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Alternatives to AoPS for Discrete Math and Calculus.

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DS is in grade 7 and currently homeschooling and will continue to do so until at least the end of grade 8 (maybe 9, 10 too). He has taken several AoPS courses, which have worked fine, and it makes sense to continue with the following 3 AoPS courses between now and end of grade 8 (mid 2020):
Intermediate Counting & Probability
https://artofproblemsolving.com/school/course/intermediate-counting
Intermediate Number Theory
https://artofproblemsolving.com/school/course/intermediate-numbertheory
Calculus
https://artofproblemsolving.com/school/course/calculus

But I wonder what alternatives we should be considering. I'm guessing there's not much for the Discrete Math (but still interested in options) but looking online there are are lot of options for Calculus, though maybe not many worth considering.

One seemingly good option I saw was MIT edX Calculus 1A, 1B, 1C
https://www.edx.org/course/calculus-1a-differentiation
https://www.edx.org/course/calculus-1b-integration
https://www.edx.org/course/calculus-1c-coordinate-systems-infinite-mitx-18-01-3x-0
https://www.edx.org/course/calculus-1c-coordinate-systems-infinite-series

 

Anyone familiar with this or other options?

Both parents know the math, so we can talk to DS about the content, but we're looking for a structured course that doesn't need us to prepare. We sometime need to keep him on task, so it helps if the course is engaging and structured. Giving him just a "too mature" textbook alone would not work well at this stage.

 

Edited by HomeForNow

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Elements of Mathematics offers a variety of math courses. I can't remember who posted on them, but I know that I've read a really good review or 2 of them here on WTM forums, but I've never used them.

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18 hours ago, Gil said:

Elements of Mathematics offers a variety of math courses. I can't remember who posted on them, but I know that I've read a really good review or 2 of them here on WTM forums, but I've never used them.

That looks interesting (I think I've come across it before) but it looks like DS is past the end of their sequence.

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Well, don't go by just the course names. Look at the descriptions for the individual courses too--there are like 18 of them. I don't think that you'll find a ton of options for discrete math or calculus taught in an engaging enough manner to hold a young childs interests. 

They don't teach a course called "calculus" or "Discrete math" but the only other online provider for challenging math enrichment that I know of, besides AoPS and EMF is Russian School of Math (RSM). They have an online program for grades 4-10, so you might check that out. But I don't expect that you'll have a lot of options if you want a quality course that is administered online, graded and engaging for your 7th grade son. It seems like EMF, AoPS or RSM would be your options.

The Prealgebra Pack (courses 1-9) sold by EMF covers more than enough niche topics that it might be worth revisiting, even for a child who has taken precalculus. It's $360 bucks but, you get a lot of proof writing, discrete math/abstract algebra taught in an engaging and interactive fashion, and it's all graded for you.

The way I look at it: in math you can always learn something new, gain insight into something you already knew, deepen your understanding, discover a new connection, refine your skills through practice, grow as a problem solver or just widen your circle of like minded people. Frankly, if I had the money, I wouldn't hesitate to enroll them and have them complete the online programs offered via EMF, RSM or AoPS. 

To date I have taught my kids math the way that I know how, using the means available to me at the time, but that doesn't mean that there isn't a better way out there. As far as online programs go,  Russian School of Math, Elements of Mathematics and Art of Problem Solving each offer an online class that, based on their reputations/samples are excellent programs that are NOT standard, run of the mill math programs so I don't expect that my kids would be bored or underwhelmed by the courses.

 

Currently, your son is on track to complete single variable calculus by ~13 years old--what do you plan for him to do next?

 

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Thanks for listing those three. I probably ought to have known those some time ago, to know the options, but AoPS has been fine.

DS would complete single variable calculus by end of grade 8. (That includes a 1 year "gap" after precalc to do other math, so we're being careful with pacing.) Some local high schools go a bit past that. A non-local high school goes a lot past that. And there's the local Uni. Both of us parents know a lot more math, but we are not natural homeschoolers, and have been driven to it by the terrible condition of most schools here.

For the near term, I think DS should do those two AoPS Discrete Math courses, as he is used to the system. But I am unsure what to do for the calculus, but that won't happen until next August or September.

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What. Is your thinking in terms of not taking AoPS cal? I'm not sure I understand why you want a different option if AoPS is a program he likes.

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^ Good question. I'm sure AoPS Calc would be fine, and that may end up what we do, but I want to explore the options. (At this point I'd say that DS will do the AoPS Interm C&P and NT first.) Unlike for Discrete Math, there are a huge amount of Calculus courses. If we ask what is worth considering given that we are happy with AoPS, then that would narrow things to a very short list, perhaps including the MIT edX course.

Also, the AoPS courses would run out soon anyway, so we need to know the alternatives.

Also there's a question of course style - whether it's heavy on difficult problem solving, or more on applications, or more on abstraction, theorems and proofs. I'm not sure what we want, but those are considerations.

 

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FYI: MIT edX univariate calc is pretty easy.  Only the kids with the worst math background at MIT would take that course, everyone else places out of it either by AP or taking the Advanced Standing Exam. My son worked his way through Multivariate calc through MIT edX and thought it was a decent course, not super hard, but not baby. Both of these classes are core requirements for all students at MIT so have to be at a level that a non-mathy maker-type kids could still do them. Once you get past these two, the MIT edX math classes get progressively harder as only the math kids will work their way up. 

Edited by lewelma
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20 hours ago, HomeForNow said:

^ Good question. I'm sure AoPS Calc would be fine, and that may end up what we do, but I want to explore the options. (At this point I'd say that DS will do the AoPS Interm C&P and NT first.) Unlike for Discrete Math, there are a huge amount of Calculus courses. If we ask what is worth considering given that we are happy with AoPS, then that would narrow things to a very short list, perhaps including the MIT edX course.

Also, the AoPS courses would run out soon anyway, so we need to know the alternatives.

Also there's a question of course style - whether it's heavy on difficult problem solving, or more on applications, or more on abstraction, theorems and proofs. I'm not sure what we want, but those are considerations.

 

I agree with Ruth. I am not sure what cal course you are going to find that is superior to AoPS.  Not sure the concern about running out of AoPS courses at that pt and having to switch. There are options then, too. He could DE at a local university or take classes through somewhere like https://onlinehighschool.stanford.edu/math

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On 1/2/2019 at 3:42 PM, lewelma said:

FYI: MIT edX univariate calc is pretty easy.  Only the kids with the worst math background at MIT would take that course, everyone else places out of it either by AP or taking the Advanced Standing Exam. My son worked his way through Multivariate calc through MIT edX and thought it was a decent course, not super hard, but not baby. Both of these classes are core requirements for all students at MIT so have to be at a level that a non-mathy maker-type kids could still do them. Once you get past these two, the MIT edX math classes get progressively harder as only the math kids will work their way up. 

Thanks. That's very helpful to hear direct experience about the level.

Edited by HomeForNow

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On 1/2/2019 at 3:42 PM, lewelma said:

FYI: MIT edX univariate calc is pretty easy.  Only the kids with the worst math background at MIT would take that course, everyone else places out of it either by AP or taking the Advanced Standing Exam. My son worked his way through Multivariate calc through MIT edX and thought it was a decent course, not super hard, but not baby. Both of these classes are core requirements for all students at MIT so have to be at a level that a non-mathy maker-type kids could still do them. Once you get past these two, the MIT edX math classes get progressively harder as only the math kids will work their way up. 

So we will stay with AoPS for their intermediate discrete math and their calculus. Thanks for everyone's comments.

I was looking at the MIT website and found this (MIT Online Math Classes)
https://math.mit.edu/academics/online/index.php
confirming that the MIT edX series of 3 calculus courses is indeed equivalent to their course 18.01 which
https://math.mit.edu/academics/undergrad/first/calculus.php
is their most "basic" version of calculus. That said, I'm sure MIT's least prepared students are still way ahead of the overwhelming majority of the students at our local state U, so I'm sure MIT's "basic" calculus is still pretty solid compared to what's taught at a lot of colleges. (Try teaching how to differentiate f(x)g(x) and f(g(x)) to those students who can't tell the difference.)

 

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Another board member (Arcadia?) has had a student use Stanford's Pre-collegiate Studies, which offers math and physics.  They are I think cheaper than Stanford Online High School.  ($1500 a course vs over 4,000).  

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14 hours ago, SanDiegoMom in VA said:

Another board member (Arcadia?) has had a student use Stanford's Pre-collegiate Studies, which offers math and physics.  They are I think cheaper than Stanford Online High School.  ($1500 a course vs over 4,000).  

 

DS14 did the multivariable differential calculus course in fall. He applied to do the heat and light course in spring semester.

https://ulo.stanford.edu/mathematics

He also takes AoPS WOOT classes for fun as a hobby. 

https://artofproblemsolving.com/school/woot

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Just to chime in about the EMF. Most of the topics in the first 9 classes are unique for that age level. Even though they are labeled "prealgebra" it's more like pre- abstract algebra. My dd far prefers it to the AoPS she's done. We do math in two streams and there hasn't been much crossover. She did a try out session with Jon Roscoe (mentioned in a post above) and really liked him, but the schedules just weren't working out at the point in our lives.

Edited by MamaSprout

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Have you checked out MEP's A level materials or high school materials?  I thought I saw at least a short unit on discrete math(s) there.  I have only used MEP 1-6, so I don't know much about it, but it would be free.

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This was posted when I was on break and traveling, so I missed it. I am not sure if you're looking for formal classes, or for books, but there are so many interesting and accessible discrete math books that would probably work fine for self-study. Many of them will have a significant overlap with AOPS, but for self-study this can be very easily dealt with by skimming the chapter and only working the interesting problems. 

I'm especially going to give a shout out to the Aimath free open textbooks (https://aimath.org/textbooks/approved-textbooks/) which include three discrete math textbooks, three combinatorics textbooks, three number theory textbooks (one of which includes some abstract algebra), and three intro to proofs texts. The "math in society" liberal arts text, while significantly easier, has some very interesting chapters on mathematics applied to social sciences. Abstract algebra isn't usually considered part of discrete math, but it would definitely be interesting for someone interested in discrete math, and there are three texts on that as well. 

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Thanks for the suggestions. (We will stick with AoPS for Discrete Math and Calculus, but will look into all these other resources.)

 

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Updating: So now DS (rising 8th grader) has finished AoPS Intermediate Counting & Probability, and is now doing AoPS Intermediate Number Theory. He should start a calculus course soon.

He could obviously take
AoPS Calculus Sep 4 - Mar 11
https://artofproblemsolving.com/school/course/calculus

But an alternative is MIT edX Calculus Aug 7 - early May in 3 parts
https://www.edx.org/course/calculus-1a-differentiation
https://www.edx.org/course/calculus-1b-integration
https://www.edx.org/course/calculus-1c-coordinate-systems-infinite-series

I was thinking to stay with AoPS, but the edX course starts in less than two weeks, so I thought to examine the choice once more, as we have to decide now. Apparently the edX course is lighter, but maybe that would take some pressure off so he could spend more time on other things.

We want DS to take the AP exam. Our home schooling efforts have been a bit of a fiasco, but if DS can start getting some STEM APs he'll have something to show for it. So while the AoPS one might be the "best" course to take (other than a hard-core theoretical Analysis course at a top uni, which is not an option, and which he couldn't handle), another course might work for learning the material and getting through the AP exam.

He doesn't necessarily need the harder calculus problem solving yet (Putnam is not til 2024), though maybe a bit more theory is good.

 

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