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 2020-08-10, 21:32 #2 chalsall If I May     "Chris Halsall" Sep 2002 Barbados 246216 Posts You just have to appreciate the investment in "sleepers", don't you? Last fiddled with by chalsall on 2020-08-10 at 21:33 Reason: s/love/appreciate/; # It involves long-term-thinking...
2020-08-10, 22:34   #3
ewmayer
2ω=0

Sep 2002
República de California

1151810 Posts

Quote:
 Originally Posted by tuckerkao It'll take some time to think the same way as this smart guy.
You say that like it's a bad thing ... and given that mathematics is inherently abstract, fancy graphics with confusingly-colored balls just give me a giant "WTF?" sense. Those of us who are older than 40 may remember previous failed experiments with "New Math" and the 70s "All is Set Theory" craze.

So let's consider your "4th graders struggle with this" example - 2/3 x 3/4. Multiply together the numerators and denominators, get 6/12 - I hope you agree this is something most 4th graders should be willing and able to master. Now I admit that getting most 4th graders to "now find the the greatest common divisor of 6 and 12 and divide each by that" is the kind of thing that should not be foisted on 4th graders, at least not in those words. But hey, you want colored balls, great - we start with 12 uncolored ones, paint 6 red, what fraction is that? More sophisticated 4th-grade minds could surely grasp "2 x 3 is the same as 3 x 2, so we can use that to rearrange the product as 3/3 x 2/4, and look! 3/3 is 1, so now we have 2/4, and both top and bottom are divisble by 2, leaving 1/2."

In your graphics I see super-confusing parti-color schemes and introduction of the Vulcan alphabet, erm I mean 'dozenal bases' - again, WTF? Sounds to me like a classic reinvent-the-wheel-so-a-bunch-of-folks-can-feel-self-important-and-make-a-lot-of-money grift. The NPR piece carefully trod around the phrase "charter school", but lots of negative language about those failing public schools. Well, you know what - like most things, starve them of resources by funneling their funding to high-paid consultants and "bold new" self-selection factories known as charter schools, and of *course* the thus-starved public schools will fail.

Sorry to be so harsh, but this reminds me way too much of having been experimented on by the New Math true-believers in my youth. I recall once in 5th grade, the math teacher pulled the 3 or 4 brightest students aside, asked us to go nextdoor to an unused classroom and spend the period looking over a proposed bold new math book the district was considering adopting for next year's 5th graders. The introductory flap summarizing the bold new method showed a square, triangle and circle in a row, followed by the bold new question "what equation does this represent?" Being fortunately not just decently smart but sensible, we just looked at each other, guffawed, and spent the rest of the hour playing board games. At the end we returned the book to the 5th-grade math teacher and said s.t. to the effect of "we have no idea what this book is about". That was fortunately the end of it - at least until the next experimental fad rolled around.

Last fiddled with by ewmayer on 2020-08-10 at 22:35

2020-08-10, 22:57   #4
chalsall
If I May

"Chris Halsall"
Sep 2002

100100011000102 Posts

Quote:
 Originally Posted by ewmayer You say that like it's a bad thing ... and given that mathematics is inherently abstract, fancy graphics with confusingly-colored balls just give me a giant "WTF?" sense.
E.Mayer... A sincere question.

When discussing economics with "normals", do you first discuss Smith, or Nash?

The latter is more complete, but the former makes more sense.

It's a bit like Newton vs. Einstien.

I would appreciate your thoughts and feedback. I've had to make decisions on what to speak about lately, and I'm not entirely sure I made the correct chose.

 2020-08-11, 01:21 #5 Dr Sardonicus     Feb 2017 Nowhere 34·43 Posts I don't remember how early in my education I learned about multiplying fractions, but I'm pretty sure one of the early things I learned was "cancellation," and I already had learned that multiplying by 1 doesn't change anything. In the example, 2/3 x 3/4 you can "cancel the threes" and drop the resulting factors of 1 in numerator and denominator to get 2/4. I think I knew by the fourth grade that 4 = 2*2, so we can again use cancellation to get 1/2. I point out that the same user has flogged the "color balls" before, in this thread and this thread, both of which were relegated to Miscellaneous Math.
2020-08-11, 05:31   #6
tuckerkao

Jan 2020

3·52 Posts

Quote:
 Originally Posted by ewmayer So let's consider your "4th graders struggle with this" example - 2/3 x 3/4. Multiply together the numerators and denominators, get 6/12 - I hope you agree this is something most 4th graders should be willing and able to master. Now I admit that getting most 4th graders to "now find the the greatest common divisor of 6 and 12 and divide each by that" is the kind of thing that should not be foisted on 4th graders, at least not in those words. But hey, you want colored balls, great - we start with 12 uncolored ones, paint 6 red, what fraction is that? More sophisticated 4th-grade minds could surely grasp "2 x 3 is the same as 3 x 2, so we can use that to rearrange the product as 3/3 x 2/4, and look! 3/3 is 1, so now we have 2/4, and both top and bottom are divisble by 2, leaving 1/2."
The Common Core Video Link, looks like the previous posted link didn't work
https://youtu.be/pZ3A6E1w1II

All of the methods you mentioned were the traditional methods which the American public school teachers currently disallow. In Common Core math, the students only do it by the color segments as shown in the video above.

When I have a dozen of color balls, I paint the 1st 4 red, 2nd 4 orange, 3rd 4 yellow, so I know where both 1/3 and 2/3 locate.

It's only hard to the American 4th graders. Greatest Common Factor and Least Common Multiple are well known to Asian 4th graders.

Last fiddled with by tuckerkao on 2020-08-11 at 05:38

2020-08-11, 05:40   #7
chalsall
If I May

"Chris Halsall"
Sep 2002

221428 Posts

Quote:
 Originally Posted by tuckerkao When I have a dozen of color balls, I paint the 1st 4 red, 2nd 4 orange, 3rd 4 yellow, so I know where both 1/3 and 2/3 locate.
And, so...

Based on what is claimed, what follows? Why is this important?

2020-08-11, 05:45   #8
henryzz
Just call me Henry

"David"
Sep 2007
Cambridge (GMT/BST)

10110010110102 Posts

Quote:
 Originally Posted by tuckerkao The Common Core Video Link, looks like the previous posted link didn't work https://youtu.be/pZ3A6E1w1II All of the methods you mentioned were the traditional methods which the American public school teachers currently disallow. In Common Core math, the students only do it by the color segments as shown in the video above. When I have a dozen of color balls, I paint the 1st 4 red, 2nd 4 orange, 3rd 4 yellow, so I know where both 1/3 and 2/3 locate. It's only hard to the American 4th graders. Greatest Common Factor and Least Common Multiple are well known to Asian 4th graders.
The thing I don't get is why that video makes the simplification step so complicated. It requires you to work out the gcd between the numerator and denominator in your head. Surely it is far easier to never multiply in the 3s in 3/4 * 2/3. The smaller the numbers the easier the gcd. Hopefully gcd has been heavily practiced before learning this.

2020-08-11, 05:50   #9
tuckerkao

Jan 2020

3×52 Posts

Quote:
 Originally Posted by henryzz The thing I don't get is why that video makes the simplification step so complicated. It requires you to work out the gcd between the numerator and denominator in your head. Surely it is far easier to never multiply in the 3s in 3/4 * 2/3. The smaller the numbers the easier the gcd. Hopefully gcd has been heavily practiced before learning this.
With the traditional methods, you can never figure out the fraction values in other bases.

[decimal] 1/3 = 0.333...

With the color balls, you can figure out [dozenal] 1/3 = 0.4, [hex] 1/3 = 0.555...

I understand that Jason Zimba have privately tried to change the educational system of the world so that the dozenal math will become the default base someday.
Attached Thumbnails

Last fiddled with by tuckerkao on 2020-08-11 at 05:56

2020-08-11, 05:55   #10
chalsall
If I May

"Chris Halsall"
Sep 2002

221428 Posts

Quote:
 Originally Posted by tuckerkao With the traditional methods, you can never figure out the fraction values in other bases.
Bovine excrement.

In early grade school, our teachers were already preparing us for multiple different bases.

Irrational numbers were just a special case.

2020-08-11, 05:58   #11
tuckerkao

Jan 2020

3·52 Posts

Quote:
 Originally Posted by chalsall Bovine excrement. In early grade school, our teachers were already preparing us for multiple different bases. Irrational numbers were just a special case.
Let's give the quiz out, how many American people actually recognize [dozenal] 1/3 = 0.4 and 2/3 = 0.8, 1/4 = 0.3, 3/4 = 0.9?

The color balls can figure out any bases without the existence of the decimal base.

Last fiddled with by tuckerkao on 2020-08-11 at 06:01

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