There have been a number of recent threads dealing with math and how it’s feared, jeered, and by somn revered.
What I want to know is why is math considered to be more difficult than other critical skills, specifically language?
There have been a number of recent threads dealing with math and how it’s feared, jeered, and by somn revered.
What I want to know is why is math considered to be more difficult than other critical skills, specifically language?
I think it depends on the student and the teacher. I found math to be the easiest class of the day until I got up to 3rd semester calculus (and that one semester of trig with a REALLY bad teacher). English was a challenge for me. I got bored with math before completing my degree and ended up with an English degree.
Here are some things that might affect this discussion.
Boys tend to do better at math than girls. When I went through the Hopkins gifted program (1978 I think) there were only two girls who qualified for the math portion and they both dropped out of it after the 1st day.
Girls tend to do better at language. There were about 75% girls in the Verbal portion of the gifted program. I was one of about 5 guys who stuck it out to the end.
Girls tend to be slightly better students on average. (I’m not sure that this has been consistently true, but in my experience it holds up especially if discount the brains and the misfits. The sort of “run of the mill” female student was usually a slightly better student than the male counterpart. I know this is a weak point.
I’m thinking that maybe because the girls who, for whatever reason, had trouble with math were usually better student, that gave math a reputation for difficulty.
Ok, as I read that back I see it’s a weak and unconvincing idea. Oh well, I told you I was better at math.
Who considers math more difficult anyway?
I think it is most difficult for Phlegmatics and easiest for Melancholies.
And I’m a sloppy typist to boot.
Math is harder for girls because they are told that it is supposed to be harder for girls. Math isn’t hard. It’s just that people believe others when they are told math is hard. The difficulty of subject matter is entirely dependent on the effort of the student.
I think there are stylistic differences between math and other subjects that make it more unfamiliar, and therefore more difficult, for most students. Unlike English and history and even many science subjects such as biology, math is not presented in a narrative format. From the day people learn to read, the overwhelming majority of the material they read is a stream of prose sentences with obvious, usually temporal, logical connections between them. (“And then Mitzi got out of bed and put on her clothes and took her baby brother out of the crib and changed his diaper and gave him his bottle and…” “If the cabin pressure drops, an oxygen mask will be released from the overhead compartment. Pull sharply on the tube to start the flow of oxygen, place the mask over your nose and mouth…” “‘You will not be fit to be seen.’ ‘I shall be very fit to see Jane—which is all I want.’…”)
Reading math, on the other hand, is much more like reading poetry, another genre that many people find comparatively difficult. Meaning is compressed into the most economical expression; apparent non sequiturs show up everywhere, revealing their relationship to the topic at hand only after a good deal of wondering and thinking; usually the meaning isn’t clear until you’ve read it over several times and thought about it. Inexperienced students unconsciously expect to read math as they would read most other subjects, and when it doesn’t make sense that way they say that math is just hard.
[tangent, hee hee]
One friend of mine who’s an excellent mathematician isn’t much of a voracious reader when it comes to ordinary prose, and I’ve hypothesized (based on the number and type of reading reversals when he reads aloud) that he may have gone undiagnosed with a mild instance of dyslexia as a kid, and turned to math partly because its compressed style and slower rate of absorption made it less frustrating for him to read. Can any other better-at-math-than-reading types out there vouch for such a correlation?
[/tangent, hee hee]
It requires analytical thinking rather than rote memorization. Answers are right or wrong, and not so subjective as might be when reading literature or studying art. That, plus most people approach the subject with the mindset that it’s going to be tough.
This is taken from an earlier thread on “Fear of Mathematics”
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I will also add something that many people pointed out. In math you build on your understanding of what you’ve learned before. So, you can’t do calculus without knowing trigonometry. Your basis must be sound. This is not the case in many other subject areas. In those instances, you can take (and possibly even learn) new things even though you’ve failed (literally and figuratively) what came earlier. Math is unforgiving in this regard.
“somn”? “somn”? Where did that come from?
:: hangs head after discovering typo in two sentence OP. ::
It would seem that the basic concepts of math are simpler than the basic concepts of language.
If I hold my hand up, extend all the fingers, and curl the pinky and thumb into my palm, any 2 year old can tell me that the number of fingers that I’m holding up is “three”.
What is a “3”? It’s an invented symbol that signifies an exact thing. A count where the number of items is three.
Language, at least those based on the roman alphabet, has another level of complication.
What is an “e”? It’s the 5th letter of the alphabet. It’s a vowel. By itself it means nothing to the language. Preface it with the letter “m” (another abstract entity) and the combined token “me” refers to self. Suffix the “e” with the “m” and the token “em” has no stand-alone meaning.
It just seems to me that the progression to learn English requires an additional step than does the progression to learn mathematics. But it’s considered easier.
Probably because it’s heard and somewhat understood long before the concept of math is introduced.
The cumulative deficit problem with math learning is based on both the analytical thinking, and the rote memorization aspects of learning. You can’t start learning higher math when you are still doing sums in your head as individual problems. You have to have learned the relationships of addition, and subtraction, and the multiplication, and factoring of two digit numbers well enough that they are not elements of new problems for you.
The crisis in math skills in our schools comes years after the elementary schools eliminated drill in simple arithmetic as a poor teaching method. Rote memorization is considered boring. That begins a deficit in skills that makes every subsequent area of learning more difficult. Memorization is a skill, and can be learned. The elements memorized earliest are most likely to be retained, and should be the most universally useful of facts. The multiplication tables, the factors, and primes, and the basic rules of quantitative functions are supremely useful in life. When you know the arithmetic without thinking about it, the algebra is simple. If you memorize the algebra, the trigonometry makes sense! Memorize the trig, and you can easily visualize the meaning of the Calculus. But if you are still doing the arithmetic as part of the problem in your head, it all starts to look like a foreign language for the simple reason that it is a foreign language. And you don’t know the vocabulary, so you can’t learn the grammar.
Memorize a few thousand lines of good poetry, and you will benefit for decades to come. And your ability to memorize, and remember, and use what you have learned will grow, as well. Being smart is waaaaay over rated. Working hard is almost always a better plan, and the results last a lot longer, and apply to a lot more areas of life. Spend the time with your children, doing the basic skills of arithmetic, grammar, and geography. They are useful things to know, and as long as grades and tests are not a part of it, it can be a lot of fun.
Tris.
Why is math harder than language? Because our brains evolved to process language. We literally have a special part of our brains designed just for language use.
But math is hard because our brains are not designed for math. We can understand it because our brains are general purpose. But we’re using abilities that evolved so we could remember where water-holes were, what degree of kinship a fellow australopithecine had, and whether the brownish leaves with large veins and crinkly edges were poisonous or not.
Same thing for all the weird “counterintuitive” physics of the very small, very large, and very fast. Sure, reletivity and quantum mechanics make no sense, but thats because our brains and bodies have spent hundreds of millions of years adapting to conditions that normally occur on the surface of planet earth. We don’t think it’s weird and counter-intuitive that rocks fall down, not up, or that the sun shines, or that water is wet, or that we remember the past but not the future. But all those things are just as bizarre as time dilation or the uncertantity principle.
I think much of the blame can be laid at the door of poor teachers. Of course, I’m working on becoming a teacher, so I’m hypersensitive to that.
All students have slightly varying learning styles that respond best to varying teaching methodologies. Some students are pick things up best by reading or listening to the teacher talk. Others need tactile stimulation or kinesthetic activities. Some, like myself, learn best if they can talk through the material.
The trouble is, traditional teaching methods, especially for higher math, tend to be strictly lecture and reading. That leaves up to half the student population out in the cold, academically speaking.
I don’t know enough about higher math to suggest lesson plans that would alter the approach successfully. I quit out after Algebra II in high school, and did a little pre-Calc in a college physics class. However, I think Math teachers could really use some new pedagogical approaches to their work.
Well said. How do we convince people this is true?
I am so frustrated that when a school district gets some money from somewhere they tend to spend it on the high school because that is where they have the most problems. When will they learn that they need to fix the elementary schools 1st?
Gosh, I liked your post so much I want to go to other threads and look to see what you’ve written in hopes of more gems.
A nit. As every good Scrabble player (and typesetter, and TeX user) knows, ‘em’ is a perfectly good word. From Merriam-Webster’s Collegiate Dictionary:
Rick
Kimstu wrote:
The integral z squared dz
From 1 to the cubed root of 3
Times the cosine
Of 3 pi over 9
Is the log of the cibed root of e.
Er, the log of the cubed root of e.
Nothing like a typo to wreck a limerick. sigh
I get A’s and B’s in other subject’s and a D- in math (lsat one wsa Geometry). I don’t know why, but I remember seeing a commercial on TV that was talking about Math Anxiety, like a problem they have doing it. It was like hooked on phonics, but for highschool kids with math trouble.
BTW I am male.
Another reason kids might have trouble with it is that their parents don’t understand it so no one can help them with it outside of school. Time and philisophical changes in teaching methods altered the way the math problems appear on homework, and a lot of parents don’t seem to recognize even fairly basic algebra. Obviously in college this is much less of an issue, but in jr. high and high school it is a problem.
Plus families can discuss most of the other subjects around the house, which greatly reiforces learning, but other than balancing the checkbook math just doesn’t come up that often.
Percentage off sales? Fractions in cooking? Which is a better buy? Angles and measurement in carpentry and arts and crafts? Gas mileage? I think math is used in a lot of contexts where it’s automatically part of the thought process.
I think the point is right that math is hard to teach. I love math but find it frustrating to teach others because if they don’t understand the one way I explain it, it’s hard to think of other ways to explain the same point. At the same time, the existence of one right answer rather than the subjective interpretation of literature, etc., is the beauty of it, and when someone does have the breakthrough it’s great.
Okay, as a disclaimer, I’m among the people to whom higher math makes lots and lots of sense (and, for the record, I’m female). But, putting that aside . . .
I think that a lot of people have mentioned the major reasons - poor teaching methods, being different from what most people spend most of their time doing, we learn language earlier.
Yes, math comes up a lot in daily life, but not nearly to the extent that language does. First graders enter school with grossly unbalanced language/math skills - they’ve been talking for several years, and have reasonably large vocabularies, but few of them can add with any sort of proficiency. And it continues throughout life like that - most of us, even people who spend large amounts of time doing math, probably excersize their language skills at least as much.
One of the points for me, though, is that I was terrible at math in elementry school. Still, when I’ve screwed up a problem, I look at the arithmatic first - cuz that’s where the problem most likely is. In around 7th grade we got into algebra, and the like, and I’ve really liked math ever since. But I think there’s a lot of people who are turned off to math way before they get to the point where it seems interesting, or before it “clicks”.
I think math is one of the harder things to teach, because to many people who are good at it, it seems second nature. I’ve had a reasonable amount of success explaining math to people, but I don’t really know what it is I do differently than anyone else.