceptual "genius" applies to mechanics and musicians who are tactile and auditory thinkers as well.) μηδείς (talk) 00:27, 17 March 2017 (UTC)[reply]

I agree that every math topic which can be taught with concrete examples should be, but I don't believe all math can be described in this way. Take my example of continuously compounded interest as an example. The best you could do is show that the annual yield goes up with more compounding periods per year, and graph several examples, and find the asymptote (limit) of that graph by visual inspection, and explain that this is what you reach with continuous compounding. That's a lot of work to allow this to be visualized. And as math gets more complex, even more tortured visualization methods would be required. StuRat (talk) 05:00, 17 March 2017 (UTC)[reply]

@StuRat: I'd suggest a set of nested cubes, the smallest one being the original investment, and the larger cubes being time slices showing the increase. μηδείς (talk) 18:30, 20 March 2017 (UTC)[reply]

That just shows something getting bigger, not a way to calculate how much bigger it gets over which time length and what effect the compounding period has. StuRat (talk) 18:45, 20 March 2017 (UTC)[reply]

I'm "not good at maths" and it took me until I was nearly 40 to actually get a diagnosis of dyscalculia. --TammyMoet (talk) 15:18, 16 March 2017 (UTC)[reply]