Where is "Here"? Thanks, Bill C ----- Original Message ----- From: David Makin [mailto:makinmagic@tiscali.co.uk] Sent: Friday, March 11, 2011 10:22 PM To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] High school calculus? Here Calculus has apparently been removed from the National under-16 syllabus which I find a little annoying (especially when successive Governments have claimed there's been no "dumbing down" of education in order to improve pass rates) *because calculus hasn't been replaced by something else*. IMHO the whole of education needs a complete overhaul - it should be designed so the same knowledge is acquired but with 100* the fun factor from the students perspective - to me this means rethink the teaching method completely so it's all done through games and challenges for the students rather than dry lecturing/dictation/textbook use etc. IMHO the real key being a massive increase in *expectations* for all years from 6 to 11. Plus get rid of the incredibly stupid and crippling modern "PC" attitude of removing all sense of competition as if it's morally or ethically incorrect - just congratulate the "winners" and commiserate with the "losers", to do otherwise teachers children something that simply is a lie and some will be unprepared for the naked truth once they leave education. (I realise that this 'PC" practice only applies to some and not all). On 12 Mar 2011, at 00:49, Henry Baker wrote:
Re _not_ teaching calculus in high school:
I have a great deal of sympathy for this view.
Some background: I was a member of our high school's math team that placed highly in the state of Ohio (first, I think, but my memory about this event isn't very good), and I won the Cincinnati math contest my senior year. My senior year, I took all AP courses (except English!), including AP math, which was calculus, more-or-less. As a result of these courses, I was able to "place" out of some courses my freshman year at MIT, including 18.01. My oldest sister's boyfriend was a college math&physics major (who later got his physics doctorate from Heidelberg), and he tried to get me to understand some of the subtleties of "epsilon-delta" calculus, but I have to say that I was not ready for it, and I didn't really understand it.
In retrospect, I should have stopped wasting all of my high school teachers' time and gone straight to MIT after my junior year in high school. Even though my high school had some of the best high school teachers in the U.S., they still were a far cry from what MIT had to offer. When I arrived at MIT & started learning _real_ math & _real_ physics, I felt like I had gone to heaven & I knew that I had just been wasting time in high school.
Calculus never excited me much in high school (or MIT, for that matter). I was far more interested in algebra & mathematical logic. For me, the coolest thing about calculus was the algebraic operations of derivation and antiderivation. I never really "understood" infinitesimal calculus until I took probability theory and especially advanced mathematical logic, where I got to understand models and cardinal numbers and different sizes of infinities. I took an extracurricular number theory course while I was still in high school and _loved_ it. Later, at MIT, I took an algebra course where we studied groups & rings & fields (including finite fields for coding theory), and was really turned on by the beauty of these constructs. I also really loved my undergraduate combinatorics course -- especially using generating functions & counting theory.
My bible for learning a lot of math that I never had in courses has been Knuth's 3-volume set. I think that if this set had been available when I was still in high school, I would have gone through and done every exercise on my own.
I could easily see giving up calculus in high school and learning more algebra -- including how to use a computer symbolic algebra system -- and more geometry in the form of computer graphics. I never understood why mathematicians of the middle 20th century wanted to wring all of the pleasure out of math by teaching everything so abstractly; a healthy dose of actual number crunching (aided by a computer, of course) is a much better preparation for calculus. (Perhaps I'm too fond of 19th century mathematics.) Also, matrix algebra -- taught correctly -- can be quite beautiful in its own right, and with excellent computer software available, it should be accessible to high school students.
At 03:59 PM 3/11/2011, rcs@xmission.com wrote:
This note is from Amy Johnston, a math-fun lurker. The funsters undoubtedly have many different viewpoints to offer. I've done a little editing.
Rich
------ From: Anna Johnston [jannaston@gmail.com] Sent: Friday, March 11, 2011 8:43 AM To: Schroeppel, Richard Subject: math fun and calculus
Hi Rich, I wanted to ask you a question (and perhaps get a gage through mathfun) -- old though it may be -- that's come up in my current circle: calculus in high school. I've read MAA articles dating back 11 years on the questionable nature of teaching calculus in high school, talked to high school teachers, mathematician parents, as well as my former colleagues at WSU. The basic thread of these conversations is that calculus should not be part of the high school curriculum. Instead there should be more breadth with a stronger emphasis on discrete concepts (combinatorics, number theory, probability, set theory, logic, proofs, etc). The reasons are:
(1) First and foremost, there are other areas of mathematics that would help students think logically while giving them knowledge far more useful in everyday life. HS Calculus, because most students don't quite have the maturity and many teachers don't have the in-depth background needed, tend to be taught in cookbook style, with more memorization and formula plugging and less understanding. Discrete math is far more concrete and useful, with great everyday examples. A solid understanding of discrete math concepts (for example, more familiarity with summations than the brief introduction they get in calculus, or the binomial expansion) would make calculus far less threatening.
(2) Secondly, society's need for calculus has been surpassed by the need for discrete math. Most kids graduating from HS don't know what a hexadecimal number is or how to read one, even though they see them regularly on product codes. Besides the screaming need for better computer literacy, most scientific fields are finding they need more discrete math than they realized. The more we learn about the universe, the more discrete it seems, from quantum physics to DNA.
(3) Thirdly, the linear push to calculus is a turn off to many students. The style of teaching most HS calculus teachers are forced into teaches students that advanced math is not about thinking but memorization.
Though this idea seems to be old, the only math AP exams are Calculus and stats. The HS teachers at Sam's school (Park HS -- private, progressive and with both abstract and linear algebra courses offered) commented that though they'd like to emphasize other areas of mathematics, it isn't possible due to their requirements from university admissions policy. Many parents view calculus as the apex of mathematics (leading back to university admissions and the AP tests), so there's pressure on them from parents as well.
The question is: Why is calculus still the perceived linear end point to HS math and what is the best way to change perceptions and curriculum?
Cheers!
Amy
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