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The Way You Learned Math Is So Old School

npr.org

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Re: The Way You Learned Math Is So Old School

#21

Post by decklin »

dhimes wrote: post #20
zwieback wrote: post #18

Either way is fine, I think, if you the child understands the underlying mechanism. I'm the father of a 3rd and 5th grader in US public schools and I think the math curriculum is very good. However, sitting down and explaining basic arithmetic is important. I also teach them to estimate and come up with a quick upper and lower bound before they start the problem. I went to school in Germany and our methods of multipl…

I agree. For learning, the method shown is fine. Why? Because it teaches and honors place value , an extremely important concept in developing numeracy. I'm fine with any method that uses that. I am not fine with something my kids call the "lattice method." The point of this method is simply to get the correct answer for multiplying large numbers. Is it clever? Yes. Does it work? Yes. But it does not teach math . If…

I'm not sure why you think this lattice method does not teach place value. The page you linked to doesn't explain (at all) why it works, sure, but the method is just a clever way of notating place. I would expect any good teacher to get his or her students to understand that, and not just mindlessly fill in numbers.

Re: The Way You Learned Math Is So Old School

#22

Post by thinkingeric »

zwieback wrote: post #18

Either way is fine, I think, if you the child understands the underlying mechanism. I'm the father of a 3rd and 5th grader in US public schools and I think the math curriculum is very good. However, sitting down and explaining basic arithmetic is important. I also teach them to estimate and come up with a quick upper and lower bound before they start the problem. I went to school in Germany and our methods of multipl…

"teach them to estimate"

I suspect that the 'calculator age' has caused kids (and kids that have now grown up to be parents) and maybe educators to over-value an increase in significant digits in calculations. It's interesting that the method of multiplication illustrated in the article is referred to as 'new' since when you use a slide rule, you operate in this way anyway. And to echo Hans Bethe, this is often "good enough".

Re: The Way You Learned Math Is So Old School

#23

Post by dhimes »

decklin wrote: post #21
dhimes wrote: post #20

Earlier quoted context omitted.

I agree. For learning, the method shown is fine. Why? Because it teaches and honors place value , an extremely important concept in developing numeracy. I'm fine with any method that uses that. I am not fine with something my kids call the "lattice method." The point of this method is simply to get the correct answer for multiplying large numbers. Is it clever? Yes. Does it work? Yes. But it does not teach math . If…

I'm not sure why you think this lattice method does not teach place value. The page you linked to doesn't explain (at all) why it works, sure, but the method is just a clever way of notating place. I would expect any good teacher to get his or her students to understand that, and not just mindlessly fill in numbers.

I would expect any good teacher to get his or her students to understand that

That's not how I've seen it used. I've seen it used as a procedure for getting the answer. Compare that to the method shown in the npr link, first line: the numerals are 2 and 3, but the numbers multiplied 20 and 30. That's what I mean by teaching place value.

In the the old-school method I learned, we respected place-value by indenting (from the right), optionally writing the zeros.

Re: The Way You Learned Math Is So Old School

#24

Post by Jach »

I don't really think the methods are important, what's important is whether students decide to learn more advanced math later (say at least up to Calculus), and more importantly whether they like doing so. Too many people say "I hate math", learning multiplication one way or another shouldn't affect that strongly.

The article has a few nice quotes I like: "Computers do arithmetic for us, Devlin says, but making computers do the things we want them to do requires algebraic thinking."

'"You cannot become good at algebra without a mastery of arithmetic," Devlin says, "but arithmetic itself is no longer the ultimate goal." Thus the emphasis in teaching mathematics today is on getting people to be sophisticated, algebraic thinkers.'

While I can do multi-digit multiplications just fine and have a high confidence in my answer, I'd much rather a calculator do it for me, allowing me a higher confidence in the answer and just being done faster to use the result for some other purpose.

Re: The Way You Learned Math Is So Old School

#25

Post by Splatchar »

mynegation wrote: post #7

At risk to be downvoted to death, I have to say that the new way of multiplication is actually _better_ than the old one, at least for kids starting to learn how to multiply. All the new multiplication algorithm does is makes implicit additions explicit, so that you do not have to keep carry-over digit in memory. 144 is 120+24 and 720 is 600+120. Sure it trains your short memory, but we are talking about 7yr olds her…

I think you've nailed it by considering the carry-overs.

With the new method there's less opportunity for error. The old way, there are two sets of carry digits: those arising in the initial multiplying, then more in the final adding up (though not in the example given). Sometimes I would try to remember them; sometimes I would write them down in various places; frequently I forgot or muddled them up somehow.

Another benefit is: the new way gives you a sense of the magnitude of the final answer more quickly. Approximations are useful. Contrast with the old method which begins by multiplying the least significant digits.

Re: The Way You Learned Math Is So Old School

#26

Post by Groxx »

hackerblues wrote: post #13
icegreentea wrote: post #5

...Does anyone actually teach their kids with that retarded method? All it does it take up more space, and shift the burden from screwing up carries while multiplying to screwing up carries while adding. And since it's so brain dead to implement, I can't see any significant amount of kids even reflecting on how 'the numbers work' based on that.

As far as I know every child in England is currently being taught this method. I'm not sure that I would leap to calling it retarded. I agree that it takes up more paper but paper isn't the most expensive thing in the world. What it does do is make explicit why the old school method works. Look at the explanation given by the article for the old method: 'Answer = 720, Because: 2x36 = 72, with a 0 added in the ones pl…

I still encounter people who try to teach long multiplication to kids by saying "add a zero in the ones place". And college students who fail to describe why they add those zeros (typically liberal arts majors (no offense. They just rarely minor in math, and many quit doing math entirely after they get the minimum to graduate)).

Re: The Way You Learned Math Is So Old School

#27

Post by madcaptenor »

To be honest, I just know 36 times 24. I've spent enough time dealing with numbers with all their prime factors small that I can just see it's 864. It might also help that I know there are 24 hours in a day, 3600 seconds in an hour, and 86,400 seconds in a day -- and I probably have a lot of random facts like this somewhere in my head that I at least occasionally pin mental arithmetic problems on.

Re: The Way You Learned Math Is So Old School

#28

Post by darthvivi »

Changing the way the multiplication algorithm is taught isn't going to fix anything.

There needs to be a fundamental change in the way mathematics is taught. Right now what most schools teach in math class resembles trivia more than mathematics. There is no appeal to intuition or understanding, because clueless symbol manipulation and memorization of formulas is apparently what really matters. It is not necessary that the student really understands what he is doing. Why is the product of two negative numbers a positive number? "That's just the rule." Why is dividing by a fraction the same as multiplying by the reciprocal? "That's just the rule." These are very simple concepts that can be both logically and intuitively presented to students, yet growing up those were the answers I received. Even high school geometry, which used to be taught decently, has now been replaced by curriculum that does not emphasize proofs or any kind of true understanding/intuition.

Unless students discover the beauty of mathematics independent of math class, or enjoy following arbitrary rules, it is no wonder they develop a dislike for mathematics.

Although the author's writing style is a little bit annoying at parts, this is a good read: www.maa.org/devlin/LockhartsLament.pdf

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