Help with Mathematical Concepts, Not Arithmetic

by Band on the Run 101 Replies latest jw friends

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  Quendi

  I've really enjoyed this thread and everyone's contributions to it whether they are "pontificating" or not. Mathematics seems to excite a lot of passion either in favor or opposed to it, and I hope this discussion will keep on going for a while.

  To address a point raised by simon17 about why true arithmetic and algebra lie "on the other side of calculus", that is because their study requires the use of analysis. Analysis courses always are offered after the calculus classes have been completed because then you understand enough to grasp how and why the Fundamental Theorems of Algebra, Arithmetic and Calculus are true.

  As for the teaching of mathematics and how poorly it's being done, don't even get me started. I will say that the practical examples some have used, such as how much paint is needed to cover a room or how much wallpaper is needed for a wall or other partition are rarely used in classroom instruction. When I taught, I would regularly pose problems like that for my students because I wanted them to understand that mathematics wasn't simply concerned with the abstract, that it had ordinary, everyday uses as well. Kids really appreciated that.

  But I also taught kids who were light-years ahead of their classmates. I remember one boy who asked me what was the definition of a real number. He was only 12 years old and was already thinking on a highly advanced level. Then there was another boy who wanted to know what kind of mathematics was used to create the digital animation features in movies like Toy Story and Titanic. Or the young woman who wrote a brilliant essay on the contributions to the field of statistical analysis that had been done by...Florence Nightingale!

  Teaching mathematics is a real challenge when you have a class of more than thirty students with widely varying abilities. The challenge is compounded nowadays with the emphasis on standardized tests that are considered a true measure of a student's mathematical understanding. Having also worked as a grader for these same tests I can tell you they are anything but that. However, they are the newest "sacred cow" in math education and their use cannot be questioned right now.

  I discovered the Khan Academy website some time ago and recommended it earlier in this thread. Sadly, the approach used there is something that professional educators oppose. I am glad this resource is available, however, as well as the ...Dummies and ...Demystified books for anyone, student or not, who wants to learn more about deep mathematics.

  Quendi
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  Band on the Run

  I am most grateful for the information. What a response! So many logical thinkers among former Witnesses. The math may have driven you out.

  Does anyone know anything about the Courant Institute at NYU? I think it is NYU. It is near their campus. A friend did advanced theoretical math there.

  No, I graduated from a women's college. We had many math and physics majors. When I started, we were not yet co-ed with the Ivy League college across the street. They had an excuse to attend the male campus for advanced classes. The women were feminine, too. I was not raised with such role models, however.

  Another weird thought that I hear from people is that thinking or studying too hard causes mental illness.
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  simon17

  Does anyone know anything about the Courant Institute at NYU? I think it is NYU.

  Yes its one of the very best math departments in the world. What did you want to know about it?
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  james_woods

  Another weird thought that I hear from people is that thinking or studying too hard causes mental illness.

  Really! I read in the Tom Wolfe book "The Right Stuff" that the original Mercury astronauts thought that physical exercise caused brain damage.

  All except for John Glenn. He was also the only one of them who did not own a Corvette.

  BTW - read that book "The Golden Ratio" by Mario Livio, no matter what Quendi says. You will like it.

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  Quendi

  @ james_woods: If you recall, I didn't tell BOTR not to read The Golden Ratio. I told her there were better books that dealt with her questions about how mathematics works. I own Livio's book myself and enjoyed reading it, but it isn't the kind of primer I would recommend for someone who is wanting to learn the nuts and bolts of mathematics. By the way, did you look at the video I pointed to earlier in this thread? What do you think about it?

  Quendi
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  00DAD

  Quendi, great video. Thanks for sharing it!

  I just want to know, where do conchs, sunflowers and dragonflies study geometry?
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  Quendi

  Let me recommend two other titles:

  A Tour of the Calculus by David Berlinski

  The Infinite Ascent: A Short History of Mathematics by David Berlinski

  The first book requires nothing more than an understanding of high school algebra and geometry. The second is a real page-turner written in a most engaging style. My non-mathematician friends really liked the second book.

  Quendi
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  james_woods

  Just joking, Quendi. No, I cannot watch videos on the IBM network.

  I was sort of hoping to hear from BOTR again.
• 

  Quendi

  @ james_woods: When you get the chance, buddy, watch that video! Since you love the Fibonacci sequence, you'll really appreciate what this video teaches. I'm very interested in your thoughts about it.

  @ 00DAD: I'm glad you were able to watch and learn from the video. Share it with others, especially those who suffer from mathphobia.

  @ BOTR: I went back to college to get my degrees (the other one is in Geography) while I was still a Witness. You can bet my move met with a lot of disapproval, but only two elders ever talked to me about it and I gave it to them with both barrels. "This is my life we're talking about," I told them, "and I'll live it as I please. As the United Negro College Fund puts it, 'A mind is a terrible thing to waste.' "

  I will say that when I graduated, one family in the congregation gave me a big graduation party as their gift to me. A lot of people came and everybody congratulated me on finishing and getting my degrees even though I was in my mid-forties. My years as a college student were my happiest in all my life in Colorado. I've never regretted getting that diploma. Since you are a lawyer, you'll especially appreciate what my mathematics advisor said to me: "Only those who study law get the kind of rigorous training in logic that we mathematicians get. In their philosophies and practice, the two professions are very much alike."

  And it is very gratifying to see the responses this thread has received. If this kind of mental energy had been allowed to operate inside the organization, it would have been completely transformed. This is not to say it wouldn't have made mistakes, but I think its most egregious errors could and would have been avoided.

  Quendi
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  Farkel

  Quendi,

  Contrary to what you may have implied, I have enjoyed your contributions on this thread. Thank you.

  : Teaching mathematics is a real challenge when you have a class of more than thirty students with widely varying abilities.

  Yes. Although I did well in mathematics, I fought it the whole way until....I took physics in my junior year in High School and then it magically became crystal clear to me how practical math could be all through life. Not only that, but I learned more about math through physics than I learned about math from taking math.

  If teachers could start students at a very young age and instill the value of knowing it through age-appropriate practical examples, perhaps more students would embrace it or at least pay enough attention to actually learn it.

  Farkel