OK, coming out of a long MDC hiatus because my mind has just been blown and I need some BTDT reassurance.
DS1, who will be 4 in a few weeks, has been on a math kick. I learned today about a fun new math tool that lets you build custom online quizzes, and over the course of figuring out how to use it in my classroom, I created a few for him. Things I know he can do... adding, subtracting, shape names, etc. I took my computer home and logged him on, and he breezed through them (as I kind of guessed he would). His interest didn't wane, though, and he begged for more. We did basic fractions, basic inequalities (a simple addition problem on either side of a missing <, >, or = sign, and started on perimeter before he got bored. All told, he sat there for well over an hour (after a full day of preschool), getting little mini-lessons from me in crayon on the back of some old bills and junk mail, then begging for "more math problems" (I tried not to use the word test) on the computer. If I had to bet money I'd guess that tomorrow he'll retain his understanding of fractions and inequalities and not remember much about perimeter due to waning interest and focus at the end.
So... now I have a three year-old (OK, an old three year-old, but still technically three) who has a basic understanding of fractions and inequalities. Not spectacular by some measures, to be sure, but also enough to raise eyebrows. I'm not as worried about what other people think as I am about "EEEEEEK, WHAT IF THEY'RE RIGHT?!"
I mean, as soon as he was clearly not interested or having fun, we stopped. In fact, I tried to get him to stop sooner, but he wanted to keep going.
So, back to my post title: It's not pushing if they're begging for it, right?
Also: Good math resources for a mathematically inclined/interested four year-old? Again, I'm not wanting to push, but as long as he loves it so, and as long as we've likely got at least the next year with me or the husband as a SAHP (moving back to WI! Taking leave of absence from teaching! Exclamation points!), we'll have the time and energy to do this kind of thing. He can read, but isn't fluent just yet. He, with a few exceptions, enjoys being read to far too much to bother with the whole "reading on his own" thing. His reading is more at the "Go, Dog, Go" level, though he successfully sounds out more difficult words and sentences. Many of the math curricula and resources I can think of require a lot more reading.