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I found it to be a nice overview, though I wish she would have touched on Singapore's New Elementary Math series. (No one ever seems to talk about that, it's like Singapore drops off the face of the earth after 6th grade. Is that because they're not as good, or because they're not as friendly to use in a home setting, or ... ? But I digress.) I'll definitely start looking into Art of Problem Solving Introduction to Algebra.
Even though Algebra I is still a way off in my particular family, I'm always on the lookout for what's coming down the pike for my kids. Gotta know what the bridge is supposed to look like when you're done if you're going to build it right.
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I am not so impressed with this list or the evaluations of each (e.g. "The choice between the top three might not be easy. In a nutshell, Jacob's book is lively, concentrates on concepts, well-admired by a lot of people for its entertaining style, and has very good and interesting exercise sets. However, it is also a bit "lite" in content."). So we have a book that is on the short list, but maybe doesn't teach as much algebra as it should?
Does anyone here have any recommendations for an algebra text that teaches real algebra? One can assume a fairly mathematically able parent. I remember hearing praise for the Dolciani texts a while back?
NOTE: Theory is good (e.g. I'd be fine with a book that talked about closure). The student/victim already has a bit of a grasp of the different number systems (whole number, integers, etc.), so this sort of stuff is okay. Proofs are acceptable, but probably not very useful for me (the student/victim will be 10½ when the algebra starts. I don't know how ready he will be for proofs ...).
-Mark Roulo
The AoPS Algebra book is quite good. You might want to do their older problem-solving books for pre-algebra.
I'm actually glad she covered Jacobs, because it is one that many, many people recommend. And I'm now getting the sense that those who are recommending it ... perhaps are not "math people." And, perhaps, that does make it a good choice for some folks, even if it's now clear to me that it's not a good choice for my house.
When asked at MSMI what algebra text Wu recommended, he answered that Dolciani et al., Algebra: Structure and Method was serviceable. He had no others he recommended.
Foerster's Algebra 1 text is good and would be suitable for a 10-1/2 year old who is ready for algebra.
Allison mentioned a Dolciani algebra book. At the Well Trained Mind forum I listed the books in the "Dolciani" sequence in a thread Dolciani/Houghton Mifflin math sequence .
For a young student with plenty of time before he needs to know algebra, the Life of Fred Beginning Algebra book may be a good starting point. It teaches algebra through the adventures of Fred, a 6-year-old boy. My son loved it. More traditional books can be tackled later.
Dolciani is my rec for independent study, however I'd start with Dolciani Pre-Alg if the child isn't used to reading and digesting a math text. I chose Dolciani because it includes both verbal, symbolic, and graphical explanations and I like to have challenge problem sets. It also breaks down the lessons more than NEM does in some places. If the student is not going to work independently, there is a few course online here that goes with the Dolciani text:
http://www.montereyinstitute.org/courses/Algebra%20IA/nroc%20prototype%20files/coursestartc.html
We used NEM1 in elementary school, then switched because the Dolciani lessons are shorter and fit our middle school afterschooling time frame better. Neither Dolciani or NEM is aligned with my state's Integrated Algebra and Geometry courses.
I homeschooled my daughter for grades 7-8, and I skipped around rather a lot. We used NEM until the last 4 months, when I decided I needed to make sure we got in everything she would need for Geometry in 9th grade, so we spent the last 4 months filling in the gaps of things we hadn't gotten to yet. The tricky bit was deciding exactly what needed to be done for it to coincide reasonably closely with algebra 1 in our district. Eventually we ended up doing:
Linear equations and inequalities
graphing lines and parabolas
factoring trinomials
completing the square
the quadratic theorem
simplifying expressions with roots
simplifying expressions with exponents
I have the advantage of being good at teaching this sort of stuff (college math prof), so I didn't worry too much about the presentation, but I wanted to make sure that she was going to remember what she learned, so she did several problems each day for several days on each topic until she felt like she really got it and it was in her memory, and then we moved on. That meant that I needed a source for problems. Some I made up, and some I stole from an intermediate algebra textbook.
They do have a class in college that is basically high school algebra 2, and it's called "intermediate algebra", and intermediate algebra books often have review sections that cover pretty much everything in algebra 1. I find it hard to know where algebra 1 ends and algebra 2 begins, really...
Anyway, I like NEM fine, and I would have kept using it if I hadn't been trying to match up with someone elses syllabus.
The reason that many folks who homeschool using Singapore Primary Math switch to something else rather than using NEM is because the sequence of topics is very different than the traditional American high school sequence. Susan Wise Bauer has a whole long discussion about it in The Well-Trained Mind.
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