How math teaching has changed

Math for 12-year-olds leaves dad feeling deep blue

By Nury Vittachi

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Readers may recall that last week I got stuck helping my son with his math homework. It was actually quite doable, as long as you had Albert Einstein, Stephen Hawking and the Deep Blue supercomputer helping you (in the parent-child sense of "doing it for you").

                This week my daughter needed help with her math. A chance to redeem myself!  SuperDad to the rescue. "Move over. I'll show you how it’s done," I said, butting her out of her seat.

                The homework for a 12-year-old, and I am not making this up, was an equation with a question below it: "In the above polynomial, what can x be equal to in the set of positive irrational numbers?"

                Huh? Suddenly, I remembered a pressing appointment elsewhere and fled the scene.

                It made no sense. I thought a "Polynomial" was a resident of the Pacific islands. And everyone knows that numbers cannot be "irrational" (a Latin word meaning "female").

Has mathematics become harder? Or have I become significantly stupider? (Don't answer that.)

You know what it is? Math teaching methods have changed over the years.
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                Teaching style in Asia in the 1930s:

Complete the following list of arithmetic tables: 12 x 12 = 144. 12 x 13 = 156. 12 x 14 = 168. 12 x 15 = 180. 12 x 16 = 192. 12 x 17 = 204. 12 x 18 = 216. Now memorize them by copying them out 100 times.
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                Teaching style in Asia in the 1940s:

Mrs A has 13 mangos. She gives six mangos to her husband and six to her son. She shares her last mango between her six daughters.  Is she being deferential enough to the men in her family?
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                Teaching style in Asia in the 1950s:

                Mrs Fong has 13 mangos. She gives 12 to her local Party work unit because property is theft. Should they shoot her for keeping one?
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                Teaching style in Asia in the 1960s:

                Amy has 10 apples. Should she eat them, smoke them or puree them so they can be ingested intravenously? Justify your answer using lyrics from Beatles songs.
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                Teaching style in Asia in the 1970s (the era of New Math):

                Amy has 10 apples. We can think of her as set A, and her apples as the subset (A/a = 10).  If Amy gives five apples to her friend Melanie (set M), who already has three apples (M/a = 3), what does the word "subset" mean anyway?
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                Teaching style in Asia in the 1980s:

                Ming Ming has a cassette recorder and a shack on the roadside.  Jaya has a cassette recorder and an Abba cassette. How long will it take them to make a fortune in pirated cassettes?

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                Teaching style in Asia in the 1990s:

                Ming Ming has ten shares of Apple Computers Inc. She wants to retire by the time she is 40. Should she (a) work hard and save money? Or (b) make a career writing viruses that attack Microsoft software?

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                Teaching style in Asia today:

                Ming Ming is starting a secondary market in selling unused hydrocarbon credits to offset global warming. She can achieve a profit ratio of 3.5 per cent net after costs of 81 per cent where x = 100 – 73/81. In the above polynomial, what can x be equal to in the set of positive irrational numbers?

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                Can anyone give me Deep Blue’s email address?
 

 

Comments

[fardel]

Do not worry , we have the exact same problem here with the maths programs
( which just happened to be the same as yours at the same time over last century).
When my daughter says the terrifying word "maths" ,I send her to have the problem translated in decent language.
Since such a translation does not exist , I am quiet for a while;

[Steve]

Seems to me, the teachers teaching new math, learned math from teachers who were teaching old math.

Something just doesn't add up.

[khirsah]

Maths in Asia has become more of a language subject. I come across several people who failed maths (exams questions set in English) terrible because English is not their native language, resulting in them having difficulties understanding the questions and answering them wrong.

[godiva]

I think I have an answer to that, Steve. Remember that post here (last 23 July 2008)how an office memo contained a totally different message from the original when it passed down from the president's office down the line? Maybe, the same thing happened to math.

Nury, is two x two in your daughter's class still what it used to be?

[Adalina Lo]

I feel sorry for these kids. Whoever writes these questions are sadists; either that, or very good businesspeople. Kids have to score well in stupid standardized tests and with such cryptic questions, tutoring and crash courses are required - big bucks are made that way.

[kidkid]

Ha ha, it's funny to see you adults all baffled by that math question! actually it's quite simple, most kids aged 12-15 could do it! just ask your kids!!!

[no one]

Now I realize that that idiotic tv show Are you smarter than a fifth grader could work with people from anywhere- adults every where cannot do the stuff that kids have to do at school

[Vince A]

"In the above polynomial, what can x be equal to in the set of positive irrational numbers?"

I didn't realise how mollycoddled kids are these days!

First they are told where the expression can be located on the page ("Above". Not below. Not on the next page)

Then they are gently reminded what kind of expression it is ("polynomial"), just in case they forget that any expression with x is a polynomial.

Then they are clued-in on the type of answer (pssst, hey bud, it's a "positive, irrational number", wink wink).

Finally, their fragile egos are protectively stroked by suggesting their opinions and feelings have some value ("what can x be equal to...?").

In my day, all we had was "Determine x", and "No erasures allowed".

[Nury]

Wow, Vince you actually understand this stuff. Pretty impressive. Are you/ were you one of those Asian mathgeeks at school?

[kavita ojha]

it,s very easy to answer if you involve your self in understanding and helping the child to understand and swim across such hurdles.

[John Simmonds]

I don't think math methods have changed too much, it is just that students feel that they shouldn't be pushed too much, otherwise they will bitterly complain. In any introductory math course in the 50's they would even cover Fourier Transforms and elliptic integrals, but now you're lucky if they let you cover up to the FTC

[fardel]

I was reprimanded by the school when my daughter was 10;
she was the only one without a calculator.

Kids can no longer use their buit-in technology: counting with fingers.
Times have changed

[Lisa]

Fardel, that's true. When I came to HK as a F.3 student, I learned that I needed to buy a calculator to do the math equations. And not just any calculator but a really expensive one with lots of special functions that we had to learn about.
After completing F.5, I've never even come close to having to deal with numbers, unless it involves mahjong/card game scores, adding up utilities/grocery bills or deciding whether it's cheaper to buy Huggies diapers at $80/56pcs or Pampers at $120/74pcs.

[sej]

I think Year 9 (HK's F3?) was I think when I last did maths with numbers. After that it was all hieroglyphics and calculators weren't much use.

[Uli]

I feel with all people who develop a huge question mark on their foreheads while struggling to understand maths. I consider myself born without that specific ability, so what the heck!
Since I am good at languages I always answered my maths-teacher in the most complicated French sentence I could think of (she didn't understand French). The first time she looked puzzled and asked what I had said. I simply smiled and told her that I understood just as much of her question as she understood my answer.
I'll say that for her: she had let me scrape through with the minimum mark necessary and I tried to work as much as I could do in order to justify her making up my marks a little.

[Albert]

Sounds like your daughter is getting a good maths education. They hadn't even taught negative numbers, let alone irrational numbers and polynomials, at my school by 12 years old (in the 90's at a 'good' private school in Australia). Instead we were doing fraction addition for the 3rd year in a row and getting marks for drawing borders on our homework with coloured pencils.

Pythagoras and his sect the Pythagoreans discovered irrational numbers around 500BCE. I bet they expected their pupils to understand them by age 12; and that was millenia before the decimal number system that we use today (which is how irrational numbers are usually taught, as a 'decimal number that goes on forever without repeating').

[Christy]

I used to understand all these stuff perfectly. I got a B in HKCEE Math, and that was just in 2007! Now two years, later, not having taken Maths in my A-Levels, all my Math knowledge has slipped away!

I was horrified to find that I could not understand your daughter's Math question...if I were to retake CE Math, I'd probably flunk the test...

[schoolkid]

If the question is "determine X", the last problem set about 'global warming business' will come to an answer...

X = 2.809... (close to a 2.81)

lol

[ij carolina]

Thanks alot for all your wonderful articles mr.nuri.I enjoy each and every one of them. You are simply a genius!...thanks again...