The curious case of the number 3435

http://www.blog.republicofmath.com/archives/4727

by wglb • 15 years ago

81 14 15 years ago

blog.republicofmath.com

Tiomaidh• 15 years ago

Why the heck don't they teach interesting, non-plug-and-chug stuff like this in high school math?

Every month, I get a little more resolute in my belief that the standard HS math curriculum needs to include a semester or two on number theory, at least for the honors track. If they're short on time, they could teach geometry in a semester (as my school did), and/or teach Algebra II + Pre-Calc in two semesters.

jmatt• 15 years ago

I agree.

I recommend "A Mathematician’s Lament" by Paul Lockhart. It's an excellent essay on math education. The entire paper is long but even the first 5 pages are great. It covers everything from the unacknowledged creativity that is involved in math to the culture and curriculum.

http://www.maa.org/devlin/devlin_03_08.html

http://www.maa.org/devlin/LockhartsLament.pdf

dwc• 15 years ago

The entire paper is long, and I grumbled at that length. Then I began reading it and couldn't stop. Now it's available in book form with the original material expanded, plus a new section at the end. This book I ordered and read quickly. This new material happens to be laying out some interesting math ideas of the kind that could be used in teaching. Fascinating. If there were a whole book of interesting ideas like that I'd buy it in a heartbeat.

EDIT: I should make clear that the second part of the book is not coursework, but a brief taste of some ideas that capture the imagination. A counterpoint to the Lament portion, if you will.

hasenj2• 15 years ago

This paper is very interesting. Deserves its own news entry on the main page.

jrmg• 15 years ago

I kind of agree - I personally might have learned better from this type of 'puzzle' - but I'm pretty sure that the response of most students would have been "Why am I being made to do this? What is the real world ourpose of it?", and they'd switch off even earlier.

tokenadult2• 15 years ago

I'm pretty sure that the response of most students would have been "Why am I being made to do this? What is the real world purpose of it?"

That's why it isn't trivially easy to be a mathematics teacher. The Russian tradition of mathematics teaching, which goes all the way back to the years when Leonhard Euler researched and taught in St. Petersburg,

http://mathsforeurope.digibel.be/Euler.html

does an especially good job of appreciating pure math for its delightful patterns and inherent beauty and elegance while at the same time being well informed by the many applications of math to science and engineering. One of my favorite textbooks for taking a balanced approached to making mathematics teaching interesting, rigorous, engaging, and practical is the late Israel Gelfand's and Alexander Shen's textbook Algebra published by Birkhäuser.

http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773

Many of the problems are HARD--the author is not afraid to pose research-level problems to first-time learners of algebra. On the other hand, some of the problems in some sections of the book are very approachable: "How to Explain the Square of the Sum Formula to Your Younger Brother or Sister." One section, "How to Confuse Students on an Exam," is laugh-out-loud funny. I love using this book in math classes that I teach as supplementary weekend classes for third-, fourth-, and fifth-grade-age pupils who like math and who want something more challenging than what is served up by the local school systems. I have clients from seven different counties in my sprawling metropolitan area. Pure math can be fun, and applied math can be fun, and both can be more enjoyable when they are taught hand in hand.

hasenj2• 15 years ago

I took some high/junior-high school in Libya: we learned set theory in grade 7. I liked math back then. It's not that I understood the point of what we were learning, but it was interesting; it was fun to ponder how to calculate the ratio of the circle's circumference relative to its diameter, and to think about how to prove the Pythagorean theorem.

Then I came to Canada and took more HS, suddenly math was a pile of confusing "things"; an enumeration of techniques for solving certain patterns of problems. Around that time I realized that I hated math.

In University we took discrete algebra with a Taiwanese prof, suddenly math was fun again. If I remember correctly, he commented once about how they learned this stuff in high school when he was back home, which wasn't very surprising, seeing as how the first half of course was pretty similar to my grade 7 math in Libya.

As far as I can tell (and I could very well be wrong), the Libyan curriculum was based on the Egyptian curriculum, which is possibly based on the British one. At least it was based on it sometime around 50 years ago.

tokenadult2• 15 years ago

we learned set theory in grade 7. . . . As far as I can tell . . . , the Libyan curriculum was based on the Egyptian curriculum, which is possibly based on the British one. At least it was based on it sometime around 50 years ago.

Set theory in seventh grade would be characteristic of the "new math" curriculum. That was taken up by quite a few schools in Britain and in the United States during the 1960s and 1970s, so fifty years ago is about right.

http://books.google.com/books?id=RVY_aIlezpAC&pg=PA60...

http://www.maa.org/spotlight/smsg.html

I liked that aspect of the "new math," which I had, pretty well, learning about set theory early and often, but I found that many of my teachers struggled to teach according to that curriculum, which didn't match their own education in math. The teachers being uncomfortable with the curriculum, and parents of pupils in that era not being sure how to help their children with homework, were among the drawback that resulted in "new math" curricula being replaced with "back to basics" curricula by the 1980s.

dkarl• 15 years ago

It's part of the general problem of the lack of stimulating material for talented students in any subject. It's not a popular priority for teachers, certainly less popular than remediation for low-performing students and measurable college-oriented "achievement" for high-performing students.

Also, this is material that less than 1% (if that) of high school students will understand. Teachers don't bother with material that only one or two students in their honors class will enjoy.

nagrom• 15 years ago

I very much enjoy this form of mathematics trivia and similarly interesting toy maths problems. They're often posted at http://www.futilitycloset.com - not just interesting numbers, but interesting geometric proofs and so on.

scythe• 15 years ago

Also, 2592 = 2^5 * 9^2.

JoeAltmaier• 15 years ago

-1

The curious case of the number 3435

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