Middle schooler wants to be a mathematician

[mckittre]

This isn't a simple question, but more a general request for advice -- my kid is 12 and I feel like I need to have my act together as he moves forward to make sure he's got a shot at doing the things he wants to do. Currently he says he wants to be a mathematician. He might easily change his mind, but I wouldn't be surprised if he means it. He really loves complicated puzzles and trying to come up with proofs, often for problems he's created entirely himself, and is happiest puzzling over the same proof for days/weeks/months at a time. And all the other things he loves (physics, computer programming), are very math-heavy as well.

His formal math education has been super scattershot -- largely consisting of me giving him things that turn out to be too easy, then skipping ahead. This year (6th grade), he's been slowly working through the AOPS calculus book with his dad, with diversions into his various puzzles and proofs. It's the first math book he'll probably get all the way through, because he does find it quite difficult. He likes working on the edge of his abilities like that, but now I'm not sure what to do with him next? He's never officially studied algebra, geometry, etc... but has always seemed to either already know what he needs or be able to fill in any gaps by quickly looking up the relevant topic. 

I figure people here are most likely to have dealt with kids like this. How should I approach the next 6 years to set him up well? (both from a learning and a college admissions perspective), while not boring him with requirements?

[lewelma]

Hi Mckittre, my older boy is also a math lover and knew by the age of 12 that he would be a mathematician. He loved proofs and puzzles.

So, question for you. When you say he has never officially studied algebra, geometry, etc, but always seems to know what he needs or can fill in any gaps, are you talking about algorithmic skills or deep problem solving skills? I ask because my son could intuit all algebraic manipulation without being taught, but it was very valuable for him to work through the good problem solving questions that you find in AoPS. Have you considered grabbing the AoPS intro algebra and Geometry books, and working through all the challengers?  And for any chapter that he is unsure of, back up, study, and do all the problems for that specific chapter, and then do the challengers. 

Edited April 8, 2021 by lewelma

[mckittre]

2 hours ago, lewelma said:

 

So, question for you. When you say he has never officially studied algebra, geometry, etc, but always seems to know what he needs or can fill in any gaps, are you talking about algorithmic skills or deep problem solving skills? 

Maybe similar to what you're describing? He always seems to know the algorithms. He's good at problem solving, but I'm sure he can get better. I think he really needs practice in writing up and explaining his proofs better, but it's hard to help him with that when I'm often not sure if I really understand his proof, or whether it's correct.

I have tried the challenge problems approach before. The only math book he ever "completed" (I don't remember when), was Beast Academy 5, where I made him do all the starred problems (he didn't touch any of the others). After that I got him to do all the challenge problems for the first four chapters of AOPS pre algebra, but he got antsy after awhile, and we moved on. Then he was desperate to learn calculus, because it was the only kind of math he'd heard of he knew absolutely nothing about. Perhaps algebra and geometry challenge problems would hold his interest, though. He says he's not at all interested in math contests, but he does like the problem solving involved in the untimed type of contest puzzles, when I've found them online. 

[lewelma]

Sounds like he needs to work on proof writing. Is there someone you know who could help? AoPS courses did this for my son. Their graders are very picky and give great feedback as to how to improve. Best money I spent, but you could also hire a specialized tutor. Maybe a university maths major?

[Not_a_Number]

Has he done any higher-level math contests? Those give you problems that you have to mull over for days/weeks.

I’d also recommend signing him up for a harder AoPS class to see how he does and whether he has any gaps. Then you’d get some feedback on whether he’s actually understanding everything or whether he has gaps. He’d also get his proofs looked at.

[mckittre]

7 hours ago, Not_a_Number said:

Has he done any higher-level math contests? Those give you problems that you have to mull over for days/weeks.

I’d also recommend signing him up for a harder AoPS class to see how he does and whether he has any gaps. Then you’d get some feedback on whether he’s actually understanding everything or whether he has gaps. He’d also get his proofs looked at.

He hasn't done any contests, but I've found problems from old higher-level contests online and given him those to puzzle over just for fun. 

The AoPS class might be a good call for next fall, to have someone look at those proofs for him. He likes that format -- he's really enjoyed their Python classes. No idea how to choose which one -- do you think I should just set him to the "are you ready" and "do you need this" tests for the whole lot? Not sure whether it's better to aim high so he's sure to think the problems are interesting, or to aim low to not overwhelm him with the work load.

I'm not likely to find any other sort of tutor -- we live in a very tiny town, and I'm confident that none of the 3 teachers (total!) at the local public school know more math than my husband does.

[Not_a_Number]

5 minutes ago, mckittre said:

He hasn't done any contests, but I've found problems from old higher-level contests online and given him those to puzzle over just for fun. 

The AoPS class might be a good call for next fall, to have someone look at those proofs for him. He likes that format -- he's really enjoyed their Python classes. No idea how to choose which one -- do you think I should just set him to the "are you ready" and "do you need this" tests for the whole lot? Not sure whether it's better to aim high so he's sure to think the problems are interesting, or to aim low to not overwhelm him with the work load.

Yeah, give him the "Are you ready?" and "Do you need this?" tests 🙂 . I'm teaching Intermediate Algebra in the summer, if that could possibly be useful? Although maybe you're just looking for next year. 

Let me know how he does with the tests! I occasionally give them to DD8 to see how she's doing, since we also do our own thing. 

 

Quote

I'm not likely to find any other sort of tutor -- we live in a very tiny town, and I'm confident that none of the 3 teachers (total!) at the local public school know more math than my husband does.

There's always Zoom tutoring, though 🙂 .

Edited April 9, 2021 by Not_a_Number

[mckittre]

Thanks, I'll do that and aim to sign him up in the fall. Summer doesn't work for us schedule-wise for a regular class -- we do far too much backpacking -- but we do school year round.

As for the higher-level math contests, do you have suggestions? I'd particularly like to find proof-based untimed stuff from past years, with solutions available. He's not interested in competing, just in the questions. Also not interested in any question that he could possibly solve in less than an hour, so not in the timed competitions. The only place I've found good untimed questions is on summer camp applications (math camp and math path). He likes those, but they don't publish solutions, so I can't really tell if he's got it right in the end. 

[Not_a_Number]

1 minute ago, mckittre said:

Thanks, I'll do that and aim to sign him up in the fall. Summer doesn't work for us schedule-wise for a regular class -- we do far too much backpacking -- but we do school year round.

As for the higher-level math contests, do you have suggestions? I'd particularly like to find proof-based untimed stuff from past years, with solutions available. He's not interested in competing, just in the questions. Also not interested in any question that he could possibly solve in less than an hour, so not in the timed competitions. The only place I've found good untimed questions is on summer camp applications (math camp and math path). He likes those, but they don't publish solutions, so I can't really tell if he's got it right in the end. 

Oh, there are tons. I'd need to know his level for suggestions, but you can look up old USAMO questions and solutions and see if those are far too hard. Or USAJMO for slightly easier ones. Or maybe USA Math Talent Search? But I don't know if I'm aiming at the right level, since those are for high school kids. 

[Not_a_Number]

Also, maybe this is too obvious, but can't he do questions from timed contests without timing them? Like, if he does AIME questions (American Invitational Math Exam), how many does he get? 

[mathnerd]

For the next 6 years, just let him explore math and learn it and feel comfortable with it to know that this is what he loves to do the most.

For a kid with passion and motivation to pursue higher level math, exposure to complex higher level problems and familiarity with proof writing are an important aspect of learning math.

The other thing that is also important is the constant exposure to mathematical thinking and concepts - one way to accomplish this is to attend math talks and math festivals. We have been attending math talks hosted by MAA for Middle and Highschoolers and math festivals like the Julia Robinson math festival and the one at Proof School (local to me) whenever we can for several years. Not only do they introduce topics that kids may never see in their entire school careers, they also make them approachable, engaging and interesting. My son also gets to meet and interact with great mathematicians during those events which again is very good exposure to motivated kids. Most of these resources are free and all it takes is some planning and time to take the kids to those events. A lot of them moved to online format during the pandemic, so it is even more easier to participate.

There are also a lot of youtube channels dedicated to math topics (numberphile, singingbanana etc) which are entertaining and informative at the same time. 

[mckittre]

Thanks both for the suggestions. I sent him those contest questions and I'll see what he thinks when he gets to them (for some reason, all I found when I first looked was the 'AMC' contests -- I know nothing about that world). And I'll see if I can find any online talks he might like (he does know about you tube channels like numberphile,  and 3 blue one brown). We absolutely do not have any in-person options, with or without a pandemic.

I do want to let him explore and see if he loves math most, of course. I just also want to have enough of a clue in steering him that whatever choice he eventually makes, he's well enough set up to take that path. 

[Not_a_Number]

10 minutes ago, mckittre said:

Thanks both for the suggestions. I sent him those contest questions and I'll see what he thinks when he gets to them (for some reason, all I found when I first looked was the 'AMC' contests -- I know nothing about that world). And I'll see if I can find any online talks he might like (he does know about you tube channels like numberphile,  and 3 blue one brown). We absolutely do not have any in-person options, with or without a pandemic.

I do want to let him explore and see if he loves math most, of course. I just also want to have enough of a clue in steering him that whatever choice he eventually makes, he's well enough set up to take that path. 

Let me know what he thinks about those contest questions 🙂 . I was once really into the serious proof-based contests, so I know a lot about that world. 

[Kanin]

My DH got his PhD in math about ten years ago. He tells lots of funny stories about getting into trouble in elementary, middle, and high school. He would get sent out of class for goofing around with his friends, and then sit in the hall reading the calculus book. He didn't do anything above and beyond regular college and got into grad school just fine. He stayed in grad school for as long as he could (7 years) because he and his friends were having so much fun hanging out and doing math. 

So I'm just saying that you don't necessarily have to cultivate anything, and if he still loves math when he's ready for college, he'll be just fine.

[bookbard]

@mckittre just waving 'hi' as I remember you from the PBH group (as well as this board). Your 2 kids are basically the same age as mine, and I remember your little girl being into Frozen at the same time as my daughter (and brainstorming ways to 'support the project')! Hope everything is going well. 

[Frances]

On 4/24/2021 at 1:35 PM, Kanin said:

My DH got his PhD in math about ten years ago. He tells lots of funny stories about getting into trouble in elementary, middle, and high school. He would get sent out of class for goofing around with his friends, and then sit in the hall reading the calculus book. He didn't do anything above and beyond regular college and got into grad school just fine. He stayed in grad school for as long as he could (7 years) because he and his friends were having so much fun hanging out and doing math. 

So I'm just saying that you don't necessarily have to cultivate anything, and if he still loves math when he's ready for college, he'll be just fine.

My graduate degree is in Statistics and my advisor was a highly gifted mathematician who was “discovered” in community college. He was the first in his family to attend college and the first time he flew was when he travelled to Cornell University for a job interview. So most definitely nothing mathematical was being cultivated during his youth. He was much sought after as an advisor because he was so down to earth and friendly and took such joy in the simple things. He seemed perpetually amazed at how his life had turned out and that he was paid good money to do what he loved.

[mckittre]

Thanks @bookbard. Things are great here. That little girl who used to love frozen just decided to go to public school for the last half of 4th grade, and my just-finished-6th grader is my only homeschooler. He's almost certainly going to homeschool all the way through. How about you?

As for my mathy kid... I don't think I need to "cultivate" anything particularly - he'll like what he likes. I'm mostly just feeling a little angst that I don't want our scattershot rabbit-hole child-led approach to education (that's worked well for him so far), to cause problems for him as he moves towards the age of transcripts and grades and college.

Most threads I read on here, even looking at advanced kids, talk about way more linear paths than he's ever followed. Kids that "did algebra" at some point, and followed some sort of designed progression of topics. My kid has either never done algebra, or has been doing it since kindergarten (when most of his math was playing the "magic function" game with polynomials while hiking). I feel like it might be easier if he gets himself to some distinct 'level' in a normal math sequence, to be able to take classes from other folks more easily, but I don't want to squash what's worked for him so far.

[Not_a_Number]

3 hours ago, mckittre said:

Most threads I read on here, even looking at advanced kids, talk about way more linear paths than he's ever followed. Kids that "did algebra" at some point, and followed some sort of designed progression of topics. My kid has either never done algebra, or has been doing it since kindergarten (when most of his math was playing the "magic function" game with polynomials while hiking). I feel like it might be easier if he gets himself to some distinct 'level' in a normal math sequence, to be able to take classes from other folks more easily, but I don't want to squash what's worked for him so far.

We've done quite non-linear things ourselves, although I do tend to make sure there are no gaps. 

You could do what I do and just give him tests for various classes (I see I mentioned that above) to see whether he needs work on any particular concepts. I do think that as you get into later math, it gets harder and harder to get by without at least a bit of guidance about what angles to approach problems from. 

Did you ever wind up doing any kind of informal evaluation? I'd do it just for your own peace of mind. He's probably further on than you think he is, and he's probably perfectly able to take classes. 

[bookbard]

On 5/27/2021 at 8:18 AM, mckittre said:

Thanks @bookbard. Things are great here. That little girl who used to love frozen just decided to go to public school for the last half of 4th grade, and my just-finished-6th grader is my only homeschooler. He's almost certainly going to homeschool all the way through. How about you?

We haven't been homeschooling (delayed entry for both, age 6, and then both were grade-skipped from 1 to 3), but we plan to for our high school here (years 7-12) as the local high school isn't very good. I look back on those early days of supporting projects around molecules and Frozen with nostalgia. My little girl (who I think is almost exactly the same age as yours) has been spending the last 2 years writing lots of fanfic based on the novels she's into. My boy (who is 8.5) spends his time jumping on the bed inventing stories in his head. They were both diagnosed gifted but in completely different ways; my boy is totally language based whereas my girl is more consistent across areas. We all spend a lot of time reading.