I don't think colleges typically offer precalculus, their math begins with calculus and they expect their students to have completed at least that much math in high school. I found "precalculus" a little weird as well because my high school also did not offer the class in the 1980s. Our sequence was: 9th grade: geometry 10th grade: advanced algebra and trigonometry 11th grade: functions and analytic geometry 12th grade: calculus

Laggy the Snail...I love it. Did you graph polynomials? trig curves? (r, theta) polar graphs? What else?

Yes, this is so true, both of me and the general population. I really dislike things that are labeled in terms of what they are not instead of what they are. Thank you.

If you have a few weeks to prepare a student for calculus, what is your list of key skills they should have mastered?

Grade

Math Olympiad for Elementary and Middle Schools is a good source of challenging problems at this level. I would use one of volumes 2-4. Start with elementary and then level up to middle school level. There are 5 questions per worksheets with detailed solutions and provide excellent learning at this age.

If you don't want to overbuy and your student has already studied the regular AoPS curriculum, then I think both books are skippable. Both were published first, before all the other curriculum books and are redundant with those. If he's already studied AoPS NT, CP, Algebra and Geometry, then volumes 1 and 2 will both have low ROI. I agree with NaN, the best thing to do to prepare is to study old exams, focusing on learning from the problems your student couldn't solve. Advise him to take care that he answers he marks are correct with high probability. When you look at the qualifying AIME scores, they vary a lot now, from mid 80s to to 120, so it's hard to strategize. But if you want to aim for a score of at least 110, that will mean 17 correct and 8 blank for a score of 114. Scoring 14 correct and 3 incorrect brings you score down to 96. He should check and double check for silly mistakes before attempting more difficult problems that take away more testing time.

I think your best bet is to encourage them to work at a hedge fund. 🤑

Agreed! I have heard elsewhere AoPS described as being for future mathematicians only, but I don't agree at all. I think even future law students can benefit from a solid understanding of logic. But then, I think all students should be taught math from a problem solving perspective, rather than memorizing algorithms.

Yep. I have students who either bombed elementary math or are just busy or in a hurry, and we skip the AoPS challenge problems, or made them optional.

You know when I was in high school in the 80s, no one really talked about our passions or what we liked or disliked. Math was hard, but we took pride in its difficulty and in what we accomplished by mastering it. Nobody liked to study, but we all wanted to get an A. (An A on an exam was accompanied by a smiley face at the top of our papers. It is no understatement that I lived for those smiley faces and was crushed if I didn't get one.) Some classes were really fun, and mostly it was enjoyable. Come to think of it, she prioritized debate team over math events, but she was still way better than the rest of us at math.

Older dd is planning to apply to med school, with a human biology major she really enjoys, and she tacked on a CS minor because it was easy at Stanford. She never AIME qualified or anything, but she was solid, and she did nearly all AoPS from middle school on. Younger dd has been AIME qualified 5 times since 8th grade. But she's basically meh about math and everything except her yorkie/maltese that follows her everywhere. She's is passionate about micro-plastics...and any plastics. Right now she's looking at a CS major when she enrolls at Stanford. I think about a kid at my high school, the smartest girl I knew, really outstanding in our math class, routinely the #1 student on the AHSME in my small state. She ended up at Harvard majoring in Russian, continuing at Oxford as Marshall Scholar. Now she's a journalist. I don't know why I'm sharing this, but it's interesting where high achieving math students end up.

Tru dat. I've actually never seen Foersters, so guilty as charged.

I think @Not_a_Number brings up a good point about pigeonholing very young students into "passionate about math" and "not passionate about math." I especially hate to see girls directed away from challenging math curricula because they are more globally gifted. My daughters didn't display much passion for math. As far as I could tell, they didn't give it much thought outside of the 30 minutes or so a day we spent on Singapore, and then later AoPS. But then, they weren't very demonstrative about anything except Sound of Music and their Polly Pockets. Just FYI, my kids definitely were not spending anywhere near an hour a day on math, and they were doing AoPS all the way through. But I was doing a lot of active teaching and explaining. If they couldn't figure out a problem within the first 10 minutes or so, we'd go over it together.

On this topic, I'm listening to a podcast episode by Malcolm Gladwell about the history USNWR college rankings. Disturbingly, it seems the magazine will punish a school if it doesn't play ball with the magazine.

Welcome to the WTM boards! I just want to let the OP know that if she is using her real name as her avatar, she may want to change it to protect her privacy.

Let me join the others in thanking you for your service. Health care workers are under a lot of pressure and are not respected by a vocal minority of idiots. I'm here to say many of us are exceedingly grateful for your work. When I feel overwhelmed I find it helpful to set small goals. Like your first goal should be to just set up a common app account, choose a user name and password and just get logged in. Check that box off your to do list and then binge watch some TV. Small goals, make a bit of progress every few days. Check in with us and we'll make sure you are on track. Another option: Your dd may benefit from a gap year. Just throwing that out. Finally, in general it's easier to start as an engineering student and then switch to liberal arts than vice versa. I would say if engineering is still on the table, she may want to start off as a freshman in that department.

Agreed!

Another thing to watch out for is that the overall rank of a university glosses over the ranks of the individual departments. This example is an overgeneralization, but a #1 ranked school for performing arts is probably not where you want to earn your EE degree. Or vice versa. (Or maybe it is, if it excels in both areas, in that case, you probably don't want to send your future chemistry major there.) And with that caveat, I think value sort of dissipates as you go down the rankings but what I would say that a school ranked #27 is not really much different from a school ranked #35, for example. But that #27 school is probably much better and probably much more competitive than a school ranked #227. Or maybe not depending on the department. Sigh. It's so hard.

Thanks for posting @gstharr, I forgot about that book. From a distance I hear that magical things happen at Berkeley Math Circle, but we live too far away. And I'm not sure it's an adequate replacement for a math curriculum, though for many kids it could be.

Math Circles vary a lot in tone and quality. I'm in the Bay Area, and I've not seen the Berkeley math circle, but have heard good things about that one and the one in San Jose. We weren't as impressed by the one at Stanford. You'll want to ask locally, as WTM is a national list. For info of interest to local homeschoolers of gifted kids, consider joining this group: http://www.sfbaghs.org/ The BAGHS parents are very supportive, but it takes a while to go through the vetting process and get admitted to the group. For a more immediate answer, I believe there are several moms on this FB group who have direct knowledge of Berkeley math circles: https://www.facebook.com/groups/emergehsc BA is more of a solid curriculum, while math circles are generally a supplement. I think Berkeley is more comprehensive however, but I do not have direct knowledge. Good luck.

I'll say I've been burned by cheap binders, or maybe just the ones I order from Amazon instead of inspecting in a store. I have at least one where the rings don't line up properly when closed...super annoying. Inspect in person before buying!

I don't have a solid understanding of "whole to parts" but the bolded description does remind me of teaching with math contests. I had a student on my MathCounts team who hated math curricula of any kind. He learned by studying the problems and my explaining how to solve them. Three years of MathCounts with increasingly harder problems can approximately equate to pre-algebra, algebra, geometry and probability, or at least is good enough.

I 😍 office supplies! Echoing others that it depends on the course. Sometimes you start with one organizational principle only to realize one week in that another might work better, maybe depending on the number of photocopied handouts (do teachers do this anymore?). It isn't an all or nothing, either. I've used paper folders + a spiral. Or you can have a big binder on the shelf for storage and keep a smaller lightweight flexible plastic binder like this one: https://www.amazon.com/Bazic-Glitter-3-ring-Binder-Pocket/dp/B00NAIVE6S/ to pack in a backpack. Some spirals include a pocket or two where you can slip in a few sheets of paper.

Here's a course-naming hack that a homeschooling parent shared with me. Put some key words from what your student learned in that along with the words "course description." With any luck you'll get links to high school courses that are similar to what you taught your student and from which you can glean an appropriate course title.