[ 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 multiday J! matches, when I want four different scores (game 1, preFJ 2, preFJ 2 cumulative, maximum potential) for three different players to line up perfectly.
The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)
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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)
Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)
I did not know this. Thanks, Stefan.seaborgium wrote: ↑Sun Dec 29, 2019 8:29 pm[ 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 multiday J! matches, when I want four different scores (game 1, preFJ 2, preFJ 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)
34x12 isn't in (A+B)(C+D) format, though.
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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)
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)
I literally never would have thought of it that way.econgator wrote: ↑Sun Dec 29, 2019 9:37 pmSo, 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)
That 1st grade math is real sneaky, I know.TenPoundHammer wrote: ↑Sun Dec 29, 2019 9:38 pmI literally never would have thought of it that way.

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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)
This is why we need to teach it this way instead of the way we currently do it, asTenPoundHammer wrote: ↑Sun Dec 29, 2019 9:38 pmI literally never would have thought of it that way.econgator wrote: ↑Sun Dec 29, 2019 9:37 pmSo, 34 isn't 30+4 and 12 isn't 10+2?
34
x12

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 opusthepenguin
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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)
They are, but they aren't in that format, are they?econgator wrote: ↑Sun Dec 29, 2019 9:37 pmSo, 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)
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.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

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)
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.talkingaway wrote: ↑Mon Dec 30, 2019 9:10 amI 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.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

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.
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)
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)
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.TenPoundHammer wrote: ↑Mon Dec 30, 2019 2:40 pmSee, 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)
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).TenPoundHammer wrote: ↑Mon Dec 30, 2019 2:40 pmSee, 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've personally always hated memorization  I love math, made a statewide 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 "downdeeup minus updeedown 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)
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.talkingaway wrote: ↑Mon Dec 30, 2019 5:01 pmFrom 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).
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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)
If it's any consolation, calculus does exactly what you're talking about when finding the areas of irregular figures. Imagine a closed, nonoverlapping, 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.TenPoundHammer wrote: ↑Mon Dec 30, 2019 6:50 pmMy 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.talkingaway wrote: ↑Mon Dec 30, 2019 5:01 pmFrom 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).
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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)
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)
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.TenPoundHammer wrote: ↑Mon Dec 30, 2019 7:25 pmI 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?
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 twodigit numbers, breaking it down into a set of essentially singledigit multiplications can be helpful to someone with their timestables memorized by rote when the numbers are crunchier.
Personally, since the timestables 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 morestep 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.
Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)
This. For example, I'd do 34x12 as (34*10)+(34*2), but I'd do 34x18 as (34*20)(34*2).seaborgium wrote: ↑Mon Dec 30, 2019 8:38 pmAnd 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.
Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)
12TenPoundHammer wrote: ↑Mon Dec 30, 2019 7:25 pmI 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?
∫ f(34)dx
0
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Re: The Official TPH Education Thread (POTENTIAL GAME DAY SPOILERS)
Since we are hijacking the TPH thread, to your point, I say AMEN!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.
https://www.smbccomics.com/comic/20100130
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 pimemorizers 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?) )
Disclaimer  repeated exposure to author's musings may cause befuddlement.