Forbes has an interesting guest editorial on its online page. Mr. Joseph Tartakovsky has decided to write an op-ed on the uselessness of studying math. I suppose that Forbes decided to run this in the interest of equal time, given that they've linked to an essay by Diane Ravitch. Tartakovsky is a law student who has no use whatsoever for math, stating "Why teach math in the age of the calculator? The device is available everywhere, from cellphones to fashionable watches."
Like any good lawyer, he backs up his thesis with facts:
"Once a visitor to the Indian prodigy Srinivasa Ramanujan (1887-1920) noted that his cab number, 1729, seemed "rather a dull one." "No," replied Ramanujan, "it is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways." He did that in his head. So what? Give me two minutes and my calculator watch, and I'll do the same without exerting any little gray cells. "
Look Tartakovsky, I hate to be the one to rain on your parade, what with publication in Forbes and all, but I think that even with two calculators and a laptop you wouldn't be able to prove Ramanujan's thesis.
He goes on and completes his proof of the uselessness of math by showing that both Benjamin Franklin and Winston Churchill were bad at math but went on to illustrious careers in spite of it.
Other than the fact that Tartakovsky has no use for math, I don't know what point he is trying to make. I only hope that as our recession worsens, he doesn't write an essay scolding big business for hiring engineers from China and India when so many people in the U.S. need jobs.
The Franklin/Churchill argument is a classic straw man.
ReplyDeleteYes, it is possible to be successful with poor math skills. It is also possible for a single parent to successfully raise a child. It is also possible for a school drop-out to become highly successful. All things being equal, however, you have a much better chance of success with good math skills, 2 (loving) parents, and by staying in school. Neither case is a guarantee, one way or the other, but the odds are definitely stacked.
The most idiotic part of his argument about 1729, however, is that without math skills he would have no way of using either a calculator or laptop to even begin to find that information. Even if he knew the method, however, he could punch in the wrong numbers, or the right ones in the wrong order, or bump the wrong button. He would end up with a completely incorrect and nonsensical answer, but think it's right.
what on earth are you complaining about? what on earth is tartakovsky complaining about?
ReplyDeletea chess gm HAS TO practice/study with a computer now, it gives a player such a advantage. computer databases and analysis has increased the skill level hugely.
automating tasks can increase progression in a field by a massive amount, even in education. i think all you're doing is romanticising education. should something like arithmetic be taught? yes, but personally, i think my arithmetic has sharpened since i've been using a calculation it's quickness with large numbers. what's the difference between learning a times table or learning with a calculator? none to me, it's the same thing. not saying it's quicker than plain pen and paper, work it out method, but i've also been doing work that's actually worth doing and interesting.
this blog can be incredibly hypocritical. promoting practice yet scorning discovery-learning, yet their definition is basically the same. then direct instruction receives praise and the fact that it's the opposite of discovery-learning is highlighted but never that it's the opposite of practice. as clear as mud.
using a calculator*
ReplyDelete""No," replied Ramanujan, "it is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways." He did that in his head. So what? Give me two minutes and my calculator watch, and I'll do the same without exerting any little gray cells. "
ReplyDeleteIt seems ironic Tartakovsky claims to need two minutes AND a calculator watch to do what Ramanujan did in his head with a glance at the numbers. Perhaps the argument would be that Ramanujan was a prodigy. What with the two minutes, and the calculator and all, it seems like Tartakovsky would have exerted more gray cells than he's aware of.
I love this part:
ReplyDeleteThe immortal example of Churchill, savior of the West, proves not only that math was unnecessary to save civilization, but that, as it nearly kept him out of the academy, math positively endangers it
Obviously, because the war effort depended entirely on Churchill's oratory, and not anything from those nerds at Bletchley Park.
Apparently, studying history is highly overrated, too.
So, do you think Forbes will run a piece on the uselessness of studying law? After all, when was the last time lawyers ever contributed anything useful to society? (Counterexample #1: politicians ;) )
ReplyDeleteReading the article, I *think* that the author was trying to write a humorous piece.
ReplyDeleteNote the claim that multiplication was covered in one week of 2nd grade (I doubt that!) after which the class proceeded to long division (in 2nd grade? Really?).
Later in the article he writes this, "Our numerals are imported from the Middle East. As the war on terror progresses, it is crucial to reduce our dependence on the region."
-Mark Roulo
Benjamin Franklin was bad at math? Has Tartakovsky seen the various publications about Franklin's "magic squares"? There was just a book published in 2007 that dealt primarily with Franklin's math talent--Benjamin Franklin's Numbers: An Unsung Mathematical Odyssey.
ReplyDeleteReading the article, I *think* that the author was trying to write a humorous piece.
ReplyDeleteIf so, many people missed the joke.
"Reading the article, I *think* that the author was trying to write a humorous piece."
ReplyDeleteHeh. I think you're right. I'll admit I went in guns a'blazin', and I consider myself to have a good sense of humor. Ah well. So often the clearer mind prevails. Glad you made that comment. It just goes to show (me) that a veracity for good education sometimes clouds the perspective in the presence of humor.
Leaving the satire issue aside, I must note that Churchill's math issues made him a disastrous Chancellor of the Exchequer, long before he became Prime Minister.
ReplyDeleteHe's trying to have it both ways, and it doesn't work. It's neither funny or satirical. I could write a funnier piece about the uselessness of math.
ReplyDelete"Joseph Tartakovsky is a contributing editor of the Claremont Review of Books and a J.D. candidate at Fordham Law School."
Now we know how much math is required for law school.
Now we know how much math is required for law school.
ReplyDeleteJust enough to convince a civil jury into believing that random variation is a statistical outlier.
Anonymous, Srinivasa Ramanujan wasn't just doing arithmetic. He was making a claim that 1729 is the smallest number expressible as the sum of two cubes in two different ways. This meant that Ramanujan had at some point carried out a mathematical proof showing that no number smaller than 1729 could be expressed as the sum of two cubes in two different ways, which is quite different to merely showing that 1729 could be expressed as the sum of two cubes in two different ways.
ReplyDeletewhat's the difference between learning a times table or learning with a calculator? none to me, it's the same thing
Not quite. If you memorise your time tables you can do basic calculations whenever you don't have a calculator. If you're dependent on your calculator you're stuffed if you don't have one with you, or your battery is flat. If you intend to spend your life entirely in front of a computer screen that's not a problem, but my life is a bit more exciting than that.
but i've also been doing work that's actually worth doing and interesting.
People have been doing work that's actually worth doing and interesting long before calculators. For example Newton developed calculus without the use of calculators. Before you criticise mathematics, try to learn a bit about it.
promoting practice yet scorning discovery-learning, yet their definition is basically the same. then direct instruction receives praise and the fact that it's the opposite of discovery-learning is highlighted but never that it's the opposite of practice. as clear as mud.
Discovery learning's definition is not basically the same as the definition of practice. See for example Wikipedia:
"Discovery learning takes place in problem solving situations where the learner draws on his own experience and prior knowledge and is a method of instruction through which students interact with their environment by exploring and manipulating objects, wrestling with questions and controversies, or performing experiments." http://en.wikipedia.org/wiki/Discovery_learning
'Practice or practise (verb form in British English) is the act of rehearsing a behavior over and over, or engaging in an activity again and again, for the purpose of improving or mastering it, as in the phrase "practice makes perfect". ' http://en.wikipedia.org/wiki/Practice_(learning_method)
In fact anonymous's statements are so ignorant that I suspect that it's an attempt at a troll.
"In fact anonymous's statements are so ignorant that I suspect that it's an attempt at a troll."
ReplyDeleteI missed those comments by anonymous, such as this:
"this blog can be incredibly hypocritical. promoting practice yet scorning discovery-learning, yet their definition is basically the same. then direct instruction receives praise and the fact that it's the opposite of discovery-learning is highlighted but never that it's the opposite of practice. as clear as mud."
This grammar and phrasing is as clear as mud.
Discovery learning, as parcticed in K-12 is a top-down process that starts with real world or thematic concepts and then works its way down towards mastery of the basics. This is a very inefficient process and mastery of the basics is less likely to happen. The resultant understanding is crippled.
Direct instruction is a bottom-up approach that ensures mastery of the basics and then uses that mastery to achieve higher-level understandings. Although there might not be much time left over for applied usage and/or thematic connections, the basic skills are still there. The student is not educationally crippled. One could make an argument for what might be called bottom-up discovery, where students apply mastered skills to new situations, but that's not what is happening in K-12.
The key is the linkage between mastery of the basics and real understanding, not conceptual understanding. The K-12 discovery approaches I've seen all deny that linkage. They call it rote or superficial learning.
The goal is to practice skills, not practice discovery. Discovery may be nice at times, but it's neither necessary or sufficient.
I found the editorial rather boring and without structure. Perhaps a bit more mathematical thinking would have created a better read.
ReplyDeleteFurthermore, maybe the author doesn't realize that calculators do arithmetic, not math. If I gave him my TI84 Plus and challenged him to a duel, I bet I could beat him to death with my pencil before he could figure out how to do math with it.
Paul B - giggle. The pen is mightier than the calculator.
ReplyDeletethis stuff isn't even meant as satire
ReplyDeleteor even necessarily humor on my reading;
it's just filler plain and simple:
chewing gum for the eyes.
you already know everything he's gonna say
before you're halfway started; what joy
in finding out you're right. i guess.
reading as if reading were tv: something
to put between the ads. blag!
He evidently needed the money. Don't we all? Hey, maybe I'll moonlight for TERC.
ReplyDeleteWho wants to stuff their pocket with a calculator when it's so much easier to carry a pencil? Technology, even 5 zillion years from now, won't matter: a calculator will never be thinner than a pencil because a calculator must have a minimum size, determined by human ergonomics, for a screen and buttons.
ReplyDeleteari-free
Well it does depend on the calculator. :) I've carried my calculator around the world with me - carry-on luggage, I would never risk it to checked. I don't care about pencils.
ReplyDeleteAlthough my love for my particular calculator can never die, I am aware that in other people's cases, those people who have not yet fallen head over heels, it is possible that new, smaller technologies may replace calculators. There's been demonstration systems of something the size of a pen that just projects light onto a surfance in the shape of a keyboard, and can then detect your typing.
to tracy w,
ReplyDeleteand why would you be able to memorise answers from a times table but not a calculator? double standard. you can master multiplication with a abacus, i see no reason why a similar effect can't happen with a calculator - http://www.youtube.com/watch?v=wIiDomlEjJw - perish the thought
and the definitions of practice and discovery' do not contradict each other, both are trial and error and involve a sort of 'scientific method' approach. behaviour is repeated until incorrect behaviour is eliminated and correct behaviour conditioned. is solving a maths problem discovery' or practice? it fits into both categories.
as for calling me ignorant, go f**k yourself(you started it).
Then there is the example of someone who has obviously partaken of discovery learning in the art of writing.
ReplyDeleteWith practice and direct instruction, one can usually find the shift key then put it to use writing sentences that make sense. With discovery alone; not so much!
Actually, I'm thinking that having sex with yourself, as suggested above would be no worse than the expository masturbation on display.
and the definitions of practice and discovery' do not contradict each other, both are trial and error and involve a sort of 'scientific method' approach.
ReplyDeleteQuite correct. Practice can yield discoveries. This goes to what SteveH calls "bottom up" type discovery. The "top down" type discovery methods are not efficient--even when direct instruction may be given along the way. "Just in time" methods don't work well for people trying to learn math. Finally, "constructing ones own knowledge" can occur with direct instruction -- "aha" moments are not restricted to discovery with minimal guidance.
as for calling me ignorant, go f**k yourself(you started it).
ReplyDeleteout of bounds
Is my existence blighted by an inability to add 15% to a check?
ReplyDeletein my experience, the answer to that question is 'yes'
Did this article appear in print?
ReplyDeleteYou know, seriously, I'm asked this question every week, sometimes twice. What the heck do I have to know this stuff for? My stock answer now goes something like this.
ReplyDeleteYou're 13 years old. There is no way to know, right now, where your life will take you but one thing is certain. Life is a journey, with many forks in its path, and at every fork we would like for you to be the one who decides which path to take. Every skill you've mastered increases the choices available to you. Every skill you've cast aside decreases those choices.
If you aren't equipped to take a path then someone else will choose one for you and they won't have your interests in mind, they'll have their own.
End of speech.....
This is the essence of a well rounded education, isn't it? I'm not sure anything beyond a small percentage is ever going to use math in their career, but it would be folly to suggest that we could divine this early enough to do anything about it. And, it's pure hubris to think that we know enough about how the brain works to forgo a discipline so devoted to structure and logical thought.
You can argue about the edges all you want but it's really hard to make a pass on this parting thought...
Humanities earliest abstractions were tick marks, pictures, music, and glyphs. Are we smart enough now to pick and choose which of these are important?
Catherine:
ReplyDeleteNo need for a blighted existence...
In Massachusetts it's 3 x the sales tax.
In New York it's a little less than 2 x the meal tax
If you're unlucky enough to travel to D.C it's 1.5 x the meal tax.
If one is challenged by fractions this makes D.C. problematic so most people just use 2 x and end up paying 20% tips. Of course bloated and Washington D.C, sort of rolls off the tongue effortlessly these days and overpaying for shabby service seems appropriate there.
No matter your arguement, basic math skills are essential. How are we going to send someone to Mar or develop better engineering skills/technologies enless we educate a group of individuals who possess the know-how to get from point A to point B? And, do we want to determine that it is OK for our public schools to eliminate the possibility for children in elementary school? Computers/calculators are not necessarily independent thinkers. The people who write the programs for them are.
ReplyDeletewww.ctcoalitionforworldclassmath.com