In preparation for Algebra, I'm trying to mentally group math programs and

[Kimber]

learn which ones are comparable. I see from ereks mom and a link she provided, that Foerster and Dolciani are in the same league, so to speak. Where does Jacobs fall relative to those two? And if your student actually works the problems in Life of Fred and not just reads the stories for fun, where do you think it would fit relative to the others? And what about Saxon?

 

 

I made the qualification about LofF because of a comment made by my Calculus I teacher in college--Calculus is not a spectator sport.:rolleyes::)

 

I am in the midst of planning for myself as well as gathering info for a friend that is pulling her 7th grader out of private school. We'll be meeting in a few days to review curriculum and I'd like to have as much info as possible.

 

I know these threads on math can be controversial, but they are a tremendous help to us moms with children approaching Algebra. WE REALLY APPRECIATE THE INFO!

 

TIA :)

[Bev in B'ville]

"rigorous" comes up is Dolciani, Forrester, Lial's and Larson. When reviewing textbooks this year I found out that our local library could get these books (even the TE's) by interlibrary loan. Check them out, but more importantly, have your dc check them out. After all, it will be his/her textbook. Each dc is different so you and your friend may/may not be able to use the same textbooks for your dc. I have two very different dc and have had to use different texts for both of them for most subjects (to my chagrin).

 

I could give my dd a text carved in stone and she wouldn't complain and she would do quite well, LOL. However, my ds is a very visual learner. He needs a textbook that "pops" visually to keep his interest, but my dd hates his textbooks. She says all that "visual stuff" is too distracting.

 

I can't really give you info on LOF, though several on this board use it and you'll probably hear from them. I also haven't used Jacob's beyond trying (and giving up) using it for Geometry (we switched to another program).

 

Hopefully others will add in their $.02.

 

L8r,

Bev

[Michelle in GA]

I agree with Bev,that those are the big 4. To that, you could add Jacobs and Saxon(although Saxon seems to be a love it or hate deal).

I am using Chalkdust, which uses Larson textbooks. I have also used Saxon, and I like that too.

[Charon]

I'd consider Singapore's to be rigorous, too.

 

 

I would be inclined to agree. (Of course, by "rigorous", here, we don't mean mathematically rigorous but rather just as a program of study.) If you want a no brainer top notch math program, couldn't you just do Singapore all the way through NEM 4 and put them in quackulus in the community college? (The program ends when their 16.) I would think that would tend to maximize their SAT scores, give them a first rate treatment of engineering math, mesh well with Singapore's top notch science program if you did that, too....

 

I, personally, don't actually do that, as it turns out. (In fact, I really do something completely different.) But, most people don't like my math program. If you are looking for something "normal", just doing Singapore pretty much without supplementing it and racing straight up through calculus at a community college would probably be my first choice. (I wouldn't even teach it myself, but rather try to get it done through a college/university and I would try to avoid AP.)

[Melissa B]

I, personally, don't actually do that, as it turns out. (In fact, I really do something completely different.) But, most people don't like my math program.

 

Looking at your signature, your math program looks similar to Myrtle's. I would like to see your complete plan written out - if you have a moment.

 

Thanks!

[Kimber]

Thanks for the info. I'll be checking back in later. Today is an errand day--dentists, foot doctor, lunch, and piano lessons--all for the next 6 hours. I really appreciate the information and will be reviewing these choices. I might actually want the no-brainer courses for my oldest child. She's bright, but not motivated in math. But for my math inclined son, I might want the unusual more intensive programs.

 

Thanks a lot,

 

Kimberly

[Charon]

Looking at your signature, your math program looks similar to Myrtle's. I would like to see your complete plan written out - if you have a moment.

 

Thanks!

 

Well, actually more like a third, but let's not go there.

 

Math Ed

 

I still need to clean up the ole website a lot. But, the basic schedule is out there up through "Algebra III". I have not made a "Pre-calculus" schedule in which we plan to use Cletus's book (listed on my website there). (Yes, I absolutely must refer to it as "Cletus's book".) We'll probably put off S I Gelfand's book until after Cletus and put BeckenBach's <i>Introduction to Inequalities</i> in there before Cletus.

 

Myrtle and I argue over geometry on a regular basis, but I think we are converging on Kiselev, actually, which is a lucky outcome since I already had made the schedule around it. She had always wanted to do 1964 Moise and Downs (a New Math text that more or less fits into our "spine", so to speak). I feel like I ought to want to do Birkhoff and Beatley which is what is listed in my tag, but originally I chose Kiselev over Birkhoff and even made the schedule for it that is on my website probably more for "aesthetic" reasons. Actually, before any of that, I was planning on doing this physicist/mathematician's book (Solomonovich, who is also listed on my website). I just think that his book is more like a first year college text, and I don't want to spend quite that much time on synthetic geometry. (I do think one can definitely do it -- it's just going to be difficult and probably take a lot more than a year to get through it with a younger kid. And, our kid is going to be 12 -- maybe 13 at the oldest -- when we get there.) That said, though, neither of us has really systematically gone through the book. My schedule could be totally unrealistic and I could be wrong about it being easier than Solomonovich. (Solomonovich is largely based on Kiselev.) At any rate, it will all get resolved soon -- our oldest is more than half way through Allen 1 right now.

 

If you get through all that, then I have been searching for a calculus text. So far, the best I have found is this text by Courant. I ended up not liking Apostol (which I used to have on my website) because of a dearth of a certain kind of problems. I do like his general approach -- it's very much a shadowing of even measure theoretic real analysis. And, he is completely rigorous in his presentation of the material from what I can tell. But, his problems just don't exercise the student on that. So, I just don't believe the student is really going to walk away with it at the end of the day. Courant does calculus the more normal way by introducing limits first and it does look like he might have some epsilon's and deltas that he expects students to wield. I need to look through the book more thoroughly. I think the Hardy book listed on my website is even more like that -- really expecting the student to be able to do the rigor. But, the real truth is if you can do something like Lay's Analysis or probably my all time first choice would be to somehow be able to do all of Georgi Shilov's books, then that is what you really need to do. (But, at that point you are committing some sort of cardinal sin of actually doing the rigor which somehow ruins the "beauty" of calculus and/or is an all around Satan-worshipping, evil thing to do, apparently. So, that's probably why I totally want to do it.) If you did all of Shilov's books, you would have a truly mathematically rigorous and fairly complete basis for doing physics, for instance. (Basically, a typical physics major should take calculus, linear algebra, ODEs, PDEs, vector "analysis" and complex "analysis". Shilov hits most of that. And, what he doesn't technically cover, would tend to be child's play to someone that was actually able to do all the problems in his book, I think.)

 

At any rate, there you go. That's the current state of my thinking on math programs in K-14 education. (It is largely centered around avoiding having to have a vague, shaky, heuristic calculus foundation for further study in math or physics.) I strongly doubt I'll be able to do it all. Frankly, I will be happy to go up through Cletus and S I Gelfand. I will even be happy to make it through the Algebra III schedule, for that matter. "Shilov?!? Yeah -- keep dreamin' buddy!" That's what I keep thinking. On the other hand, I didn't expect to be doing Frank Allen and Gelfand with an 11 yo math-hating, ADHD, dyslexic child, either. So, you never know.

[Guest Katia]

My dd is using LOF Advanced Algebra along with TT Geometry to keep up her algebra skills this year.

 

After having completed TT Algebra 1 and Algebra 2, she has not found anything new (except logs) nor has she had any trouble working the problems. So, simply by her experience, without me having any math ability or background, I would say that LOF is on a similar plane as TT.

 

Having emailed the author of LOF, he does not agree. He says LOF is much more advanced than TT and even contains more than Saxon. But, unless he is just a wizard at explaining upper level math to kids.........I can't see how.

 

My dd is a normal, average math person; not a wiz and she struggles through TT, so, for her to have no problems with LOF........I'll let you draw your own conclusions. Perhaps the author is a genius and we are missing all the rigor in his books. I'll be very sad if that is the case, because we really are just using LOF for a supplement.

 

Dd likes it a lot, if that counts for anything :) It's a great supplement; not boring and not too many problems. It takes her about 1/2 hr. per lesson.

[Jane in NC]

 

If you get through all that, then I have been searching for a calculus text.

 

Have you looked at Michael Spivak's Calculus? Not Calculus on Manifolds, but his text called simply Calculus? Lovely book of a rigor that you may find to be satisfactory.

 

In his introduction Spivak writes: "In American universities, "calculus" courses are so varied in content and viewpoint that only tradition dictates that the same title be given to all. Some of these courses cover only the most rudimentary techniques, sedulously shunning all theory." He goes on to say that this book is his attempt at a text that is used in the US for a so called honors course but is a typical British or European text in content. His problems include some of what you would expect to find in a calculus text to challenging proofs that would keep graduate students scratching their heads.

 

This is not a book for a typical high school student, but it is a volume that I enjoy owning and have consulted often.

 

By the way, my edition is the first and I have no idea of what changes have been made in subsequent books.

[Charon]

Have you looked at Michael Spivak's Calculus? Not Calculus on Manifolds, but his text called simply Calculus? Lovely book of a rigor that you may find to be satisfactory.

 

In his introduction Spivak writes: "In American universities, "calculus" courses are so varied in content and viewpoint that only tradition dictates that the same title be given to all. Some of these courses cover only the most rudimentary techniques, sedulously shunning all theory." He goes on to say that this book is his attempt at a text that is used in the US for a so called honors course but is a typical British or European text in content. His problems include some of what you would expect to find in a calculus text to challenging proofs that would keep graduate students scratching their heads.

 

This is not a book for a typical high school student, but it is a volume that I enjoy owning and have consulted often.

 

By the way, my edition is the first and I have no idea of what changes have been made in subsequent books.

 

 

Yes, I do know of Spivak's text. Those seem to be the big three: Apostol, Courant and Spivak. My dad recommended Apostol to me and I eventually got it and was initially excited about it. But, my excitement faded when I realized what was going on with the problems. Just for example, Thomas and Finney has the rigorous definition of a limit in it. It's not like these texts aren't written by mathematicians. The point is that Thomas and Finney clearly doesn't require the student to actually use epsilons and deltas abstractly to prove a result. In fact, both Thomas and Finney and Courant do this silly business of "if epsilon is 1/1000 then find an delta such that...." The epsilon-delta argument is not supposed to be used for some kind of approximation techniques like that. Or, at any rate, you are not doing the epsilon-deltas if you are doing that kind of thing -- that completely misses the point. I can't believe these turkeys (yes, I just called Courant a turkey) actually try to pass that off like that. (Although, it may be that Courant is just trying to ease into real epsilon-delta proofs -- I need to look at the book more closely.) So, Apostol just having a rigorous presentation but not the problems to back it up is a pretty **** serious ommission. (I' sure his book is better than Thomas and Finney but probably not because of all the rigor the student is not expected to know.)

 

Spivak is the only one of the three I don't have a copy of. I've seen Spivak listed as the top choice of the three, and I've seen it listed as the last choice of the three. Is there anyway you could look in your copy and tell me what you think about how the limit is handled? Or, how Rolle's Theorem and/or the Mean Value Theorem is done, for instance? It is okay if he does a proof by picture first or looks at a sequence of points for a while to heuristically talk about limits or continuity or whatever. What I want to know is if he ever does give a slew of problems that go like "Use the formal definition of a derivative to prove that the derivative of x^2 is 2x," or "Prove Theorem 1.3" (and when you look at that theorem it is real theorem)... that kind of thing. If it is just one starred problem at the end of some section. That's not enough. If it is use theorem <blap>, theorem <blap> and theorem <blap> to show that <blah blah blah> -- where you apply several theorems and then it just becomes a simple (or even if it is not so simple) calculation, then that isn't a "proof". (That's just another hairy calculation.)

 

Just before I buy it (and I'll probably end up buying it anyway), I just want to know what to expect there. I care a lot less about whether or not Spivak can do an epsilon-delta proof. (For crying out loud!) I want to know if the student is expected to.

[Ruth in Canada]

I'd add Jacobs to your list, particularly if you have a kid who likes words and/or a kid who really appreciates jokes. Jacobs recommends Foerster for algebra II.

[Kimber]

It may be poor memory from too many nights up with the littles, but don't the Singaporeans themselves think that NEM is not very good. I believe I read that many moons ago, and since then, I have dismissed it as an alternative.

 

But from your post and others, I gather that while NEM has its flaws, it's still better than most of what is mainstream here or at least as good?

[Charon]

It may be poor memory from too many nights up with the littles, but don't the Singaporeans themselves think that NEM is not very good. I believe I read that many moons ago, and since then, I have dismissed it as an alternative.

 

But from your post and others, I gather that while NEM has its flaws, it's still better than most of what is mainstream here or at least as good?

 

 

I think the Singaporeans acknowledge that it is "engineering math". It is plenty good at that. Everything is "engineering math" unless you either get high enough up (like graduate math texts or the right kind of senior undergraduate text) or you really find something exotic like the New Math from the 60s or something. So, unless you are really trying to do something like what I am doing (teach rigor in a way that leads up to rigorous calculus, for instance), I really don't know of much of a better program than NEM for teaching you engineering math. (Although, I have to admit that I haven't really thoroughly purused it, since, after all, I'm not using it. I have looked at it quite a bit, though.)

[Kimber]

Thanks for all of the responses,

 

I've got a little time to figure this math stuff out, so I've begun collecting math texts based on the feedback here. I've just purchased:

 

Elementary Mathematics a Logical Approach by Paul Sanders, published 1963

An Introduction to Inequalities by Beckenbach Bellman 1961

Modern algebra: structure and method (Book One) by Dolciani

Algebra I: Expressions, Equations, and Applications by Foerster

Principles of Mathematics by by Allendoerfer, C. B. And Oakley, C. O. (1955)

 

 

I'm not sure what the Sanders book is about, but for the price of $10 or so, I figured it was worth the purchase.

 

All of these old books were cheaper to buy than new texts. I already own Jacobs, answers and all, that I purchased for $25 at a used book sale. I've taught Saxon at co-op for 3 years and own those as well. I'll

pick up NEM with my store credits for returning our used curriculum. And I'll go ahead and buy Life of Fred.

 

I've got a lot of reading to do. I plan to pass this off to my dh too and hope that he will help me review.

 

I really appreciate the help and guidance. When I decided to homeschool, I never thought I'd be relearning all of this material. But it's a joy!

 

Thanks again,

 

Kimberly

[Charon]

Thanks for all of the responses,

 

I've got a little time to figure this math stuff out, so I've begun collecting math texts based on the feedback here. I've just purchased:

 

Elementary Mathematics a Logical Approach by Paul Sanders, published 1963

An Introduction to Inequalities by Beckenbach Bellman 1961

Modern algebra: structure and method (Book One) by Dolciani

Algebra I: Expressions, Equations, and Applications by Foerster

Principles of Mathematics by by Allendoerfer, C. B. And Oakley, C. O. (1955)

 

 

I'm not sure what the Sanders book is about, but for the price of $10 or so, I figured it was worth the purchase.

 

All of these old books were cheaper to buy than new texts. I already own Jacobs, answers and all, that I purchased for $25 at a used book sale. I've taught Saxon at co-op for 3 years and own those as well. I'll

pick up NEM with my store credits for returning our used curriculum. And I'll go ahead and buy Life of Fred.

 

I've got a lot of reading to do. I plan to pass this off to my dh too and hope that he will help me review.

 

I really appreciate the help and guidance. When I decided to homeschool, I never thought I'd be relearning all of this material. But it's a joy!

 

Thanks again,

 

Kimberly

 

 

Incidentally, out of all those books and all the books on my website, I think that Beckenbach is special. For one thing, the subject of inequalities is actually pretty key to real analysis (i.e. calculus done correctly). So, there may be something to the topic in that regard. But, what really makes it so special is the fact that it is accessible to a typical parent in a way that other books treating axiomatics really aren't. But, it is simultaneous a real example of axiomatics. It is completely correctly axiomatic about the notion of ordering. Not pretty close. Not an attempt to push the student in that direction in the hopes that one day maybe they can finally do it right. This is it -- the correct axiomatic method for developing that. And, it isn't "presented in a way that is accessible" -- it just is an accessible topic to present. It really has provided a clear example for Myrtle and me to talk about programs with -- how Jacob's just shows the student a number line as opposed to what it takes to really do it correctly.

 

It is also an example of how not every axiom that the student is going to have to use is spelled out -- just the relevant ones for the book and the rest are just taken for granted. And the student doesn't just do axioms all day every day. They do the axioms and then they do the results. It's all done axiomatically but not just as a big exercise in proving the obvious. It really is a very good example of what it's really like to do math. You solve problems rigorously. I feel like this provides the most concise example possible, probably, of "what I'm talking about" all the time on these boards and elsewhere. At any rate, I just thought I'd mention that about that book, in particular. (I really didn't appreciate it, myself, at first until Myrtle started working through it, and I started really examining those first few chapters and then the following chapters. That's really a great book by a great mathematician.)

[Kimber]

Most of what you say, I have to read and study to understand. I have never been taught "real" math only engineering math. I can remember in high school one of my teachers referencing some proof that was in our ps text. She told us it was too hard for us now and we'd see it later. I immediately took the book home and worked on it. I just have dig down deep to find that interest again.

 

The thing that I've learned from your posts and Myrtle's is that parents have to really dig in and do the math. You can't know what your children are learning until you dive in and work the problems.

 

My calculus 1 teacher, many many moons ago, said the very first day that ,"Calculus is not a spectator sport." That has more meaning to me now than it ever did. As parents, we can't tell what's happening in the text until we get in there and work the problems. It's highly unlikely that as parents we really understand the methods use to teach the math until we actually "tasted" the text ourselves.

 

I was trying to avoid this. I was hoping to coast through these middle high and high school years based on my comfort with math. But that's not really going to get for us what my husband and I want for our kids. Lucky for me though, while my dh isn't involved with homeschooling, he loves doing math.

 

I'll be hanging out on your website a little more. I'll definitely remember your comments about An Introduction to Inequalities by Beckenbach Bellman. We may not be able to take the road that you and Myrtle are traveling down, but we might be able to incorporate enough of the "new math" so that our kids are prepared for a career in math if that is their field of choice.

 

Thanks to you and Myrtle and the rest for sharing all this information. I'm a little simple minded sometimes and need all the help I can get.

 

Kimberly

 

 

 

 

 

Kimberly