I find this interesting - I too discovered the square root at 5 - but I had little help from my parents and actually I reverse engineered it to find out how it worked. square rooting from 0 up to 10 and scratching my head for a while trying to work out why 0, 1, 4 and 9 were special...
Calculators are great. The first time I encountered one I learned more maths than the next 4 years of school would teach me in mere hours...
I'm not sure how but mass education seems to have made difficult and scary concepts like decimals and negative numbers, which are so intuitive that they require little or no explanation when naively encountered 'in the wild'.
Everyone should let their kid play with a calculator I think. :)
I'm also strongly in favour of encouraging children to learn for themselves through experimentation. Explaining things is difficult, and at that age - you may not remember - but learning things is not. Not to mention that when you do reinvent the wheel you get a truly deep understanding, rather than some rote memorisation tricks to pass highly targetted exams.
My experience around the same age (well, maybe more like 6) was with early BASIC home computers circa 1980, and once I learned "FOR loops" and "print" and saw all these weird "function" things in the manual complete with handy example code, I started randomly seeing what happened when I used functions and got all wound up that sqr() crashed on negative numbers and almost never was a "even round result" except for certain numbers and another thing I found hilarious at the time was repeatedly taking the square root of ANY postive number the computer would accept, would eventually, sooner or later, round to exactly "1". Playing with log and antilog was another weird experience, as was early probing of the boundaries of the scalability of factorials (so, why does it crash on any factorial bigger than 70 or so?) I also learned that trig is hard. I learned more about math from a TRS-80 model3 at age 6, than until I went to university.
Calculators are great. The first time I encountered one I learned more maths than the next 4 years of school would teach me in mere hours...
I'm not sure how but mass education seems to have made difficult and scary concepts like decimals and negative numbers, which are so intuitive that they require little or no explanation when naively encountered 'in the wild'.
Everyone should let their kid play with a calculator I think. :)
I'm also strongly in favour of encouraging children to learn for themselves through experimentation. Explaining things is difficult, and at that age - you may not remember - but learning things is not. Not to mention that when you do reinvent the wheel you get a truly deep understanding, rather than some rote memorisation tricks to pass highly targetted exams.