>> PI day — Mar. 7, 2013.
>> The Math Museum In
>> New York City — Mar. 4, 2013.
If so, as the incomparable Kipling said: “You’re a better man than I am, Gunga Din!”.
I guess unlike me, an old man pushing 60, who learned his 3 Rs in the 1950s (in a third world country), you must know all about ‘Number Bonds‘. Just this year, looking at Teischan’s homework I became vaguely aware that they were doing this stuff called ‘number bonds’. Initially all I had seen was the two dangling ball efforts to deconstruct an integer and I had no problems with that since I do think that kids should appreciate how a number comes to be what it is. Now to be fair, ‘number bonds’ is part of the new, ‘new math‘ – the so called ‘Singapore Math‘ (and in case you don’t know, ‘Singapore‘ is a tiny Asian country, really best known for its infamous capture by the damn Japs during WW II, when it, like my home country was a British colony). Singapore Math is being taught all over the place, not just in Alton.
Then yesterday Deanna showed me this homework that Teischan was struggling with. It took my breath away. I never realized that they were going to use the two dangling balls to do arithmetic operations. So, have a look at this.
They had done the top 2 in class, on the blackboard. She had supposedly transcribed the method and answer from the board onto her sheet. Number 2 was wrong and we asume she copied it wrong.
Though I had never seen subtraction done this way, I could work out how they got ’14’ for #1 and the (correct answer) ’12’ for #2.
Then I noticed that we had a problem! Number 3 and 4 (’17.’ & ’18’ on the sheet) were very different to the other three, and the two they had done in class. Can you spot the difference? Yes, the ‘ones’ number of the second operand is BIGGER than that of the first operand. To use the same technique as for one & two, you would have to use a NEGATIVE NUMBER, in this case ‘-4′ which when added to the ’10’ will give you the right answer ‘6’! But even I, with my high expectations of kids, do not really expect 6 and 7 year olds to be that conversant with negative numbers. IF you don’t use negative numbers, then you have to use a DIFFERENT technique to handle numbers 3 & 4!
I had no idea what that different technique would be. So I did what I always do when I am stuck. I Googled. I found this excellent video tutorial, with exactly the right example, at ‘onlinemathlearning.com‘. Here it is. You have to watch it.
Notice the BIG ‘No!’. I was mortified.
There is an exception to the method. This is for 6 and 7 year olds.
I have two issues with using this strange, two dangling ball approach for teaching kids subtraction.
1/ This method does NOT ELIMINATE the need to do subtraction! Ah? Kids still have to do subtraction with this approach. So what is the gain. I would be all in favor if this method eliminated the need to subtract and said kids could do subtraction by just adding numbers. Now that isn’t as crazy as it may sound to the uninitiated. Logarithms. Now that is real math. We (as kids who didn’t have calculators) used logarithms because ‘logs’ allowed you to do complex multiplication and division using just addition and subtraction. That is neat and useful. You eliminate a complicated process with an easier, better mastered technique. Not so with the two dangling balls. You still have to do the damn operation — in this case subtraction. Plus, how do they teach subtraction. They count the difference between the two numbers. If so, why bother with the two dangling balls. Just count the difference to begin with!
2/ Having an exception to deal with a common occurrence is beyond unacceptable. The abiding, (to some of us sensually stimulating) beauty of maths is its predictability, its uniformity. You can’t have a so called ‘easy method’ that has exceptions to deal with common occurrences. This is plain crazy.
Yes, I am the first to admit that I am an old fashioned and stuck in my ways. But, I see no problems with the way we learned our arithmetic, algebra, geometry and trigonometry. We had no electronic calculators or even mechanical ones. We learned things by rote and repetition, over and over and over again.
This was the dedication in one of my recent books.
P.S.: I collect old logarithmic/trigonometric tables (i.e., the so called ‘log’ books) and old slide rulers. Send me pictures and quote me a price. Yes, every once in awhile, late at night, when I feel that I am due a treat, and have a few dollars stashed away, I log onto eBay and see what they have. Got a real beauty of a slide rule, cheap, very cheap, a couple of months ago — making use of the eBay, ‘make an offer’ feature.
March 14, 3/14, Next Thursday Is World ‘PI Day’: A Celebration Of The Joys of Math. Happy Pi Day (Or For Some Of You, Happy Pie Day).
>> The Math Museum In New York City
>>— Mar. 4, 2013.
Next Thursday, at least in the U.S. (and maybe in Canada, though I am not sure whether they actually have calendars up here), it is 3/14 or 3.14. In the rest of the world, in the U.K. and Sri Lanka, it is 14/3 or 14.3. But, since the U.S. rules the waves 3.14 is World Pie Day — and for those of you who are not into pi, just celebrate it as World Pie Day and have a pecan or meat pie and think of POOR me.
I love Pi. Always have since I was introduced to it when I was about 8. I also love pie, both sweet and savory — but alas and alack I haven’t touched a pie, not even nibbled on the crust of one, in 6 weeks! Yes, I have managed to lose 11 pounds. I am down to 178 pounds. So, I am no longer as obese as I used to me, but that at the expense of apple, pecan, lemon and cherry pies, not to mention savory meat and French pies. Getting old sucks. Being pre-diabetic just makes it worse. But, I will celebrate Pi.
Pi is one of the two most important, pivotal, sacrosanct, physical constants in the Universe. The other ‘c’ – the speed of light (as in e = mc²). But, most people can’t remember c. c = 186,282 miles per second. I am not sure how many people even remember ‘G’ — the gravitational constant.
Pi is neat. Very neat.
When I want to have fun with my brain, I try to imagine early philosophers, who believed that all things in nature, divinely inspired, had perfect order. Just think of them, laying out little pieces of string trying to correlate the circumference of a circle to its radius. They must have thought that they were doing something wrong. How could it not be a exact number. Was God playing games?
I try to imagine whether in another world, another planet, in another galaxy, or even in the Milky Way, Pi might be different? I don’t think so.
Having been born a Buddhist, I was never expected to believe in an almighty, all seeing, all powerful God. Thank God. But, Pi to me, was yet another example that there is no all knowing, all seeing creator ‘up there’. Because, nobody with even a modicum of sense would have come up with Pi! Pi is chaotic. That is its abiding, never ending beauty. Infinite, mysterious, beguiling and beautiful. Pi.
Growing up, given my age, we didn’t have electronic calculators. I got my first electronic calculator, a bulky Casio, around 1972. I think it cost my father U.S. $200. I started with using 22/7 for Pi.
In 1971, in my first year at University, doing computer technology, one of the assignments we had was to calculate Pi to as many digits as we could in 3 seconds of compute time. No, we didn’t have dedicated computers. The PC was exactly a decade out. We used time-sharing systems. Computer usage was measured by the Milli-second and billed. 3 seconds compute time, which might equate to 5 minutes of elapsed time, was a lot. Oh! We also programmed using punched cards. They were batch jobs. You submitted a deck of cards and waited for that job to be run and the printout to be delivered to your pigeon hole. I can’t remember what algorithm we used. We programmed it in Fortran IV. I do remember spending 2 weeks refining and polishing my code, 3 to 4 times a day, to get more digits in the 3 seconds we got. Yes, I have to confess, I beat the rest of the class. I was a zealot. Total maniac. I worked on my programming like a man possessed. It was beyond an obsession. I had a very unusual 3 years at University for my 1st degree. To say it was WILD would not even capture 10% of it. There were those that claimed that I was horizontal for 75% of time at University — and it wasn’t inebriation because I didn’t take up alcohol until I got my 1st degree (though the drinking age was 16 or lower) and I never did drugs (though my inseparable best friend, 1968 to 1969, when living in Paris, was Charlie ‘Byrd’ Parker Jr., yes, THE Byrd’s son). [I think they exaggerate. It was probably only about 60%, though it might have looked longer to others.] Yes, I could program while horizontal and always had a notebook by my side to write down algorithms that would come to me in my sleep or in moments of inspiration. Yes, I was strange, even more or than now. Plus, I had a shaggy, uncut head of curly black hair, and an unwashed, smelly genuine, bona fide, from Afghan coat. No wonder IBM offered an ‘unconditional’ job when I was 19. With or without degree. Whenever. Just call this number. And I spent 10 months trying to avoid that … writing letters to all the African game reserves asking for a job as a game warden! Just think. If I had got ONE offer, I would have been gone. None of this. All their fault.
Anyway, next Thursday. MATH DAY. Pi day. Alas I will still not indulge with a pie. But, lets celebrate.