AoPS Calculus

[Roadrunner]

A friend is pulling a junior out of school. She is bright but has only so far done school math, which is easy. They want to take Calculus next. Would you recommend AOPS calculus  to a student who has never done AoPS before?  

Edited December 14, 2018 by Roadrunner

[regentrude]

No, I would not. Of all the AoPS texts, this is the most theoretical. It is unlikely that her high school math prepared her for a this kind of rigorous approach.

I'd get a more mainstream text like Stewart.

Edited December 14, 2018 by regentrude

[lewelma]

Even my ds who is very theoretical, did calculus with AoPS text AND redid calculus with an applied text, Anton. 

[Roadrunner]

9 hours ago, lewelma said:

Even my ds who is very theoretical, did calculus with AoPS text AND redid calculus with an applied text, Anton. 

 

Redid or supplemented? 

[lewelma]

Ah, good question.  DS has self-studied math since he was 8, so I'm not totally sure.  His initial plan was to take multivariate calculus at the local university, and they used Anton for univariate.  He wanted to use AoPS to learn Calc, because he loves AoPS. But I was concerned that he would not have a clear understanding of the engineering applications and problems, so I told him to do Anton also.  I got him the Anton problem sets for Univariate from the local uni, and he did them, or as many as he deemed required.  As I remember, he spent 4 months with AoPS calc, and then 2 months with Anton after AoPS.  After that, he did not touch calculus for 3 years, and walked in and took the final exam at MIT without studying, and passed it.  So apparently, this approach made calculus stick.  He did say, however, that he didn't remember much of the calculus during the exam, and instead derived it on the spot, which did make the exam a bit time pressured.  🙂  The ability to derive calculus after a 3 year gap would definitely be due to the AoPS textbook, and how it teaches calculus. 

Edited December 18, 2018 by lewelma

[8filltheheart]

On 12/18/2018 at 11:36 AM, Roadrunner said:

Redid or supplemented? 

I don't know if your question here is for your own student or for the student you posted about, but I don't know that kids growing up with AoPS need to either redo or supplement AoPS cal other than format for the AP exam. I know that our ds did not use anything other than AoPS and has never had an issue with other math courses or applying it to physics.

[Roadrunner]

4 hours ago, 8FillTheHeart said:

I don't know if your question here is for your own student or for the student you posted about, but I don't know that kids growing up with AoPS need to either redo or supplement AoPS cal other than format for the AP exam. I know that our ds did not use anything other than AoPS and has never had an issue with other math courses or applying it to physics.

 

The word “redid” shook me a little. 😉

[regentrude]

29 minutes ago, Roadrunner said:

The word “redid” shook me a little. 😉

FWIW, both my kids redid calculus 1 at college, after using AoPS for high school. 

[lewelma]

Sorry to make you worry.  I wanted him to do some Anton so that the transition to the university multivariate class would be smooth (it was part 2 of a 2 semester course using the same book). I think that ds did it because he was really fascinated by all the applications and was excited to dig even deeper into Calc. 🙂 

I often like to write about alternative approaches so that people don't think there is only one right way. My son took 3 years to do AoPS Intro Algebra, and he did calculus with 2 textbooks sequentially.  I think that this is worth noting because he is a high end math student, and sometimes people think that best is fastest or most efficient or uses the most rigorous texts. Homeschooling is great because you can take the time you need, and do it the way that is best for *your* student. 

Edited December 21, 2018 by lewelma

[Roadrunner]

 

17 minutes ago, lewelma said:

Sorry to make you worry.  I wanted him to do some Anton so that the transition to the university multivariate class would be smooth (it was part 2 of a 2 semester course using the same book). I think that ds did it because he was really fascinated by all the applications and was excited to dig even deeper into Calc. 🙂 

I often like to write about alternative approaches so that people don't think there is only one right way. My son took 3 years to do AoPS Intro Algebra, and he did calculus with 2 textbooks sequentially.  I think that this is worth noting because he is a high end math student, and sometimes people think that best is fastest or most efficient or uses the most rigorous texts. Homeschooling is great because you can take the time you need, and do it the way that is best for *your* student. 

 

Well as a non math non science parent with a math kid, I am always at a loss at those discussions. I try to piece together information on what is best to do from various comments and while I started out asking about a friend, I am now thinking about my own kid. He is young and has only used AoPS and thrived with it. And as we approach the end of, I wonder about comments like this. Should we also be repeating it? Why? Why do others do it? Are there certain texts worth repeating with (for a deeper dive) or let him move forward and then once he is in college he can do some more repetition there? For a parent with a liberal arts background it all can seem so confusing. And it isn’t all that obvious what a student needs either.  So basically that’s the place my questions are coming from.  It’s my attempt to understand why people make choices they do with math/science.

[lewelma]

My decision was based out of my own insecurities.  DS was young, and going to be walking into a second class in a sequence of 2 as his first university class ever, and I had just been reading on this board that university grades from highschool follow you to university. So I did it out of fear, I guess. However, because my ds is way ahead of me in math, I can only give him my best guess and then he directs his learning.  He was not so keen on Anton after having completed AoPS calc, but I just showed him some of the cool applications by flipping through the book one afternoon, and that was all it took to hook him.  As I said above, I don't know how much he did, but I know he enjoyed it because he did it -my mathy kid doesn't study stuff that he finds too easy or of no value.  He just won't do it. So that is how we came to AoPS first and Anton second.  If he had said 'No' to Anton, I would not have required it. In many ways, he knows what is best for him, and I generally try to play devils advocate and then support his final decision.

[8filltheheart]

Well, I don't know much about upper level math and science, but I do know my kids. I know when they really understand something and when they are just getting things right bc they are going through the motions. I also trust their self-evaluation for what they think they need. 

My ds went from AoPS to DE at VCU. I know he would have been bored to tears repeating cal, but his options for courses weren't heavy theory based ones like at some other schools. Your next step may be one step forward for now and then back again for review depending on the school. His challenge came from physics, not math.

Fwiw, if he is taking his classes through AoPS, asking the instructor what they think is the next right step might be an option. 

[Gil]

On ‎12‎/‎14‎/‎2018 at 11:36 AM, Roadrunner said:

A friend is pulling a junior out of school. She is bright but has only so far done school math, which is easy. They want to take Calculus next. Would you recommend AOPS calculus  to a student who has never done AoPS before?  

Unless I knew something additional about this "bright" students ambitions and abilities, sure, why not?

A student who has "never done AoPS before" is simply some student who, to the best of our knowledge, hasn't used AoPS books or their website. It doesn't mean they aren't a good problem solver, that they aren't capable of finding creative or efficient approaches to problem solving in physics/programming/mathematics or even just random problems they come across in their everyday life in cooking/arts/music/etc.

It doesn't tell us that they are or aren't mathematically curious or mathematically ambitious. It doesn't tell us if they are the sort to read, re-read and deeply read something until they understand it* (Which is where a lot of students struggle, period.)  It doesn't tell us if they enjoy math puzzles or technicalities. It doesn't tell us if they had a teacher at any point after leaving elementary school who gave them engaging problems or taught things from an axiomatic point of view or anything else or got them stoked on math or anything else. It doesn't tell us if they used to do math contests in school or if they've always wanted to do one but couldn't for any number of reasons. It doesn't tell us what role peer pressure or social "rules" have played in their academic development up to this point.

It doesn't tell us if they are the kind of person to look up information when they're confused or seek out an extra explanation or if they're the kind to play with ideas or examine their thoughts.

So, if I knew a family who were looking to homeschool their "bright" High-schooler and they told me that they needed a calculus course, I'd tell them that they can get an older edition of a "standard" all-in-one Calculus text such as Stewart or Thomas on eBay or Amazon for <$10.00ppd, but there is also a series out there called Art of Problem Solving, that is about $60, but supposed to be more challenging than "standard" texts, it's out there and it exists.

Of course AoPS Calculus is only Single Variable and it's the last book in a series marketed as one of the "deeper" and "more rigorous" math programs available in the US for home purchase, give them the Name/Link so that they can take a look if they're interested. 

They can check out the website for themselves, read through the samples of the books and if they like the samples, they can take a placement test for and/or order which ever book they like whether it's Calculus, Precalculus or some other volume. Of course it may turn out that she doesn't WANT to do AoPS, can't appreciate the approach, doesn't understand the text, or anything else that prevents her from using the books beneficially, but at least she and her family will have been given the option of considering the option of AoPS Calculus for themselves.

 

[Guest]

I think that someone who has had school-type math texts would find the AoPS approach a pretty jarring change. Not an impossible one, necessarily (kids go from PS math to MIT and similar theoretical math majors frequently, after all), but AoPS is very different from the typical math book that expects a teacher to do the actual instruction.