I've been doing math lessons with my 3-year old using the 100-bead abacus. Usually we do a few problems where she tells me a number to make and I tell her a number to make, back and forth. Today she asked me to make 51, and I asked her to make 68. These went smoothly since she's getting pretty good at this now.
Then we did a few "more than" problems. I said, "Let's say your sister has 5 cookies and you have one more than her. How many do you have?" This is a new concept to her so we need to do it slowly and carefully with the abacus: first make her sister's cookies, then let her have the same amount, then give her one more.
Then we do a few subtraction problems such as 7 − 4. She moved 7 beads, then "took away" or moved the other way 4 beads, and how many were left? 3 beads. I showed her also 50 − 10 = 40.
She started doing her own problem, "Let's do 9 − ..." and while she was thinking, I quickly proposed "... minus nine". Nine minus nine. Well, she moved nine beads, then COUNTED the beads one by one moving them the other direction, and was left with none... and what a SURPRISE it was to her! She had to start giggling!
I immediately showed her another one, 4 − 4. She did 10 − 10 herself. And THEN I showed her 100 − 100, which made the greatest giggles of all!
It was just so cute so I had to share. Plus, now you know several ways how to teach math concepts with the abacus.
Tampilkan postingan dengan label zero. Tampilkan semua postingan
Tampilkan postingan dengan label zero. Tampilkan semua postingan
Kamis, 28 Agustus 2008
Jumat, 08 Desember 2006
Nullity and dividing by zero by professor James Anderson
Recently this was highlighted at Slashdot and Digg.com both.
A math professor James Anderson has made a new 'number' or entity that he calls NULLITY, in order to solve problems such as 0/0, which traditionally is left undefined.
Basically he first defined 1/0 as infinity, -1/0 as negative infinity, and 0/0 as nullity, using Φ (Phi) as a symbol for it. He said this nullity lies outside our normal number line, not on it.
I watched the video shown on BBC news, and there he went on to show what happens with the "age-old" problem of 00, (zero to zeroth power) using just normal rules of arithmetic plus these definitions:
Anderson said in the comments following the main article on BBC that two other professors have helped him develop axioms for this new theory, and one of them checked them for consistency.
So.... a new theory. It doesn't sound that earthshaking to me; in fact I wonder if somebody in times past hasn't already tried this...?
(And yes, there exists a system for an "extended real number line".)
In the BBC 'divide by zero' article, you can leave comments, and lots of people have. Most of those seem to be on the mocking angle, putting down the theory.
That truly disappointed me! The same attitude seemed to prevail in people's comments at Digg.com.
Haven't we learned? The best I can remember from math history, negative numbers were certainly disliked and resisted for a long time, becore accepted by mathematicians.
And similarly when complex numbers came on the scene - Descarteds coined the term 'imaginary' as a derogatory term.
It seems that no one knows an application or use for this idea - at this time. But so what? It's no reason for ridiculing someone's theory. He has even consistent axioms written for it.
People have found uses for negative and complex numbers; they've proven very useful. Time will tell if this theory is of use or not; that's not my expertise or business at all. But I just wish people wouldn't be so quick to judge.
A math professor James Anderson has made a new 'number' or entity that he calls NULLITY, in order to solve problems such as 0/0, which traditionally is left undefined.
Basically he first defined 1/0 as infinity, -1/0 as negative infinity, and 0/0 as nullity, using Φ (Phi) as a symbol for it. He said this nullity lies outside our normal number line, not on it.
I watched the video shown on BBC news, and there he went on to show what happens with the "age-old" problem of 00, (zero to zeroth power) using just normal rules of arithmetic plus these definitions:
00 = 0(1 − 1) = 01 × 0-1 =(0/1)1 × (0/1)-1
Now, for every number, the 1st power is the number itself, while the -1 power is its reciprocal:
= (0/1) × (1/0) = (0 × 1) / (1 × 0 ) = 0/0 = Nullity.
Anderson said in the comments following the main article on BBC that two other professors have helped him develop axioms for this new theory, and one of them checked them for consistency.
So.... a new theory. It doesn't sound that earthshaking to me; in fact I wonder if somebody in times past hasn't already tried this...?
(And yes, there exists a system for an "extended real number line".)
In the BBC 'divide by zero' article, you can leave comments, and lots of people have. Most of those seem to be on the mocking angle, putting down the theory.
That truly disappointed me! The same attitude seemed to prevail in people's comments at Digg.com.
Haven't we learned? The best I can remember from math history, negative numbers were certainly disliked and resisted for a long time, becore accepted by mathematicians.
And similarly when complex numbers came on the scene - Descarteds coined the term 'imaginary' as a derogatory term.
It seems that no one knows an application or use for this idea - at this time. But so what? It's no reason for ridiculing someone's theory. He has even consistent axioms written for it.
People have found uses for negative and complex numbers; they've proven very useful. Time will tell if this theory is of use or not; that's not my expertise or business at all. But I just wish people wouldn't be so quick to judge.
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