I'm not dead yet.*
Awesome thread in Drexel about pure math in high school.
http://mathforum.org/kb/thread.jspa?threadID=1909041&tstart=0
I wouldn't come out of six months hibernation to recommend a boring thread to you! Pay attention to the "Calculus isn't really a part of math" rearing its ugly head.
*I'm not in remission yet and still have a lot of problems. Daily severe fatigue, lightheadedness, difficulty concentrating, joint pain, nausea, lower back pain are just some of the problems. I think they will switch me to a more aggressive treatment by next month and follow up on that tumor, it's inflammation not cancer. I might have another one on the other side of my body from what I can tell. There is a miracle drug (not curative though) based on adult stem cell technology that is in phase III clinical trials and it looks like it might be available to the public in the next two or three years so I am very optimistic.
My son is coming close to finishing Frank Allen's Algebra I as well as Suppes Mathematical Logic. That logic book may be the all time best book I've used in homeschooling. Next on our list is an old 1960s Moise and Downs Geometry book and Suppes' Introduction to Logic. As usual I am extremely skeptical about having a seventh grader work on college level material, but I'm willing to go slow and give it my best.
WIP Wednesday: Wingspan
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I am knitting wingspan. I am using my serenity sock yarn in chili. It is
a pretty lavender and green patterned fingering weight yarn. I think it is
turn...
16 comments:
If you're optimistic, then I'm going to be (about you), too!
Very interesting about pure math. It seems to be offered as a matter of routine at the local public school, a surprising (to me at least) percentage of students fail the course, many of the rest require a tutor, and it is apparently impossible, as taught, to manage with a graphing calculator. Seems like a recipe for disaster to me.
In fact, when my brother in law, a public school teacher, heard we were going to home school, he asked, "What about the Pure Math"? I told him we're going to concentrate on Algebra, Geometry, and if the kids have the ability and interest, pre-calc and Calculus. The curriculum set up by the province seems guaranteed to have students fail and to come out liking math even less than when they started...
Wonderful news, Myrtle -- keeping my fingers crossed for you!
I wish you well. If it is Crohn's disease, I can share with you the fact that I know a professor who has, despite that disease, maintained a very high level research program for the nearly three decades I have known him.
Becky, "pure math" (as I understand it, having been a math major as an undergrad) has nothing whatsoever to do with the sort of computations done by a graphing calculator. I also can't imagine teaching it in high school unless the student already had proved their way through Euclid.
On your main topic, I couldn't find the statement you were referring to. I would, however, agree 100% with the statement quoted in the first post: "What you have to realize is that mathematicians don't do calculus,
at least in the sense of freshman/sophomore calculus." The calculus is a tool for doing physics. Mathematics is about creatively proving how to take the Lebesgue measure ("integrate") a particularly unusual set, or exploring the properties of a Lie algebra.
Well, pure math doesn't have to be the most general case. I think mathematicians screw this up all the time when they consider the matter in terms of K-12 education. When you say we should be teaching rigor, they think rigor-and-generality. But, the regular old Reimann integral is every bit as rigorous as the Lebesgue integral. Of course, where the generality is required, then also the rigor is usually necessary, as well. But, that doesn't mean you can't have rigor even if you don't absolutely have to have it in order to solve some ultra-pathological problem.
Mostly, it is just a simple choice. The practical reality is that you end up having to sacrifice breadth for that kind of depth. And, that is the sum total of the rub, right there. People just have to be able to say "We covered...." They just can't give up that breadth. But, it is a false claim, really, if the student is really tested on that topic by real problems that aren't just made up by teachers under contrived and controlled conditions. And, this is particularly true about calculus.
To draw an analogy, it is like judo. There are something like 67 official judo throws and 29 official grappling techniques in Kodokan judo. But, I once read someone analyzing years of Olympic and international judo tournaments to see how many different throws any given world class judoka could actually score on another world class judoka with. For any given judo player, that amounted to about 4 throws and 2 pins/submissions. So you want to "know" the throw? That's one thing -- you can probably learn all 67 fairly quickly. You want to really know the throw, as in, can actually use it effectively in a real match? Then, you can spend your entire life perfecting only just a few. In fact, I was once told that there are really only three throws: one back, one forward and one to the side -- the rest is just stylistic differences.
great to see you again.
(and this is indeed an awesome thread.)
Glad to see you back! I'm sorry, though, that the doctors haven't been more successful in treating you. I hope you get a chance at that new drug, and that is is effective.
I'm off to look at the math thread, though at the rate we are currently moving we will never make it to calculus at all.
Another thought provoking post! Thanks for taking the time to post it. I hope that things all become more and more clear for you on the health front.
Wow--good luck with the treatments. I hope they get you feeling better (and of course, not dying).
If you're using Moise's geometry, you might also want to check out Geometry from Euclid to Knots by Saul Stahl. It's not as old (and not as cheap), but it's a really good reference and textbook. I bought it when neither of the two geometry books I was using (one of them was the Moise book) could adequately explain triangle similarity, so I interlibrary loaned all of the geometry books I could find, and this was the best.
It's been awhile since I visited your blog, but I've always liked reading about your resources and the way you teach your kiddos. They are bound to do very well.
I'm sorry to hear about your health problems, though.
You might already know this, but if it's Crohn's that's causing problems, eating helminths might help. It's a treatment that's in the works and has been used with some success. Google Crohn's and helminths and that should get your started. The more scientific stuff can be found at Crohn's sites.
The stem cell research sounds promising, too.
Hope you're feeling better soon.
Good to see pure math introduced at a younger age. Any thoughts on introducing more mathematical applications? I've always found that as a great way to connect kids to real world problems.
Rathanharan,
It was math "real world" math applications that completely turned me off from math as a kid.
For an example of a problem that motivated both me and my son to learn more math and had nothing to do with the real world, see this entry:
http://myrtlehocklemeier.blogspot.com/2007/02/quick-trick-brick-stack.html
More important than "real world" problems are interesting problems that spark the imagination.
"Imagine that prospective teachers of literature in a certain country are made believe through their professional preparation that all fairy tales, fables, fantastic stories are useless. When told a fable, where animals speak to each
other, they cannot comprehend and enjoy it in a normal way, as all children do, but exhaust their imagination in figuring out how could it happen in real life: perhaps, animals were especially trained to speak? perhaps, they were made some operation?
perhaps, it were disguised people? etc. This is similar to the approach of some American educators towards word problems: they insist that it should be possible for the situation and for the question asked to take place in reality." Andrei Toom
thanks for the toom quote;
good to see you.
I have been thinking of you. I spent last week with 10 other BC Calculus teachers bemoaning the idea that we teach quick math, not real math. We all vowed to do more proofs and more starting from basics with analysis.
Just checking in to see how you're doing...
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I missed your illness, and I'm sorry to hear of it.
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