My son is one year old, so it is perhaps a bit too early to worry about his mathematical education, but I do. I would like to hear from mathematicians that have older children: *What do you wish you'd have known early? What do you think you did particularly well? What do you think would be particularly bad? Is there a book (for children or parents) that you recommend?*


(This a community wiki, so please give *one* advice per answer, as usual.)


### Background


I ask here because I believe that the challenges a mathematician faces in educating a child are special. For example, at least [some websites](http://www.bbc.co.uk/schools/parents/work/primary/numeracy_and_science/maths_at_home_primary.shtml) and [books](http://books.google.com/books?id=6GxoPgAACAAJ) address the parents' fear of not knowing how to solve homework, which keeps them from becoming involved. On the contrary, I fear I might get too involved and either bore my son or make him think he likes math when in fact his skills are elsewhere.


Christos Papadimitriou [said](http://linkinghub.elsevier.com/retrieve/pii/S1574013709000185) in an interview that, even though his father was teaching math in high-school, they never discussed math. I wonder if that means his father didn't teach him how to count and I wonder if it's a good strategy. (It certainly turned out well in one case.)


Timothy Gowers (in [Mathematics, a very short introduction](http://books.google.com/books?id=DBxSM7TIq48C)) says that it was inappropriate to explain to his son, who was six, the concept 'zero' using the group axioms. (Or something to this effect, I don't have the book near to check.) That was surprising to me, because I wouldn't have thought that I need to restrain myself from mentioning abstract concepts. (**Update.** Here's the quote: "[The non-abstract] way of thinking makes it hard to answer questions such as the one asked by my son John (when six): how can nought times nought be nought, since nought times nought means that you have *no* noughts? A good answer, though not one that was suitable at the time, is that it can be deduced from the [field axioms] as follows. [...]")


There is a [somewhat related Mathoverflow question](https://mathoverflow.net/questions/5139/how-have-mathematicians-been-raised). This one is different, because I'm looking for advice (rather than statistics/anecdotes) and because my goal is to give my son a good math education (rather than to make him a mathematician). I also found an [online book](http://www.math.com/parents/articles/helpmath.html) that seems to give particularly good generic advice. Here I'm looking more for advice geared towards parents that are mathematicians.


In short, I'm looking for *specific* advice on how a mathematician should approach his/her child's math education, especially for the 1 to 10 age range.



How do you approach your child's math education?
I would recommend a great book by [Alexandre Zvonkine](http://www.labri.fr/perso/zvonkin/), "Math for little ones", but it is only available in Russian ([here](http://www.mccme.ru/free-books/zvonkine/zvonkine.html)); however, two articles by Zvonkine which were published earlier are translated into English, see [here](http://www.de.ufpe.br/~toom/others_articles/engeduc/Zvon-eng.pdf). (You might also want to check other materials [linked](http://www.de.ufpe.br/~toom/others_articles/engeduc/index.htm) on Andrei Toom's webpage.)


And, as a tiny bit of more general advice, you know about Piaget's works, right? They are highly relevant when trying to teach kids anything at all, I think.


