I think he should definitely take them on paper. Someone who's looking at engineering needs to be absolutely rock-solid on algebra, geometry, and precalculus. If he cannot get the careless errors under control, all of his major classes (calculus, physics, and the engineering classes) are going to be pretty unmanageable. What grade is he? Is he applying to colleges for the fall? I would rather see a freshman with a solid knowledge of precalculus than one with Cs in precalc and calc. The people who enter having struggled through precalc and calc usually place into my calculus class when they take the placement test, and they often struggle as they know about half of calc (which means that they THINK they know a fair amount of calculus, and therefore don't study enough) and half of precalc. I would talk to his teacher about this as well. I just looked up TPS math classes. I notice that they have a pre-calculus problem-solving class. Is he enrolled in that and is that adding that an option? It looks like it would be cheaper than hiring a tutor.

Left-to-right is how I naturally compute. The numbers come out in the correct order for writing them down, and estimation is more natural this way as well. This is nothing I was ever taught but simply the way that made sense to me. I think this is also partially because I started algebra so young that I tend to apply algebraic algorithms -- and when adding polynomials, it tends to be taught to combine the highest order terms first. Side note -- when I was first taught long division, I was taught it as an algorithm (by the PS math teacher), and I just did NOT get it. I could neither remember the steps nor get them in the right order. When my algebra teacher taught long division of polynomials, it was as though a light bulb went off in my head. "Oh! THIS is what they were trying to get me to do before! It's just all the x's were 10s!"

We check ID's at exams (at university) for precisely this reason. Frankly, the homework is worth only a small percentage of the grade, so a student who pays someone else to do their homework is only hurting themselves. So we don't really look for cheating on the homework, other than extraordinarily blatant copying. We rely on the in-class proctored exams (which are worth far more of the grade) to fail those students who may be cheating on the homework. Laundrycrisis: You are not far off -- reducing cheating is one major reason that is done. Another reason is to work with students who genuinely cannot do the work without that level of help. When the administration is demanding that the professors figure out how to get more students passing, this way is easier to stomach for many than simply changing the passing marks.

Good point. I have heard really good things about Timez attack for multiplication as well.

"How can a child do prime factorization, but struggle with simple division???" Because division is boring and prime factorization is interesting. Frankly I did not have my multiplication facts down myself until I was in Calc III. Under no circumstances would I stop ALL learning and go back to nothing but facts. This would be like taking a child who is reading well but struggling with spelling and sending them back to read nothing but Hop on Pop until their spelling improves. I would keep doing what you are currently doing and provide high levels of encouragement for math facts improvement. (stickers etc.?)

One of my friends got into a UK university by submitting a year of good (4.0) grades from a local college in lieu of A levels/APs. Would that be an alternative? Or maybe high school in Germany would work, if she could exchange for a year and then take a "13th grade" year?

I realize you've already made your decision, but just to add in for anyone else reading who has a similar question: I have heard professors talk about instantly rejecting otherwise qualified graduate applicants because they brought their mother to an interview. For undergraduate it might be okay (although even then it's better for the student to handle it while the mother goes for coffee), but for graduate school, at many schools it's a complete no-no.

Well, my (homeschooled) brother didn't care and refused to even try, either. He didn't like math, either, so that wasn't a carrot. This went on until he was about 9, at which point he found something that he desperately wanted to read and everyone else refused to read to him because they were bored with the topic. It took him a week to hit grade level and a month to hit college-level. But he had been constantly exposed to elevated language through read-alouds and discussions, etc. Perhaps one of the reasons he refused to try was because he was the youngest and people would always read to him because "I can't"?

Here's a decent, cheap (if you're willing to go used) textbook that might be of interest. It is aimed at uni students but avoids higher level mathematics. http://www.amazon.com/Introduction-Astrobiology-Iain-Gilmour/dp/0521546214/ref=sr_1_3?s=books&ie=UTF8&qid=1355943257&sr=1-3&keywords=astrobiology I would probably start reading *until* he finds he needs chemistry knowledge to understand what he's reading, and then cover the chemistry. (given that he's 7th grade)

Look into the Great Illustrated Classics as well. Many of my very favorite books I read there first, and having an overview of the plot (I'm looking at you, Tale of Two Cities) kept me from getting completely lost in the prose.

That's why my mother put me directly into pre-algebra after I quit school in 2nd grade. It worked fine for me. I did the comprehensive arithmetic review/gentle intro to algebra over the next year and a half and then started algebra. I was SO bored trying to do grade-level stuff.

If she is nearly done with Algebra II, I'd look into statistics.

AOPS has written a textbook that would be a good start. For following up, I enjoyed this book very much: http://www.amazon.com/Elementary-Number-Theory-David-Burton/dp/0073383147 but I would definitely definitely definitely get an older edition. You can get the fifth edition used for 3.42. Before you advanced to Burton's book, though, I would say you should have algebra 2 under your belt. Some number theory textbooks have more prerequisites than others. If you run into a specific book at a used-book store or something, I can look it up.

A solid course in proof-based geometry would be good. Some exposure to set theory would be a good idea as well. Here's a few books with low prerequisites, written for high school students. (disclaimer: I have not read them, but none are unduly expensive and they have been recommended by people whose opinion I respect.) http://www.amazon.com/Shape-Space-Chapman-Applied-Mathematics/dp/0824707095/ref=sr_1_1?ie=UTF8&qid=1355543513&sr=8-1&keywords=weeks+shape+of+space http://www.amazon.com/Intuitive-Topology-Mathematical-World-Vol/dp/0821803565/ref=sr_1_1?ie=UTF8&qid=1355543404&sr=8-1&keywords=prasolov+intuitive+topology http://www.amazon.com/First-Concepts-Topology-Mathematical-Library/dp/0883856182/ref=sr_1_2?s=books&ie=UTF8&qid=1355543984&sr=1-2&keywords=steenrod+topology Topology, imo, would be an excellent elective for a mathematically mature high school student who was aimed at a career in STEM and potentially mathematics. It would also really set them up for success in real analysis.

Depends on what she likes about it. If it's the proofs, look into a 'proofier' algebra. If it's the fact that it's more visual, look into visual explanations of algebra concepts. Unfortunately I don't have a textbook recommendation because I make up my own explanations for my visual students. If it's that she's weak in arithmetic(especially fractions) and geometry has less of it, remediate.

Elements of Math would be great. So would AOPS discrete math books. AOPS Problem solving books in general. You might also find Mathematics: a Human Endeavor interesting (easy to pick and choose topics of interest). I will say, though, that she will probably find any high-school level classes very trivial if she's worked through these harder courses. Other ideas: I notice she's 8. When I was that age, I *loved* math for smarty pants and the I hate mathematics book. Awesome introductions to a lot of stuff.

If he continues to want to be a computer scientist, I'd look into a discrete math/programming math course rather than (or in addition to) diffeq. This course is a rude awakening to some CS majors because it's so very different than what they've studied before, and the material really isn't included pre-college in most sequences.

It might be a decent idea to get used to the non-saxon phrasing while repeating material she mostly knows already. It really depends on if your dd is the type who gets bored with stuff she already thinks she knows, and prefers to get pushed into the deep end, or if she's the type who gets overwhelmed by excessive challenge. Another option, btw, might be to start the saxon calculus yourself at a gentle pace with plans to do calc 1 at the university anyway. Another option might be to get a decent university precalculus textbook (cohen, lial, et cetera) and work through that in a diagnostic-prescriptive manner (i.e. do the odd problems out of the chapter reviews, and if anything is wrong, review that section).

I would also look into taking a math or english summer course at the community college if he's up for it. It'll ease him into things, and he'll have a chance to start out with just one course. Community colleges have some really good teachers and nearly invariably have small classes. He could knock out a fair number of gen eds in one year. The deadlines are also much later, and if he has the FAFSA filled out and ready to go (or you have it essentially filled out so all that's needed is data entry) he could qualify immediately.

I would not worry so much about having courses planned for senior high school. There *will* be courses of interest, and the precise courses will depend on your student's intended major. Your student might also need extra time to process, and take more than a year to finish algebra 1. (This is not at all unusual when starting young). That is perfectly okay! Don't try to lock into a progression now.

Having re-read your original post, college algebra sounds reasonable as well and a bit less of a struggle than precalc. The CC might also have a "math for liberal arts" or "quantitative literacy" course which should also work.

I think environmental science would be fine. Another science elective you might look into is nutrition. She also might enjoy finishing off chemistry by looking at some of the units from OCW's Kitchen Chemistry class. For math, precalc at the CC might be extremely challenging if she struggles in math. It moves a lot faster at the CC than at a high school. I would suggest that for someone who's looking at a culinary career (or a non-STEM career in general) statistics might be more useful and hopefully transferrable -- check with receiving schools -- but I see far more situations in everyday life or in non-technical careers where some understanding of statistics would be useful than situations where some understanding of trigonometry would be useful.

There are plenty of kids who've become mathematicians without having BA. Now, I do think it's absolutely wonderful and if the child could possibly be talked into it, it'd be good. But if he's in full I WON'T mode, I think it'd be more productive to use one of the many other good curricula out there than insisting he must do THIS ONE. I do think he sounds like an ideal fit for AOPS when he gets through arithmetic.

If he is looking at college, I would strongly suggest finishing geometry. Why isn't Saxon Adv. Math an option? If he did well with Alg I and II, that would complete his geometry credit.

I would say that if she places into Algebra II, she should have credit for Algebra I. Award it by examination if it makes you feel better.