mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Miscellaneous Math

Closed Thread
 
Thread Tools
Old 2020-08-10, 21:27   #1
tuckerkao
 
Jan 2020

59 Posts
Default Jason Zimba vs the Creature From the Dozenal Abyss

I read this article, it seemed like this guy has reshaped the educational system of the United States since the Obama Administration -
https://www.npr.org/sections/ed/2014...mmon-core-math

Jason Zimba - The creator of Common Core Math -
https://media.npr.org/assets/img/201...e-s800-c85.jpg

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

Tutorial video of the simple multiplications of 2 common fractions -
youtube]pZ3A6E1w1II


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 - Screenshot 1 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 - Screenshot 2 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
Attached Thumbnails
Click image for larger version

Name:	Decimal 2 3rds times 3 4th Equals 1 Half.png
Views:	36
Size:	28.7 KB
ID:	23002   Click image for larger version

Name:	Dozenal 2 3rds times 3 4th Equals 1 Half - Shiny Color Balls.png
Views:	29
Size:	43.9 KB
ID:	23003  

Last fiddled with by xilman on 2020-08-12 at 19:03
tuckerkao is online now  
Old 2020-08-10, 21:32   #2
chalsall
If I May
 
chalsall's Avatar
 
"Chris Halsall"
Sep 2002
Barbados

9,311 Posts
Default

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...
chalsall is offline  
Old 2020-08-10, 22:34   #3
ewmayer
2ω=0
 
ewmayer's Avatar
 
Sep 2002
Rep├║blica de California

2×13×443 Posts
Default

Quote:
Originally Posted by tuckerkao View Post
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
ewmayer is offline  
Old 2020-08-10, 22:57   #4
chalsall
If I May
 
chalsall's Avatar
 
"Chris Halsall"
Sep 2002
Barbados

9,311 Posts
Default

Quote:
Originally Posted by ewmayer View Post
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.
chalsall is offline  
Old 2020-08-11, 01:21   #5
Dr Sardonicus
 
Dr Sardonicus's Avatar
 
Feb 2017
Nowhere

66078 Posts
Default

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.
Dr Sardonicus is offline  
Old 2020-08-11, 05:31   #6
tuckerkao
 
Jan 2020

1110112 Posts
Default

Quote:
Originally Posted by ewmayer View Post
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
tuckerkao is online now  
Old 2020-08-11, 05:40   #7
chalsall
If I May
 
chalsall's Avatar
 
"Chris Halsall"
Sep 2002
Barbados

9,311 Posts
Default

Quote:
Originally Posted by tuckerkao View Post
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?

No need for YouTube links.

Please expand on your idea.
chalsall is offline  
Old 2020-08-11, 05:45   #8
henryzz
Just call me Henry
 
henryzz's Avatar
 
"David"
Sep 2007
Cambridge (GMT/BST)

2·2,861 Posts
Default

Quote:
Originally Posted by tuckerkao View Post
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.
henryzz is offline  
Old 2020-08-11, 05:50   #9
tuckerkao
 
Jan 2020

738 Posts
Default

Quote:
Originally Posted by henryzz View Post
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
Click image for larger version

Name:	1 Over 2 in All Bases.png
Views:	10
Size:	18.2 KB
ID:	23004   Click image for larger version

Name:	1 Over 3 in All Bases.png
Views:	6
Size:	22.3 KB
ID:	23005   Click image for larger version

Name:	2 Over 3 in All Bases.png
Views:	3
Size:	23.8 KB
ID:	23006   Click image for larger version

Name:	1 Over 4 in All Bases.png
Views:	3
Size:	21.9 KB
ID:	23007   Click image for larger version

Name:	3 Over 4 in All Bases.png
Views:	3
Size:	18.4 KB
ID:	23008  


Last fiddled with by tuckerkao on 2020-08-11 at 05:56
tuckerkao is online now  
Old 2020-08-11, 05:55   #10
chalsall
If I May
 
chalsall's Avatar
 
"Chris Halsall"
Sep 2002
Barbados

9,311 Posts
Default

Quote:
Originally Posted by tuckerkao View Post
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.
chalsall is offline  
Old 2020-08-11, 05:58   #11
tuckerkao
 
Jan 2020

3B16 Posts
Default

Quote:
Originally Posted by chalsall View Post
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
tuckerkao is online now  
Closed Thread

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Dozenal near- and quasi- repunit primes sweety439 And now for something completely different 22 2020-07-21 14:49
Smallest multiple of n satisfying given condition in dozenal sweety439 sweety439 0 2020-06-11 06:36
Mersenne numbers in Dozenal base tuckerkao Lounge 7 2020-02-11 04:44
Jason's sieved ranges(for the prp and llr addicts with Intels) jasong Sierpinski/Riesel Base 5 8 2005-04-29 05:13

All times are UTC. The time now is 22:57.

Wed Sep 23 22:57:30 UTC 2020 up 13 days, 20:08, 0 users, load averages: 1.73, 1.60, 1.65

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.