Jann in TX, Myrtle, Charon and other "Mathy Minds"

[Pongo]

Cross post from K-8.........

 

I love reading your math threads. It is a real blessing to have "Mathy" people on this board. I feel like I'm at a Super Wal-Mart when I come here. It looks as though math is a really tough subject to get a handle on, at least for me. I was wondering if you had the time is you could list a curriculum recommendations in

[1]Non-Math (Child must have DVD's at upper levels)

[2]Okay until Alg.(Child could handle if DVDs or possible well laid out solutions manuals are available)

[3]Pretty Confident (I can handle rigorous, possible outsource with a tutor or hand over to Dad if help needed)

 

I'll start only to show what I mean, please by no means should anyone follow my lead I am one of those that sputters out at Alg.

 

[1],[2] or [3]

1-6 Pick an Elementary curriculum and stick with it (Ones I have used Bob Jones, Singapore, MUS)

 

[1]

7th Teaching Textbooks or Chalkdust (Uses Larson text)

8th Pre-Algebra Video Text all the Way through

9th

10th

11th

12th

 

[2]

7th Lial Basic College Math, Chalkdust or Video Text

8th Dolciani Structure & Method 1

9th Geometry (no clue what to use)

10th Dolciani Structure & Mehod 1

11th Pre- Calc ((no clue what to use)

12th

 

[3]

 

I can't even Imagine........

[Jann in TX]

Since your children are still young you have plenty of time to choose the program that suits their learning style/abilities.

 

Some of the programs on your list are VERY inexpensive--you can easily pick up a used copy of Lial's Basic College Math for less than $7 shipped. The Dolciani texts are also inexpensive (I found my copy for under $5). Look around for a 'contact' who can let you sample the video based programs. Nothing helps more than actually sitting down and holding the programs in your own hands (or watching them). I also suggest letting your children be involved as well--but you have the ultimate choice.

 

Right now there are so many choices (especially in Math) and in the next few years there will be even more as home video support becomes more and more common (even with PS texts!).

 

It is impossible for me to list the perfect sequence/publisher for any group of students (mathy or non-mathy...). Just about any series can work for a student--as long as the limitations (of the student AND the series) is known.

 

I currently have a student with learning differences (my own daughter), unmotivated but very capable students, and highly motivated but not quite sure of their abilities students all using Lial for Algebra. They are ALL doing very well. These same students would have similar success if they used other programs like Foerster's or Larson or Dolciani as long as the support they needed was available.

 

Video support is great--as long as the student can learn from them. Text support is great (a strong point of Lial) as long as the student will LOOK and READ the lesson. Parent/tutor support is great as long as the student feels free to ask questions and the parent/tutor is able to answer them!

 

Keep an open ear out for new programs and programs that others can recommend--but it is really really important that you go with a program that works with YOUR student...and what works with one of your children may not be the best approach with all of them.

[Charon]

I don't really make recommendations for [1] and [2], mostly because you don't need one if you fall into that category. Do teaching textbooks or something easy and just forget about it -- stop even worrying about whether your math program is good or bad at all. If you fall into that category, and you really still want advice, then my advice is to get out of that category. It's not that hard -- it isn't as hard as learning Greek or Latin -- that's for sure. At any rate, my recommendations fall into three categories of my own (which may seem like "hard", "harder" and "harder than that" in no particular order):

 

1) You want a normal program and want your kid to be successful with any math-related endeavors they may persue outside of the program.

 

 

 

Then do Singapore up through NEM 4 and put your kid in Community College. It is a "no brainer". It pretty much covers everything (though it might be a little light on trig or this or that -- if it really bothers you, you shouldn't have to supplement very much to completely remediate it). The brain comes in when you teach/TA it. You are going to have to be able to solve those problems and explain them to your kid. But, outside of that, you should have no anxieties like "But, what if they bomb the SAT??" or "What if they can't handle a normal Calculus class??"

 

 

2) You don't care about normal or college or the SAT. You just want the straight dope, no bull**** answer that doesn't depend on a whole lot of social crap to be even remotely valid.

 

 

 

Then, what you do for arithmetic is practically irrelevant -- do something, though, like up through Singapore 6B -- don't just skip it. You will start out around 9-12 years old with "mathematical logic" ala Patrick Suppes'

An Introduction to Mathematical Logic

. Do a couple of his other books all the way up to axiomatic set theory. Add in some number theory from the Art of Problem Solving, perhaps (real early on -- perhaps in your arithmetic). Add in some kind of Euclidean Geometry like

Kiselev's Geometry

. Do all that until your child is ready for something like Joeseph Gallian's

Contemporary Abstract Algebra

or I N Herstein's

Abstract Algebra

. Now a lot of mathematicians, and definitely a lot of math teachers, will screech like a pack of harpies at you for doing something like that, but rest assured, they are all mostly full of it. All they are doing is observing the fact that you are bucking the system and want to know just who the hell you think YOU are?? However, it is true that you will have to stop along the way at times if you hit some intense algebraic manipulations since your child will not have much, if any, experience with that while these texts are written for people that really have. At that point, you may have to to just make up some problems to get the practice in on the relevant mechanics for a while. This kind of thing will only happen a few times before your student is pretty handy with a formula. Once you are at that point, you should be able to follow that up with a stronger Algebra text (like

Abstract Algebra

by Dummit and Foote) and something like

Topology

by James Munkres. Finally, wrap it all up and call it a day with

Principles of Mathematical Analysis

by Walter Rudin. You may have to go really super slow at first, but it can be done this way, and it may well take you until the kid is around 20 to pull it all off. No one really seems to know for sure because it appears as though no one has ever had the stones to do this. Also, go ahead and follow all this up with a really tough Analytic Mechanics or something -- some senior level physics text on classical mechanics -- just to make sure the material is really made applicable for your student.

 

 

3) Okay, so you do care about college and the SAT, but you don't care about normal. And/or, you can't do the real no bull**** program -- no really, you really cannot do it, as in, not able to as opposed to just feeling a little too neurotic or lazy to because it probably really does take a PhD in math to do well, for one thing.

 

 

 

Then, that's a toughie, but I really like these books by Allen and Pearson from the New Math era. Pretty much everything I'm doing here is in my tag line. Though it is often criticized as such, it really isn't Abstract Algebra. Nevertheless, there is some pretty good stuff like proving that the inverse is unique (like you would do normally only in an abstract algebra class). What other high school

algebra

does two column proofs? Probably 1960s Docliani or something (in other words, some other New Math text from the 60s). I am totally infatuated with Kiselev's Geometry -- a classical Euclidean-style Geometry text. That kind of geometry is always a good one for the axiomatic method. In fact, Euclid basically invented axiomatics in the Elements -- that's why it was such a big deal. And, of course, I like and have always liked Gelfand's books because the problems are really pretty d*** good -- better than Frank Allen and probably better than NEM. In fact, I really can't think of a book with better problems. I found at least one of his problems in a graduate text on complex analysis, for instance. (But, it's totally "doable" in the context it appears in Gelfand.) The problem with Gelfand is that there really are problems in there that if you were to do it truly rigorously, you would need to use Mathematical Induction, say, which he doesn't teach you and is a bit too hard porbably for most American 9th graders. In fact, for that matter, Allen probably isn't really

completely

rigorous. Ordering, for instance, is better done in Beckenbach's book (also listed in my tag line and something we plan to do after or towards the end of Allen, but that we have nonetheless started informally introducing already). If you can get your kid doing S I Gelfand's

Sequences, Combinations, Limits

-- all the problems

on their own

, then there is little doubt in my mind they could just skip the calculus and go straight to something like Lay's Analysis.

 

 

Just aside from all of this -- forget about high school, having a "rigorous program", or anything like that for a moment. The three main subfields of math are Abstract Algebra, Topology and Analysis. Okay: not calculus. This race to calculus is really all about a race to engineering not to mathematics. You would think that the freshman calculus sequence would have some kind of bearing on math as a field. But, it really profoundly doesn't. In fact, the whole of undergraduate math lives in the service of other fields, most notably physics and engineering. Some students go to graduate school in math never having taken a course in real analysis! That is outrageous! Because when they get there, they will be in for a rude awakening when their whole success or failure is based on a bunch of stuff that bears almost no resemblence to anything like freshman calculus and looks like real analysis all day every day. That was the big weed out qualifying exam at Ohio State. And, it probably still is. (Not that calculus is a bad course or anything -- just that it isn't like "what mathematicians do". It is more like "what physicists and engineers do". It's all the theorems of real analysis without the proofs, so it isn't doing math so much as using math -- usually to shoot a cannon ball or something -- some sort of a physics problem. Hopefully, I haven't slighted calculus too much....)

[Nan in Mass]

For a non-math child, I think it is important to do something like Singapore Primary Math (there are others, I just haven't looked at them) that teaches how numbers work and some strategies for problem solving, not just arithmetic algorithms. Otherwise, it will be very, very hard for that child to get through more advanced math like algebra and geometry. A child who is mathematically minded is going to be able to figure out the thinking behind the algorithms, so it won't matter as much which program is used.

Just my opinion, after struggling with a non-math child.

-Nan