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27 Feb 2006 - 00:25

why do kids like math?


This is something I've been thinking about for awhile now, but hadn't gotten around to bringing up.

How do you get a kid to like math?

I didn't worry about it much when Christopher was in grade school, because I was boss; Christopher had to do what I said.

I'm still boss here in middle school - the boss of last resort at least - but it's a fight to the death, and the day when Christopher makes his own decisions about what he likes and doesn't like, and will and won't pursue, isn't far off.

Is he going to graduate high school with a superb grasp of K-12 mathematics?

If his father and I have anything to say about it, the answer is yes.

But I'm not sure how much we will have to say about it 4 years from now.

Another thing: as the British report on the UK's dwindling supply of mathematicians and applied math types points out, if we hope to increase the number of people who are good at math, we have to increase the number of students who want to be good at math. We don't have a math draft, after all.


from the report:

At this point we should perhaps comment on an apparent contradiction underlying our analysis.

(i) We know that many students find mathematics hard.
(ii) Yet our goal is to attract more students to the study of mathematics.

A crude “consumerist” model of education might lead one to conclude that one has no choice but to “drop the price” – that is, to concentrate on making mathematics “easier”. Yet we have repeatedly emphasised both (a) the need to strengthen basic technique and to expect more students to integrate one-step routines into multi-step wholes, and (b) the urgent need for a massive increase in the number of students taking A level Mathematics. How can such talk be realistic? And how can it be achieved?

These are serious questions – provided they are not merely rhetorical. Resolving the present crisis will not be easy; but, as we shall try to indicate, there is no essential contradiction in the analysis.

First, one has to understand that the long term challenge of ensuring a natural flow of home-grown mathematically competent graduates is quite different form the short term goal of selling off an unfashionable product simply by “dropping the price”.

Second, one has to recognise that a modern economy is mathematical in so many ways that we really have no choice but to find ways of producing a reliable flow of mathematically competent graduates – unless, that is, we are content to become a dependency of those countries that do appreciate the essentially “mathematical” character of a modern economy.

Third, we need to remember that the number taking A level Mathematics as recently as 1989 was more than 50% larger than at present, so there is no obvious logical reason why the goal is unrealistic.



So the question of motivating or inspiring kids to like math, and to want to pursue it, is important.

Constructivists seem to have given this question thought, and I've seen at least two real-live kids around here who love TRAILBLAZERS, and are having the time of their life with it. (I've seen more a few more who dislike it...)

Even so, if I had to bet, I'd bet that the answers constructivists have come up with are wrong, for the reason Dan K points out:

My daughter threw a (minor) fit today about having to do an extended response math homework problem. "I got the right answer," she wailed. "I did it in my head. Why do I have to write a paragraph about it?" I know I would have been as least as whiny back in my youth. I'm a mature adult now, so I enjoy learning stuff just to learn it. I can remember, though, wanting to get by with as little work as possible back in school (I still don't like working too much). To me, some of the best things about math, as opposed to other subjects, were 1) there's a right answer; 2) no term papers; and 3) no essay questions. Modern educators have eroded those benefits.

I agree.

I agree, because people who are good at math so often say that the thing they loved about math when they were kids was that there was a right answer.

For a particularly spectacular example, consider Lisa Randall ($?)

There used to be an ice cream parlor in the student center at the Massachusetts Institute of Technology. And it was there, in the summer of 1998, that Lisa Randall, now a professor of physics at Harvard and a bit of a chocoholic, and Raman Sundrum, a professor at Johns Hopkins, took an imaginary trip right out of this earthly plane into a science fiction realm of parallel universes, warped space and otherworldly laws of physics.

They came back with a possible answer to a question that has tormented scientists for decades, namely why gravity is so weak compared with the other forces of nature: in effect, we are borrowing it from another universe. In so doing, Dr. Randall and Dr. Sundrum helped foment a revolution in the way scientists think about string theory - the vaunted "theory of everything" - raising a glimmer of hope that coming experiments may actually test some of its ineffable sounding concepts.

Their work undermined well-worn concepts like the idea that we can even know how many dimensions of space we live in, or the reality of gravity, space and time. The work has also made a star and an icon of Dr. Randall. The attention has been increased by the recent publication to laudatory reviews of her new book, "Warped Passages, Unraveling the Mysteries of the Universe's Hidden Dimensions," A debate broke out on the physics blog Cosmic Variance a few weeks ago about whether it was appropriate, as a commentator on NPR had said, to say she looked like Jodi Foster.

"How do we know we live in a four-dimensional universe?" she asked a crowd who filled the Hayden Planetarium on a stormy night last week.

"You think gravity is what you see. We're always just looking at the tail of things."

Although it is the unanswerable questions that most appeal to her now, it was the answerable ones that drew her to science, especially math, as a child, the middle of three daughters of a salesman for an engineering firm, and a teacher, in Fresh Meadows, Queens. "I really liked the fact that it had definite answers," Dr. Randall said.

source:
Scientist At Work | Lisa Randall: On Gravity, Oreos and a Theory of Everything by Dennis Overbye
NEW YORK TIMES
November 1, 2005, Tuesday


So here we have the Holy Grail, the object of millions of dollars of NSF-funded curriculum-building and conference-hosting, a Woman in Physics - at Harvard, no less!

What got her interested in math?

The fact that it had definite answers.



000EB657-C6C7-1331-841D83414B7FFE9F_1.jpg

Lisa Randall



update: more from Dan

I'll also add that math is not the only realm in which there are right answers. Some kids of all ages enjoy playing games like Trivial Pursuit or the home version of Who Wants to be A Millioinaire? It's not because you're going to get rich winning the home edition. It's because it's fun to get the right answer. That's the whole point of the game.


And don't forget variable reinforcement!



maths in England
maths in England, part 2
more maths in England, part 2
top students in England, US, & Singapore
why do kids like math?
another brilliant person who liked getting right answers (scroll down)
Catherine's cousin talks about Everyday Math

Call for national debate on maths teaching GUARDIAN
Where will the next generation of UK mathematicians come from? (GOVT REPORT: pdf file)

The Beauty of Branes SCI AMER
On Gravity, Oreos and a Theory of Everything NYTIMES (possibly $)
On Gravity, Oreos and a Theory of Everything NYTIMES (pdf file)



dingbatWSJ2.jpg


extended response problem from IL state test
extended response problem 1
extended response problem 2
extended response problem 6
extended response problems 7, 8, 9
direct instruction & the rigor conundrum
Dan's daughter reacts to extended response problem
defensive teaching of Singapore bar models
open-ended problems in math ed
problems that teach - "Action Math"
email to the principal



-- CatherineJohnson - 27 Feb 2006

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I don't think you can make anyone like anything. You can put some people off things, e.g. by making them very confusing, by mocking anyone who does something wrong (that worked extremely well for putting me off singing), etc. But actual liking seems to be as much an internal process as an external one).

I was a student member of the Institute of Electrical Engineers when I was at uni, and I remember one letter in their newspaper about encouraging kids to study engineering. It sounded like an old, crusty member, who said that he'd taken part in a programme to encourage kids into engineering back in the 1960s, and ever since then the proportion of university students doing engineering had tracked downwards.

Sorry, no help here.

-- TracyW - 27 Feb 2006


Actually, on second thoughts.

It will help if Chris finds high school maths understandable, due to you building up a good base of knowledge as you are doing now.

You can emphasis that doing maths will keep many options open, and is a subject where he doesn't need to worry about working out what things the teacher wants him to say and what he doesn't.

-- TracyW - 27 Feb 2006


Here's one way to make kids like math, possibly -- give them unrewarding experiences in language-based subjects.

What makes any kid like anything, I think, is the feeling of being rewarded for doing it. The reward can either be implicit ("math is like puzzles") or explicit ("I got the school award for best story").

In my case, I had (shall we say) a hard time, at times, with writing assignments. Not that I hated writing -- I like it, and am pretty good at it. But I could bust my butt to get a good grade on a writing assignment (I did occasionally bust my butt in college), and still get a mediocre grade. The teacher's reasons for grading me that way often seemed capricious, too. Sometimes it seemed to happen because they had something against me, for some reason I couldn't understand.

Whereas when I got a proof right, I got it right, by golly, and I had a position to argue from if I didn't get a good grade. Or if I had it wrong, it was my own fault, indisputably. From the moment I went into math, I appreciated that about it; it didn't matter what you thought of me, you had to admit it when I got the answer right.

So, if you are a kid who frequently gets rewarded for writing, you may well not appreciate this about math; that the results are indisputable; you're right, or you're wrong. This is one of the most important and lovable things about math.

On the other hand, if your most salient gift is for bs -- you probably won't like math.

-- CarolynJohnston - 27 Feb 2006


You might encourage him to pity people who aren't good at maths.

Trade stories with Ed over the dinner table about uneducated people you have run into who can't do basic arithmetic, or who can't tell the difference between speed and acceleration. Look up jokes about maths and tell them over the dinner table.

Bribe Chris's older cousins (or equivalent) to make quotes in his hearing about maths being the queen of the sciences, and other maths-praising subjects, and to make scathing remarks about people who are proud of not being good at maths.

-- TracyW - 27 Feb 2006


I've been meaning to write about this.....one way of looking at this question is to ask: WHY DO I LIKE MATH?

After all, I spent my entire adult life not YEARNING to LEARN ALL THE MATH-MATH-MATH I MISSEDIN SCHOOL!!!....(though it bugged me to no end that I couldn't do statistics; that much is true).

So what the hell am I doing liking math so much I'm writing a damn blooki about i?

I think what happened in my case may be as simple as the principle of variable reinforcement: I got hooked.

I got right answers just often enough, and just variably enough, that I got hooked on getting right answers.

I strongly suspect that you'd get a LOT of kids liking math — as many as are naturally inclined to like it — if you made sure this principle was always at work in every math class you taught.

That would mean:

a) you have right answers

b) kids don't always get the right answer

c) kids don't always get the wrong answer, either

I wonder what would happen if you put kids on the same reward schedule they use in Vegas?

Maybe you'd have a whole country HOOKED ON MATH.

-- CatherineJohnson - 27 Feb 2006


It sounded like an old, crusty member, who said that he'd taken part in a programme to encourage kids into engineering back in the 1960s, and ever since then the proportion of university students doing engineering had tracked downwards.

No good deed goes unpunished!

-- CatherineJohnson - 27 Feb 2006


Tracy - yes, definitely, TRY to get a solid base of fundamental knowledge & math facts built up

At a minimum, you need to not turn kids off, which is what happens every day in every way here in the US it seems...

-- CatherineJohnson - 27 Feb 2006


Tracy: what do you think of this section?

the crude economic model is all wrong!

(you have to scroll down)

-- CatherineJohnson - 27 Feb 2006


is a subject where he doesn't need to worry about working out what things the teacher wants him to say and what he doesn't

That's going to become more and more appealing, I imagine

-- CatherineJohnson - 27 Feb 2006


Bribe Chris's older cousins (or equivalent) to make quotes in his hearing about maths being the queen of the sciences, and other maths-praising subjects, and to make scathing remarks about people who are proud of not being good at maths.

I think I should commission some Soviet realist artwork depicting stupid bourgeois who don't know anything about math

-- CatherineJohnson - 27 Feb 2006


But I could bust my butt to get a good grade on a writing assignment (I did occasionally bust my butt in college), and still get a mediocre grade. The teacher's reasons for grading me that way often seemed capricious, too.

boy, no kidding

I've come to love the 'independence' of the student from the teacher and from the whole b.s. edu-world he has to spend the first 20 years of his life negotiating.....

WAIT TIL YOU SEE THE NEW HELICOPTER PARENT ARTICLE I FOUND

(it's about college....)

-- CatherineJohnson - 27 Feb 2006


Their crude economic model is very crude.

It ignores the other suggestion any successful Econ 101 student would make to encourage students to study maths - raise the benefits of doing maths in order to get more students studying it. E.g. pay a fixed sum to everyone who passes a first year uni maths course. (Econ 313 will teach you that this will create an incentive for universities to make really simple first year uni maths courses.)

I suspect that they framed simplifying maths to encourage more students to take it as a "crude economic model" for debating reasons. No one supports a "crude model", and a fair chunk of educators wouldn't support any economic model, so the readers are led to disapprove of making high school maths more easy right from the start.

Having read this Wiki for a while, I'm convinced the solution is to improve maths education in primary school, not fiddle around with rewards or requirements at high school. It means making maths easier for students in high school because they already thoroughly understand arithmetic.

-- TracyW - 27 Feb 2006


TracyW?: "Having read this Wiki for a while, I'm convinced the solution is to improve maths education in primary school, not fiddle around with rewards or requirements at high school. It means making maths easier for students in high school because they already thoroughly understand arithmetic."

I agree 110 percent.

Our state is pushing "Physics First" in high school. I want Math First or Fractions First in grade school. The solution is easy, but lower schools do not like the solution. They will not give up social promotion, full-inclusion, and fuzzy math curricula.

Contradiction:

(i) We know that many students find mathematics hard.

That's for a variety or reasons, from pathetically poor math curricula to the fact that some people just have difficulty with numbers and being exact. Some people just can't deal with details. Besides, learning to write is "hard". Learning and making sense of history is "hard". Learning is "hard". Easy learning is a goal, not a prerequisite.

(ii) Yet our goal is to attract more students to the study of mathematics.

Is this really the goal of education? This leads to fuzzy, top-down approaches to math and science in the lower grades that make kids think that they have to "like" a subject before they can learn something. I want my son to know that there are lots of things to learn that may not seem very important or interesting right now. And, that there will be many things that he has to do that will probably be a waste of time. Although I will fight for better teachers and curricula, my son has to be able to deal with the occasional bad teacher (and boss, in the future).

This doesn't mean that you don't try to make the material interesting or easier to learn. It just means that you don't adapt or change the subject to make it easier.

" ...we have to increase the number of students who want to be good at math."

Fix K-8 math and this will take care of itself. (What TracyW? said) If my son gets to hate math in middle school, that's fine, but he darn well better do the work and get good grades.

Having said all of that, I think that I would have liked much more detailed information on careers in high school. Not just listening to a few parents talking about their jobs, but a detailed look at specifically what different jobs and fields require, what kind of pay is involved, and what kind of time commitment is needed. High school kids need to know about the concept of "career path".

I had a big discussion with my nephew (who got a degree in computer science last year) about how his first job will greatly influence his career path. He thought that all job experience was equal. I told him that many paths depended on what kind of experience he had. If he takes a job as a DBA (database administrator), then it's not going to make it easier to become a game programmer.

-- SteveH - 27 Feb 2006


I'm sure I have a serious, witty, and insightful answer in me somewhere, but right now, the only thing I can think of is that Lisa Randall does look a lot like Jodie Foster.

-- IndependentGeorge - 27 Feb 2006


Having read this Wiki for a while, I'm convinced the solution is to improve maths education in primary school, not fiddle around with rewards or requirements at high school. It means making maths easier for students in high school because they already thoroughly understand arithmetic.

we can all tattoo that one to our foreheads....

-- CatherineJohnson - 27 Feb 2006


First thoughts: Let me propose a path:

   Learning to mastery -> Getting the Right Answer -> Liking Math
The spiralling curriculum is exactly the wrong thing, because the student never achieves the first step.

I see math as being like music: You have to practice-- and master-- the basic skills before it starts being fun. (And there's some drudgery in mastering the basics.)

But without mastery, every year you face another round of the same old no-fun things you couldn't do the year before. Talk about negative reinforcement!

Second thought: Re SteveH?'s comment about knowing career paths. While the concept of a career path as a "succession of related jobs" may be valuable, it's also limiting. When I graduated H.S., there wasn't any such thing as a "game programmer" (except possibly the person who scheduled the game shows on network television), and while there were probably "database adminstrators" out there, they sure weren't called that (the first article on relational databases was only published in 1970). My point? Someone's ideal job may not even exist yet. All you can do is use your education time to accumulate as much knowledge in your area of interest as you can, realize that there will still be new things to learn even after the degree, and try not not close any doors.

-- OldGrouch - 01 Mar 2006


I'll also add that math is not the only realm in which there are right answers. Some kids of all ages enjoy playing games like Trivial Pursuit or the home version of Who Wants to be A Millioinaire? It's not because you're going to get rich winning the home edition. It's because it's fun to get the right answer. That's the whole point of the game.

-- DanK - 01 Mar 2006


"All you can do is use your education time to accumulate as much knowledge in your area of interest as you can, realize that there will still be new things to learn even after the degree, and try not not close any doors."

I guess that's my point about career paths - that you have to worry about closing doors. It's real tempting to take the fancy job when your boss pats you on the back, but that job might send you off on a one-way trip. For my nephew, this might mean not taking the first job that someone offers him. You even have to worry about getting paid too much for what you do.

My wife (Unix SysAdmin?) worries about what goes into her yearly review, but I tell her that she only has to worry about her up-to-date skills, her value to her company, and her value in the marketplace. Openings come up in any business, but you have to be very careful about what skills you will be learning as much or more that the amount of money you will be getting.

-- SteveH - 01 Mar 2006


On the other hand, I've never had any career plan beyond "keep learning stuff" and "do difficult stuff" and so far it's working out reasonably well. I frequently get surprised at how the things I've done in the past turn out to be useful in this (apparently unrelated) job.

E.g. I've worked as a programmer, and what I learnt there is turning out to be useful in understanding some of the problems around changing how electricity is bought.

-- TracyW - 01 Mar 2006


Learning to mastery -> Getting the Right Answer -> Liking Math

The spiralling curriculum is exactly the wrong thing, because the student never achieves the first step.

And not achieving step one along with purposely teaching by trial and error (i.e., discovery learning) prevents the satisfatisfaction of getting lots of right answers. Result: frustration and not liking math.

-- KDeRosa - 01 Mar 2006


Old Grouche

I see math as being like music: You have to practice-- and master-- the basic skills before it starts being fun. (And there's some drudgery in mastering the basics.)

One of Carolyn's friends, a mathematician who teaches at Purchase College, told me that the mathematicians think of themselves as being more akin to the music department, not the English department. (Purchase is mostly an arts college.)

He said, absolutely, that all of the math professors saw what they did as 'performance' — as doing math.

-- CatherineJohnson - 02 Mar 2006


Having read this Wiki for a while, I'm convinced the solution is to improve maths education in primary school, not fiddle around with rewards or requirements at high school. It means making maths easier for students in high school because they already thoroughly understand arithmetic.

This is sure the way I feel about it.....Barb Oakley's 2nd daughter is evidence of this.

She's the one who isn't a naturaly born Math Brain, and who did KUMON for years and years.

As a result she's always the speedy one in her high school math classes; she's the kid who helps the other kids.

She's almost done with high school now, and has decided to go into some kind of math-related field.

-- CatherineJohnson - 02 Mar 2006


I graduated college into a recession. There were zero jobs, and I had to get a job.

So I applied at an employment agency where they gave me a typing test.

I typed 90 or 100 wpm.

The interviewer told me that employers would want to know why I, a graduate of Wellesley & Dartmouth, 'wanted to type' for a living.

I said, 'Because I'm good at typing,' which was true. I was good at typing, so I liked typing. I still like it.

He got a big frowny face when he heard that.

It was the wrong answer, he said.

-- CatherineJohnson - 02 Mar 2006


I became a fast typist because my dad was constantly telling me, 'Learn to type so you can support yourself in case anything happens to your husband.'

Of course now there aren't any typing jobs.

So I'm learning math.

-- CatherineJohnson - 02 Mar 2006


For the same reason.

-- CatherineJohnson - 02 Mar 2006


I think that I would have liked much more detailed information on careers in high school.

Definitely.

-- CatherineJohnson - 02 Mar 2006


JodieFoster.jpg

-- CatherineJohnson - 02 Mar 2006


Lisa_Randell.JPG

-- CatherineJohnson - 02 Mar 2006


OK, Independent George, now that we've cleared that up....Comment away!

-- CatherineJohnson - 02 Mar 2006


Someone's ideal job may not even exist yet.

That's one of the reasons I'm pushing the math around here.

My guess is that the various predictions that math is going to become more important to a number of jobs, not less, are right.

At least, that's where I'm putting my nickel.

-- CatherineJohnson - 02 Mar 2006


I think Bayesian statistics are going to be EVERYWHERE.

-- CatherineJohnson - 02 Mar 2006


I'll also add that math is not the only realm in which there are right answers. Some kids of all ages enjoy playing games like Trivial Pursuit or the home version of Who Wants to be A Millioinaire? It's not because you're going to get rich winning the home edition. It's because it's fun to get the right answer. That's the whole point of the game.

WITANDWISDOM !

-- CatherineJohnson - 02 Mar 2006


I became a fast typist because my dad was constantly telling me, 'Learn to type so you can support yourself in case anything happens to your husband.'

I learnt to touch-type at school - mostly because the school computers at primary school were so pathetic (in the '80s), that the typing program was as good as the games got. I thought it was ridiculous having typing classes in high school (1/2 a year in third form (age 13) was spent on keyboard skills, and you could take it as an option), but yet it's been a major advantage to me. When I'm writing something for work, the limiting factor is how fast I can think, not how fast I can type.

My father taught himself to touch-type some time in the '80s for similar reasons.

I was the fastest typist in keyboard skills, but I hated it. Admittedly mostly because the typing teacher tried to make me cut my finger nails, which I refused to do for a class I didn't even want to take in the first place. I don't think being good at something and liking it necessarily go together. Although it was very nice being the fastest typist despite not following my teacher's advice.

-- TracyW - 02 Mar 2006


Ken

And not achieving step one along with purposely teaching by trial and error (i.e., discovery learning) prevents the satisfatisfaction of getting lots of right answers. Result: frustration and not liking math.

You're so right — trial and error.

This takes me back to the evolution of thinking about animal behavior.

For years everyone thought animals learned through trial and error.

Then whats-his-face, at Stanford (the name will come to me) said to himself: so how does it work, learning by trial and error IN THE JUNGLE?

answer: not very well

Turns out animals do a HUGE amount of observational learning.

That was the secret Irene Pepperberg used with Alex the parrot.

She had him learn through social rivalry and observation, not through classic reinforcement.

-- CatherineJohnson - 02 Mar 2006


I dropped out of a touch typing class in high school; it was too boring...

I taught myself to touch type a few years ago, but I'm still not very good at it.

-- CarolynJohnston - 02 Mar 2006


When my father was in high school in Chicago back in the late 1930's, his mother told him to take typing and shorthand courses. While in the Navy during WWII, his skills (especially shorthand) earned him a position as a Secretary to one of the ship's officers. I think he later was on Admiral Halsey's staff as well.

He served primarily on the New Jersey, a battleship, and he was always grateful that his battle position was in the bowels of the ship, and not on deck, during battles.

He liked to tell that story to emphasize that we should always be open to possibilities and learning, because you never know where it might take you.

-- KarenA - 02 Mar 2006

WebLogForm
Title: why do kids like math?
TopicType: WebLog
SubjectArea: ElementaryMath
LogDate: 200602261924