I think that given what the instructor has said, the best course would be to have one year of Intro to Calculus and one year of Calculus BC.

This really varies. I have seen a fair number of students come in and take my precalculus or calculus class who were very upset at having to take it, when they claimed they had had calculus in high school. They had never really done limits, and strongly resented having to do work with the limit definition of the derivative (which is what explains why it works). They had no idea what the derivative was or how to apply any of the derivatives they loved taking. They knew that there was this magical thing called "the derivative" and how to get it (on polynomials), but not what to do with it once they had it. They had no recollection of anything involving trigonometric functions, products/quotients/compositions of functions, or indeed anything more difficult than a polynomial. In short, there were tremendous gaps in their knowledge, made worse by their refusal to learn anything that hadn't been in their high school (non-AP) calculus course, because "I already took this course". Even at the university level, there are different levels of calculus, and someone who took applied calculus would not be prepared for engineering calculus. OP: I would ask the teacher of the online course how it compares to the BC calc syllabus. A lot of non-AP courses don't even cover the full AB syllabus, and it is not at all uncommon at high schools to do either intro to calculus and then calc BC, or calc AB and then calc BC. I would strongly consider the teacher's advice.

Nifty! Thanks!

Intro to Algebra is the text for *their* Algebra 1 and 2 courses.

I would not change her from Saxon at this point. She seems to be understanding it and applying it beyond the scope of the text. If your DD would like, you could consider supplementing with the original AOPS texts -- The Art of Problem Solving, Volume 1: the Basics is the first one, and the second is The Art of Problem Solving, Volume 2: and Beyond. These texts were intended to supplement problem-solving and additional topics for someone who was talented in math, enjoys math, could be doing math competitions, but was already doing well with a standard curriculum, which sounds exactly like your DD. She could also do this at a very slow pace if she liked, so it would not need to stop her from doing enviro science -- and it would be easy to do a chapter or two, then shelve it for a while, then do more when the pace slacked up. If you think this might also be an option, I would get the sample chapters (most of chapters 5 and 15 are excerpted) and have her skim them to see if she thinks she would enjoy it.

No, Intermediate Algebra is definitely intended to follow Introduction to Algebra. Intermediate Algebra is their Algebra 3, while the Introduction to Algebra text contains Algebra 1 and 2. There is overlap of topics, but that doesn't mean you should skip the book.

I would agree that for most students, skipping grades in homeschool just to get done more quickly isn't a good idea. Honestly, if a student is not prepared to excel -- not just to succeed, but to excel -- in their new grade, I don't think it should be done. A possible exception could be a 15 year old who has a vocational goal and is chomping at the bit to get started. But I would NOT argue the same about doing algebra early, or reading excellent books early, as long as the child is enthused about doing so. I *would* agree that it applies if the student is doing algebra early with a non-challenging program, planning solely on racing through the material and getting to a weak calculus at 11. But if the student is doing well in good and challenging courses, such as AOPS or some of the other good texts, and still flying through them, let them fly! For many students, moving slowly through non-challenging material, rather than teaching thoughtfulness and deep understanding, teaches them that they don't have to study to learn, and if they do have to study, it must be because they're stupid/not good at that subject. An ex was a perfect example of this -- he was actually quite talented at mathematics, but because it was the only subject he had ever had to work at before A levels, he believed he was stupid at it. tl;dr summary -- Skipping grades, honestly, is more for unusual circumstances, but accelerating *subjects* to an appropriate level of challenge is usually a good idea.

Children who read early because they were pushed even out when the others get instruction. Children who read early because they are in the gifted range are unlikely to even out unless they give up on school.

It would depend on the interest and ability level of the student, as well as what math they'd already had. My first step, however, would probably be the AOPS C+P and NT texts, which I would consider, taken together, as a one-year discrete math course. Discrete math is nowhere near as standardized as algebra, geometry, and calculus courses, so there is a wide variety of material that could legitimately be included.

Keep plodding. It's better that he finish Algebra 1 with understanding than hurry through and struggle in more advanced courses due to lack of foundation.

Most of the students in El Ed hope to become a kindergarten or first grade teacher. Seriously. It's not just student teaching -- this is the placement that they all want, so her chances of finding a job there are smaller. She canNOT guarantee that she will teach the grades she wants. While it's true that they'll teach what she needs in college, her basic arithmetic/algebraic skills need to be there first. If she doesn't pass the placement test she'll end up having to take several semesters worth at college developmental math. Even if she passes it, if she doesn't have the basic skills needed she may need to take it more than once. You can't teach everything in one semester. Her test scores sound good, except for the weird geometry score. I would check with a placement test and see how much algebra she remembers, though. Again, I would make sure to do at least math review in 12th grade as well, to try to avoid non-credit developmental classes in college.

What OhElizabeth said. If she wants to go for El Ed, she MUST work on shoring up her pre-algebra and algebra 1 skills. Not just understanding how to do problems, but WHY and HOW to do problems, because she is going to NEED to explain this to children in multiple ways and not just stick to 'because that's what the back of the book says.' She will not only need to pass the class, but understand it well enough to pass the state certification exam and not get flunked on student teaching. I know she will hate it, but she should also take math her senior year. It does not have to be 'hard' but something that will require continuing use of algebra 1 skills. I would suggest re-doing algebra 1 for 11th grade and a non-rigorous algebra 2 for 12th grade. Otherwise, she runs a very serious risk of forgetting her algebra 1/pre-algebra and placing into non-credit, remedial classes. I haven't taught this class (I usually teach algebra and calculus classes) but I will ask my officemate who has taught it for some more advice for your dd in a day or two. :)

The Compass test is a placement test used by universities, including community colleges. Basically, what it's designed to do is to see how much math a student *remembers* from what they have had in high school (many have had precalculus or even calculus and still place into beginning algebra because they have retained nothing). It is often taken once the student has been admitted, and will determine what level of math class they need to take. For example, at the local community college, a student may place into arithmetic, pre-algebra, algebra 1, algebra 2, college algebra, trigonometry, or calculus. Here is the brochure -- http://www.act.org/compass/pdf/COMPASSOverview.pdf -- and on page 7, there are details about math. Here are some sample test questions -- http://www.act.org/compass/sample/ -- so that you can see what it's like.

If she's looking at college, I would still strongly, strongly recommend doing more algebra. Most colleges require at least a general education math class, and if she can't place into it she will have to take remedial algebra in college, when she hasn't done algebra in 4 years. This will make the remedial math class very difficult for her. Also, planning her high school focused on one specific college just seems like a bad idea. My personal recommendation would be to work on redoing algebra 1 this year -- update your TT as others suggested -- she may find that it goes much better with more maturity. This will also prepare her for the SAT, as she will need algebra for that.

The "limiting" part comes in if they didn't do as well in their first degree. I see nothing wrong with acceleration if the child is really excelling, but if they graduate at 16 with a 2.9 gpa (please note, this is purely hypothetical) I cannot see this as being beneficial. I can see it as being a real issue if they later want to go to graduate school/med school/any other place where the GPA is seriously looked at. Furthermore, many kinds of aid are only available to those doing a first degree. With respect to their plan, the part that I object to is their billing it as something that even very average kids can do. I do not, in any way, think that a very average kid is ready for full-time college that young, even if their parent accompanies them. There are some courses they could take, sure. For example, our 'math for liberal arts' class would be easily accessible to a reasonably prepared middle-school student who had already had a solid pre-algebra course. But these are the non-majors courses -- the courses for students to take to get their general education requirements accomplished. Not the courses for math majors.

I agree. If she has a solid foundation in alg 2/geom, she could spend the summer doing college algebra. If she does not have a solid foundation in alg 2/geom, she should shore that up first, but that will not leave time for her to do college algebra. As others have already said, college algebra is NOT just algebra 2!

I would be a lot more inclined to go with some of the more recently written books that are intended for high school age students who are not reading at a high school level. AGS and Power Basics are two of the best-known, and I know that they're available for purchase for homeschoolers. I understand your love of old books -- I really do. I love and collect vintage textbooks of all kinds. But I just don't think that, when this is going to be a student's only exposure to the topic, using textbooks with un-updated information is going to be the best option.

Hmm doesn't she still have the college algebra textbook? I would redo work from that.

Exactly. I could write an exam where 92% is an A where 30% of the class would get an A, or an exam where 70% is an A where probably 5% of the class would get an A.

Gosh, I thought matrix algebra was a lot more boring than calc-based prob/stats. The prob/stats class was one of my favorite ever.

I think mandating study time until he's back above a 3.5 sounds like a good idea. If he were maintaining a 4.0 and studying less than that I wouldn't be concerned. But accepting B's and studying less is a bad habit to get into.

I don't know about teamwork. I really do think though that being involved in some physical activity is extremely good. Does she have something else that she would like to replace it with? Otherwise, you could suggest to her that if she doesn't like basketball, she can come up with a feasible alternative and you'll be happy to consider it. ETA: Personally I loathe team sports and being forced to do them would have just been torture. But I really love martial arts, I'm so glad I found it as an adult and I wish I'd found it sooner. This may color my thinking.

But why does preparing oneself for the worst-case scenario *have* to involve utterly forsaking a calling? Why can it not involve searching for ways to pursue what one is called to do and still be able to put food on the table? Why cannot we have a mix of pragmatism and romanticism instead of pure romanticism?

I think you would have gotten a lot fewer vigorous responses if you hadn't bolded the part about teaching piano and suggested that a world renowned concert pianist would have been a more appropriate goal. I absolutely do agree that focusing on a student's natural talent and inclination is imperative, but I still don't see why aiming for skill at giving piano lessons as well as just practicing the piano filled you with such horror. As for "why dissuade a child from their field of study", I don't think people were suggesting *stopping* them from studying a field they loved as much as encouraging them to *also* study something practical. For example, a relative of mine studied a musical instrument (which she loved) and accounting as double majors. I have a friend who loves photography who took training as an auto mechanic, and does the photography on the nights, weekends, and days off. I have another friend who is substitute teaching because that is flexible enough for her to pursue her musical career. I have another friend who's obsessive about martial arts who does part-time work as an occupational therapy assistant. All of these people put their energy and their best time into their passions, but *also* found something else that they could handle doing which was employable.

I wouldn't go back to Saxon -- it already didn't work once, why try again? If she prefers SM, why not look into their Discovering Math series?