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"The Math Myth and Other STEM Delusions"

  1. Feb 29, 2016 #1

    Andy Resnick

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    Last edited: Mar 1, 2016
  2. jcsd
  3. Feb 29, 2016 #2
    Hacker brings up the issue that has been or is being debated still. In our hurry to increase the number of scientists and engineer back in the sixties our educational system left behind the majority of citizens who only need the fundamentals of numeracy. Hacker has contriubted to the NY time in the past with this article "Is Algebra Necessary"

    In an article by Don Byrd, he discusses one of the early articles on the problems of teaching math by Paul Lockhart "A Mathematician's Lament " musing in part on what if we taught music like we teach math. It would be unthinkable.

    Bryd singles out two problems, over use of abstraction i.e., use of symbols, and poor environment for student engagement i.e. not creating an environment that stimulates students curiosity and interest.


    Keith Devlin further https://www.maa.org/external_archive/devlin/devlin_03_08.html [Broken] using it as a springboard for his https://www.maa.org/external_archive/devlin/devlin_07_11.html [Broken] , adapting Lockart's use of the proper teaching of music as a paradigm for math.

    So when will educators get the message that we cannot all be mathematicians?
     
    Last edited by a moderator: May 7, 2017
  4. Mar 1, 2016 #3

    Astronuc

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    I had an interest in math and science, and I found algebra, geometry, trigonometry, analytical geometry and calculus fairly easy. However, the majority of students in high school weren't particularly interested in those subjects. In high school, I expected to go to university and do math and physics, which is pretty much what I did, but then migrated to nuclear engineering, which is more or less applied nuclear physics. So for me, STEM was absolutely necessary.

    There were programs for kids who could only manage basic math, like consumer mathematics and some simple algebra.

    If numeracy is a problem, perhaps there are problems with the way math is taught and/or a lack of support at home.
     
  5. Mar 1, 2016 #4
    Did you have a support system in regards to math?
     
  6. Mar 1, 2016 #5

    Astronuc

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    My parents gave me a lot of encouragement, but more in terms of getting me into summer programs (during summers between 7, 8, 9, 10 grades) at a local university, which did have math and science courses, an the summer program got me access to the university library. My parents bought an encyclopedia, which had a lot of natural history and historical information, which included articles on topics in chemistry, physics, and other subjects, including biographies of mathematicians, scientists and political figures. My parents bought my brother and me a chemistry set, and my folks bought me one of those 100-in-1 electronic kits.

    Besides the university library, my dad took me to the city public library and another university library, but also to a technical book store where I was able to buy textbooks on analytical geometry and calculus, basically so I could teach myself some calculus. I did a lot of self study, and by grade 11, I was beyond my parents in mathematics.

    The second high school I attended had a really good program in math. My 11th grade (algebra, trigonometry, analytical geometry) teacher worked closely with my 12th grade (calculus) teacher, and they worked closely with the chemistry teacher who had an MS in chemistry. The three of them prepared major works (MW)/honors and AP courses for 30 to 40 students, who were planning to go to the top universities in the country. We had numerous students going to Harvard, Yale, Princeton, MIT, Caltech, Stanford, Cornell, . . . , but some stayed in state and went to UT or TAMU.
     
  7. Mar 2, 2016 #6

    Andy Resnick

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    I think there's increased interest in reviving this type of program, in Ohio they are calling it 'financial literacy'. I envision the content in this type of program to be more than just arithmetic and algebra drills, but also include some statistics. In crude terms, the idea is to teach rational consumerism.
     
  8. Mar 2, 2016 #7
    Those programs have its merits but I feel there is some danger involved.
    The big problem is students that are not interested in maths in the least.
    Some classes will consist of students so uninterested it will be next to impossible to captivate and motivate students to do well.

    A lot of those students will remain uninterested whatever efforts we do, helping them understand the maths necessary to allow people to spend rationally or do some quick calculations like finding the amount of carpet needed.

    A final remark is the fact that all students seem to benefit from at least a few stronger students in the group (stronger as in faster, more inquisitive and more enthousiast). Unfortunately I only found a reference in a dutch book.

    tl;dr
    Introducing such a program needs a lot of consideration in advance.
     
  9. Mar 2, 2016 #8

    Astronuc

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    There was/is a similar program in the high school my son attended. I think it was termed 'consumer math' or something like that.
     
  10. Mar 2, 2016 #9
    My primary and secondary education ( '47 - '59) of course was exactly this scenario. I think it did spur especially the average student (me at the time) to exert more effort. In my schools and at this time I suppose most where graded on a straight scale. You know what you had to do to get an A. You knew who the good students were. So yes I think there is a benefit for a heterogeneous group. Did it affect all students in the same way I cannot say. Did it to paraphrase Goethe -make a man better because you took him as he should be not as he is?

    A common critique of the type of class is that the less able students hold up the class and bore the more able students. But this criticism begs the question "Is the course overly sensitive to the needs of the less able students"? Could the course especially an elementary one be structured so as to remain significantly challenging to the able students without demoralizing the less able. Certainly at some point one must create separate pathway according to ability and/or interests. That brings up the question of when should this occur.
     
  11. Mar 2, 2016 #10
    I am unsure what is taught currently here in New Jersey, for instance, but 'financial education' would be an extremely valuable lesson for most....issues such as compound interest when saving, economic growth and GDP, stocks, bonds, borrowing costs of credit cards, incorporating businesses to limit liability, wills, unemployment insurance, Roth versus traditional IRA's, defined contribution versus defined benefit plans, leasing versus buying, financial security, retirement saving, health savings plans, life,disability and liability insurance, effects of government debt and deficits and borrowing, strong versus weak currency, diversification of investments, risk/reward, etc.
     
  12. Mar 2, 2016 #11
    Yes, consumer math or financial math is useful to the more mathematically inclined too. Certainly not from the mechanics of the math but certainly from the context that are relevant to applications. Sometimes one has to pull facts out the the provided statistics or numbers i.e., do some math, to get a handle on their significance.
     
  13. Mar 3, 2016 #12

    Astronuc

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    Mine was in the 60's.

    Reflecting on the earliest years, my first and second grade classrooms had cuisenaire rods.
    https://en.wikipedia.org/wiki/Cuisenaire_rods

    They were very practical with respect to learning the relationship of numbers, e.g., 5 x 2 (or 2+2+2+2+2) = 2 x 5 (or 5+5) = 10. One could understand addition and subtraction. I don't know if is sank into my classmates as readily.

    In second and third grade, I had a classmate with whom I competed. On rainy days, when we had indoor recess, he and I used to write numbers (1, 2, 3, . . . .) on a personal chalk board to see who could achieve the highest number during the recess period. He always got to higher numbers. It was also good way to start to see relationships between numbers, e.g., multiples of 2, 3, 4, 5, . . . I think we just naturally discovered patterns. I don't think our other classmates were invested in such activities. By the time I got to number lines, counting and natural numbers, reals numbers and so on, I had a pretty easy time with understanding numbers, i.e., arithmetic was pretty easy, whereas many classmates struggled at various levels.
     
  14. Mar 3, 2016 #13
    There seems to be some connection between having some visual representation of numbers and learning their relationships.. What about the Abacus as a teaching aid?
     
  15. Mar 3, 2016 #14

    Andy Resnick

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    One of the 'new' ideas is called 'competency-based instruction'. In this model, students progress at their own pace, determined by passing exams. This is fairly easy to implement on computer-based instruction (math, spelling, etc). My dystopian view is that it helps train students to be mindless cubicle-dwellers, interacting only with computer programs.
     
  16. Mar 3, 2016 #15

    bcrowell

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    [A moderator deleted almost all of this post, so that what remained was not an accurate indication of my thoughts. Therefore I've deleted the small amount of remaining content.]
     
    Last edited: Mar 5, 2016
  17. Mar 4, 2016 #16

    billy_joule

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    Well hopefully there's some middle ground as the traditional one size fits all approach has been clearly failing. I find the modern classroom to be much less cube-farm-like, there's a lot more active participation, collaboration and group work while still being assessed individually, back in my day it was sit down shut up and do your sums! And everyone took the same tests. My 'day' was the 90's - 00's so pretty recent, I'm comparing changes in the school I attended that my daughter now attends.

    I don't think anything I learnt though high school and university math made me a more well informed voter (bar a small amount of statistics).
    What did hurt my political viewpoint was not taking a single humanities or social science class since I was 14 (as is fairly normal for engineers in my country). Taking only math & science classes gave very little insight into how the 'real' world works.
     
  18. Mar 4, 2016 #17
    Do you have kids? Kid make bad choices and not wanting an education is one of them. You can't dump them on the street where they will make many more bad choices. There is a reason that education is compulsory and its not to just to babysit them. You want as many functional and educated adults as possible. All cultures have rites of passage to prepare kids for adulthood and in civilized society schooling is one of them.

     
    Last edited by a moderator: Mar 4, 2016
  19. Mar 4, 2016 #18

    Astronuc

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    That would be taking it to the extreme.
    Yes, children, young adults, and even some adults, make bad choices. However, the sooner someone reaches an individual, the sooner hopefully the individual will learn to make better choices.

    I think it is necessary to make arithmetic/mathematics, science, humanities relevant, and it seems for many, it is not.

    Perhaps I was fortunate, because I knew, probably from first grade, that my education was relevant, and that I could some day be one of those adults who practiced math and science. I have encountered so many in the past, and I encounter so many as a professional, who struggle in this world.
     
  20. Mar 5, 2016 #19

    Fervent Freyja

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    I imagine that the No Child Left Behind Act of 2001 has had much to do with many issues of this sort. I was around 12 when this was implemented into the school system, standards were lowered in order to meet progress reporting but there was no longer much support for children that loved to learn. They become an additional "problem" for the teachers and were suddenly pulled from accelerated/gifted programs.
     
  21. Mar 5, 2016 #20
    On the one hand, I agree that not every student needs or wants to be a mathematician. On the other hand, students often don't know what they want or need at this age and a lot will opt for "consumer math" as an easier path through school just because they get indoctrinated into thinking math is "hard" or "geeky". The proposal to reduce the math taught strikes me as elitist. I'd rather see math instruction that makes the problems relevant -- why do you need algebraic skills? Because there are practical applications in adapting recipes when you're cooking (or brewing), hunting, fixing your car, hiking in the woods, etc.
    The big problem I see isn't that schools teach math, it's the way some of them teach it. Most of the problems I've seen circulating as "Common Core" are just asinine (of course, the problems sets people object to are the ones most likely to be circulated) and I have to wonder about the practical experience of the people who generated them. I know I am more "math-friendly" than most as a working engineer but I have also worked with teenage boys for nearly 30 years and have always endeavored to make any skills I teach both relevant and interesting. I haven't seen how my nephews are taught but some of the homework problems I've looked at are just abominable.
     
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