The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)

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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)

Post by seaborgium » Sun Dec 29, 2019 8:29 pm

1stlvlthinker wrote:
Sun Dec 29, 2019 7:14 pm
(Edit: Apparenly J Board shrinks whitespace?)
[ code ] tags not only put the enclosed text in a monospaced font, but preserve the appearance of multiple spaces. They're indispensable for me when I do wagering suggestions for final games of multi-day J! matches, when I want four different scores (game 1, pre-FJ 2, pre-FJ 2 cumulative, maximum potential) for three different players to line up perfectly.

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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)

Post by pinkfreud » Sun Dec 29, 2019 9:12 pm

seaborgium wrote:
Sun Dec 29, 2019 8:29 pm
1stlvlthinker wrote:
Sun Dec 29, 2019 7:14 pm
(Edit: Apparenly J Board shrinks whitespace?)
[ code ] tags not only put the enclosed text in a monospaced font, but preserve the appearance of multiple spaces. They're indispensable for me when I do wagering suggestions for final games of multi-day J! matches, when I want four different scores (game 1, pre-FJ 2, pre-FJ 2 cumulative, maximum potential) for three different players to line up perfectly.
I did not know this. Thanks, Stefan.

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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)

Post by TenPoundHammer » Sun Dec 29, 2019 9:31 pm

econgator wrote:
Sun Dec 29, 2019 3:25 pm
Hell, you can use FOIL to multiply two-digit numbers:

34x12= (30x10)+(30x2)+(4x10)+(4x2)=300+60+40+8=408
34x12 isn't in (A+B)(C+D) format, though.
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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)

Post by econgator » Sun Dec 29, 2019 9:37 pm

TenPoundHammer wrote:
Sun Dec 29, 2019 9:31 pm
econgator wrote:
Sun Dec 29, 2019 3:25 pm
Hell, you can use FOIL to multiply two-digit numbers:

34x12= (30x10)+(30x2)+(4x10)+(4x2)=300+60+40+8=408
34x12 isn't in (A+B)(C+D) format, though.
So, 34 isn't 30+4 and 12 isn't 10+2?

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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)

Post by TenPoundHammer » Sun Dec 29, 2019 9:38 pm

econgator wrote:
Sun Dec 29, 2019 9:37 pm
TenPoundHammer wrote:
Sun Dec 29, 2019 9:31 pm
econgator wrote:
Sun Dec 29, 2019 3:25 pm
Hell, you can use FOIL to multiply two-digit numbers:

34x12= (30x10)+(30x2)+(4x10)+(4x2)=300+60+40+8=408
34x12 isn't in (A+B)(C+D) format, though.
So, 34 isn't 30+4 and 12 isn't 10+2?
I literally never would have thought of it that way.
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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)

Post by econgator » Sun Dec 29, 2019 9:44 pm

TenPoundHammer wrote:
Sun Dec 29, 2019 9:38 pm
I literally never would have thought of it that way.
That 1st grade math is real sneaky, I know.

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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)

Post by 1stlvlthinker » Mon Dec 30, 2019 12:19 am

TenPoundHammer wrote:
Sun Dec 29, 2019 9:38 pm
econgator wrote:
Sun Dec 29, 2019 9:37 pm
TenPoundHammer wrote:
Sun Dec 29, 2019 9:31 pm
econgator wrote:
Sun Dec 29, 2019 3:25 pm
Hell, you can use FOIL to multiply two-digit numbers:

34x12= (30x10)+(30x2)+(4x10)+(4x2)=300+60+40+8=408
34x12 isn't in (A+B)(C+D) format, though.
So, 34 isn't 30+4 and 12 isn't 10+2?
I literally never would have thought of it that way.
This is why we need to teach it this way instead of the way we currently do it, as

34
x12
------
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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)

Post by opusthepenguin » Mon Dec 30, 2019 5:44 am

econgator wrote:
Sun Dec 29, 2019 9:37 pm
TenPoundHammer wrote:
Sun Dec 29, 2019 9:31 pm
econgator wrote:
Sun Dec 29, 2019 3:25 pm
Hell, you can use FOIL to multiply two-digit numbers:

34x12= (30x10)+(30x2)+(4x10)+(4x2)=300+60+40+8=408
34x12 isn't in (A+B)(C+D) format, though.
So, 34 isn't 30+4 and 12 isn't 10+2?
They are, but they aren't in that format, are they?

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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)

Post by talkingaway » Mon Dec 30, 2019 9:10 am

1stlvlthinker wrote:
Mon Dec 30, 2019 12:19 am

This is why we need to teach it this way instead of the way we currently do it, as

34
x12
------
I agree - that's what a lot of the "new math" is about - understanding over rote, which I support 100%. The problem is that almost any method used to teach multiplication, when inappropriately applied, can become an algorithm. If you understand WHY you're writing down the 8 here, then the 6, and then start a new line where you write a 0 and then write a 4 followed by a 3...then there's some understanding behind the algorithm.

Conversely, if you do a "box method" where you write "30, 4" in a row and "10, 2" in a column, and just mechanically do the partial products and add them all up - but you don't understand WHY adding the four partial products should give you the desired product, you're just creating a new algorithm that's a little clunkier and takes up more room on a piece of paper.

And understanding why the distributive property actually works is a whole nother bag of worms. I like to use an example of buying a slice of $4 pizza and a $2 soda for 7 kids. You can do (4 + 2)7 = 6*7 = 42, getting the price per kid first, and then multiplying by the number of kids. Or, you can do 4*7 + 2 * 7 = 28 + 14 = 42, totaling the pizza first and then the sodas. Since you're counting the same thing in two different ways, they must be equal, hence (4 + 2)7 = 4*7 + 2*7. Change the "kids" to "4 boys and 3 girls", and you've got FOIL.

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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)

Post by 1stlvlthinker » Mon Dec 30, 2019 11:44 am

talkingaway wrote:
Mon Dec 30, 2019 9:10 am
1stlvlthinker wrote:
Mon Dec 30, 2019 12:19 am

This is why we need to teach it this way instead of the way we currently do it, as

34
x12
------
I agree - that's what a lot of the "new math" is about - understanding over rote, which I support 100%. The problem is that almost any method used to teach multiplication, when inappropriately applied, can become an algorithm. If you understand WHY you're writing down the 8 here, then the 6, and then start a new line where you write a 0 and then write a 4 followed by a 3...then there's some understanding behind the algorithm.

Conversely, if you do a "box method" where you write "30, 4" in a row and "10, 2" in a column, and just mechanically do the partial products and add them all up - but you don't understand WHY adding the four partial products should give you the desired product, you're just creating a new algorithm that's a little clunkier and takes up more room on a piece of paper.

And understanding why the distributive property actually works is a whole nother bag of worms. I like to use an example of buying a slice of $4 pizza and a $2 soda for 7 kids. You can do (4 + 2)7 = 6*7 = 42, getting the price per kid first, and then multiplying by the number of kids. Or, you can do 4*7 + 2 * 7 = 28 + 14 = 42, totaling the pizza first and then the sodas. Since you're counting the same thing in two different ways, they must be equal, hence (4 + 2)7 = 4*7 + 2*7. Change the "kids" to "4 boys and 3 girls", and you've got FOIL.
Yeah, I fully agree, and I think this is where most of our elementary teaching falls short. I hear a lot of elementary school teachers almost brag about how little "advanced math" they understand, as in "I never did well at algebra" but it's ok since they can master the operations of arithmetic.

Conversely, you'd never hear me as a math teacher say, "I can do English up to the 9th grade level." There might need to be more education of teachers to help them understand why it's important to look for understanding, not just algorithms. At one point, I wanted to create a blog or a website for this, but I don't really have the time.

Also, the reason I hate FOIL is because it locks people into a 2x2 formula. Sure, it works for the most common case, multiplying binomials, but is hard to extend.
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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)

Post by TenPoundHammer » Mon Dec 30, 2019 2:40 pm

See, what gets me is that the only way to make things "easier" is to splinter them into a bunch of smaller problems, which just sends my brain running in the other direction from the heaps of work that have just been added.
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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)

Post by pinkfreud » Mon Dec 30, 2019 4:37 pm

TenPoundHammer wrote:
Mon Dec 30, 2019 2:40 pm
See, what gets me is that the only way to make things "easier" is to splinter them into a bunch of smaller problems, which just sends my brain running in the other direction from the heaps of work that have just been added.
I think many trivia lovers would not view this as "work." Teasing out information in this way is what we often regard as "fun," which is one reason why we love Jeopardy! and watch it with such enthusiasm. I do not intend this as criticism, but your mindset seems to differ from that of a typical Jeopardy! fan.

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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)

Post by talkingaway » Mon Dec 30, 2019 5:01 pm

TenPoundHammer wrote:
Mon Dec 30, 2019 2:40 pm
See, what gets me is that the only way to make things "easier" is to splinter them into a bunch of smaller problems, which just sends my brain running in the other direction from the heaps of work that have just been added.
From what I understand, this is actually the backbone of computer science: you have a really big problem. The task is invariably broken up into "black boxes" that you come back to later. If you need to find the square footage of a house, you break it up into fining the area of each room. From there, you can break each individual room up into finding is area - either with a simple formula (if your room is a rectangle), or by breaking each room up into components and finding those areas (ie if you have a room that's a triangle conjoined to a square).

I've personally always hated memorization - I love math, made a state-wide team in high school, but I'd say the only two "complex" formulas I ever memorized rote are the quadratic equation and the formula for the derivative of a quotient. I can still hear my calc teacher saying "down-dee-up minus up-dee-down over downdown". But even simple stuff, like the formula for "the number of integers between integers x and y, inclusive", is silly to memorize, and easy to get wrong. If you have x=20 and y = 34, understanding that when x=1, the answer is simply y, and then noting that subtracting the same number from x and y will give you a simpler problem, will quickly get you to the right answer of x' = 20 - 19 = 1, y' = 34 - 19 = 15. If you just memorize y - x + 1, then you might forget whether it's "inclusive of both endpoints", "exclusive of both endpoints", or one of each.

My biggest mathematical pet peeve: the weird awe over memorization of pi. Serves no purpose, and it's just a waste of time and brain space. At least memorizing the order of the Presidents gives you a bearing of when things happen in history, and memorizing world capitals gives you a sense of place in this world. Memorizing pi just gives you a string of pseudorandom numbers that have no practical application in this day of modern electronics.

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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)

Post by TenPoundHammer » Mon Dec 30, 2019 6:50 pm

talkingaway wrote:
Mon Dec 30, 2019 5:01 pm
From what I understand, this is actually the backbone of computer science: you have a really big problem. The task is invariably broken up into "black boxes" that you come back to later. If you need to find the square footage of a house, you break it up into fining the area of each room. From there, you can break each individual room up into finding is area - either with a simple formula (if your room is a rectangle), or by breaking each room up into components and finding those areas (ie if you have a room that's a triangle conjoined to a square).
My problem is I try to take things one brick at a time, but even the individual bricks are too heavy for me. So I just keep breaking the brick into smaller and smaller pieces until I'm left with a pile of powder that I can't do anything with.
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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)

Post by talkingaway » Mon Dec 30, 2019 7:08 pm

TenPoundHammer wrote:
Mon Dec 30, 2019 6:50 pm
talkingaway wrote:
Mon Dec 30, 2019 5:01 pm
From what I understand, this is actually the backbone of computer science: you have a really big problem. The task is invariably broken up into "black boxes" that you come back to later. If you need to find the square footage of a house, you break it up into fining the area of each room. From there, you can break each individual room up into finding is area - either with a simple formula (if your room is a rectangle), or by breaking each room up into components and finding those areas (ie if you have a room that's a triangle conjoined to a square).
My problem is I try to take things one brick at a time, but even the individual bricks are too heavy for me. So I just keep breaking the brick into smaller and smaller pieces until I'm left with a pile of powder that I can't do anything with.
If it's any consolation, calculus does exactly what you're talking about when finding the areas of irregular figures. Imagine a closed, non-overlapping, irregular, possibly curvy figure on graph paper that has one square per cm^2 - you can estimate its area by counting the number of squares that are entirely within the figure. It's not exact, but it's close. Now copy that onto another piece of graph paper that has 10 squares per cm^2 - your resolution increases, as does your accuracy. You have more squares, but each square covers less area. Continue ad infinitum/ad nauseam, and you get the exact area of the figure - an infinite number of infinitesimally small squares - or, in your case, brick powder.

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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)

Post by TenPoundHammer » Mon Dec 30, 2019 7:25 pm

I still don't see how smashing 34x12 into a billion smaller problems is supposed to be "easier". Isn't the point to make LESS work, not MORE?
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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)

Post by seaborgium » Mon Dec 30, 2019 8:38 pm

TenPoundHammer wrote:
Mon Dec 30, 2019 7:25 pm
I still don't see how smashing 34x12 into a billion smaller problems is supposed to be "easier". Isn't the point to make LESS work, not MORE?
Multiplication of 34 * 12 as I learned it is 34 * 2 + 34 * 10 (the latter portion is more like 34 * 1, a column to the left, but whatever). It's not too tough to do mentally since the component multiplications don't have any carrying.

Turning it into a FOIL problem is 30 * 10 + 30 * 2 + 4 * 10 + 4 * 2. In this case this method doesn't confer much advantage over the classic way described above, but to find the product of two-digit numbers, breaking it down into a set of essentially single-digit multiplications can be helpful to someone with their times-tables memorized by rote when the numbers are crunchier.

Personally, since the times-tables I learned went up to 12 * 12, I would probably solve this quickest by adding 12 * 4 to 12 * 30. But I could also see 12 * 12 * 2 + 12 * 10, or even 12 * 12 * 3 - 12 * 2.

You might see these as more work because there are more apparent steps than the pencil and paper, columns of numbers method, but the point of these more-step methods is that the steps may be more manageable, especially when working mentally. And the point of having different ways of doing it is that someone who becomes familiar with more than one way can learn to recognize which way would be better from one problem to the next.

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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)

Post by mas3cf » Mon Dec 30, 2019 9:24 pm

seaborgium wrote:
Mon Dec 30, 2019 8:38 pm
And the point of having different ways of doing it is that someone who becomes familiar with more than one way can learn to recognize which way would be better from one problem to the next.
This. For example, I'd do 34x12 as (34*10)+(34*2), but I'd do 34x18 as (34*20)-(34*2).

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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)

Post by Volante » Mon Dec 30, 2019 11:11 pm

TenPoundHammer wrote:
Mon Dec 30, 2019 7:25 pm
I still don't see how smashing 34x12 into a billion smaller problems is supposed to be "easier". Isn't the point to make LESS work, not MORE?
12
∫ f(34)dx
0

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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)

Post by twelvefootboy » Tue Dec 31, 2019 12:16 am

talkingaway wrote:
Mon Dec 30, 2019 5:01 pm


My biggest mathematical pet peeve: the weird awe over memorization of pi. Serves no purpose, and it's just a waste of time and brain space.
Since we are hijacking the TPH thread, to your point, I say AMEN!
https://www.smbc-comics.com/comic/2010-01-30

I feel the same way about the Spelling Bee - it is reduced to rote memory of obscure words that are not educational to learn. At least the pi-memorizers already know their hobby is pointless.
(This attitude is nohow related to the fact I can't remember my four digit PIN or a 7 digit phone number long enough to access my phone keys and dial it. I could if I HAD to (I hope?) :roll: )
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