This is one reason the comments are SOO much more important than the numbers. If I saw a comment with anything like 'easiest prof ever!' I knew that would be a bad match for me.

From what I heard when talking to them, it mattered most if it looked like you were trying to get 'easy' classes. The specific example they gave to me was that a student with an associate's from a community college who had taken some courses there would be much better off than one who had done four years at a good school but taken summer med school courses at the community college. As always, YMMV.

You get used to it REALLY quickly. I had to learn it for typing my dissertation and there are so many good points about it. For one thing, when you need to use the same equation in multiple places you can just copy and paste. When you realize that one line doesn't make sense and needs to be changed you don't have to copy the whole thing again. et cetera.

Basic math -- if they cannot do the four basic operations (add, subtract, multiply, divide) I would look into Power Basics Basic Math book. If they are a little more advanced you could consider Lial's Basic College Mathematics. Both of these books contain a thorough review of arithmetic and are designed for developmental learners. Lial's covers a bit more pre-algebra. ETA: This is assuming that the reason they're behind in math is primarily due to lack of time put in. If the reason is learning differences then these may not be suitable.

Foerster is a good and solid program but you'll still have to grade his work and make sure problems aren't being glossed over. There is nothing wrong with continuing pre-algebra review while you do algebra problems. Heck, it could be one problem per day with a repeating weekly cycle -- e.g. monday, do a multiplication, tuesday, do a long division, etc. where as long as the one problem is perfect there are no extras.

I would have him work on redoing algebra 1 with a tutor while he takes geometry next year.

In addition to what everyone else said: Your dh is not really correct about what she'll have to take in college. It is true that if she majors in English she won't need more than a 'math for liberal arts' type class, or possibly college algebra. However, these courses usually have a prerequisite of Algebra 2 and make use of high school geometry (i.e. assuming that at least the basics have been taken in high school), and if she has not had those in high school she will need to take them at a community college. Furthermore, there are many majors your dd could discover that require at least some mathematical competency. But with that being said -- I also really do not think that I would rush a weak math student through a summer pre-algebra class. JMO, but I think that summer classes are appropriate to two classes of students: Strong students who are trying to accelerate, and weak students who took the class previously and came close to passing, but not quite. For a struggling student, taking a class at double pace is not really appropriate. It would be totally reasonable and eminently desirable, though, to start pre-algebra during the summer at regular pace to minimize the well-known summer loss due to leaky teenage brains.

I agree with BOTH of these a lot. The number of prospective elementary school teachers who will vigorously resist learning arithmetic and how it works because "I'm just going to teach kindergarden and you don't need fractions there" is both astonishing and sad. We are not talking requiring them to learn calculus, we are talking requiring them to learn to do fractions, long division, multi-digit multiplication and addition, and explain why it works (as if they were teaching children). I also totally agree with introducing simpler concepts earlier instead of holding back on algebra until they're ready for advanced concepts. As a matter of fact I think we should introduce linear equations very early (in a simple form) and continue working on them (introducing slope close to when we do triangles and doing lots of work on them) throughout several years. I think a lot of issues really boil down to not understanding why linear equations work.

I would review the algorithms before I panicked and switched curriculum. If he learned it and could do it before he shouldn't need more than a quick review. If he "chunks" then forgets MUS is probably not going to be a good fit anyway with the extensive mastery approach. As Arcadia says learning for a test and then forgetting is very habit-forming and it takes a while to break.

When you say "finish his high school reqs", how much math and science will he have had? He will need exceptionally good grades in college to be competitive for med school, so you'll want to make sure that he's had a decent high school class biology, chemistry, and physics, because he'll need to take all of those courses in college and get good grades. For math, he should have as much math as he can handle, but at least through precalc and preferably an introduction to calculus. That way his freshman year classes will be an easier transition. If his high school requirements won't have him through bio, chem, phys, and precalc, then he should definitely take the extra year to be prepared.

I would agree.

Keys really isn't enough to be a full algebra 1 course and will cause difficulties when trying to continue on to Alg 2. What has she done for pre-algebra and how did she do?

What everyone else said: AOPS is for super mathy kids who love math. It could work with a moderately mathy kid who loves math or with a super mathy kid who's ambivalent. There are loads of other programs which provide solid conceptual instruction and an excellent foundation for the future (even for STEM majors) which would be much more suitable for a less mathy kid. Personal recommendation: Finish CLE through pre-algebra. Re-evaluate at that point and find a good algebra program.

The New Mathematical Library has one: http://www.maa.org/ebooks/nml/NML34.html This one also has a lot of applications. It's been revised and updated extensively.

I don't know as much about the NZ system of higher education, but isn't it more similar to the UK system where students enter with a declared major and take courses only towards that? I believe that the mathematics courses in such a system usually are significantly more theoretical and proof-oriented than the ones in the US, where at most universities (especially community colleges and smaller state colleges) students with multiple goals (med school, engineering, physics, geology, math) all take the same calculus I class. If I'm wrong, ignore me :)

I do not think I said anything that even implied that students should race through an easy curriculum. As a matter of fact, I have repeatedly recommended the opposite. Now, none of these curricula were available when I was a child, and my parents did the best that they could with the materials they had available. I have said (in this thread, even), that if AOPS had been out I think I would have been far better served by working through those materials instead. I will really disagree with the bolded. If the child has sufficient mathematical talent, even these intellectually engaging curricula (and I like all of these curricula very much) may not be enough without acceleration.

Yes, absolutely, and this exacerbates the issue. Not only are all your kids clever (and they ARE at the very least clever to be able to do this) but most of the people you know has clever kids who are at least a few grades accelerated -- it's very easy to jump from that to 'everyone else is just like me'. ("you", btw, is in general here and not in specific)

Well, I actually don't think you would need to do lof frac/dec. But if you do do them, I would do them before aops. I think that they'd be a step down if you did them during. I was reading your original post as 'we really are determined to use all of these resources'. :p

I see this as well. Furthermore, a lot of said posters have no real idea about how higher education works, and will cavalierly say things like "Oh we are going to do an online high school diploma (with no post-algebra courses) and then do an online college degree in general studies and we are going to be all done by the time they're 16 and after that they can do med school or law school if they want" and blissfully ignore the reality that this is not an education that will get you into anything other than a job which requires "any degree". Pfui.

Honestly I would suspect that this is because she spends so much of her time with her own children that they seem very normal to her. It is a very normal attitude to develop -- you compare yourself to the people you see regularly. There are similar studies showing that when people have primarily overweight/primarily underweight friends their sense of a normal body image also skews.

Obviously he is young now. I'm not sure how good the local university is, but unless it's quite good (flagship state university or something) he would probably be better off to only do math courses there, and when he's maxed them out (which he probably will, again, unless they're really good), then apply to somewhere really good to take 4 years of math electives while doing research etc. This also preserves options longest should he change his mind and decide something else is his true love. I would also look at (once calc is passed) doing mandatory major courses at the university and post-calculus electives with the mentor. For example, linear algebra is a required course and will probably be rather boring to someone who has already self-studied the class. Something like game theory or graph theory or who knows what will be an elective that will strengthen his transcript for university admission and provide a fun and interesting challenge yet not put him in the rather awkward place of having to sit through a class he has already taken.

Well, in a way it was a good thing. I doubt my parents would ever have looked into homeschooling if the school had not been so resistant :)

FWIW, this is what happened to me in PS. They wanted me to do page after page of single-digit addition problems and it was so damn boring. I had no motivation whatsoever. Then they wanted me medicated for ADD because I spent all my time staring out the window instead of doing math. They also wanted to keep me back a year because I was young for grade and 'failing math'. Yeah.

Two things: I know this is not your child, but I would recommend very strongly against 'getting math out of the way' if it means doing AP calc at 12 and then never touching math again. I think a kid who is talented but totally uninterested would be better served by going through a standard, honors sequence (which, if they are talented enough to pass AP calc at 12, they could do the standard sequence with very little effort). Even for one who was originally interested but is no longer, I would recommend decelerating by doing half-courses (so, for example, someone who completes algebra 2 in 8th grade but really doesn't want to do more could do half of precalc each in 9th and 10th, half of calc each in 10th and 11th, and legitimately transcript it as college algebra, precalculus, calc 1, calc 2) instead of just stopping. As for yours, there is a student in graduate school with me who finished his undergraduate at 18. There is another one who entered university at 17 but had already taken 8 courses (4 years) of university-level math. Both of these are very strong students and doing well. But they waited to enter university full-time until they were on university level in ALL subjects, not just math. It sounds like your mentor is outstanding so you have some wiggle room. :)

With a young, gifted child there's no reason to head straight for the run of the mill high school math program. There are many electives that can be done after only algebra 1. AOPS does a counting and probability course and a number theory course, and there are other courses that could be done early if the parent, tutor, or mentor is capable. IMACS has books in mathematical logic and set theory that could be completed even prior to algebra and definitely after algebra 1. Once geometry is completed there are more advanced courses in geometry which could be completed. After algebra 2 some more advanced courses in counting and probability (aops), number theory (many elementary textbooks would now be accessible to someone who completed the AOPS introductory course and a solid algebra 2 course), statistics, graph theory, etc. After precalculus it opens still more and after calculus still more. Specific courses chosen could depend on the child's interests -- for example, a kid primarily interested in biology could, after algebra 2, self-study some matrix algebra and then do a basic course on game theory w/evolutionary/ecological applications (I find this fascinating myself), while a kid interested in physics would want to head more towards calculus and then afterwards look at subjects like differential equations, linear algebra, mathematical statistics. I would also recommend reading The Calculus Trap (an online article) about why you shouldn't just rush a gifted kid through the standard curriculum on the way to calculus.