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-   -   Jason Zimba vs the Creature From the Dozenal Abyss (https://www.mersenneforum.org/showthread.php?t=25827)

 tuckerkao 2020-08-10 21:27

Jason Zimba vs the Creature From the Dozenal Abyss

2 Attachment(s)
I read this article, it seemed like this guy has reshaped the educational system of the United States since the Obama Administration -
[URL="https://www.npr.org/sections/ed/2014/12/29/371918272/the-man-behind-common-core-math"]https://www.npr.org/sections/ed/2014/12/29/371918272/the-man-behind-common-core-math[/URL]

Jason Zimba - The creator of Common Core Math -
[IMG]https://media.npr.org/assets/img/2014/12/19/06-jasonzimba_schaer-056-edit_slide-5e038b09161c4f9e2ebd6b3111e3c7aaa250cb4e-s800-c85.jpg[/IMG]

It'll take some time to think the same way as this smart guy.

Tutorial video of the simple multiplications of 2 common fractions -

The 4th grader fractions of Common Core math is a major challenge for lots of American students because their brain processors have to function this way - [COLOR="Red"]Screenshot 1[/COLOR] below

Thus, lots of fragments are generated and cause intellectual confusions much similar as the obstacles placing on the roads for the car drivers.

I must admit this screenshot takes me more than 2 hours to create to make sure no internal mistakes have been made such as the graphical mis-alignments or math errors as the results of the endless decimal recursions.

I process the Common Core fractions using the dozenal base - [COLOR="DeepSkyBlue"]Screenshot 2[/COLOR] below

No fragments have been generated, I can still convert my answers back to the decimal base afterward.

Screwdriver, Screw, Hammer, Nail, how should you use these 4 materials together?

Decimal Base + Traditional Math = Screwdriver + Screw
Decimal Base + Common Core Math = Screwdriver + Nail
Dozenal Base + Traditional Math = Hammer + Screw
Dozenal Base + Common Core Math = Hammer + Nail

 chalsall 2020-08-10 21:32

You just have to appreciate the investment in "sleepers", don't you?

 ewmayer 2020-08-10 22:34

[QUOTE=tuckerkao;553164]It'll take some time to think the same way as this smart guy.[/QUOTE]

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.

 chalsall 2020-08-10 22:57

[QUOTE=ewmayer;553172]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.[/QUOTE]

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.

 Dr Sardonicus 2020-08-11 01:21

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 [url=https://www.mersenneforum.org/showthread.php?t=25357&highlight=balls]this thread[/url] and [url=https://www.mersenneforum.org/showthread.php?t=25247&highlight=balls]this thread[/url], both of which were relegated to Miscellaneous Math.

 tuckerkao 2020-08-11 05:31

[QUOTE=ewmayer;553172]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."[/QUOTE]
The Common Core Video Link, looks like the previous posted link didn't work
[URL="https://youtu.be/pZ3A6E1w1II"]https://youtu.be/pZ3A6E1w1II[/URL]

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.

 chalsall 2020-08-11 05:40

[QUOTE=tuckerkao;553214]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.[/QUOTE]

And, so...

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

 henryzz 2020-08-11 05:45

[QUOTE=tuckerkao;553214]The Common Core Video Link, looks like the previous posted link didn't work
[URL="https://youtu.be/pZ3A6E1w1II"]https://youtu.be/pZ3A6E1w1II[/URL]

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.[/QUOTE]

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.

 tuckerkao 2020-08-11 05:50

5 Attachment(s)
[QUOTE=henryzz;553217]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.[/QUOTE]
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.

 chalsall 2020-08-11 05:55

[QUOTE=tuckerkao;553218]With the traditional methods, you can never figure out the fraction values in other bases.[/QUOTE]

Bovine excrement.

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

Irrational numbers were just a special case.

 tuckerkao 2020-08-11 05:58

[QUOTE=chalsall;553219]Bovine excrement.

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

Irrational numbers were just a special case.[/QUOTE]
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.

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