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Self taught vs instructor led math


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My 15yo son has always been good at math. He worked through Singapore 1-6, Miquon, and Beast Academy by the end of 5th grade, and after that has been doing some of the AoPS books on his own: Pre A, Alg1, Geo, and is now doing the Int Alg. He is missing about 1/3 of the answers but is able to find his mistakes most of the time. But there are occasional review and challenge problems that he just has no idea how to tackle and no idea why they chose the solution in the book. I’ve always had this worry in the back of my mind that he was missing out on something by not having an instructor. 
 

All of that leads to my actual question, when is it time to switch to an instructor led math class? Thoughts and experiences welcome! 

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If you can't lead him through it yourself, then I'd say this year is time to find a tutor or friend to be able to occasionally consult and next year it's time to switch to an actual instructor. Not a video instructor or a grading service, but a human.

But that's just my personal take. A lot of people on this board are convinced that kids can learn multivariable calculus and differential equations from videos and that if they're having trouble, you should just jump in and learn it too. It's amazing if you and your kid fall into that category, but it's also okay if you don't.

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53 minutes ago, Farrar said:

If you can't lead him through it yourself, then I'd say this year is time to find a tutor or friend to be able to occasionally consult and next year it's time to switch to an actual instructor. Not a video instructor or a grading service, but a human.

I would agree with this. There is, imo, tremendous value in an actual person with whom you can ask questions and have an interactive discussion.

FWIW, I also think there is value in having an actual human who can give feedback on format, clarity, and process...even if you totally get the math. Math at this level is a language not just a set of axioms. When you solve a problem you are communicating a sequence of ideas, and understanding conventions and clarity for how to communicate that in a manner that other humans (including you-two-weeks-from-now) will understand takes practice and feedback.

 

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But there are occasional review and challenge problems that he just has no idea how to tackle and no idea why they chose the solution in the book.

I will also add that these books are HARD. Not knowing how to solve some of the review, and especially the challenge, problems is just part of the deal. From my own education and practice, and having taught it twice, I think I'm pretty comfy with the topics in AoPS IntAlg. And yet, there are some problems I will be unable to solve. I look at the answer and think "oh. I see how you did that...and yes, that works. But I would _never have thought of that on my own'. I would not take this to mean, necessarily, that he's missing something or not understanding the material. They are, on purpose, hard problems and I wouldn't expect someone to just get them all. He'd probably still benefit from a human to work with, though.

 

 

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I agree the green intermediate books are a big step up in difficulty.  (Putnam problems!)  That is material that you will start to see on the AMC 12.  You might have him take an old one every so often to see if the material is sticking.  1/3 sounds like not much, unless you are including the Challenge Problems, which I wouldn't worry to much.  (Did I mention the Putnam problems?)  He should be getting most of the Exercises and Review Problems correct.  

How well does he document his solutions?  Does he use stream of consciousness math notation or is his logic clear?

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Thank you for sharing your thoughts! We have a family friend who has a PhD in math, worked in banking all his life, homeschooled 3 children, and just retired. He was very interested in working with my son. Happy to see where this goes. 😊😊😊

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It sounds like you've gotten good advice. Your son sounds a lot like mine, who is now 16 and self-taught a lot of math.

We actually started using AoPS online classes mainly for the pacing (with the online classes he could go about twice as fast!). But I've noticed recently how lonely math feels for him sometimes. This summer, as he was working through AoPS Calculus problems to go with the class, he asked one of us to sit with him a lot of the time. We were on a road trip, so one of us would just sit next to him in the middle while he talked through each problem, and the other would drive. Usually he didn't actually need help, so much as companionship. Math can get lonely, especially when you're spending many hours on it each week and none of your peers understands.

You may also be able to find in-person opportunities around you for dealing with hard math. Ours, unfortunately, got shut down due to COVID.

I think not being able to solve some of the challenge problems in AoPS is par for the course. Can he discuss those on the boards? FWIW, the AoPS online classes do SO FEW problems compared with the book (maybe 10 per week?). It turned out that was fine for my son and that I was just giving him tons of extra work he didn't need when I was assigning him lots of problems.

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Not being able to solve some of the challenge problems is absolutely expected! That's why they're "challenge" problems. 😉 But I do think that there's no substitute for live instruction. Your family friend sounds great; so does @EmilyGF's suggestion of the AoPS boards. (They have "office hours" every weekday, where they make sure that every question from the last 24 hours gets a response from an instructor!)

To shamelessly plug: AoPS started up a "virtual academy" during the pandemic (I teach there!) and that might be worth checking out, too. If your son loves it, fantastic; if he doesn't find it helpful, you know he wasn't missing anything after all.

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It looks like you've found a good solution, but to answer the initial question, the time to move to an instructor led class (or to get a tutor) is when you can no longer be the human in the room to answer questions.  When this is will vary wildly depending on the kid, the parent, and the resource(s) you're using.

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You have received great advice from the pp. I will also add that it might be good to start looking at collaborative groups for your child. I find that for math especially, kids learn a lot by working with other students at their level. This might be through a math team or working on a long project like AOPS had at one time. Having peers really enrich the math experience. 

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This is the first year we went with a class with math. He just didn't want to go through AOPS on his own anymore...and it was being an issue with mom giving feedback and correcting his problem sets. We got through part of Intermediate Algebra (enough to get us through Algebra 2 topics). Geometry was never my favorite and was never his favorite topic when it would come up prior to this. So, it was a good time to switch over. He also wanted a lot more independence/personal ownership in his schooling through classes as well. 

Edited by calbear
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18 hours ago, Lilaclady said:

You have received great advice from the pp. I will also add that it might be good to start looking at collaborative groups for your child. I find that for math especially, kids learn a lot by working with other students at their level. This might be through a math team or working on a long project like AOPS had at one time. Having peers really enrich the math experience. 

I would love to find a way to make this happen, but I can’t find a math team or group to be a part of. A local university offers a math circle which he has participated in when scheduling would allow. We don’t really know any other teens/kids who are at his level. 🤷🏻‍♀️

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We switched to an AoPS class for Intermediate Algebra for my eldest - he is taking it right now. Like your son, he self-taught Beast Academy and the earlier AoPS books. We switched for a couple of reasons. Most importantly, he enjoys their classes enormously (he had taken their Python classes earlier). We also prefer to have an official record for at least some of his Math. He's still trying to work through all the book problems (I hope he can keep it up - the class moves fast!). We'll see what we do after he is done with this class.

You could try a class and see how he likes it. Otherwise, your retired PhD friend seems like an excellent resource.

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59 minutes ago, Mom_to3 said:

We switched to an AoPS class for Intermediate Algebra for my eldest - he is taking it right now. Like your son, he self-taught Beast Academy and the earlier AoPS books. We switched for a couple of reasons. Most importantly, he enjoys their classes enormously (he had taken their Python classes earlier). We also prefer to have an official record for at least some of his Math. He's still trying to work through all the book problems (I hope he can keep it up - the class moves fast!). We'll see what we do after he is done with this class.

You could try a class and see how he likes it. Otherwise, your retired PhD friend seems like an excellent resource.

What Intermediate Algebra class is he in, if you don't mind me asking? 

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I might be totally wrong in how we handled this, but my oldest did fine self studying AoPS with just the books and his own brain and occasional questions for my engineer DH. We didn't discover AoPS til after Alg 1 and 2 and Geometry (which I felt confident enough to facilitate and which he finished by the end of freshman year) but he did NT and C&P and Precalc and Calc on his own. He preferred this to taking a class because he could savor the math and spend hours on one proof and go at his own pace.

He got 90%+ of the regular problems correct, but the challenge problems sometimes stumped him.

He did fine in all his upper level undergrad and graduate level math courses.

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On 9/27/2021 at 1:49 PM, daijobu said:

Like @Momto6inIN we are also an "only the books" AoPS family.  My kids took a handful of online AoPS classes, mostly the test prep, or if they had a friend taking one, they'd join in.  But I think studying the textbooks is a superior option if you have it.  

My oldest also just did the books. The classes were at a terrible time for us on the East Coast so I never really looked into it. He will likely major in Math in college. 

I pushed him to have a tutor for Calculus just because it felt wrong to me to self-teach and I knew I couldn’t support him anymore. We found a recent college grad who was a Math major. She had been homeschooled herself. They met online once a week and worked through problems together. They did both the Calculus book and the Intermediate Counting and Probability books together. What we found is that he probably could have done them alone but having someone to talk about Math with once a week really made for a better deeper experience for him.In the end he took the Calc BC AP test and did well so it worked out for us. 

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