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I bought this book last year and found it really interesting with respect to how children interact with math as their brain develops: Math from Three to Seven [1]. There are a lot of little experiments and games that teach kids basic concepts and show how specific reasoning develops. I'm looking forward to doing some of them with my son in a few years.

[1] https://www.amazon.com/gp/product/082186873X/ref=oh_aui_sear...

Book looks like out of print but PDF is here: http://www.msri.org/people/staff/levy/files/MCL/Zvonkin.pdf

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