Confused how teach geometry and importance of teaching geometry in 21st century.
I'm teaching high school math to homeschoolers and I'm looking for how to make geometry year meaningful. I'm having a "crisis of confidence" because from my viewpoint, algebra was 10x more useful for future math and science work. The only thing I can remember that was useful from geometry was a few volume and area formulas. That can justify maybe a month but not a whole YEAR of geometry!?!? cs P.S. Yes yes I know that geometry is meant to teach logical reasoning. Maybe one can get that from chess, debate club and other activities as well if not better? People also say geometry is where you learn proofs. Couldn't proofs be just as easily emphasized in all the other math classes?  _______________________________________ Christian Seberino, Ph.D. Email: chris@seberino.org _______________________________________
well, there's future usefulness and practicality to motivate your homeschoolers. and there's also inthemoment fun, beauty, and joy of doing it. check out Strogatz's recent New York Times column: "I bet I can guess your favorite math subject in high school. "It was geometry. "So many people I’ve met over the years have expressed affection for that subject. Arithmetic and algebra — not many takers there. But geometry, well, there’s something about it that brings a twinkle to the eye." see the full article at http://opinionator.blogs.nytimes.com/2010/03/14/squaredancing/ beyond being cool, maybe geometry helps develop spatial imagery and visualization? Jeremy On Thu, Mar 25, 2010 at 10:40 PM, <chris@seberino.org> wrote:
I'm teaching high school math to homeschoolers and I'm looking for how to make geometry year meaningful.
I'm having a "crisis of confidence" because from my viewpoint, algebra was 10x more useful for future math and science work.
The only thing I can remember that was useful from geometry was a few volume and area formulas. That can justify maybe a month but not a whole YEAR of geometry!?!?
cs
P.S. Yes yes I know that geometry is meant to teach logical reasoning. Maybe one can get that from chess, debate club and other activities as well if not better? People also say geometry is where you learn proofs. Couldn't proofs be just as easily emphasized in all the other math classes?
 _______________________________________
Christian Seberino, Ph.D. Email: chris@seberino.org _______________________________________ _______________________________________________ Edusig mailing list Edusig@python.org http://mail.python.org/mailman/listinfo/edusig
On Thu, Mar 25, 2010 at 11:39:08PM 0400, Jeremy Gray wrote:
well, there's future usefulness and practicality to motivate your homeschoolers. and there's also inthemoment fun, beauty, and joy of doing it.
I'm glad you said that. I was simultaneously coming to same conclusion. Still it is nice to hear it from someone else. If I tried to "wow" my students and make the class fun and engaging without trying to be "practical" maybe I'll be ok. cs
On Thu, Mar 25, 2010 at 7:40 PM, <chris@seberino.org> wrote:
I'm teaching high school math to homeschoolers and I'm looking for how to make geometry year meaningful.
Most geometry taught in high school is flat, planar. This is a problem in an age of HDTVs, LCDs. If you wanna blow some time on a meandering meditation on just this theme, 'Beyond Flatland', here's something I wrote last night. This takes off from a 1997 Math Summit held here in Oregon, with Keith Devlin, Roger Penrose, Ralph Abraham and other luminaries. http://groups.yahoo.com/group/synergeo/message/58095 (maybe just scan the opening paragraphs, then decide if it grabs ya  I'm talking to an inner circle, using some shoptalk, so probably a yawner).
I'm having a "crisis of confidence" because from my viewpoint, algebra was 10x more useful for future math and science work.
10th grade geometry distills just some of the Euclidean stuff. There's precious little topology, no V + F = E + 2, no Descartes Deficit, no sphere packing, gnomon studies, hardly much about polyhedra, their duals, little to nothing about Phi... I agree with ya, a big rip off. Fortunately, the Internet is brimming with cool stuff, so much to see and do. Lots of great Java applets, no reason to avoid them (we're not language bigots). Geometry in the sense of events in space is about geography, which (going big) includes astronomy and (going small) internal organs, cells, molecules down to whatever particles. In other words, geometry applies to the whole kit 'n kaboodle so can't be "irrelevant to science" no matter how hard we try. My advice: remember to stay spatial, with planar as subset (special case) of spatial. Regarding Python in particular, I recommend getting into VPython. Also POVRay if you have the time, and VRML. I've got lots of writings on this at my web site, complete with source. Recommended: 'The Book of Numbers' by Conway and Guy. Lots to program around.
The only thing I can remember that was useful from geometry was a few volume and area formulas. That can justify maybe a month but not a whole YEAR of geometry!?!?
cs
I've spent many years with the Python + Geometry combo. One payoff is I generated most of the graphics at my web sites and am therefore free to upload them to Wikipedia and Wikieducator, where the authorities tend to be sticklers about intellectual property. Given all these cool graphics are mine, mine, mine, I feel at liberty to spread them. Thank you Python. Thank you other free tools.
P.S. Yes yes I know that geometry is meant to teach logical reasoning. Maybe one can get that from chess, debate club and other activities as well if not better? People also say geometry is where you learn proofs. Couldn't proofs be just as easily emphasized in all the other math classes?
If you're free to work in a home schooling setting, then you can blend the topics a lot more, as student interest meanders. 'The Geometrical Foundation of Natural Structure: A Source Book of Design' by Robert Williams would be a good title to start with. It's not a textbook. Dover Press books tend to be quite affordable though, this one not too hard to obtain. If you're into lore or stories, which I consider central to any credible curriculum, then maybe the Siobhan Roberts bio of Donald Coxeter would be work getting and sharing with students. There are some juicy stories in there, gossip about Escher's son I think it was, trying to break into the radome business... radomes were those DEW line things across Canada, a manifestation of the cold war.... Lots more to say, but since this is a topic I've worked on a lot, I need to hold back, not open the floodgates. Lots here in the archive. Thanks for joining us. Oh, and if you get the Litvins text, Math for the Digital Age and Programming in Python, then you'll find stuff on graphs (in the sense of networks), mostly planar, but it's easy to turn graphs into polyhedra with the wave of a magic wand. Turtle Art / Turtle Graphics... Springie.com. Darwin @ Home. Gregor helped me with getting Python turtle to draw the planenet for a Tmodule (back to my shoptalk), 120 of which build a rhombic triacontahedron (an important shape with thirty 1 x phi diamond facets). Per Robert Williams, once you start jamming polyhedra together, you're into lattices, and that's Linus Pauling style chemistry, nanotechnology, crystallography  no shortage of relevant pages and projects. Happy camping! Kirby
 _______________________________________
Christian Seberino, Ph.D. Email: chris@seberino.org _______________________________________ _______________________________________________ Edusig mailing list Edusig@python.org http://mail.python.org/mailman/listinfo/edusig
As a somewhat recent highschool graduate (2005) I must say that I don't think that all the countless proofs we did in geometry helped my logical reasoning that much. I think that programming helped that 100x more than geometry did. Jason On Thu, Mar 25, 2010 at 4:40 PM, <chris@seberino.org> wrote:
I'm teaching high school math to homeschoolers and I'm looking for how to make geometry year meaningful.
I'm having a "crisis of confidence" because from my viewpoint, algebra was 10x more useful for future math and science work.
The only thing I can remember that was useful from geometry was a few volume and area formulas. That can justify maybe a month but not a whole YEAR of geometry!?!?
cs
P.S. Yes yes I know that geometry is meant to teach logical reasoning. Maybe one can get that from chess, debate club and other activities as well if not better? People also say geometry is where you learn proofs. Couldn't proofs be just as easily emphasized in all the other math classes?
 _______________________________________
Christian Seberino, Ph.D. Email: chris@seberino.org _______________________________________ _______________________________________________ Edusig mailing list Edusig@python.org http://mail.python.org/mailman/listinfo/edusig
Beautiful! Thank you for making this statement. Lots of people making decisions in education need to hear this. On Thu, Mar 25, 2010 at 10:08 PM, Jason Axelson <bostonvaulter@gmail.com>wrote:
As a somewhat recent highschool graduate (2005) I must say that I don't think that all the countless proofs we did in geometry helped my logical reasoning that much. I think that programming helped that 100x more than geometry did.
Jason
On Thu, Mar 25, 2010 at 4:40 PM, <chris@seberino.org> wrote:
I'm teaching high school math to homeschoolers and I'm looking for how to make geometry year meaningful.
I'm having a "crisis of confidence" because from my viewpoint, algebra was 10x more useful for future math and science work.
The only thing I can remember that was useful from geometry was a few volume and area formulas. That can justify maybe a month but not a whole YEAR of geometry!?!?
cs
P.S. Yes yes I know that geometry is meant to teach logical reasoning. Maybe one can get that from chess, debate club and other activities as well if not better? People also say geometry is where you learn proofs. Couldn't proofs be just as easily emphasized in all the other math classes?
 _______________________________________
Christian Seberino, Ph.D. Email: chris@seberino.org _______________________________________ _______________________________________________ Edusig mailing list Edusig@python.org http://mail.python.org/mailman/listinfo/edusig
_______________________________________________ Edusig mailing list Edusig@python.org http://mail.python.org/mailman/listinfo/edusig
 "Computer science is the new mathematics."  Dr. Christos Papadimitriou
Another thing to consider is that there is a lot of different math: algebra and geometry are quite different and someone being good at one might not be good at the other. As a former high school math teacher and one who saw his kids recently go through high school, I believe that many geometry courses these days deemphasize the logical part of geometry in favor of a more computational form. Development of proofs is useful for reasoning skills, beyond simple logic. Finally, geometry is useful for learning about the world. My $0.02 rich enbody@cse.msu.edu chris@seberino.org wrote:
I'm teaching high school math to homeschoolers and I'm looking for how to make geometry year meaningful.
I'm having a "crisis of confidence" because from my viewpoint, algebra was 10x more useful for future math and science work.
The only thing I can remember that was useful from geometry was a few volume and area formulas. That can justify maybe a month but not a whole YEAR of geometry!?!?
cs
P.S. Yes yes I know that geometry is meant to teach logical reasoning. Maybe one can get that from chess, debate club and other activities as well if not better? People also say geometry is where you learn proofs. Couldn't proofs be just as easily emphasized in all the other math classes?
 _______________________________________
Christian Seberino, Ph.D. Email: chris@seberino.org _______________________________________ _______________________________________________ Edusig mailing list Edusig@python.org http://mail.python.org/mailman/listinfo/edusig
Check out GeoGebra OER community. There will be a US conference this year, and the online resources and groups are good, too. A lot of my students appreciate geometry through the following lenses:  Origami  Computer graphics, especially programming cool visuals for games  Escher, Dali, and other "surreal" space transformations  we are doing a lot of it in our "Alice in Wonderland" class, hehe. We watch videos a lot, too. Mobius transformation: http://www.youtube.com/watch?v=JX3VmDgiFnY Bach on Mobius strip: http://www.youtube.com/watch?v=xUHQ2ybTejU Cheers, Maria Droujkova http://www.naturalmath.com Make math your own, to make your own math. On Thu, Mar 25, 2010 at 10:40 PM, <chris@seberino.org> wrote:
I'm teaching high school math to homeschoolers and I'm looking for how to make geometry year meaningful.
I'm having a "crisis of confidence" because from my viewpoint, algebra was 10x more useful for future math and science work.
The only thing I can remember that was useful from geometry was a few volume and area formulas. That can justify maybe a month but not a whole YEAR of geometry!?!?
cs
P.S. Yes yes I know that geometry is meant to teach logical reasoning. Maybe one can get that from chess, debate club and other activities as well if not better? People also say geometry is where you learn proofs. Couldn't proofs be just as easily emphasized in all the other math classes?
 _______________________________________
Christian Seberino, Ph.D. Email: chris@seberino.org _______________________________________ _______________________________________________ Edusig mailing list Edusig@python.org http://mail.python.org/mailman/listinfo/edusig
participants (7)

chris＠seberino.org

Jason Axelson

Jeremy Gray

kirby urner

Maria Droujkova

michel paul

Richard Enbody