The term: New Math

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  • #26
jim hardy
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If i'm correct in my understanding,,, Einstein started out with Euclidean geometry which builds from observations of constructs.....What before why.... rules evolving from observations....

And I wasn't demeaning him at all. He was a thinker.

Re new math -I stand by my assertion : "what before why" produces larger numbers of math capable kids.
I arrived at that from my own observations in early 1960's.
Are there any new studies that disagree?
 
  • #27
AlephZero
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I did some "new math" in the 1960s at school in the UK. I don't think it did me any lasting damage.

This thread reminds me of a story from one of my Univ. lecturers. He had decided his own kids ought to learn math concepts as early as possible. So one day he was walking along the riverside with his 4 year old kid, watching some rowing eights training. He pointed out to the kid that there were the same number of oars as the number of rowers, and this was called a one-to-one correspondence.

A few days later they were on the river bank again and he asked his kid if he could remember what a 1-to-1 correspondence was. With great confidence the kid answered, "It's a special sort of boat".
 
  • #28
WannabeNewton
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I dunno, WBN - I never thought much of "Abstract Art" . Boston's "Museum of Bad Art" is full of it.

This is the mechanized age.

I respect those who think on higher planes . They advance science. And I wish I could understand my little book on 'irrational numbers'.
But 99% of us are more involved in maintaining the wheels and cogs of civilization.
Einstein was not a skillful handyman. Among his most prized possessions was a small reflector telescope some students built as a gift for him.
The Boston thing made me laugh quite a bit haha. I'm not saying applied math is useless; by all means I mean the opposite because it drives our world :D. What I was talking about was more along the lines of the kind of teaching where you are thrown some formulas and have to memorize them and plug and chug come exam time. I don't see any utility in that kind of teaching. By abstractness I meant more along the lines of focus more on concepts rather than actual numbers.

Perhaps as an example, explaining the concept(s) and diagrams behind the fourier transform of an impulse-response system into the frequency domain would probably be more helpful in solidifying the theory behind why it is useful and why it works as opposed to just giving say a mass-spring system with some numerical parameters and saying "here, go find the fourier transform and give me the amplitude of the response in the frequency domain!"
 
  • #29
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Perhaps as an example, explaining the concept(s) and diagrams behind the fourier transform of an impulse-response system into the frequency domain would probably be more helpful in solidifying the theory behind why it is useful and why it works as opposed to just giving say a mass-spring system with some numerical parameters and saying "here, go find the fourier transform and give me the amplitude of the response in the frequency domain!"

Pretty sure we're talking about grade school here.
 
  • #30
WannabeNewton
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Pretty sure we're talking about grade school here.
Pretty sure Jim was talking about engineers and inventors.
 
  • #31
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Pretty sure Jim was talking about engineers and inventors.

Good point. Yeah, understanding is important for engineers and inventors.
 
  • #32
MarneMath
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My father is an Engineer and I had a conservation with him regarding new math many years ago during my high school time. From what I gathered, he felt completely discouraged in his mathematical abilities for a good part of his education, because he never understood the purpose behind of stating axioms while solving algebraic equations or looking at problems in terms of sets. If it wasn't for the fact that a family friend, who worked at NASA explicitly told him that 'while there is a use for this kind of thought, at the end of the day, as an engineer, it's your ability to use math to solve real problems, not made up ones, that matter.' that got him to stay and eventually obtain an engineering degree instead of working the family avocado farm.

Looking back at my own educational experience, I can say with a high degree of confidence I would've felt the same. I disliked most of abstract algebra, I disliked most of my theory based probability, and I wrote my thesis with the sole intent of taking an abstract idea and making it concrete for myself. In the end, the mathematics has always just been a tool for me to analysis real world data. I think education needs to accept that for a lot of people, mathematics is just that, if not less.
 
  • #33
jim hardy
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In the end, the mathematics has always just been a tool for me to analysis real world data. I think education needs to accept that for a lot of people, mathematics is just that, if not less.

Thanks all - that was exactly my line of thought.
 
  • #34
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I'm glad to hear you say that because I also didn't recognize anything in that wiki article, nor do I have any memories of it being strange or confusing. I was beginning to think all of my childhood memories of math were false.
Maybe you and I both happened to go to schools that were administered the placebo.
 
  • #35
dlgoff
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The beauty of math and the challenge of math is in the abstractions ...

It's been too long to really appreciate your quote, but not so long as to remember I began feeling exactly the same somewhere around differential equations. :smile:
 
  • #36
lisab
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My father is an Engineer and I had a conservation with him regarding new math many years ago during my high school time. From what I gathered, he felt completely discouraged in his mathematical abilities for a good part of his education, because he never understood the purpose behind of stating axioms while solving algebraic equations or looking at problems in terms of sets. If it wasn't for the fact that a family friend, who worked at NASA explicitly told him that 'while there is a use for this kind of thought, at the end of the day, as an engineer, it's your ability to use math to solve real problems, not made up ones, that matter.' that got him to stay and eventually obtain an engineering degree instead of working the family avocado farm.

Looking back at my own educational experience, I can say with a high degree of confidence I would've felt the same. I disliked most of abstract algebra, I disliked most of my theory based probability, and I wrote my thesis with the sole intent of taking an abstract idea and making it concrete for myself. In the end, the mathematics has always just been a tool for me to analysis real world data. I think education needs to accept that for a lot of people, mathematics is just that, if not less.


Avocado farm, are you kidding me?!?!?! That would have been freakin' AWESOME :!!) :!!) :!!)!!!
 
  • #37
MarneMath
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Avocado farm, are you kidding me?!?!?! That would have been freakin' AWESOME :!!) :!!) :!!)!!!

It's a nice little place down in south Texas. We also do bell pepper. To this day, the world Abuelo y Abuela is synonymous with pepper with me, and I can smell the morning fields with dew.
 
  • #38
jim hardy
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dlgoff said:
but not so long as to remember I began feeling exactly the same somewhere around differential equations.

I LOVED Diffy-Q because it explained how so many things work.
The next course, vector calculus, was simply too much for me. One finds his limits....
I do admire and envy those who can handle abstract math. My earlier remarks were not a put-down, just it's not for everybody including me.

There are doubtless people who understand the Laplace Transform.
To me it's only a useful tool that I don't understand.

Fourier transforms we worked out by hand as exercises in AC circuits class. Prof gave us an arbitrarily shaped wave and we developed the first five or six transform pairs by ruler, pencil and sliderule.
That enabled me to believe it was indeed true that a periodic wave can be represented by a polynomial in sines. A most useful concept.
But my plodding brain had to see at it from that direction before I could accept the derivation.
I thank goodness for that practical classroom exercise !
 
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