Jason Zimba vs the Creature From the Dozenal Abyss
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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/themanbehindcommoncoremath"]https://www.npr.org/sections/ed/2014/12/29/371918272/themanbehindcommoncoremath[/URL] Jason Zimba  The creator of Common Core Math  [IMG]https://media.npr.org/assets/img/2014/12/19/06jasonzimba_schaer056edit_slide5e038b09161c4f9e2ebd6b3111e3c7aaa250cb4es800c85.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  [URL="youtube]pZ3A6E1w1II"]youtube]pZ3A6E1w1II[/URL] 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 misalignments 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 
You just have to appreciate the investment in "sleepers", don't you?

[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 confusinglycolored 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 4thgrade 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 superconfusing particolor schemes and introduction of the Vulcan alphabet, erm I mean 'dozenal bases'  again, WTF? Sounds to me like a classic reinventthewheelsoabunchoffolkscanfeelselfimportantandmakealotofmoney 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 highpaid consultants and "bold new" selfselection factories known as charter schools, and of *course* the thusstarved 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 truebelievers 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 5thgrade 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. 
[QUOTE=ewmayer;553172]You say that like it's a bad thing ... and given that mathematics is inherently abstract, fancy graphics with confusinglycolored 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. 
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. 
[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 4thgrade 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. 
[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? No need for YouTube links. Please expand on your idea. 
[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. 
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[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. 
[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. 
[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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