This is why that stupid way to multiply isn't so stupid after all


#1

Originally published at: https://boingboing.net/2017/11/03/this-is-why-that-stupid-way-to.html


#2

I’ve seen this locally too. Teachers start showing the kids how to have some basic number sense and parents flip the fuck out. It’s long division or the highway for them apparently.

An example of the “new math” that is going to ruin the children: You want to subtract 57 from 73. You could do it the old way by carrying the one and subtracting 7 from 13 and then 5 from 6 and add them together. Works, but there’s a fair bit of mental load. Option 2 is to add 3 to the 57 to make it 60, subtract 73 from 60 to get 13, and then add the 3 back on. The second way is apparently witchcraft and grounds to pull the kids from school for homeschooling.


#3

Well, if the goal was to have them do the multiplication fast then why have them use an O(n^2) algorithm? at least use something O(n^1.6)

But more seriously, the area version builds intuition for place value and the distributive property (for when they are in algebra).


#4

Obligatory https://www.smbc-comics.com/comic/why-i-couldn39t-be-a-math-teacher


#5

Remembering the additional exponents in the addition stage has always been the flaw of that technique. Luckily it is usually pretty obvious (your answer is off by several orders of magnitude usually) if you know what to look for. Kids tend to struggle with it though.


#6

This is a dumb method for two digit multiplication. The straightforward way is to see that 36 x 12 = 24 x 24 - 12 x 12.

But if you’re really lazy like me, you can just notice that 36 x 12 = 4 x12 x 12 - 12 x 12 = 3 x 12 x 12 and go back to watching cat videos instead.

KIDS THESE DAYS


#7

In my day we added 43 to 73 and knocked a 100 off in post-production.


#8

Some things never change. From Wikipedia concerning “New Math” in the 1960s, when I was in school: “Parents and teachers who opposed the New Math in the U.S. complained that the new curriculum was too far outside of students’ ordinary experience and was not worth taking time away from more traditional topics, such as arithmetic.”


#9

Showed my college age son my old high school slide rule and how it worked. It was obvious to him how it worked but he said, well if you are multiplying 47,000 by 650 how do you keep the decimal places straight. I responded you just did, it’s really not that hard. It was like we were speaking different languages


#10


#11

Huh. That’s my shortcut in my head to juggle fewer numbers. Some people think I’m good at math 'cuz I can do operations in my head quickly. (I’m not)


#12

Option 3 is to add 3 to both 57 and 73 and subtract 60 from 76. If you envision the subtraction as finding the distance between the numbers on a number line (or ruler), this option is the same as sliding the problem a little further down the ruler without changing the distance between the numbers.


#13

That’s where Spinal Tap’s money went?


#14

Me, too, as is the method documented in the post. Just the way I’ve always done it in my head; glad it works for others!


#15

Those who have a strong interest in dividing people have not left education untouched. One party’s effort to bring US math education up to the same standard as other nations (i.e. the dems) has to be - MUST be deeply distrusted!
So, for example, if an initiative such as Common Core is introduced, and that plan includes forms of mathematics not widely taught in schools previously… Well, flame on :stuck_out_tongue:


#16

Well, Mr Snelgrove, I happen to know that in the future I will not have the slightest use for algebra, and I speak from experience.

:sunglasses: Peg Kelcher


#17

Third quarter of the video is the important bit. The objections to these “new” ways to teach math are ultimately rooted in a misunderstanding about what the real learning objectives are. (And a lack of ability on the part of parents who never learned how to be good at math because they were never taught math very well to imagine that hey, in 30 years maybe somebody thought of a better way to teach this stuff.)

If the learning objective for a two-digit multiplication problem is “get the right answer”, then the way we learned it 40 years ago is a pretty good way to teach that. But that’s a stupid learning objective in an era when you everyone has a voice-activated supercomputer in their pocket. When the learning objective becomes much more sophisticated and genuinely useful, something like “understand what’s actually happening to two-digit numbers when you multiply them”, then making students memorize a mindless algorithm is a terrible way to teach it. Stacking two two-digit numbers atop each other and memorizing the FOIL pattern completely obscured the fact that it’s exactly the same mathematical operation, whereas drawing the four quadrant box makes this much more useful concept explicit and obvious.

Siri and Alexa have made pretty much any “memorize this thing” learning objective a complete waste of time, in all of primary, secondary, and tertiary education. Time to update curricula to reflect that, and to craft learning objectives that involve not memorization of facts that everyone has instant access to, all the time, but instead demand genuine conceptual understanding and application of those concepts.


#18

Relatedly, you have to be able to figure out what’s the right question to ask said supercomputer. That seems to be as much – or more – of a stumbling block.


#19

I just got my dad’s old “Versalog” slide rule, it all looks like greek to me but I look forward to someday having the time to learn how to use it (I’m assuming there are instructions on the internet somewhere).


#20

Gershon Legman, in Rationale of the Dirty Joke, just had to tell this clean one: The Professor is lecturing. “Today, class, we will learn the use of the slide rule. Through its operation, we may easily and with precision multiply any two numbers together. Any two numbers. May I have two numbers, please?”

The inevitable voice in the back (I think he had a whole chapter on that) shouts, “TWO TIMES TWO!” Without breaking stride, the Prof continues. “We simply slide this scale so that the one lines up with the two, and then we slide the hairline to line up with the two on the other scale, and our answer… (he squints) …is three point nine, nine, …eight. But we’ll call it four.”