algebra? help!

[BZmom]

Have anyone used Introduction to Algebra

by Richard Rusczyk? any input will be greatly appreciated. my ds just finished singapore 6 and horizons 6. he is good at math. should i move him to algebra? or pre-algebra? or NEM1? very confused! thanks.

[Myrtle]

The diagnostic test for Rusczyk's Algebra is here: http://www.artofproblemsolving.com/Books/IntroAlgebra/pretest.pdf

 

and seems to require that the student already know how to solve linear equations and work with radicals before beginning this book. This isn't covered in Singapore primary school math.

 

The post-test which the author has a link to is indicative of the kinds of problems that the student will solve after working through the book and seems to cover topics normally taught in Algebra II.

 

I would want to go through this book topic by topic and see if it isn't really more of an algebra II book before starting my child in it.

 

The Singapore primary math series does not cover all the topics normally taught in arithmetic but does finish up these topics in the first few chapters of NEM I. I would recommend either finishing up those chapters before switching programs or taking the placement test for whatever you plan on switching to.

[mellifera]

We are using Jacobs Algebra, so I can't comment on the curricula you're thinking of using. The only thing I noticed is occasionally there are gaps in his math that the book assumes he knows. I have a fairly good knowledge of math, so I can explain the gaps when we come to them. He's solid enough on math that that's usually all I have to do for him to get the concept.

[Nissi]

Myrtle, I have been looking at "Introductory course to Geometry" by Ruszcyk for my ds. The website says it is an honors course. I also have the Jurgensen's Geometry text. Would you recommend the Ruszyk Geom. course? I like the fact that it is an online course.

Thanks,

Nissi

[Myrtle]

Myrtle, I have been looking at "Introductory course to Geometry" by Ruszcyk for my ds. The website says it is an honors course. I also have the Jurgensen's Geometry text. Would you recommend the Ruszyk Geom. course? I like the fact that it is an online course.

Thanks,

Nissi

 

 

Our starting point for evaluating synthetic geometry programs were these two questions:

 

1. Did a mathematician write the text? Not a high school math teacher, not math ed, not a contest winner, not ghost writers, nor even a curriculum specialist, but a real mathematician.

 

2. What set of axioms or postulates are used? Foundations of Geometry

 

I think what Adrian has on tap for analytic geometry is Gelfand's Functions and Graphs, and Method of Coordinates.

[Storm Bay]

Our starting point for evaluating synthetic geometry programs were these two questions:

 

 

I think what Adrian has on tap for analytic geometry is Gelfand's Functions and Graphs, and Method of Coordinates.

 

At one time Adrian talked about Mark Solomonovich. Since I missed Geometry in school, I don't know if this is for a different type of Geometry or not. But then, there is no answer key for it, so people like me wouldn't be able to grade papers. Is he planning to do both, or has he changed? I do remember that he recommended more than one Gelfand book, but my list is hidden somewhere right now. All I know is that I love Gelfand's Algebra and wish I'd had it, or something like it, when I was in school.

[Myrtle]

Karin,

 

Adrian likes Solomonovich geometry because it has translations and he says that Solomonivich "does it correctly" rather than via handwaving. However, it's way of the head of our oldest son.

 

If you guys have finished Gelfand's algebra I and enjoyed it you might also enjoy Beckenbach's Inequalities. I'm finally getting around to finishing up the axiomatic part of that and I've really enjoyed it. Like Gelfand, he gives you a few tough problems to work on. So far it's involved algebraic manipulations which you already know from algebra I, the manipulations are easy enough but the solutions aren't straight forward. One new topic that is introduced is mathematical induction which will be used in a few times in later chapters I think. Adrian has just spent the past few weeks lecturing on the parts that I didn't understand so he's up on what's going on in that book if anyone ends up with any specific questions or getting stuck

 

It has solutions guide in the back although it's not always specific enough to be helpful. So far I've not needed it for the problems themselves but I did need to get help with induction and the very first part of the book but it's been much easier since then.

[Storm Bay]

Karin,

 

Adrian likes Solomonovich geometry because it has translations and he says that Solomonivich "does it correctly" rather than via handwaving. However, it's way of the head of our oldest son.

 

If you guys have finished Gelfand's algebra I and enjoyed it you might also enjoy Beckenbach's Inequalities. I'm finally getting around to finishing up the axiomatic part of that and I've really enjoyed it. Like Gelfand, he gives you a few tough problems to work on. So far it's involved algebraic manipulations which you already know from algebra I, the manipulations are easy enough but the solutions aren't straight forward. One new topic that is introduced is mathematical induction which will be used in a few times in later chapters I think. Adrian has just spent the past few weeks lecturing on the parts that I didn't understand so he's up on what's going on in that book if anyone ends up with any specific questions or getting stuck

 

It has solutions guide in the back although it's not always specific enough to be helpful. So far I've not needed it for the problems themselves but I did need to get help with induction and the very first part of the book but it's been much easier since then.

 

No, we haven't finished Gelfand's Algebra 1 yet. She's finishing a different one. We took a break because at 11 my dd wasn't ready for the long problems. We're going back to it in March, though because she's nearly 13, which is the age I think Adrian recommended this for. She's just been doing Lial's, etc. She's been putting time in with other courses so that she's doing something. I wish I'd known about the Russian books you mentioned--I've taken a look and am planning to get them for my 9 yo later this year. I spend a lot of time planning the future math thing. Not as much as you, but since I'm so happy with Gelfands' I've kept Adrian's first list of suggestions in a notebook stashed away in some mysterious place. At least, the first list of his I ever saw. Before you and he started posting about new math.

 

I will look at Beckenbach's Inequalities. I've been seriously thinking of buying a course with a DVD, but hate the cost and am not sure if it's worth it or not. It would help with those heavily hormonal days. Gelfand's is the only Algebra she will let me do with her and only on days where she's not as strongly hormonal. She loves the thinking of Gelfand's and learning the theory. I'm so busy that I would go to Adrian's answer key and am still not completely used to using ^, etc as we let it go so long. I think that if Beckenbach has an answer key, that will be more helpful, but I might need something more detailed. Are inductions logic based? As I said, I missed Geometry in all the school switches I did.

[Myrtle]

Mathematical Induction is a kind of proof used with a particular kind of problem. Sometimes you see a series expressed as 2, 4, 6, ..., 2n with the last term expressing the what any given number in the series will look like. Sometimes you have to make a general statement that thus n such is true for all of the numbers in this series. Well, it's easy enough to prove about an actual number such as 2 or 4 or 6, but how do you prove something to be true about a nonspecific number? Mathematical induction helps you to do this. It's a syllogism that uses the counting numbers and if you accept the premise and allow a member of the audience to randomly choose any number in the series, you will prove that it's true for that number and then wave your magic wand and it's true for any other number in the series.

 

 

It's very much logic based. Too much. I wish it were more math-based.

 

Here is my blog entry struggling with it. There were a people trying to respond to me to explain it. Once I really had a problem that I liked and needed induction to prove the general case then how exactly it worked made more sense.

[Charon]

No, we haven't finished Gelfand's Algebra 1 yet. She's finishing a different one. We took a break because at 11 my dd wasn't ready for the long problems. We're going back to it in March, though because she's nearly 13, which is the age I think Adrian recommended this for. She's just been doing Lial's, etc. She's been putting time in with other courses so that she's doing something. I wish I'd known about the Russian books you mentioned--I've taken a look and am planning to get them for my 9 yo later this year. I spend a lot of time planning the future math thing. Not as much as you, but since I'm so happy with Gelfands' I've kept Adrian's first list of suggestions in a notebook stashed away in some mysterious place. At least, the first list of his I ever saw. Before you and he started posting about new math.

 

I will look at Beckenbach's Inequalities. I've been seriously thinking of buying a course with a DVD, but hate the cost and am not sure if it's worth it or not. It would help with those heavily hormonal days. Gelfand's is the only Algebra she will let me do with her and only on days where she's not as strongly hormonal. She loves the thinking of Gelfand's and learning the theory. I'm so busy that I would go to Adrian's answer key and am still not completely used to using ^, etc as we let it go so long. I think that if Beckenbach has an answer key, that will be more helpful, but I might need something more detailed. Are inductions logic based? As I said, I missed Geometry in all the school switches I did.

 

I'm fixing that, by the way, as well as some other errata. I actually learned some HTML so I can properly put exponents in the upper right corner now and stuff like that. My biggest problem is that at one point I decided to turn over a new leaf and stop doing Linux and started doing it all in MS Word. Boy did that put a litany of junk in my HTML! I go on these long hiatuses where I don't do anything to my website and then go on a big work-on-the-website binge. I am entering one of those binges, now. I may be able to get through most of those solutions reformatting everything this time around. Eventually when I get that all fixed up, I will probably do all the problems in his Trig book. I think I might even do all the problems in Baby Rudin and a few other books, too. (But, that's definitely beyond the scope of high school at that point and well into the future.)

[Storm Bay]

Thanks, you two. I hadn't realized that Charon is Adrian--haven't got around the highschool board enough, or something. fwiw, I like logic based things, and this will make it easier for me to use with dd.

[StephanieZ]

My now-11yo /then-10yodd finished 6B about 6-9 months ago. (She's v good at math, etc.)

 

I wanted dd to take 6 mos doing 6A&B IP and some other review stuff, but she was SOOOO eager to start NEM that I caved. It went fine until the real algebra started in ch4. Then, dd could totally understand and apply each individual step/tool/idea but she'd make a little error somewhere or forget one thing and then those complex problems would all end up wrong. It was disheartening. I think it was really an intellectual maturity thing; a need to be extrememly careful/accurate. . .

 

Soo, we stepped back from NEM for a while. She's working through Key to Algebra which is going very well. Very simple, step by step, and reteaching a lot of those NEM techniques in a very methodical way. Nearly completely self-teaching and a big confidence builder. DD wants to go back to NEM, so we'll do that in a few more month when she's done with Key To (or at least a few more levels of it).

 

Meanwhile, we're also enjoying the Joy of Mathematics DVDs to keep dd's thinking cap on. We're watching a lecture and then playing around with the tools/tricks/techniques presented. Not trying to master the concepts totally but just to enjoy the mind-expansion aspects of it.