# Hey... why didn't I think of that!?

July 9, 2003 3:46 PM Subscribe

The Lizzie Method : 16-year-old Elizabeth Seagle figured out a better way of factoring quadratic equations. What do the Me-Fi mathematicians think? Will it be taught in future textbooks? Personally, I never touch the stuff.

*the quadratic formula, a complex and tricky device that mathematicians try to avoid whenever possible.*

This is news to me. If a quadratic has an obvious factorization you can "unfoil" then you use that. If not, using the quadratic formula is more than kosher. And not all that complex and tricky.

I don't see new mathematics in Lizzie's method, just a slight differentiation in procedure, akin to the difference between doing 63 x 11 as:

(60 x 11) + (3 x 11) = 660 + 33 = 693

vs writing:

63

x 11

-----

63

630

------

693

That's not to say it isn't useful. Many students may take more to one way than another, despite the fact that differences are largely cosmetic.

posted by namespan at 4:06 PM on July 9, 2003

Lizzie's method won't work for double root or imaginary root cases. That's the whole problem.

What's wrong with just saying for some function:

the solutions are:

posted by bshort at 4:06 PM on July 9, 2003

What's wrong with just saying for some function:

the solutions are:

posted by bshort at 4:06 PM on July 9, 2003

That is no simpler than the quadratic f.

HELLO I am a newspaperwriter I know nothing about math, how are you highschoolteacher who knows nothing about math, what! You say you have a brilliant student, photogenic too?

Hello hello there university professor, would you like your name in the paper? Just tell some lies into my hand, fudge a little, the readers love this.

The sad thing is that she probably didn't/can't even derive it from the original but just stumbled across the resemblance.

WHY oh why have I just written three paragraphs about this bullshit.

posted by shabrem at 4:08 PM on July 9, 2003

HELLO I am a newspaperwriter I know nothing about math, how are you highschoolteacher who knows nothing about math, what! You say you have a brilliant student, photogenic too?

Hello hello there university professor, would you like your name in the paper? Just tell some lies into my hand, fudge a little, the readers love this.

The sad thing is that she probably didn't/can't even derive it from the original but just stumbled across the resemblance.

WHY oh why have I just written three paragraphs about this bullshit.

posted by shabrem at 4:08 PM on July 9, 2003

I believe by "mathematicians" the ps.-journo meant "untalented high school students".

posted by shabrem at 4:09 PM on July 9, 2003

posted by shabrem at 4:09 PM on July 9, 2003

(sorry, should have <pre>'d that columnar multiplication example to make '63' appear over the last two digits of '630')

posted by namespan at 4:10 PM on July 9, 2003

posted by namespan at 4:10 PM on July 9, 2003

*Newman’s excitement over the discovery led her to submit Lizzie’s name for recognition in the “Who’s Who Among American High School Students” publication.*

Score!

posted by furiousthought at 4:11 PM on July 9, 2003

Sorry. Not impressed. This is exactly the way I did them in high school, and I got yelled at for not doing them the "right way". I had all sorts of unique ways to solve equations, which led to correct answers. I would do them on scratch paper the way I wanted to, and then write them out on homework and tests the way the teacher wanted them. I don't recall anyone heralding me as a genius.

Wait ... I was listed in "Who’s Who Among American High School Students" for four years, I was cute, I was smart ... why didn't anyone write a puff piece about me? LOL!

posted by Orb at 4:18 PM on July 9, 2003

Wait ... I was listed in "Who’s Who Among American High School Students" for four years, I was cute, I was smart ... why didn't anyone write a puff piece about me? LOL!

posted by Orb at 4:18 PM on July 9, 2003

When I graduated high school, the "“Who’s Who Among American High School Students” publication sent me a letter, congratulating me, and asked if I wanted to be in their fine tome. For the low, low price of $29.99, I could get my own copy too!

No thanks.

“Who’s Who Among American Scam Businesses" is more like it.

posted by Fofer at 4:20 PM on July 9, 2003

No thanks.

“Who’s Who Among American Scam Businesses" is more like it.

posted by Fofer at 4:20 PM on July 9, 2003

Well, the article was written by an intern at the Metro Times, too, not a full-fledged journalist. So I think some tiny amount of slack must be given. But not too much.

Quadratic equations made my head hurt in 8th grade and they still make my head hurt.

posted by eilatan at 4:23 PM on July 9, 2003

Quadratic equations made my head hurt in 8th grade and they still make my head hurt.

posted by eilatan at 4:23 PM on July 9, 2003

*“Who’s Who Among American Scam Businesses" is more like it.*

Ironically, I think the fact that I realized this in high school validates the idea that I was a standout. But hopefully not.

posted by namespan at 4:25 PM on July 9, 2003

That was pretty retarded (the article). They listed a bunch of "problems" with current methods, and implied that Lizzie's method had none of these problems. In reality, it shares all of them. It's a fine method, and one that I think many people have used when the question was "find the roots, but don't find the factored form", but this was only news because the journalist is afraid of math.

posted by hammurderer at 4:28 PM on July 9, 2003

posted by hammurderer at 4:28 PM on July 9, 2003

*Quadratic equations made my head hurt in 8th grade*

Math education seems to be

**far**advanced in the US compared to the UK! We only got as far as basic trigonometry by the time I left school at age 16 (and I was in the highest 'set'). Quadratic equations, polynomials, and functions are left to A (advanced) level (ages 17+18) Mathematics. And calculus only barely gets a look in at that level too. So bravo to her.

Why does Math get such little coverage in a British education?

posted by wackybrit at 4:29 PM on July 9, 2003

*...We only got as far as basic trigonometry by the time I left school at age 16 (and I was in the highest 'set'). Quadratic equations, polynomials, and functions are left to A (advanced) level (ages 17+18) Mathematics...*

Wackybrit - You must be kidding. I was factoring polynomials and solving for roots by the time I was in 8th grade, and that didn't seem particularly early.

posted by bshort at 4:34 PM on July 9, 2003

wackybrit: My impression is that whereas U.S. math education is heavily focused on calculus (i.e., even if a student never gets as far as calculus in high school, the curriculum still consists of the preparatory steps), giving short shrift to other branches of mathematics. Don't some European curricula include more number theory, probability, geometry, etc.? Put another way, aren't "only got as far as basic trigonometry" and "factoring polynomials" apples & oranges?

posted by Zurishaddai at 4:39 PM on July 9, 2003

posted by Zurishaddai at 4:39 PM on July 9, 2003

*What do Me-Fi mathematicians think?*

I think that it's easy to verify that Lizzie's method works, but it's interesting to note that no one - Lizzie included - attempts to explain why it's valid. They're just happy that it works. And there's the rub. If math educators (who, notably, seem far more excited about this method than the mathematicians quoted in the article do) decide to adopt this method when teaching factoring, I hope that they explain that (as some posters have said) it's just a rehashing of old methods presented in a slightly different format.

Key quotes, for me, as a math grad student and instructor:

*“I just started playing around with the numbers,” Lizzie remembers, “and trying to see what I could do with them until I ended up getting the answers that were [on the answer key].” When she found a way that worked, Lizzie figured the lesson had been learned.*

It's cool that she figured this out, but for every Lizzie, there are ten students

*in classes I've taught*who try to reverse-engineer their answers by looking at the answer key, figure out something that works, feel content that they've gotten the answers at the back of the book, and then wonder why their method has failed to work on a similar-but-different question that they later encountered. It makes it that much harder for math teachers to explain the nature of mathematical justification. And this part is just sad:

*“…[M]ath is one of those things where people don’t really question it so much because everyone’s taught, ‘Well, this is the formula; you have to use it,’” Lizzie says.*

I hope that not everyone's taught that they should do math by mindlessly plugging numbers into formulas, but I wonder sometimes.

posted by isomorphisms at 4:42 PM on July 9, 2003

Good for her, even if it does turn out to be a limited or previously thought of method. Not many kids get to show their teachers something they really don't know. Especially math teachers.

posted by carter at 4:42 PM on July 9, 2003

posted by carter at 4:42 PM on July 9, 2003

In Ontario, we did polynomials in grade nine(13-14) and quadratics in grade ten (14-15), but calculus, probability and linear algebra by OAC (17-18). As a result, you do what is second-year calculus in America in first year university here (though there's usually a semester of catch-up for students outside the province).

posted by Pseudoephedrine at 4:43 PM on July 9, 2003

posted by Pseudoephedrine at 4:43 PM on July 9, 2003

I shit ye not. I left High School with an A*, the top grade, in Math, yet now, five years later, it is taking me

Another oddity about the British system is that the Math syllabus changes from decade to decade. Until the mid 80's, it was common practice to teach about 'sets'. In my High School, however, we were told to ignore the pages about 'sets' as they were 'irrelevant'. Now I'm out of school, and I've seen what 'real' mathematicians do, I've learnt sets aren't as irrelevant as they thought! You need to know what a 'open set' is even to understand something as basic as a manifold, so I've been trying to catch up with the rest of the world, thanks to my flawed British education.

I must admit, we

Maybe, although I'd say trigonometry is childs play compared to polynomials.

posted by wackybrit at 4:46 PM on July 9, 2003

*forever*to understand what the heck all this polynomial nonsense is about.Another oddity about the British system is that the Math syllabus changes from decade to decade. Until the mid 80's, it was common practice to teach about 'sets'. In my High School, however, we were told to ignore the pages about 'sets' as they were 'irrelevant'. Now I'm out of school, and I've seen what 'real' mathematicians do, I've learnt sets aren't as irrelevant as they thought! You need to know what a 'open set' is even to understand something as basic as a manifold, so I've been trying to catch up with the rest of the world, thanks to my flawed British education.

*Don't some European curricula include more number theory, probability, geometry, etc.?*I must admit, we

*did*spend most of our time doing geometry, probability, and statistics, as opposed to calculus (which we never got to) or advanced algebra (which we got to in 11th grade). Perhaps, in some ways, this is good because geometry and statistics are more useful to people doing ordinary things.. whereas calculus is almost useless unless you're in a technical profession, where you'd have learnt calculus at University anyway.*Put another way, aren't "only got as far as basic trigonometry" and "factoring polynomials" apples & oranges?*Maybe, although I'd say trigonometry is childs play compared to polynomials.

posted by wackybrit at 4:46 PM on July 9, 2003

*Lizzie's method won't work for double root or imaginary root cases.*

It won't even find irrational roots, unless the user is adept at finding such roots by inspection in the second step of her procedure:

*Find the two numbers that will multiply to 36 and*

also add to 13, the middle number.

also add to 13, the middle number.

This is the "and then a miracle happens" step; it is by no means general (again, unless you can see complex and irrational roots by inspection). Find for me the two numbers that will multiply to 36 and also add to 14, for instance. Or multiply to 36 and add to -2.

I remember spending hours and hours of junior high math (She's doing this stuff in high school?!? I thought introductory algebra had been mostly moved into junior high.) factoring quadratics by inspection. What is that supposed to teach, anyway? Show the students how to complete the square, use the method to derive the quadratic equation, and bingo: you have the topic handled in an hour.

It's this emphasis on the pointless repetition of meaningless mechanical exercises that leaves so many students hating math.

posted by mr_roboto at 4:46 PM on July 9, 2003

I'd like to hear her explain Fermat's Enigma that way:

Um, like, I was playing with the numbers and it just seemed to work, so I tried a few more and it worked for them too!

posted by jonah at 4:48 PM on July 9, 2003

Um, like, I was playing with the numbers and it just seemed to work, so I tried a few more and it worked for them too!

posted by jonah at 4:48 PM on July 9, 2003

What's available in terms of Math Education in american public secondary schools varies widely by school, standardization attempts notwithstanding. Vector calc and basic analysis and discrete math and linear algebra are available in some programs. Many, probably most, cap out at calc I.... though you do, interestingly enough, get the odd program with discrete math classes and no calc.

Which may well not be any worse. I severely dislike the characterization of calculus as the pinnacle of mathematics, which I think it derives somewhat from its position in secondary ed (ok, ok, and its astounding usefulness).

posted by namespan at 4:52 PM on July 9, 2003

Which may well not be any worse. I severely dislike the characterization of calculus as the pinnacle of mathematics, which I think it derives somewhat from its position in secondary ed (ok, ok, and its astounding usefulness).

posted by namespan at 4:52 PM on July 9, 2003

We were doing Calc C/D senior year. This kind of basic algebra was taught to us in 8th grade. Really, though, how hard is it to plug in three numbers into an equation? Don't they even let highschooler's use calculators nowadays? So even take the square root is easy-as-pie. God, kids these days have it so damned easy.

Hey, look! I figured out a neat-o way to solve for compound fractions. Take this example:

Instead of doing this:

I can just multiply the denominator by the whole number, and then

posted by Civil_Disobedient at 5:01 PM on July 9, 2003

Hey, look! I figured out a neat-o way to solve for compound fractions. Take this example:

Instead of doing this:

I can just multiply the denominator by the whole number, and then

*add*it to the numerator. Wow! So much easier! Can I get my Field's Medal now?posted by Civil_Disobedient at 5:01 PM on July 9, 2003

*Lizzie's method won't work for double root or imaginary root cases.*

Unless the roots are imaginary and complex conjugates.

*Well, the article was written by an intern at the Metro Times*

Next up: Metafilter dismantles Iraq coverage in the Washington Post Kids' Page.

posted by eddydamascene at 5:04 PM on July 9, 2003

I found a way of doubling numbers easily. Take your number, say 7. Add 0.001 to it. Square the number. Then dig around in the 'bit of the answer after the dot' for your real answer! So..

7.001 * 7.001 = 49.014001

And the answer 14 is right there! You can double any number this way!

posted by wackybrit at 5:24 PM on July 9, 2003

7.001 * 7.001 = 49.014001

And the answer 14 is right there! You can double any number this way!

posted by wackybrit at 5:24 PM on July 9, 2003

My favorite quote from the article is this one:

Can't they at least find a writer who knows a *little* math?

posted by caveday at 5:30 PM on July 9, 2003

*The other two methods -- the "split method" and "guess and check" -- provide shortcuts, but only for equations that factor; that is, equations that yield real numbers, as opposed to imaginary ones.*Can't they at least find a writer who knows a *little* math?

posted by caveday at 5:30 PM on July 9, 2003

wackybrit - LOL!

As far as the journalism goes, it doesn't disappoint me nearly as much as does Ms. Newman, the math teacher, who apparently thinks this is some amazing discovery that

posted by kickingtheground at 5:41 PM on July 9, 2003

As far as the journalism goes, it doesn't disappoint me nearly as much as does Ms. Newman, the math teacher, who apparently thinks this is some amazing discovery that

will soon find its way into the notebooks of future math students everywhereand is worthy of publication. A math teacher should know better.

posted by kickingtheground at 5:41 PM on July 9, 2003

**wackybrit**

*Another oddity about the British system is that the Math syllabus changes from decade to decade. Until the mid 80's, it was common practice to teach about 'sets'.*

I went through that in the early 70s - it was the period when they'd introduced set theory and Boolean algebra as 'New Maths' (actually pretty old maths that had finally crawled into the syllabus). But we did do quadratics pre A-Level.

posted by raygirvan at 5:42 PM on July 9, 2003

*Orb, you do realize they invite everyone, don't you?*

They publish everyone who is nominated and passes the criteria ... whether or not you pay them for the book. I didn't. Since it was a scam, I suppose I should have returned the scholarships I received from being listed in both the high school and college versions (the ones that paid for my first two years' tuition). Didn't sound like a horrible scam to me then, nor does it now. I paid nothing and did nothing beyond what I was doing anyway to get into a good school, and I got my tuition paid for two years. If it was a scam, then it was one that paid me well.

posted by Orb at 5:46 PM on July 9, 2003

Will this be on the test?

posted by crunchburger at 6:06 PM on July 9, 2003

posted by crunchburger at 6:06 PM on July 9, 2003

*Until the mid 80's, it was common practice to teach about 'sets'.*

Sets education does more harm than good -- what we need to teach these kids is abstinence.

posted by eddydamascene at 6:10 PM on July 9, 2003

*I would do them on scratch paper the way I wanted to, and then write them out on homework and tests the way the teacher wanted them.*

amen! I hated it when teachers would grade the work and not the answers. who started that? lets hurt them.

posted by mcsweetie at 6:20 PM on July 9, 2003

Yes, the quadratic formula is hard if it's just a random scribble that you're supposed to memorize. We derived it. Seems Ms. Newman is looking for a method that her students can use to get the right answers (and boost her score) on standardized tests, but doesn't care whether they actually learn anything about math. Sigh...

posted by kewms at 6:27 PM on July 9, 2003

posted by kewms at 6:27 PM on July 9, 2003

Independent of whether or not this constitutes groundbreaking mathematics, I think it's a big mistake to assume it's better to derive a formula than to memorize it. It's much easier for most people to pick up a general theory from a lot of examples than the other way around. After twenty times plugging numbers into this initially meaningless formula, you'll start to notice patterns among the answers, then wonder where the formula came from. By then, you'll have a good enough feel for it for the answer to make some sense.

posted by transona5 at 6:32 PM on July 9, 2003

posted by transona5 at 6:32 PM on July 9, 2003

I think those who're harshing on Lizze should pay her a little more respect. She's essentially made a clever observation about the relationship between the coefficients of a 2nd degree polynomial and the solutions, and she can describe what the relationship is, albeit in procedural terms. The fact that this observation isn't particularly novel to the mathematics world means that she doesn't deserve a Fields Medal, but it doesn't mean she's not bright. If she learns to talk a certain way, she'll start sounding like a mathematician.

Whether it deserves news coverage, on the other hand, is another matter, which is where I suspect the real snarkiness is directed.

posted by weston at 6:51 PM on July 9, 2003

Whether it deserves news coverage, on the other hand, is another matter, which is where I suspect the real snarkiness is directed.

posted by weston at 6:51 PM on July 9, 2003

I have a minor in math, and I say Lizzie is the

posted by user92371 at 7:05 PM on July 9, 2003

*belle of the ball!*HUZZAH!posted by user92371 at 7:05 PM on July 9, 2003

Well, she gets appreciation from me. Anything that makes math easier for kids = more gooder. Personally, I don't care though. I just got credit for the last course in my math requirement for my major. That means that never, ever again, will I give a second thought to any of that stupid *expletive deleted*. The best part is that I don't even remember anything that I learned!

posted by tomorama at 7:29 PM on July 9, 2003

posted by tomorama at 7:29 PM on July 9, 2003

Sigh... I so envy math geeks. You deal with actualities, certainties, right and wrong answers. From my side of the fence it looks pretty inviting sometimes.

Can any of the mathematicians here tell me if there are programs out there that take mathphobic adults back through the curriculum, starting at, say, Grade 6, where I gave up? I think we were doing something to do with fractions, but I've repressed the memory. Actually, this is a serious question. I want to learn some of this stuff, and work the other side of my brain, the one that isn't full of Benjamin and Kristeva.

posted by jokeefe at 7:30 PM on July 9, 2003

Can any of the mathematicians here tell me if there are programs out there that take mathphobic adults back through the curriculum, starting at, say, Grade 6, where I gave up? I think we were doing something to do with fractions, but I've repressed the memory. Actually, this is a serious question. I want to learn some of this stuff, and work the other side of my brain, the one that isn't full of Benjamin and Kristeva.

posted by jokeefe at 7:30 PM on July 9, 2003

jokeefe: resist the dark side!

I saw 'A Beautiful Mind' during the winter. After the credits rolled, I was psyched about going to class the next day. I thought "math is interesting stuff, I'm going to try and understand it!"

Then I went to class the next day and found out that Parametric Equations and Methods of Convergence sucked just as much as the day before.

posted by tomorama at 8:11 PM on July 9, 2003

I saw 'A Beautiful Mind' during the winter. After the credits rolled, I was psyched about going to class the next day. I thought "math is interesting stuff, I'm going to try and understand it!"

Then I went to class the next day and found out that Parametric Equations and Methods of Convergence sucked just as much as the day before.

posted by tomorama at 8:11 PM on July 9, 2003

Interesting that the article undermines itself in the text:

'A mathematics professor at the University of Michigan believes that that’s exactly the case. Responding to an e-mail inquiry, the professor writes, “This method was the standard method taught when I was in school, and I suspect that in many parts of the USA it is still the standard method.”

'The professor asked to remain anonymous, saying he didn’t wish to rain on anyone’s parade.'

Guess that wasn't worth following up on, eh Metro Times Intern Reporter Person

posted by Big Fat Tycoon at 8:20 PM on July 9, 2003

'A mathematics professor at the University of Michigan believes that that’s exactly the case. Responding to an e-mail inquiry, the professor writes, “This method was the standard method taught when I was in school, and I suspect that in many parts of the USA it is still the standard method.”

'The professor asked to remain anonymous, saying he didn’t wish to rain on anyone’s parade.'

Guess that wasn't worth following up on, eh Metro Times Intern Reporter Person

posted by Big Fat Tycoon at 8:20 PM on July 9, 2003

transona5: I think that really depends on the person. I and many other people learn concepts much easier than formulas. I was always the kid who derived formulas on the exams because I can't memorize a formula to save my life. Most people probably are as you say, though, and I think that many problems in education can be attributed to the fact that people don't recognize that students have different relative strengths in learning concepts vs. concrete facts.

posted by cameldrv at 8:23 PM on July 9, 2003

posted by cameldrv at 8:23 PM on July 9, 2003

*Didn't sound like a horrible scam to me then, nor does it now. I paid nothing and did nothing beyond what I was doing anyway to get into a good school, and I got my tuition paid for two years. If it was a scam, then it was one that paid me well.*

Whoa, whoa, whoa, now, hey now, hang on there, slow down.

"Who's Who Among American High School Students" paid your tuition? Was there some form I forgot to fill out?

posted by soyjoy at 8:38 PM on July 9, 2003

"I was always the kid who derived formulas on the exams because I can't memorize a formula to save my life."

I used to do that. Then I got treated for ADD. Now I can do both!

posted by shabrem at 8:40 PM on July 9, 2003

I used to do that. Then I got treated for ADD. Now I can do both!

posted by shabrem at 8:40 PM on July 9, 2003

**jokeefe**: I don't know if there are courses that will really try, but I could suggest some books. Start with Keith Devlin... I'd especially recommend his Mathematics: The Science of Patterns. It's not Annie Dillard, but for writing about Mathematics, it's pretty close. The reading is easy, very prosy and even a bit chatty, with lots of context and good exposition for the mathematics. When you read it, don't force yourself to try to swallow something before you go on... re-read what catches your interest and your eye. See if you can approach Math with the spirit of play for a bit, because in something of the way that poets play with words to try to articulate emotion and experience and insight, mathemeticians play with symbolic thinking and logic to articulate pattern, structure, and insight.

posted by weston at 9:20 PM on July 9, 2003

soyjoy: They have always given scholarships, and they aren't really small either. Of course, tuition was WAY cheaper "way back then".

posted by Orb at 9:30 PM on July 9, 2003

posted by Orb at 9:30 PM on July 9, 2003

*amen! I hated it when teachers would grade the work and not the answers. who started that? lets hurt them.*

I'm in line with the math dorks who love to understand how all the little things work. Much like some other people here, I never could memorize formulas. In calculus and physics and all those fun courses, I learn much better by knowing HOW the stuff works in theory and figuring out eveything else from there (calculus actually does make sense if you have the right teacher- its amazing!!!)

posted by jmd82 at 10:11 PM on July 9, 2003

Heather G. was in my geometry class. She never returned my love, and I can only hope that she's regretting it now that I'm fat and middle-aged. Wait a minute..

I just switched to Adderall. Stuff is awesome.

posted by mecran01 at 10:40 PM on July 9, 2003

**Shabrem:**: "I used to do that. Then I got treated for ADD. Now I can do both!"I just switched to Adderall. Stuff is awesome.

posted by mecran01 at 10:40 PM on July 9, 2003

*They publish everyone who is nominated and passes the criteria ... whether or not you pay them for the book. I didn't. Since it was a scam, I suppose I should have returned the scholarships I received from being listed in both the high school and college versions (the ones that paid for my first two years' tuition). Didn't sound like a horrible scam to me then, nor does it now. I paid nothing and did nothing beyond what I was doing anyway to get into a good school...*

Criteria? What criteria? AFAIK the only "criteria" they have is that you actually graduated! IE:

*Everyone I knew*got the distinguished invitation. (Dunno about anyone else, scholarship or not, I'd still snicker if I saw "Who's Who Among American High School Students" on a resumé.)

I must know what good school has "Who's Who Among American High School Students" scholarships. Or is it just applied as credit to whatever good school you got accepted? And how does it work for the college version? I mean, do they pay the scholarship in advance, with the expectation that you'll be getting into "Who's Who Among American College Students" in the future?

Sounds like you were just lucky enough to get in early enough to profit from this veritable pyramid scheme.

Anyway, good on you for the accolades and working 'em to your best advantage. Got a few silly scholarships myself; who the hell are the "Daughters of the American Revolution" anyway?

posted by Fofer at 10:42 PM on July 9, 2003

great link, bluno. Worth me chiming in for the first time in a while.

Good, that's what's supposed to happen. When you're in school.

Of all the good side discussions on this thread, I like what transona5 and cameldrv are talking about, and that's called 'teaching for understanding.' Unfortunately, it's the witch's spell, the stuff teachers tend not to teach, because they've got (high?) standards (and low expectations) to meet at the state/district level. When teachers taught for understanding, and developed the 'number sense' and put students through deep, interesting problems...the kids were interested and they learned.

What Lizzie has done is use a number sense she developed early on to solve a deep problem (quadratics/polynomials) in a way she can understand better than dry formulas. Kudos to her and her teacher(s) for that much.

I hope Lizzie's scholarly interest and skills, whatever they may be, don't get squashed along with her confidence when mathematicians (even the armchair ones here) rain on her parade.

p.s. Cool math link to the 43 proofs of the Pythagorean Theorem. (Proof #5 by President James Garfield in 1876 (link) 5 years before taking, and dying in, office)

posted by msacheson at 11:00 PM on July 9, 2003

*"Things kind of stick in my head when I learn them."*Good, that's what's supposed to happen. When you're in school.

Of all the good side discussions on this thread, I like what transona5 and cameldrv are talking about, and that's called 'teaching for understanding.' Unfortunately, it's the witch's spell, the stuff teachers tend not to teach, because they've got (high?) standards (and low expectations) to meet at the state/district level. When teachers taught for understanding, and developed the 'number sense' and put students through deep, interesting problems...the kids were interested and they learned.

What Lizzie has done is use a number sense she developed early on to solve a deep problem (quadratics/polynomials) in a way she can understand better than dry formulas. Kudos to her and her teacher(s) for that much.

I hope Lizzie's scholarly interest and skills, whatever they may be, don't get squashed along with her confidence when mathematicians (even the armchair ones here) rain on her parade.

p.s. Cool math link to the 43 proofs of the Pythagorean Theorem. (Proof #5 by President James Garfield in 1876 (link) 5 years before taking, and dying in, office)

posted by msacheson at 11:00 PM on July 9, 2003

In my UK school, by age 18, I hadn't quite reached calculus level, but was quite adept at "If Johnny has eight apples and eats three, how many is he left with"?

(multiple choice answers: a. two; b. five; c. frogspawn.)

posted by skylar at 2:31 AM on July 10, 2003

(multiple choice answers: a. two; b. five; c. frogspawn.)

posted by skylar at 2:31 AM on July 10, 2003

From what my old high school guidance counselor told me, Who's Who actually used to be a legitimate operation, until somehow they lost the trademark or something like that, and then lots of bogus services sprung up that called themselves "Who's Who". Might have been in the 80s. I don't know all the details; that was five years ago.

posted by nath at 2:45 AM on July 10, 2003

posted by nath at 2:45 AM on July 10, 2003

Actually, there are more than 43 proofs for the pythagorean theorem out there. I saw one by da Vinci that involved a really neat tiling of the plane. I'm sure the number of unique proofs is at least in the hundreds.

posted by meep at 3:35 AM on July 10, 2003

posted by meep at 3:35 AM on July 10, 2003

I guess I have had too much math education because I prefer the "Split-Method" specifically because each of the last three steps can be justified in terms of elementary mathematical principles and operations (substitution, factoring, distributive principle).

The lizzie method just reeks of betty-crocker math with such phrases as "bring each denominator over to its x"(huh, you mean multiply the equation by the denominators and simplify?) and even ends with "Voila".

The end result of this kind of thinking is that those people who actually are interested in UNDERSTANDING math (you know, mathematicians.) end up being taught and graded by Mrs. Newmans who "tried it out a couple of times" before declaring "that's frickin amazing".

What actually is frickin' amazing is that neither of the explanations of the two methods bother to justify WHY it is necessary to have two numbers whose product is 36 and whose sum is 13(because 6*6=36 and 13 is in the middle, duh...). If this was actually done then not only would both methods be obvious and easily justified but the derivation of the quadratic equation would also follow...

I am a bitter, bitter, math guy...

posted by nasim at 4:33 AM on July 10, 2003

The lizzie method just reeks of betty-crocker math with such phrases as "bring each denominator over to its x"(huh, you mean multiply the equation by the denominators and simplify?) and even ends with "Voila".

The end result of this kind of thinking is that those people who actually are interested in UNDERSTANDING math (you know, mathematicians.) end up being taught and graded by Mrs. Newmans who "tried it out a couple of times" before declaring "that's frickin amazing".

What actually is frickin' amazing is that neither of the explanations of the two methods bother to justify WHY it is necessary to have two numbers whose product is 36 and whose sum is 13(because 6*6=36 and 13 is in the middle, duh...). If this was actually done then not only would both methods be obvious and easily justified but the derivation of the quadratic equation would also follow...

I am a bitter, bitter, math guy...

posted by nasim at 4:33 AM on July 10, 2003

wackybrit: I'm British and my experience is completely different to yours. I was happily solving quadratic equations for my GCSEs (ie, at 16) and there's nothing particularly hard about them.

We only got on to calculus at A-level though.

When I was about 15, I came up with an easier way for me to square whole numbers under 100 in my head. For numbers of the form ab (ie, 10*a+b), then

(ab)^2 = a^2b^2 + 20ab

eg, 43^2 = 4^2,3^2 + 20 * 4 * 3

= 1609 + 240

= 1849

I knew it was just a re-working, but I found it easier to do in my head.

posted by salmacis at 5:28 AM on July 10, 2003

We only got on to calculus at A-level though.

When I was about 15, I came up with an easier way for me to square whole numbers under 100 in my head. For numbers of the form ab (ie, 10*a+b), then

(ab)^2 = a^2b^2 + 20ab

eg, 43^2 = 4^2,3^2 + 20 * 4 * 3

= 1609 + 240

= 1849

I knew it was just a re-working, but I found it easier to do in my head.

posted by salmacis at 5:28 AM on July 10, 2003

*I left High School with an A*, the top grade, in Math*

Surely you mean that you left secondary school with an A* GCSE/O-Level in Maths? (Really, I find 'translating' British stuff to American equivalents irritating and misleading, because it's not as if doing a GCSE means you 'major' in a subject. And 'math' is what Catholics with lisps attend.)

And I was doing quadratics in secondary school. Hated the fuckers. And the writer of this piece probably had the same problem.

posted by riviera at 5:59 AM on July 10, 2003

Heh. Everyone knows that Blair Hornstine discovered this method first. Her lawyers will be in contact...

posted by paddbear at 6:14 AM on July 10, 2003

posted by paddbear at 6:14 AM on July 10, 2003

Gah, what a lot of cynics we've got here. Yes, it's a fluff story, but it's just a city rag trying to meet their human interest quota. Would you rather have the paper do the normal thing and write their token super-special high schooler story about another tri-sport varsity athlete who still has time to pad their college app by baking cookies for the old folk's home?

Do you all have any idea how rare sci-math stories are in mainstream journalism? I'm not a math whiz and, actually, I discovered that factoring was exactly the gap in my knowledge that was screwing me time and time again in Calculus. I'd never even heard of the Split Method before now and all I recall is a maybe a day's lecture about some mysterious thing called completing the square in 11th grade . For all I know, the "Lizzy Method" might have saved me from graduating a year late after trying to meet my calc II requirement.

The story even says that the method might not be all that original afterall. What more do you want?

Here we've got a teacher that actually cares about giving individual students individual choices about what methods work best for them, a teacher that's encouraging and working to reward her student's creativity. Jebus H. Crisco, that's a miracle in and of itself. Add in the genuinely modest student and you've got a nice feel-good story to pass along to your friends. Is it a waste of newsprint? Maybe. Probably. But it's certainly better than 99.9% of the other fluff that's out there.

posted by Skwirl at 6:41 AM on July 10, 2003

Do you all have any idea how rare sci-math stories are in mainstream journalism? I'm not a math whiz and, actually, I discovered that factoring was exactly the gap in my knowledge that was screwing me time and time again in Calculus. I'd never even heard of the Split Method before now and all I recall is a maybe a day's lecture about some mysterious thing called completing the square in 11th grade . For all I know, the "Lizzy Method" might have saved me from graduating a year late after trying to meet my calc II requirement.

The story even says that the method might not be all that original afterall. What more do you want?

Here we've got a teacher that actually cares about giving individual students individual choices about what methods work best for them, a teacher that's encouraging and working to reward her student's creativity. Jebus H. Crisco, that's a miracle in and of itself. Add in the genuinely modest student and you've got a nice feel-good story to pass along to your friends. Is it a waste of newsprint? Maybe. Probably. But it's certainly better than 99.9% of the other fluff that's out there.

posted by Skwirl at 6:41 AM on July 10, 2003

*“Who’s Who Among American Scam Businesses" is more like it."*

That may well be true - I don't claim to know, but I do know that a certain young lady's parents were awfully impressed when I was dating their daughter back in the late 70's that I was in there. I bet I could have done much better with the Mom than I ever did with the daughter . . .

posted by kcmoryan at 6:57 AM on July 10, 2003

oh, the lizzy method, must get my ears syringed......

posted by johnnyboy at 7:51 AM on July 10, 2003

posted by johnnyboy at 7:51 AM on July 10, 2003

*Surely you mean that you left secondary school with an A* GCSE/O-Level in Maths? (Really, I find 'translating' British stuff to American equivalents irritating and misleading, because it's not as if doing a GCSE means you 'major' in a subject. And 'math' is what Catholics with lisps attend.)*

Sure, if you want to argue semantics. I have always called it High School. 'Secondary school' is a ridiculous term, since secondary means 'of lesser rank; not primary; inferior'. Not to mention the fact I went to 'Middle School', which doesn't fit into the 'primary, secondary' scheme.. although arguably this means 'Primary School' should be called 'Low School', but I digress.

Leaving school with all your GCSEs is

*somewhat*like graduating US High School, since despite the two year difference, they both mark the first point where you can leave school for real and say "I did these subjects, and I have official proof of my abilities with them."

Either way, I prefer US English, and I choose to primarily write in it. It's far easier to expect an Englishman to interpret US English than to twist a poor American mind around our dialect. ;-)

posted by wackybrit at 8:07 AM on July 10, 2003

Uhhh....

That method's harder than what I do.

You know what I do?

Assuming I've bothered to program the quadratic equation into my calculator, I plug the three numbers in. Otherwise, I just graph the equation on my calculator - the zeroes of the equation are the factors. If I do it by hand it'd take me 3 seconds tops because I don't need to show the steps, which is less time than that method would take.

/Took Calculus his Junior Year of High School.

posted by Veritron at 8:45 AM on July 10, 2003

That method's harder than what I do.

You know what I do?

Assuming I've bothered to program the quadratic equation into my calculator, I plug the three numbers in. Otherwise, I just graph the equation on my calculator - the zeroes of the equation are the factors. If I do it by hand it'd take me 3 seconds tops because I don't need to show the steps, which is less time than that method would take.

/Took Calculus his Junior Year of High School.

posted by Veritron at 8:45 AM on July 10, 2003

Uhhh....

That method's harder than what I do.

You know what I do?

I ask the nerd sitting next to me.

posted by Fofer at 8:58 AM on July 10, 2003

That method's harder than what I do.

You know what I do?

I ask the nerd sitting next to me.

posted by Fofer at 8:58 AM on July 10, 2003

If this were being taken seriously, it would never be named the Lizzie Method. This is just an attempt to go "Aww, look, the cute little girl can do clever math stuff." Insulting.

posted by dagnyscott at 9:36 AM on July 10, 2003

posted by dagnyscott at 9:36 AM on July 10, 2003

This method doesn't impress me either... Much better to know the quadratic equation, because you can remember it using a song!

<waltz>

There will come a time as you go through the course

To conquer your task mathematic,

That every so often you will be obliged

To compute the roots of a quadratic.

Suppose that it's given in typical form,

With a, b, and c in their places.

The following formula gives the result

In all of the possible cases.

Take negative b, and then after it put

The ambiguous sign "plus or minus,"

Then square root of b squared less four times a c

(There are no real roots when *that's* minus!)

Then 'neath all you've written just draw a long line,

And under it write down 2 a.

Equate the whole quantity to the unknown

And solve in the usual way!

</waltz>

posted by starkeffect at 10:41 AM on July 10, 2003

<waltz>

There will come a time as you go through the course

To conquer your task mathematic,

That every so often you will be obliged

To compute the roots of a quadratic.

Suppose that it's given in typical form,

With a, b, and c in their places.

The following formula gives the result

In all of the possible cases.

Take negative b, and then after it put

The ambiguous sign "plus or minus,"

Then square root of b squared less four times a c

(There are no real roots when *that's* minus!)

Then 'neath all you've written just draw a long line,

And under it write down 2 a.

Equate the whole quantity to the unknown

And solve in the usual way!

</waltz>

posted by starkeffect at 10:41 AM on July 10, 2003

weston, thanks for the advice, and I will check out your recommendations. Bonus points for calming my shaky English major nerves by mentioning poetry...

posted by jokeefe at 11:05 AM on July 10, 2003

posted by jokeefe at 11:05 AM on July 10, 2003

*I hated it when teachers would grade the work and not the answers. who started that? lets hurt them.*

Yeah! When I was asked to reduce 16/64 to lowest terms, I cancelled out the 6's to get 1/4. I totally should've gotten full credit for that!

posted by DevilsAdvocate at 11:40 AM on July 10, 2003

First time I've read EVERY single comment in a thread... kudos..And everything I'm about to say has already been spoken (notably by weston, Mr_roboto, msacheson, dagnyscott), but here goes:

There are three discrete parts of this conversation a)the Lizzy method b)the reporting of the Lizzy method and c)US vs UK Math.

a) The name "the lizzy method" disgusts me, but I think a hearty pat on the back is in order. She may not be able to express herself well verbally, but anyone who defies "conventional" mathematical wisdom (that applies to you too, Veritron) gets a thumbs up in my book.

b) Guess what? Some stories aren't stories! the USA Today is full of them. Everyone's absolutely right, the homely girl sitting next to me who figured this sorta stuff out in the womb is NEVER going to be featured in an article. That's life.

c) I remember my math education. Not the math itself, but the education. I remember specifically talking about factoring using fake Star Wars Voices... ("Solve for X you must" "Oh, I'm afraid the calculator will be fully operational when your friends arrive!"), so yeah, I imagine it's quite different on the other side of the Atlantic... :D

posted by hoborg at 12:13 PM on July 10, 2003

There are three discrete parts of this conversation a)the Lizzy method b)the reporting of the Lizzy method and c)US vs UK Math.

a) The name "the lizzy method" disgusts me, but I think a hearty pat on the back is in order. She may not be able to express herself well verbally, but anyone who defies "conventional" mathematical wisdom (that applies to you too, Veritron) gets a thumbs up in my book.

b) Guess what? Some stories aren't stories! the USA Today is full of them. Everyone's absolutely right, the homely girl sitting next to me who figured this sorta stuff out in the womb is NEVER going to be featured in an article. That's life.

c) I remember my math education. Not the math itself, but the education. I remember specifically talking about factoring using fake Star Wars Voices... ("Solve for X you must" "Oh, I'm afraid the calculator will be fully operational when your friends arrive!"), so yeah, I imagine it's quite different on the other side of the Atlantic... :D

posted by hoborg at 12:13 PM on July 10, 2003

" the homely girl sitting next to me who figured this sorta stuff out in the womb is NEVER going to be featured in an article. That's life."

Yes, but that doesn't mean I can't bitch about it. That's life too.

posted by shabrem at 1:13 PM on July 10, 2003

Yes, but that doesn't mean I can't bitch about it. That's life too.

posted by shabrem at 1:13 PM on July 10, 2003

I loved finding shortcuts in math problems in school. 'course, this was defeated by teachers demanding that I show all of the work on paper (guh, so easy to do it in your head. Like multiplying large numbers left-to-right instead of the usual r-to-l.) and the occasional teacher who would scream at me for reading ahead in the math textbook ("I'm teaching the class! Not the book! Put it away!" --actual middleschool quote). Not that I'm smart by any measure. Their teaching methods just sucked.

posted by stavrogin at 11:32 PM on July 11, 2003

posted by stavrogin at 11:32 PM on July 11, 2003

The method she uses is usually called Vieta's theorem, which states that the equation a x

-b/a and multiply to c/a:

x

x

The factored form of the equation is (x - x

Lizzie's method says the solutions are x

a x

a x

Divide the first equation by a

An even faster way than Lizzie's method to solve the problem would be to first divide the equation

a x

by a:

x

and then find two numbers which add to the negative of the new middle coefficient, -b/a, and multiply to the new last coefficient, c/a.

I'm a math teacher and find it hard to believe that Lizzie's teacher doesn't seem to know this theorem, which is taught in 9th grade in Germany, by the way.

posted by amf at 6:26 AM on July 12, 2003

^{2}+ b x + c = 0 is solved by two numbers x_{1}and x_{2}which add to-b/a and multiply to c/a:

x

_{1}x_{2}= c/ax

_{1}+ x_{2}= -b/aThe factored form of the equation is (x - x

_{1}) (x - x_{2}) = 0.Lizzie's method says the solutions are x

_{1}and x_{2}witha x

_{1}a x_{2}= a ca x

_{1}+ a x_{2}= -bDivide the first equation by a

^{2}and the second by a, and you get the equations of Vieta's theorem mentioned above.An even faster way than Lizzie's method to solve the problem would be to first divide the equation

a x

^{2}+ b x + c = 0by a:

x

^{2}+ b/a x + c/a = 0and then find two numbers which add to the negative of the new middle coefficient, -b/a, and multiply to the new last coefficient, c/a.

I'm a math teacher and find it hard to believe that Lizzie's teacher doesn't seem to know this theorem, which is taught in 9th grade in Germany, by the way.

posted by amf at 6:26 AM on July 12, 2003

*The method she uses is usually called Vieta's theorem*

Viete's method is a blatant copy of Sharaf al-Din al-Tusi's, which was taught in the 12th century in Mosul.

posted by eddydamascene at 6:55 PM on July 15, 2003

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This thread has been archived and is closed to new comments

~~article~~puffball.She combined three steps. It's something I'd be proud of my university students for figuring out on their own. That's about it.

My god! Did they really say

plugging numbers into the quadratic formula, a complex and tricky device that mathematicians try to avoid whenever possible.? Kill me now.posted by gleuschk at 3:58 PM on July 9, 2003