Can you recommend a book to learn to teach math to a child?
I am looking for a book which contains some ideas on introducing a child to mathematics. I am not particularly looking for a textbook to be used as part of the teaching (though feel free to mention one if it's particularly good), but for a book suggesting teaching methods and approaches (the ultimate purpose is homeschooling).
Crucially, the emphasis should be on actually teaching mathematics, not grinding through mindless exercises (in the spirit of Paul Lockhart's Mathematician's Lament).
Clarification: I am looking for material that focuses on teaching children which are already old enough to be proficient with counting and some basic arithmetic but maybe not ready yet to eat a lot of formalism, so in the 5-12 year old range?)
Math From Three To Seven by Alexander Zvonkin is an excellent book that chronicles the author's experiences running a math circle for his children and their friends from the ages 3 to 7. It does not purport to be an instruction manual, but there are many great ideas and all activities are described in detail. Here's a preview.
And just to give some credence to his lessons' effect: his son Dimitri is also a mathematician!