This is what is driving it for us. DS15 is utterly miserably in the "honors" track in public HS, and struggling for purchase on an adequately challenging course load for next year. It isn't that the school doesn't offer good subjects - it's that the content is watered down, tests are pitiful (what the heck is the point of a group test!?!?!?), and his grades are in jeopardy of slipping from disengaging from class. So directional U, here we come.

This, this, and more of this. Basic trig will suffice for calc 2 except for substitutions - you need to be very comfortable with trigonometric identities and derivations.

Concurrent enrollment is the only option we have been given in our area, anyway. If you look at the DC courses offered at UTPB, for instance, they're all valid toward core curriculum requirements. The UT-Austin Extension options might be reduced, as well as some JC options.

If you are using multiple sources, you don't need to do all the regular problems - you're bringing in lots of practice already. There is value in doing the derivations and examples alongside the book, though. You might have a different approach, but the process is valuable. I would go straight to the Intro to Algebra book, and look to take a break before Intermediate Algebra, possibly by using the C&P and NT texts. For shipping, can you save by ordering multiple books at once?

I think this is not the point? Yes, some states don't even require it, and yes, you can get through trig without much geometry - the question seemed to be whether geometry was relevant and "covered" in trig...

Good for you - it is absolutely rubbish, and for kids not progressing into higher math, may be the single most important math course they will take. It's the only one that cannot be executed through rote procedure, and the only one that mandates the development of logical thought. For kids progressing into certain science, engineering, and architecture topics, geometry is absolutely indispensable - and I mean the parts not "covered in trig," which is an almost comical turn of phrase in itself.

"Plugging in" the number is actually a bit of a trap in rational expressions. It only works reliably when the variable can be isolated in either the numerator or denominator. In this example, think about a multiplied function. You should have seen lim( fg ) = lim( f ) x lim( g ), so you can break the complex problem into a product of known limits. It's not an intuitively obvious problem if you've never seen the approach. I would just chalk it up to "well, now we've seen a new technique - let's remember to consider it in the future."

Correct. It is extrapolated from a normalized sample across all grade levels. You can see a lot of info about it on the Iowa site: http://itp.education.uiowa.edu/ia/InterpretingResults.aspx

For us, it's all of these things plus the content being deeper / more satisfying for our kids. As to when to start and how many to take, it really depends on the student and situation. Anywhere from 0-20 of them, sometimes balanced across four years, and sometimes loaded toward the back.

Switching between algebra I & algebra II might be tricky. Much of the traditional algebra II is in the "Introduction to Algebra" text. The "Intermediate Algebra" text has the balance of algebra II plus a whole lot more. If you are thinking about it, you might need to have him work through some examples and challengers in the early chapters of the first text... After that, it can be self-taught, but a tutor should be at the ready. Most kids need some support, because they aren't used to fighting through challenging math problems.

For classroom settings, it is essential because one teacher cannot simultaneously observe 30 individuals. That limitation is lifted for home schoolers and tutored sessions.

One last point: making a child write down all steps actually punishes them for using working memory. It's good they can solve complex problems in their heads. What is difficult - for the teacher - is understanding where they need help when they do. If you know they aren't cheating, work on this issue, instead of the mental math non-issue. You can even write down steps as they state them. It well help demonstrate the value of putting pen to paper. (BTW, yes, we make the kids use pen, not pencil - a good mathematician should not destroy his/her work, even if it hits a dead end).

This is the right idea. Don't sweat the detailed steps until he can't progress without them. It should be desirable to write down steps in order to free his brain to think. For now, it's inconvenient for the teacher, not the student. If he can do advanced problems without writing, he IS doing the steps - in his head. Don't worry - it will get harder. I wouldn't even assume algebra 2 is that point. Our boys (both) needed AoPS challengers and tougher physics problems to get them to write. They do write.

I don't think it is an apples-to-apples comparison. Some find biology very easy and physical science difficult; others the reverse. To me, it's like asking, "which is easier: music or English?"

For tantrums, this is true. For disorders, it can have exactly the opposite effect, and entrench the disorder. It's why I recommend a professional opinion.

At 7, we didn't pressure at all. Younger DS went to regular B&M school, and we waited until he started asking for more. We started home schooling at 8, and he accelerated like mad. Sometimes, it's like food - picky eaters will try things if the options are available around them. The only thing you can't do is tell/ask them to try the options. They will eat something. If it becomes severe - not just a problem for parental sensibilities, but really a problem for the child - then I would recommend visiting with a professional. "Highly sensitive" could actually be an anxiety disorder.

Very generous! Those F&Y sets are great. Combined with the MIT-OCW videos, you've got a full curriculum there without needing too much teacher oversight. We'd take you up on the offer, but we've already got the 10th edition set, so we're good to go. Now, if you have some nice intermediate mechanics, quantum mechanics, or the like with solutions, well... ;) (10yo cosmologists are tough to feed)

The college-level algebra course. Precalculus originally was a review of concepts of college algebra and trigonometry needed to succeed at higher levels of math. Now, it roughly covers essential content from college algebra not covered in algebra 2. Even then, there is content in college algebra that isn't covered in a typical precalculus course. In a junior college, the sequence is typically beginning algebra (algebra 1), intermediate algebra (algebra 2) and then college algebra. College algebra is the first course not considered remedial.

Maybe "possibly," but I wouldn't assume "nearly definitely." :) Ours did each in one year, with a side helping of advanced geometry each year. ETA: Intermediate Algebra has proven a bit meatier, especially toward the end. It is going beyond the 9-month plan, but will still be within a year. I'd say that the first book doesn't quite cover the typical algebra 2 course, but the two algebras together cover algebra 1 through college algebra.

I can't imagine it ever being considered unacceptable. It is a relatively easy course, though, and won't apply to math, engineering, or most science degrees. Those will request either specific content (e.g., biology), or a calculus-based probability course. For both of our kids, we won't do it because it's of low value to them. They have done/will do AoPS counting and probability, and then calculus-based probability and mathematical statistics. Generally speaking, though, stats is a great course to take in high school, either before or after calculus.

After calculus? Yes. Before calculus? Business math would be fine. If business math is still desired, I'd suggest mathematical economics (assuming that the stats prerequisite has been met - otherwise, take stats).

Sometimes, there isn't a lot of choice to be had. It may be a choice between miserable kid or having to scramble for later options. We've got a 10yo who already knows a bit of calculus, but is nowhere near college-ready. We can't bring ourselves to make him do 4th grade arithmetic. For the OP, there are still a lot of options available. I do second the thought of showing increasing rigor. "Cop out" courses will look exactly like that. Unfortunately, that means looking for something that is college sophomore level or better. ETA - Additional thought to ponder: at this age, a talent for math may not have turned into a love for it just yet. I have a math degree, but until my second year of college, I had no interest in pursuing math. I only did so because my degree required it. Fortunately, I connected with the right professor, in the right class, and realized that I loved the artistry of the creative genius behind the theory. If there is *any* chance of this, don't sell her short. Find a local college, or sign her up for an online remote option, and let her take something more advanced. Calculus III (multivariate / multivariable calculus) is widely applicable. If she liked stats, she can take calculus-based prob & stats. Some colleges have introductory courses for higher math, and many have discrete mathematics (check computer science departments, who occasionally host the course). There will be something both interesting and challenging.

I think it matters which test. One thing that is often surprising is how the "grade level equivalents" are calculated. On most of them, it represents the grade level at which average performance on the exact same test matches your child's (i.e., it's not an above-level test). It doesn't mean a child is operating way above level, but it does mean that they score way above level. It's a pretty good evidence that the child is gifted, and likely operates above level. On above-level tests, the student is compared to a different population. Our favorite (of those) is the Woodcock-Johnson, because it tests through increasing levels until the child misses six straight. That is compared against a representative sample across many age groups. The SAT or ACT, as mentioned above, are also good examples of this. The reason it matters is that "beyond high school" on the former means more testing is warranted and recommended. "Beyond high school" on the latter means the child is already accelerated beyond expectations. Are you comfortable sharing the test used? If it's something like the WJ, then acceleration only requires brief reviews and shoring up of weaknesses. It will move quickly. If it's one of the other tests, and your child is content with her education, then there's no need to do anything other than what you already are - just keep an eye out for boredom and be prepared to change course as appropriate. (edited for typo)

I'd shoot for discrete math or multivariate calculus. Both would be practical to other majors, and both looked at as serious content. Game theory would be another interesting option, particularly if she likes politics or economics.

We'll have to keep an eye on those. Thanks!