Algebra books (and a geometry question thrown in)! Myrtle or Charon? Others?

[jeri]

Ok, my 11 yo just finished RM6 today. Great book! She also finished SM through level 6, including lots of the supplement books. So, now I need to give myself permission to let her stop math for the year. I can do that, right? ;)

I have NEM1 and NEM2, and an Algebra Structure and Method book (Brown, Dolciani, Sorgenfrey, Cole) published in 1990, and and Algebra, Book 2 with Trigonometry (Pearson, Duffy, McCaffery) published in 1981. So, how do I make these work for next year? Has anyone ever combined US and Singapore math? Do I have the "right" editions of Dolciani's algebra or should I be looking further? And if I should look elsewhere, what edition should I be getting?

As for geometry, I have a book called, creatively enough, Geometry. It was published in 1978 and is authored by Jurgensen, Donnelly, Maier, adn Rising. Is this book "acceptable" or should I splurge and get Basic Geometry (the yellow book)?

Thanks for any and all of your input!

Jeri

[Myrtle]

Ok, my 11 yo just finished RM6 today. Great book! She also finished SM through level 6, including lots of the supplement books. So, now I need to give myself permission to let her stop math for the year. I can do that, right? ;)

I have NEM1 and NEM2, and an Algebra Structure and Method book (Brown, Dolciani, Sorgenfrey, Cole) published in 1990, and and Algebra, Book 2 with Trigonometry (Pearson, Duffy, McCaffery) published in 1981. So, how do I make these work for next year? Has anyone ever combined US and Singapore math? Do I have the "right" editions of Dolciani's algebra or should I be looking further? And if I should look elsewhere, what edition should I be getting?

As for geometry, I have a book called, creatively enough, Geometry. It was published in 1978 and is authored by Jurgensen, Donnelly, Maier, adn Rising. Is this book "acceptable" or should I splurge and get Basic Geometry (the yellow book)?

Thanks for any and all of your input!

Jeri

The Dolciani that we like is from the New Math era..from about 1962 to early 1970s. They have a peculiar way of thinking about algebra that isn't seen so much any more.

The most interesting seems to be Dolciani's Modern Analysis (pre-calc) which was co-authored with Edwin Beckenbach. And we've speculated that it was Beckenbach's contribution that has made it so great. Beckenbach was a very good mathematician who also on the side wrote for high school students. He was such a good writer that the MAA now has established an award in his name called the Beckenbach Award for mathematical expository writing which is given to authors of exceptionally well-written math books.



If I were to use NEM I would need to take a second look at the trig, it may need to be beefed up (And since you like Russian mth, Gelfand's Trig (http://books.google.com/books?id=mHVH2OIkbKsC&pg=PP1&dq=Gelfand%2Btrigonometry&sig=habvJVa7TJzP7qgLLx-tvB3PQ3c#PPA18,M1)is recommended on the Sing math site as well) I would also want to spend more time on formal mathematical justification than is spent in NEM (but this reflects my liberal arts slant on things more than what it takes to get through engineering calculus. One way to do that would be an old fashioned proofy geometry class in which the student justifies assertions by refering to axioms and theorems. Patrick Suppes does this also in his First Course on Mathematical Logic (http://books.google.com/books?id=lxYbp1_d0DoC&printsec=frontcover&dq=Suppes%2BFirst+Course+on+Mathematical+Logic&sig=uFmTgmG3ubp9nHaMeOxphs61G70#PPA240,M1), but using the properties of the real numbers rather then geometry.

It also looks like you'll need some sort of a precalc after NEM...not sure. I'm not seeing topics such as logs, polar coordinates, sequences and series, etc. in the NEM series.

[Jane in NC]

The most interesting seems to be Dolciani's Modern Analysis (pre-calc) which was co-authored with Edwin Beckenbach. And we've speculated that it was Beckenbach's contribution that has made it so great. Beckenbach was a very good mathematician who also on the side wrote for high school students. He was such a good writer that the MAA now has established an award in his name called the Beckenbach Award for mathematical expository writing which is given to authors of exceptionally well-written math books.



If I were to use NEM I would need to take a second look at the trig, it may need to be beefed up.

If anyone wants to beef up their trig, the Dolciani/Beckenbach Modern Trigonometry book is one way to go. It is by far the most complete treatment I have found on the subject and presents much more interesting (challenging) problems than other trig texts. Lots of proofs, identities, and good physical applications.

This book is not for the faint hearted. My son, who has survived Dolciani Algebra I and II, has hit a wall with the Trig, a similar wall to that which I hit using the Dolciani/Beckenbach Analysis in high school. There is a turn to the theoretical that required more of a mental leap than I had in me initially. I somehow stayed with the program and came out a math major. While I don't think that my son is headed in this direction, I want him to have the tools to understand more than mathematical algorithms.

By the way, I believe that the wall we have hit is temporary and not insurmountable. There are times when the abstraction of notation and the nature of relationships take time to penetrate.

Jane

[jeri]

Ok, so the plan is to look for an earlier edition of Dolciani, then look for Dolciani/Beckenbach for my mathematical children. But I guess I will keep my original books in case my non-mathy children need something. Nothing lost since I got them all at Goodwill!

Oh, I so wanted to love NEM! But I guess I can use them for problem sets even if the explanations aren't fantastic, right?

Jeri

[Myrtle]

Ok, so the plan is to look for an earlier edition of Dolciani, then look for Dolciani/Beckenbach for my mathematical children. But I guess I will keep my original books in case my non-mathy children need something. Nothing lost since I got them all at Goodwill!

Oh, I so wanted to love NEM! But I guess I can use them for problem sets even if the explanations aren't fantastic, right?

Jeri

I use NEM problem sets to supplement what we are doing and for word problems. I have a daughter who is not "mathy" and we plan on slowly plodding through these old books with her as well. In fact, knowing the "theory" can fix some of that unmathiness to an extent.

These older books don't just have a better explanation, in fact, the explanations may seem more technical and in that sense "worse", but they are also arranged the topics according to the structure and properties of the real numbers rather than according to technique being learned.

For example, in Singapore's NEM you can see the topic of division of polynomials and also the topic of set theory. In these older American books (not any old American book though) the set theory is taught first and the algebra is then taught in the context of sets of integers, rationals, reals, so that you see connections between topics earlier on.

[Karin]

In these older American books (not any old American book though) the set theory is taught first and the algebra is then taught in the context of sets of integers, rationals, reals, so that you see connections between topics earlier on.

Yes, I agree. This is how I learned math, and the transition from set theory to Algebra was a very easy one to make (I was mathy.)

[WTMCassandra]

Wow! A genuine math whiz. Is there a teacher's edition available (with answers)? Do you know the ISBNs of the text and teacher's manual?

Since you're a genuine math whiz, and I'm a high school newbie, may I hijack this thread for just a minute? What text would you suggest for calculus for an engineering hopeful?

And while I'm at it, what about algebra? We're considering a combination of Professor B and LOF, and moving to VideoText Interactive for Geometry (Prof B does not do geometry), again combined with LOF.

[Jane in NC]

Well...I cannot help you with a number of your questions since I do not use the teachers editions, solutions manuals, etc.; hence I lack ISBNs. Further, I know what I like (Dolciani) and have no experience with LOF, Video Text, etc.

As far as Calculus texts are concerned, I would give the university engineering programs in your state (or those to which your student is attracted) a call to ask them what they use. I like the old Swokowski book. I am currently tutoring a Calc student who is using the Larson text which is not bad. At this point I am not sure what book my son will use as he and I have not yet discussed whether he will take an AP exam or whether he would prefer to pursue a more theoretical route (as opposed to engineering applications).

Sorry not to be more helpful.

Jane