I used Genki in college and liked it. FWIW, my college course only covered 4 chapters per semester.

I agree 100%. I have had multiple students where my class was the only class that kept them from straight A's for the semester. But they weren't A students in my class.

OK, I'm not sure that a new curriculum is really the answer but it may be. Lial's (beginning or introductory are both okay) has pretty good explanations and lots and lots of practice. Too much, as a matter of fact, doing about 1/4 of the problems should be about right. They're also cheap. If she would like DVD lectures Chalkdust is well-regarded as well -- it goes with Larson's series of texts which are also widely used, but I've never personally used them.

How solid are her pre-algebra skills such as fractions? What types of mistakes does she tend to make?

Teaching is really hard to get around -- they want you in the classrooms reasonably early so they can watch you interact with the kids. It's pretty common, though, to do coursework at a CC and then transfer -- transfer students often need to take 3 years though because of Ed classes not available at the CC's.

Either way there will be forgetting -- with the break off from calculus she'll forget it and with the break off from trig she'll forget that. If she's going to take the AP credit in college I'd do Calc as a senior so she won't have time to forget. Otherwise I'd go ahead and do it as a junior.

Yep. Because kids who deliberately drop out go in one category, and kids who try and fail go in another category. It's much less detrimental to the school to have students drop out than to fail to graduate. Schools have gotten in trouble in other places for basically forcing students into 'homeschooling' in order to get them off their graduation records.

I think that doing AOPS Intermediate Alg and then taking Alg II would be incredibly redundant. I sorta like the idea more of just continuing with aops algebra and trying to place out of both algebras.

You might look into Key to Algebra as another pre-algebra. It covers a fair amount of an algebra 1 course, but not in sufficient depth, so you'd still need to do an algebra 1 afterwards, but it could be useful as a preview and for maturity issues. If you chose this I'd do once-a-week arithmetic review with fractions etc. as well.

Good. Yeah, it's a bit limiting if students don't take it. I think mandating that math through precalc needs to be *offered*, by DE if nothing else, is reasonable. But I don't think we should be making students leave without a credential just because they can't do higher algebra. Plus, it'll let us make the courses more rigorous for students who *are* planning on going to college.

The algebra's new so a lot of people haven't used it yet. If you like horizons I wouldn't switch away. A lot of people switch programs between algebra 1 and 2, and the only really big issue would be if you were transferring from a weaker one to a stronger one.

I agree with Ruth on pretty much all aspects.

I assume, since you're doing the precalculus course (That's what the Stewart book really is) you're solid in lower-level algebra, geometry, and pre-algebra. Working on math is a definite biggie -- it's the number one reason I see people fail out of engineering schools. I'd get some good, solid grade 12 chemistry/physics textbooks aimed at people in your province -- there should be some solution guide that's suitable for self-study. When you're self-studying with a solution guide, make sure not to look at the solution guide before you've attempted the problems. Even if you do get stuck, look at the first line of the solution to see if that helps, then go back to working by yourself. I see far too many students who are studying with a solution guide and think they're doing fine because they understand how to watch someone do it, but not how to do it themselves. Do you need to take exams on these courses? If so, I'd make sure to get an exam-specific prep book as well, after you've studied.

Why isn't he ready for algebra? Lack of problem-solving skills? Lack of stamina for longer problems? Lack of pre-algebra skills? Recommendations will vary depending on reasons.

Haven't used it, but it has some really bad reviews -- here's a collection. http://www.nychold.com/imp.html

Yes. Quite honestly, I also see a large difference between "may not wear a bikini" and "may not swim because even a burkhini is too immodest." I would consider the second one excessive (though not abusive) and the first one a reasonable difference in parenting styles.

Would it help to split up your lesson? To do half in the morning and half in the afternoon? Maybe then it wouldn't feel quite so long and she'd make fewer errors because her brain is just tired.

As far as "remembering which number to flip", here is what I would do if I had a habit of forgetting. I do know that 4 / 2 = 2. So that means that if I'm going to do (4/1) / (2/1) I should definitely get 2. If I flip the first one, I have (1/4)(2/1) = 2/4 = 1/2. Uh oh! If I flip the second one, I have (4/1)/(1/2) = 4/2 = 2. Oh, that must be the one I flip. I didn't have an issue remembering this, but there were other places where I continually forgot and had to do a quick check with something where I *knew* the answer to remind myself I was doing the problem right. For example, does f(x-c) translate to the left or the right (for c > 0)? Well, ... y = x^2 has a 0 at x=0. y = (x-1)^2 has a 0 at x=1. Oh, it must move to the right.

Yeah, I use it, but you really don't need it. If I were doing bookkeeping without a calculator you're darn straight I'd use it, but there's not a lot of need for that outside Amish communities and the like.

You may also be able to gain advanced standing but not credit, for some of the classes. One of my friends attended a school where they did not accept his transfer credits, but after an interview with the department chair, the courses he had taken were waived and electives substituted in their place in his degree plan. In many ways, this is an ideal solution if graduating faster is not the goal, because the student has more room to do interesting electives, an internship, undergraduate research, etc.

I don't think most kids could just be handed the book and learn well. They need regular corrections so you catch errors before they become ingrained. Why not see how she does on the placement test for TT3, TT4? I'd recommend a computer-based self-grading program instead if you really don't have time to teach.

If you like Galore Park, why not pick up their texts? You wouldn't have to worry about spelling/minor language usage differences and ought to be able to transition to GCSE fairly well afterwards if you completed their sequence. And since they're UK-based they'd probably arrive very quickly.

Yes. Yes, they can. I think having her explain back to you what you just explained may help. Be prepared for a lot of uncomfortable silence and 'ummm' the first time you try it. Difficulty with word problems is often caused by not understanding what the operation means. I have a lot of students who can easily compute 1 and 3/4 divided by 2 if I tell them to compute it, but if I say "A cake recipe requires 1 and 3/4 cups of sugar. How much is required for half a recipe?" will get flustered and start doing crazy stuff with the numbers. I don't have any real remedy other than more practice.

Just because you're explaining it conceptually doesn't mean she's listening to your explanation. She may just be going 'ladidadida' until you get to the 'how to do it' part and then turning on her ears.

I've heard of people placing anywhere from 65 to alg 1 depending on how well the Singapore was understood -- you really need to take the placement test.