Just because they start algebra early doesn't mean they need to move forward at one year per grade. They can take 2 years or even 3 to do algebra and enjoy themselves with something that's an appropriate challenge level. I would be the last person to advocate early algebra for all. I absolutely agree that most aren't developmentally ready. But the kids who are ready should have the opportunity instead of re-doing arithmetic until they hit some arbitrary age marker. Isn't that part of homeschooling -- to give an education that's customized to the child?

If you have already earned an associate's degree, many universities will force you to transfer in as a junior. If you have already earned a bachelor's degree, you will be ineligible for a lot of financial aid should you decide to continue undergraduate education in a different field.

FWIW, I see no issues with a 15 year old who wants to be a nurse aiming their university career at that, and so starting to knock out courses which are often required such as psych 101, speech 101, etc. As a matter of fact, that seems like a GREAT idea. What I see as a lot bigger issue is a 12 year old limiting their future by taking 'lite' versions of courses or by achieving substandard grades because they are in a hurry to get a degree. This would apply especially to having 12 year olds go through programs which give them a bachelor's degree in general studies or something similar. This would also apply to overemphasizing vocational development at a young age. It is much more difficult to get financial for a degree once the first degree has been attained, so a child who does a young degree in (purely for hypothesis) computer information systems, and then decides that they want to be a doctor/engineer when they're 20, has a long and hard road ahead of them, mostly self-paid.

I think that in this case I would say "Gosh honey, that is confusing. But looking at the solution book it seems they meant pages 7 through 14. Can you try it again knowing that they meant that?"

Hey, there are plenty of adults who do that -- Society for Creative Anachronism? :D

I wouldn't switch to CLE with a talented child who gets it with very little teaching. The spiral and the fact that CLE doesn't get to algebra until 9th grade would probably make much less fun. Frankly I would leave him in Singapore. I'd also start using IP (intensive practice) instead of the workbook. If it's too challenging, go back to the workbook. If you need something easier for someone raised with the American way of math education Math Mammoth would be a good choice to switch to. Also if he likes comic books I would look into Beast Academy. I would probably do this after Singapore 3 though. As for "how to accelerate", just keep giving him the next level. For example, you said he just finished Singapore 2 -- start him on Singapore 3 now.

Chiming in with everyone else -- even the college English placement test I took just said 'bubble in which sentence is correct', so if you knew which one was correct by inspection you were fine.

I. Dup, what are you using right now with your kid who seems math-inclined and what indications have led you to believe he's math-inclined? That would enable more specific recommendations.

You are actually right -- but it's usually discrete math with very little theory and with applications to business. Sort of like the commonly taught course 'calculus for business and social sciences'. The customary prerequisite is college algebra (like business calculus, which also has a prerequisite of college algebra).

I (personally) started Algebra at age 9. Here is my math career. I have an early fall birthday, so I have listed my age at start of the school year. 3 - ungraded private school (technically enrolled as prek), worked through about 2nd grade curriculum. The teacher just kept giving me worksheets and I went through them very fast to earn lots of gold stars. 4 - changed states, placed in first grade. 5 - changed states again. Due to cutoffs in new state they strongly wanted to put me in kindergarden. They ended up 'compromising' on first grade. 6 - in public school second-grade half of the year, deschooling half of the year. 7 - worked through comprehensive arithmetic textbook in diagnostic-prescriptive manner. Also did hands-on equations. 8 - pre-algebra. 9 - algebra 1 and 2. 10 - geometry and precalculus. As you can see progression in early years was by no means linear due to the fact that my mother was still trying to work with the school system. ETA: If AOPS had been around then I think I would have been much better served by switching to that after the pre-algebra course (so doing their pre-algebra at 9). It would have been 100% right for my learning style and introduced me to more challenging mathematics. But it wasn't. The textbooks that were used were moderately conceptual but nowhere near as challenging.

Finite math is usually a lower-division math class, about the same level as survey of calculus/applied calculus/precalculus.

I would also ask the school's advice. I would second the other people's recommendation of conceptual physics.

I wouldn't fret about sticking to a classical education. I would make sure she keeps doing math because even if she just wants to go get an associate's in agriculture, she'll need to do math. Does she enjoy the botany you're doing at home? Can you enroll her at a cc or local 4-yr for animal science/plant science courses? I would totally let her satisfy her high school science requirements like that.

Ok, I just looked at their course catalog. Not sure which program you mean, but -- Associates in electronics and computer technology - basic algebra and applied physics. Bachelors in: Computer engineering technology -- precalc, calc 1-2, college physics 1-2 Computer information systems -- college algebra, statistics Electronics engineering technology -- precalc, calc 1-2, college physics 1-2 Network and communications management -- college algebra, statistics If he's looking at the associates, he can probably stop now. If he's looking at one of the bachelor's that requires only algebra and statistics, what I'd strongly recommend instead is trying to take the college algebra and statistics online his senior year. Then he'd be REALLY done and not trying to get back into math in college after a year off.

If it works for them and the kids are happy and thriving, great. One of the graduate students in my program just turned 18 and had a very succesful undergraduate experience. The things I'd watch out for are -- in my opinion -- someone who starts college early aiming at a degree rather than just a few courses NEEDS to be good enough to be in the top, in order for it to be advantageous. I wouldn't start them if they're just going to be average. It doesn't do any good to have an 18 year old who wants to apply to medical schools but has a 3.1 undergraduate GPA, when they could have been in the very top if they'd started a bit later.

Human Bio after taking AP Bio will probably be a little weak. Does her school offer an AP Environmental Science? Would she find that more interesting than Physics? Or possibly taking AP Chemistry, which will usually get credits at least towards general education?

This is a great idea and FWIW, Foerster's is a very solid course.

What do you mean computer type college route? If you mean computer science, math is required for computer science degrees and taking a year off math is a bad idea. They almost always require discrete math and at least applied calculus, often statistics and engineering calculus and sometimes linear algebra. It will not look at all good for college admissions to see someone who has obviously 'checked out' in math and science and yet wants to major in a STEM field. If he were majoring in art history it might be different.

Zaccaro's books (including Real World Algebra, for sure) might be interesting as well. Jacobs is a good choice for younger algebra students. It's not 'lite' but it's humorous, and you can always slow down if he's not getting it -- I believe a fair few people here have done it over two years.

Because most students who don't have at least one parent with a degree don't make it to college, much less to the level that would enable them to aim for top colleges. Colleges are trying to increase their ethnic and class diversity, and first-generation students are disproportionately minority and disproportionately poor. When a kid from an affluent family (or a poor family with a lot of social capital, especially education) does well in school, it's sort of what's expected. When a kid who has to navigate applications themselves, course selection themselves, doesn't get tutoring because parents are low-income, etc. does well in school, it's unexpected because most don't. (There are other opportunities open to students whose parents did go to college, for example, legacy admits)

I would not have been interested in joining such a club as a college student. I joined clubs which had to do with my academic interests, and in graduate school my sporting interests. It would be possible to set up such a club but you'd need a collection of interested students. Most universities are pretty open to clubs with low membership as long as you're not asking them for cash, so if all you needed was a meeting room it should be pretty easy.

It's not that it's virtually the same -- aops is considerably more extensive. But doing fractions/decimals/percents would be a step down, and he should be already very good with all of the above if he's ready for aops pre-algebra. The aops pre-algebra assumes )(iirc) competence in linear equations but the hands on equations should suffice for that.

I'd finish RS and the fred decimals and percents before starting AOPS. If you want to continue fred I would do the pre-algebra courses alongside aops instead.

If College Math will transfer I'd do that. It will probably be more applicable than college algebra. Intermediate algebra is unlikely to transfer.

Nothing wrong for a kid to be more advanced in one subject than another. Overall though I'd prefer a program with a more conceptual bent for a young accelerated learner.