Algebraic and calculus concepts may be better way to introduce children to math
(Disclosure: I'll be working with Maria on the calculus series for kids.)I'm a big fan of the conceptual approach. One of the largest problems I see with math education is that we don't check if things are really clicking.I graduated with an engineering degree from a great school, and still didn't have an intuitive understanding for i (the imaginary number) until I was about 26.Go find your favorite tutorial introducing imaginary numbers. Got it? Ok. It probably defines i, talks about its properties (i = sqrt(-1)) and then gets you cranking on polynomials.It's the equivalent of teaching someone to read and then having them solve crossword puzzles. It's such a contrived example! (N.B., this anguish forced me to write a tutorial on imaginary numbers with actual, non-polynomial applications, like rotating a shape without needing trig. See https://news.ycombinator.com/item?id=2712575)Calculus needs these everyday applications and intuitions beyond "Oh, let's pretend we're trying to calculate the trajectory of a moving particle."
They're out there: my intuition is that algebra gives a static description (here's the cookie), while calculus describes the process that made it: here's the steps that built the cookie. Calculus is the language of science because we want to know how the outcome was produced, not just the final result. d/dx velocity = acceleration means your speed is built up from a sequence of accelerations.