Why? What's wrong with the old way?
The what now?
Why? What's wrong with the old way?
You can do partial products in your head waaay faster than the old way. But the old way still works.
I can do most 3 digit * 3 digit in my head in about 10 seconds.
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Finally, there is a question on these messageboards that I can answer with completely authority!
There isn't a reason. The old way is fine. The new way was good too. And the way after that, and the one after that. We math authors just have to make up new ways so that the publishers will let us rewrite and sell our books again. It's sort of like 4th Edition.
Somebody finally got told that the old way was just distribution, so now people want to FOIL.
Finally, there is a question on these messageboards that I can answer with completely authority!
There isn't a reason. The old way is fine. The new way was good too. And the way after that, and the one after that. We math authors just have to make up new ways so that the publishers will let us rewrite and sell our books again. It's sort of like 4th Edition.
I KNEW IT!!!!!!
The what now?
I believe it is where they send you half he book now and the other half later. Or maybe the final edit.
Who? What? When? Where? How? Why?
Finally, there is a question on these messageboards that I can answer with completely authority!
There isn't a reason. The old way is fine. The new way was good too. And the way after that, and the one after that. We math authors just have to make up new ways so that the publishers will let us rewrite and sell our books again. It's sort of like 4th Edition.
I can't speak to the authorship portion of things, but as a math teacher I'm ok with whatever method the student uses (so long as it is mathematically sound meaning it will in fact always work). I has a girl tell me that she does multiplication in a "messed up" way. She made this little grid with diagonals in it and got her product and it was the correct product. It took me a minute but I managed to figure out why it worked. I told her that her way was just fine and she should keep doing it since it works for her . There was nothing wrong with how she does things even if it looks different from what I was doing at the board. This is high school mind you (and also I think it came up once or twice during a brief stint teaching remedial course at a community college). I've seen different methods for doing most basic arithmetic. I think (since I seldom payed much attention to names for the different methods) I personally tend to use partial products most of the time (mainly as that is the method I was taught). As for why, probably because someone got a new idea for how math should be taught and it seemed fresh and new at the time. In my brief time as an educator I am discovering that certain concepts seem to go through cycles in education. That, however, is an entirely different discussion which I would undoubtedly find frustrating and pointless.
I can't speak to the authorship portion of things, but as a math teacher I'm ok with whatever method the student uses (so long as it is mathematically sound meaning it will in fact always work). I has a girl tell me that she does multiplication in a "messed up" way. She made this little grid with diagonals in it and got her product and it was the correct product. It took me a minute but I managed to figure out why it worked. I told her that her way was just fine and she should keep doing it since it works for her . There was nothing wrong with how she does things even if it looks different from what I was doing at the board. This is high school mind you (and also I think it came up once or twice during a brief stint teaching remedial course at a community college). I've seen different methods for doing most basic arithmetic. I think (since I seldom payed much attention to names for the different methods) I personally tend to use partial products most of the time (mainly as that is the method I was taught). As for why, probably because someone got a new idea for how math should be taught and it seemed fresh and new at the time. In my brief time as an educator I am discovering that certain concepts seem to go through cycles in education. That, however, is an entirely different discussion which I would undoubtedly find frustrating and pointless.Finally, there is a question on these messageboards that I can answer with completely authority!
There isn't a reason. The old way is fine. The new way was good too. And the way after that, and the one after that. We math authors just have to make up new ways so that the publishers will let us rewrite and sell our books again. It's sort of like 4th Edition.
As someone whose burgeoning interest in math was crushed by the unfeeling "do it our way and show your work or you're wrong" regime, all I can say is MATH SUCKS!! FIGHT THE POWER!!!
As someone whose burgeoning interest in math was crushed by the unfeeling "do it our way and show your work or you're wrong" regime, all I can say is MATH SUCKS!! FIGHT THE POWER!!!
Protip: Any teacher that would give you large amounts of grief over that likely doesn't understand math very well. Feel good about yourself. :)
I prefer the gully dwarf method:
1+1+1+1+1+1+1+1+1+1=2 no more then 2
As someone whose burgeoning interest in math was crushed by the unfeeling "do it our way and show your work or you're wrong" regime, all I can say is MATH SUCKS!! FIGHT THE POWER!!!I can't speak to the authorship portion of things, but as a math teacher I'm ok with whatever method the student uses (so long as it is mathematically sound meaning it will in fact always work). I has a girl tell me that she does multiplication in a "messed up" way. She made this little grid with diagonals in it and got her product and it was the correct product. It took me a minute but I managed to figure out why it worked. I told her that her way was just fine and she should keep doing it since it works for her . There was nothing wrong with how she does things even if it looks different from what I was doing at the board. This is high school mind you (and also I think it came up once or twice during a brief stint teaching remedial course at a community college). I've seen different methods for doing most basic arithmetic. I think (since I seldom payed much attention to names for the different methods) I personally tend to use partial products most of the time (mainly as that is the method I was taught). As for why, probably because someone got a new idea for how math should be taught and it seemed fresh and new at the time. In my brief time as an educator I am discovering that certain concepts seem to go through cycles in education. That, however, is an entirely different discussion which I would undoubtedly find frustrating and pointless.Finally, there is a question on these messageboards that I can answer with completely authority!
There isn't a reason. The old way is fine. The new way was good too. And the way after that, and the one after that. We math authors just have to make up new ways so that the publishers will let us rewrite and sell our books again. It's sort of like 4th Edition.
While I agree that we shouldn't stifle students who have creative approaches, there is also value in knowing how to do it in a more traditional way. The fact is that as we move to other courses, and the content gets more complicated, the instructor is going to keep going back to the traditional methods to explain things. If a student is used to do things (correctly) in their own fashion, it may make it harder for that student get help in more complicated problems because the person trying to help them may not know what they are doing. It is like one person working in base 8 and the other in base 10. Both could be right, but they would have difficulty talking to one another.
Huh? What? What?
What is it you young people in your newfangled lingo are going on about? What kind of method is that you go on about and who uses it?
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I can't speak to the authorship portion of things, but as a math teacher I'm ok with whatever method the student uses (so long as it is mathematically sound meaning it will in fact always work).
I totally agree. In fact, it's always good to know different methods for doing the same thing because one way doesn't necessarily work for all students. Of course, it's much easier for all of us to teach math the way that we do it, but too many of our methods are only shortcuts that rely on an understanding of place value that too few students have.
But I do write math for publishers and I can absolutely promise you that they insist that I change up strategies to whatever is the trend of the moment, so that they can repackage the same exercises and sell the book all over again. Basic math doesn't change that often, so why do school districts spend money on new math books every five years? It makes you wonder.
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The what now?
partial product and partial quotient method of multiplication and division
A month ago, a lady at work told me about this "NEW WAY" of multiplying that her kid had to do, and then asked if I knew what the hell they were talking about.
So I looked at it and couldn't figure it out.
THEN, another lady on facebook I knew in high school was bemoaning partial product and partial quotient.
So....I put 2 and 2 together.....
and googled it and figured it all out.
It's just kinda disconcerting; I'm always looking forward to this kinda stuff in my kid's homework, so he can ask me how to do it, see me baffled, and either think:
1)my dad's a dummy
or
2)hell; my dad can't do it and he's older than Justin Beiber. If he doesn't know how to do it, it must be umpossible.
Maybe I need to repeat 4th grade. Hell; it'd be nice and stress free.
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Finally, there is a question on these messageboards that I can answer with completely authority!
There isn't a reason. The old way is fine. The new way was good too. And the way after that, and the one after that. We math authors just have to make up new ways so that the publishers will let us rewrite and sell our books again. It's sort of like 4th Edition.
Thanx for the explanation though.
Guess I need the textbook too. ;)If I can just know what these new things are, I can google them.
I actually once APPLIED GEOMETRY TO REAL LIFE to figure something out; so I'm pretty trainable.
This is new? It's a little bit different from what I've learned (mostly by using a few more steps), but I don't see how this is New And Exciting.
What's the method this is replacing?
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I was a math teacher for a couple of years, and I still couldn't even begin to tell you what "the new math" is.This is new? It's a little bit different from what I've learned (mostly by using a few more steps), but I don't see how this is New And Exciting.
What's the method this is replacing?
Well this is the 3rd "new" math I have seen.
My hatred for math rivals my hatred for Facebook and Joss Whedon put together.
I was a math teacher for a couple of years, and I still couldn't even begin to tell you what "the new math" is.This is new? It's a little bit different from what I've learned (mostly by using a few more steps), but I don't see how this is New And Exciting.
What's the method this is replacing?
It won't do you a bit of good to review math. It's so simple, so very simple, that only a child can do it.
My hatred for math rivals my hatred for Facebook and Joss Whedon put together.
Now, now, calm down, LOL-Cheshire, this is quite tame stuff. It's not really math, it's just figuring out numbers. It's not the brutal stuff you get when you leave numbers behind.
And with little tricks like this, the numbers business, when it does arise, will be less of a hassle.
And those pesky numbers have the terrible habit of turning up over and over again.
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This is new? It's a little bit different from what I've learned (mostly by using a few more steps), but I don't see how this is New And Exciting.
What's the method this is replacing?
Cross multiplication.
It's kinda confusing without an instructional video for me, but I'm probably not as smart as you.
My hatred for math rivals my hatred for Facebook and Joss Whedon put together.
So you secretly love math too, huh? ;)
I KNEW IT!!!!!!Finally, there is a question on these messageboards that I can answer with completely authority!
There isn't a reason. The old way is fine. The new way was good too. And the way after that, and the one after that. We math authors just have to make up new ways so that the publishers will let us rewrite and sell our books again. It's sort of like 4th Edition.
Even though I hate wotc, and want to agree with Mama Loufing's fine argument, I have to ask you to try the following experiment.
There is a reason, but it may not be what you think: "the Partial Product method can be performed mentally faster than the "Old Method." Here is an experiment you can do to impress your friends:
The SET UP:
1. Teach yourself the partial product method. Do 100 practice problems to get very well practiced at it.
2. Re-remember how to do multiplication the "old way". Do 100 practice problems to get very well practiced at it.
3. Randomly generate 60 new multiplication questions. Give both numbers being multiplied 1-3 digits. Split them into two groups of 30.
The EXPERIMENT:
1. You are now going to perform the multiplication in your mind only and time yourself how long it takes you to do each individual question. Each problem will done only in your head without writing any work down. After which you will do a hypothesis-test to verify there is a difference in the time it takes you to perform multiplication in your mind using the "old method" and the Partial Product method.
2. First, a little organization. For the first group of 30 you will us the "old method", and for the second group of 30 you will use the partial product method. Get a stop watch, or find a webpage with a timer on it you can trigger by pressing a mouse button.
3. Group 1 - "Old Method". Do each problem in your mind only, one at a time until you arrive at the correct answer. Time and record in seconds how long it takes for each individual problem. You should end up with 30 trials.
4. Group 2 - Partial Product Method. Do each problem in your mind only, one at a time until you arrive at the correct answer. Time and record in seconds how long it takes for each individual problem. You should end up with 30 trials.
The ANALYSIS:
1. Calculate the Mean and Variance for your two groups of data. One Mean and Variance for the time it took you to perform multiplication in your head using the "Old Method", and another Mean and Variance for the time it took you to perform Partial Product multiplication.
2. Perform an alpha = 0.05 Hypothesis test that the Partial Product method can be performed mentally faster than the "Old Method".
.
3. ( ALTERNATIVE ANALYSIS ) If you can not do a hypothesis test, then just post the Mean and Variance of you data groups here. Then, I will do it for you.
.
The CONCLUSION:
1. Post the results of your experiment, and tell us all how you did.
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Ha! Great idea, high G! I hope a few people try this.
Actually, something like this has been done, and there is no question that the partial products method is superior for the reason that it can be done mentally very easily (which means it is congruent with the way we think) and it reinforces place value concepts. If you can do the partial product method, you really get what the numbers mean. The traditional method is just marks on paper. One other reason that the partial products method is superior: Errors are less likely to be in higher place value columns. I'd rather make a $1 error than a $1000 error.
The real question is: Since we know the partial products method is so sound educationally, why did we stop using it and switch to the method most of us learned? As far as I know, the reason was that some children had trouble with the partial products method because they didn't have sound number sense. Our traditional method was an attempt to get younger children to get right answers whether they understood it or not. It was part of our factory model of education.
Most people are unaware that education methods cycle and recycle instead of improving in a linear fashion. The methods we choose have less to do with how children learn and more to do with the child-product we want to manufacture.
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When did they switch to cross multiplication?
I hate math, I'm no genius, I'm better than some;
English was easier for me, but I've been able to deal with math ever since I learned to approach it from a mindset of wanting to kick its ass, wanting to crush it, see it driven before me, and hear the lamentations of its mates....that sorta thing.
So, I make it personal-like, and it helps.
And every time it plans a night raid on my camps, I plan to kick math's ass really really hard.
When did they switch to cross multiplication?
I hate math, I'm no genius, I'm better than some;
English was easier for me, but I've been able to deal with math ever since I learned to approach it from a mindset of wanting to kick its ass, wanting to crush it, see it driven before me, and hear the lamentations of its mates....that sorta thing.
So, I make it personal-like, and it helps.And every time it plans a night raid on my camps, I plan to kick math's ass really really hard.
1.
Cross multiplication is a "technique" to solve equations. This term gets used sloppily to mean other things, especially in finding common denominators. But, cross multiplication is used to solve an equation when you have exactly two terms on either side of the equal sign, and in one of the terms is the variable you want to solve for.2/x = 7/9
Cross Multiplying yields:
7x = 18 => x= 18/7.
2.
Having a violent mindset towards learning math is actually kind of a good thing.
Math is used to make decisions by powering up your reasoning skills. You want to be good at math, so you can out-think other people, and take their gold.
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Tensor is right. Cross-multiplication applies to fractions and proportions (also vectors).
The four methods that have been taught for multiplication of multi-digit numbers are (1) the partial products method, (2) the lattice method, (3) the short method (the traditional method), and (4) the Egyptian method.
Everyday Math, a series developed in Chicago, which came out around 2003, encouraged a return to partial products. Why? Because it became obvious, that students were having trouble with our standard division method and most teachers were beginning to experiment with the partial products method of division. So it made sense to change the way we multiply also.
I wonder which method is used in Golarion. Probably the Osirion method.
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My next question is this:
hearkening back to the old Soviet Union way of selecting for Olympic champions,.....
with myself, anyway, it seemed that there were two different types of math; geometry which really came naturally to me, and.......everything else.....i.e. algebra/trig/calculus/whathaveyou. I could DO these things, but it never seemed natural to me; I also have weak ankles and flat feet so I'd never be much of a hockeyplayer (growing up in Florida haha). Does this make any sense past my own possibly anecdotal observation, and, if so, if I was to notice this proclivity in my own kids, what sort of field of study would lend itsself to this particular proclivity?
What would one hypothetically steer a kid with a "mind for geometry" towards?
As an aside, I'm aware of the concept of "helicopter parent," and as such, probably need to take the 'bird back to the horizon some, but I try to be mindful of this and let the teachers do what they're doing, seeing as they went to school for it and all. ;)
My next question is this:
... Does this make any sense past my own possibly anecdotal observation, and, if so, if I was to notice this proclivity in my own kids, what sort of field of study would lend itsself to this particular proclivity? ...
Some math is easier because it is more visual. Geometry falls into this category. Since, we can actually touch blocks, and draw triangles "geometrical reasoning" seems more natural. And quite frankly, in human history geometry was the launch-pad for the development of all math (think Euclid's Elements.)
Mathematics such as trig and calculus are not as visually oriented, and rely on analytical reasoning SKILLS supported by your MEMORY of all the definitions. Visualizing geometry is built into our brains, but calculus skill has to be learned through training.
Skills takes practice and repetition to strengthen. For a lot of people, all this practice is boring, and interest easily wains. (An analogy is exercise, doing push ups and sit ups is boring, makes you sweaty, and hurts. But long term practice makes you sexy and strong!)
Anyways, long term mastery of calculus and trig (for example) requires regular practice to build your skill and memory. The result is powerful decision making ability that can be used to out-think other people, and take their gold; Or program computers, or design an investment portfolio, etc.
Gold is sexy and strong. So make sure your kids practice (finish) all their homework -- make it a fun game. Use flash cards to assist memorizing all the math definitions, and draw lots of pictures to assist their minds in visualization.
What would one hypothetically steer a kid with a "mind for geometry" towards?
The study of Mathematics. Including Art, History, and Military Science.
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(lol)
I worked like 7 am to 10 pm yesterday, so I'm punchy.
I don't know why I wrote Trafalgar for Waterloo, but infantry squares at Trafalgar would kinda be silly, unless they were sahuagin, and I still think the powder woulda got too wet.
"Waterloo" doesn't mean it was a sea battle, heath! Sheeesh!
This is new? It's a little bit different from what I've learned (mostly by using a few more steps), but I don't see how this is New And Exciting.
What's the method this is replacing?
Cross multiplication.
It's kinda confusing without an instructional video for me, but I'm probably not as smart as you.
Cross multiplication seems something you do with fractions, and this partial product seems to be something used to multiply larger numbers.
is this where someone should say "Mathlete's of the world unite?"
Because I am not going to.
Isn't the word "mathochist"?
The four methods that have been taught for multiplication of multi-digit numbers are (1) the partial products method, (2) the lattice method, (3) the short method (the traditional method), and (4) the Egyptian method.
Ah!
I also learned the short/traditional method, then. I'm not an expert, but partial product looks a lot like short method.
Lattice looks weird, and involves a lot of painting lattices - I'd rather spend my time multiplying, thank you. But nice for the art majors to get their own method ;-)
The egyptian methoid is interesting, too. But, then again, I know the binary numbers up to 2^15 or so by rote :D and generally like computers and their weird little ways, so I'm biased.
What would one hypothetically steer a kid with a "mind for geometry" towards?Architecture?
We will need those geodesic domes, for when we all migrate to Mars.
Then to INFINITY AND BEYOND!
Which infinity?
Since we're talking about math in this thread, you can't just say something like infinity and then not specify which one :P
(lol)
I worked like 7 am to 10 pm yesterday, so I'm punchy.
I don't know why I wrote Trafalgar for Waterloo, but infantry squares at Trafalgar would kinda be silly, unless they were sahuagin, and I still think the powder woulda got too wet."Waterloo" doesn't mean it was a sea battle, heath! Sheeesh!
Trafalgar Square?
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Huh, I didn't know this is a thing.
I've pretty much always done math problems in little chunks, and then put all the pieces together afterwards, because my suckage at math cannot be expressed without exponential notation.
In crayon.
Also, interesting to note that Joss Whedon has a Facebook page. Thanks, Freehold DM!
I've pretty much always done math problems in little chunks, and then put all the pieces together afterwards, because my suckage at math cannot be expressed without exponential notation.
Actually, that's what mathematicians do all the time.
There's a joke about it where a mathematician is asked how he'd react in certain situations.
"You're in a burning building. There's a window which is closed and locked. What do you do?"
"I smash a window, and then escape."
"Now you're in a burning building. There's a window which is open. What do you do?"
"I close and lock the window. Now I can refer to a problem I already know the answer of."
Huh, I didn't know this is a thing.
I've pretty much always done math problems in little chunks, and then put all the pieces together afterwards, because my suckage at math cannot be expressed without exponential notation.
In crayon.
Also, interesting to note that Joss Whedon has a Facebook page. Thanks, Freehold DM!
AAAAAUUUUUUUUGGGGGHHH!!!!
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When I was in High School my teachers insisted that Math was important. I'd always argue: "But if I need to do math there'll be a calculator handy."
They'd respond: "Not during a test there won't be." (Unless there was like final exams always allowed).
Nowadays everyone carries a mobile phone, and every mobile phone has a calculator app of some description. I ALWAYS HAVE A CALCULATOR DAMMIT! I was ahead of my time.
Where am I going with this?
I'm an English major dammit! I don't have time for useful skills like Math!
I ALWAYS HAVE A CALCULATOR DAMMIT!
Can your calculator proof conjectures? ;-P