Thursday, November 3, 2011

Math problems of the week: 21st century geometry vs. 1960s geometry

I. The first and last pages of the Discovery Geometry (2003) Chapter Review of the "Reasoning in Geometry" chapter , pp. 138 and 140 [click to enlarge]:



II. The Weeks & Adkins A Course in Geometry (1961) Chapter Review of the "Proof" chapter, p. 55 [click to enlarge]:


III. Extra Credit
If you had to ditch a geometry course in order to make room for an entrepreneurship course, would you be more likely to ditch the Weeks & Atkins course, or the Discovering Geometry course?

2 comments:

Lsquared said...

Discovering Geometry, huh? I may have to take the other side on this one. I have found Discovering Geometry to be fairly well thought out, and having fewer of the disappointments I find in most of the "standards based" texts. Granted problems 1-10 are losers, but #26 is a pretty good problem, and # 24 and 25 are very nice checks on student reasoning and understanding (important for angle measure theorems). I ignore, of course, the journal and portfolio prompts, since that's what I would do if I were teaching out of this book.

Part of the problem is I'm not really impressed with your page from Weed and Atkins. Problems 8 and 6 are good. 5 and 7 are OK too, maybe. 8 and 7 are actually not too different in complexity from # 26 in the other book--only expressed with more words and fewer pictures. The rest of it seems to be mostly algebra, with, perhaps, a few trappings of geometry thrown in for show.

You don't really get a sense of where the books are going from these pages necessarily. Discovering Geometry keeps skimming the line between proof and not-proof until the end of the book where it finally spends some quality time with theorem proving (I believe this chapter is the first "real" chapter in the book--by which I mean, I'd skip chapter 1 if I were teaching out of it). It really depends on the background of the students whether you need to spend all that time practicing snippets of logical reasoning before you really get to proofs. The book does have some real proofs all along, though, so there are plenty of places where a class could take it deeper. I don't know that it's the book I'd choose, but I wouldn't find it hopeless to teach out of... I'm not sure I wouldn't prefer it to, say, Holt Geometry, and it's miles above Integrated Mathematics.

Weed and Atkins might be OK too, though I haven't spent any time with the book except to look at your one page excerpt, which is not bad but not impressive either.

I have an old copy of Moise and Downs, though, that I got on the recommendation of someone on the kitchen table math blog,and that's clearly a more thorough course than Discovering Geometry (though I'm not particularly fond of its choice of an axiom set).

I, of course, wouldn't ditch either course for a course in entrepreneurship, which I find no evidence is something we know how to effectively teach. I'm sure such a course would end up being pointless and frustrating for almost everyone.

Barry Garelick said...

Weeks and Adkins is similar to Moise Downs in thoroughness. Regarding problem #26 in Discovering Geometry--it may be good, but it isn't clear whether the student has been given enough information and prior knowledge to even begin to know how to solve it. And regarding the so called simplicity of the Weeks-Adkins problems, bear in mind that it is page 55 and the beginning of the book. Weeks-Adkins is very proof based and they have very difficult problems--but they also provide the students with the information they need in order to do the proofs.

What specifically do you not like about Moise Downs axiom set?