Yep, we all have to hit the wall and that’s where we find out what we’re made of. It can be a valuable experience with the right people around to help.
My son (7 years old) is gifted in Math and as a parent I find it extremely hard to decide how much I should push him (register him to math competition, weekend math club ...) and how much I should just let him get 100% on exam and not accelerate the learning.
As you can imagine, there is a whole world of kids like your kid who love math and want to do nothing more than math.
If you're interested I can chat with you or recommend resources here if you decide to help your kid do more math.
My own kid went to MathPath (middle school camp by same people as Epsilon Camp). Loved it. “Yes, dad really, I want to spent a whole month of my summer doing math.” The social experience is great for kids to be with other kids that like math.
I'm a thoroughly useless adult, so it was a waste of money on their part, but it does happen. Or at least it used to.
Of course you still hit the wall later. But I see all the reports of how terrible it is to be gifted and am so grateful that my experience was different.
If I'm honest, I never ran into an intellectual wall. I did choose a comparatively 'easier' path, but that was more because I had a wide breadth of interests and choosing something easier meant I'd have more time to indulge my various interests. I was still getting interviews for tenure track positions out of grad school and when I did try to work post-graduate school, my first position was at an Ivy where I was the only one on staff who didn't come from an Ivy League school. (I was too lazy/too absorbed in my own things to do what was required to go to one.)
I ended up disabled in my last semester of graduate school - the 'wall' in my case is my body being unable to accommodate the social/networking demands of an academic or high powered private research career rather than my running into a topic I felt was beyond me. Particularly combined with being on my own in a HCOL area as that lifestyle required: Doing all your life management on your own with no safety net along with running at that high of an intellectual level is near impossible when you have a severe disability. (I have MS.)
I've been 'stuck' intellectually once in my life, and it was the result of a medication we tried for symptom management, and I found the feeling horrifying, if I'm honest. It was the first time I'd run into a problem where I had to sit there and think and still couldn't come up with a way to proceed, versus running into a problem and just being too damn lazy to bother. (Being able to see what I would do to solve the problem is very different from being motiviated to do so.) Apparently, most people feel that way fairly often? It made me way more sympathetic to people who didn't like school or who don't like learning.
No one told me that math is really 90% about writing proofs, all those homework problems I did were just the weed-out stuff, the academic equivalent of Leetcode.
So when I got put into some “real” academic math as a teen, I crashed and burned hard. I didn’t have a tutor and it never would have occurred to me to ask for one, so that was that.
When I was 18 years old in my first year of college, after my first semester grades came in, a guidance counselor set up a 1-on-1 with me to talk about the Rhodes Scholarship process and what my research interests were.
My response was: 1) what the heck is a Rhodes Scholarship and 2) how could I possibly have “research interests” as an 18 year old college freshman.
That was the final chapter of society considering me “gifted”, but it was just as well, I couldn’t imagine any greater success beyond getting a job and being able to afford my own apartment.
Mostly because a lot of my personal interests/ability to self-develop was related to Internet access. (My parents made VERY QUESTIONABLE financial choices and opted to pay for Internet access instead of food or clothing so I might have been freezing and my clothes all had holes in them but I could go online to talk to other smart kids.)
Also because I remember me + my parents being sat down when I was in elementary school and having my options talked about. In middle school once I was proven to have programming and math aptitude during the dot com boom, educational experts came to us and discussed specific gifted learning options (including things like private schools, skipping grades, or even pulling me out of school altogether for private instruction). None of this was initiated by my parents - it was brought to us. This was in the 90s.
I did teach myself programming in the 90s, after my friend loaned me his floppy disk with all his QBASIC stuff. Then dabbled in PHP, MySQL, etc.
We had one computer programming class in high school and I never got to take it because I had too many other electives. I don’t think it would have done much for me by the time I could have taken it.
It never really occurred to me as a teen that I could use the internet for getting really good at academics or broader “self-development” - I guess I just cared about video games and making money. Parents’ attitude was as long as I was getting As and going to college they didn’t need to do anything.
The best way to guarantee a gifted kid wastes a lot of their potential is to be in an environment that is too easy. It creates a devastating mental habit that won’t trigger until later in life, like college. Whenever they try to do something that doesn’t come easy, their brain will try to shut down out of a kind of frustration. They won’t know how to overpower it. It will cause depression, anxiety, shame and low self worth later on. Because the gifted kid will know they are wasting their potential, but blame themself for not being good enough to deal with it. It feels like being broken.
All of this is created by being rewarded for maxing out the rewards of a trivial environment. Someone needs to patiently and compassionately teach them to value overcoming appropriately sized challenges. To find and operate on the edge of their potential and ask for help to operate beyond those limits.
So yeah, grit and asking for help. Intelligence is mostly wasted without it.
- your child has a wall. At 7 he is not hitting that wall.
- that wall is probably mostly related to the pure math concepts, and probably less to his actual age when he encounters them. This is my assertion and I cannot prove it but let’s assume it is true. Precalc or calc is a typical wall moment, but for others it might be geometry or trig.
- one response to an eager math learner is to move them through the curriculum faster. They are happy, because everything is fun prior to the wall! You get to be the parent of that kid who is great at math! Let’s put the pedal to metal!
- what acceleration means is that your kid will hit the wall at 13 instead of 15, or 14 instead of 16, etc.
- those two years can make a big difference. Accelerating might be positive, in that they hit that at an age where you can support them better. It might be negative, in that they now have a crisis that their peers can’t relate to. Not accelerating might mean that they respond to the wall by pouring their energies into age-appropriate activities instead, like listening to loud music or being grumpy.
So no easy answers here. We did not think ahead clearly, and pushed forward, and had some decisions to make later. In retrospect I think it turned out fine, but I wish I had known that I was pulling the wall forward in time.
Moving through the curriculum faster is a common approach but it's also risky, because that's how the gaps are created that can then hinder your understanding later. Of course if you have reached true mastery of a given topic, moving forward is preferable to being bored to death, but assessing whether that applies can also be difficult at times.
If he likes to do math you make it available, if he would rather play with legos instead of doing math you let him do that in his free time.
You can encourage learning and problem solving without it having to be math, or pushing.