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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?)

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    $\begingroup$ This is a good question, but it would be helpful to know roughly what age and/or level of mathematics we're talking about. I understand the request is for books to help teach math, but knowing the type of math we're talking about is relevant. $\endgroup$
    – aes
    Commented Nov 26, 2014 at 21:48
  • $\begingroup$ I'll add a clarification $\endgroup$
    – Arthur B.
    Commented Nov 26, 2014 at 21:53
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    $\begingroup$ This doesn't answer your question, but you might be interested in looking at the archives of the Los Angeles Math Circle to find interesting and challenging math handouts for elementary school students. $\endgroup$
    – littleO
    Commented Nov 26, 2014 at 22:14

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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!

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  • $\begingroup$ Wonderful, I actually posted an link to an excerpt of this book, but I didn't know what the book was. I think I actually may have had Dimitri as a "colleur" in 2000. $\endgroup$
    – Arthur B.
    Commented Jan 7, 2015 at 15:05
  • $\begingroup$ The full book seems available here: msri.org/people/staff/levy/files/MCL/Zvonkin.pdf $\endgroup$
    – Arthur B.
    Commented Jan 7, 2015 at 20:49
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The book "Beast Academy" which have been published by a very well know Company " Art of Problem Solving". in the discretion they said its good for kids in grade 3rd. but I used with my son in 1rd grade and he like it. The most important this about this book which also is series. its fun ( nice colorful Cartoon) and its total different from what they teach it in school. as a dad and Ph.D student I still enjoy every part of this book.

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FWIW, I have some online mathematics exercises / tutorials (autocorrected), ranging from kindergarten to college, at: http://www.public-domain-materials.com/folder-student-exercise-tasks-for-mathematics-language-arts-etc---autocorrected.html

Also, the material is public-domain. You can copy the entire website if you like and alter it to fit your own purposes.

edit: Also: DadsWorksheets.com:

"This site has math fact worksheets, place value problems, addition without carrying, subtraction without borrowing, suites of multiplication tests using various methodologies, fractions and more. It’s done wonders for my kids. I hope it does the same for yours."

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The best book I have found so far is Polya's "How to solve it."

This article has also seems like a great resource: http://www.ams.org/bookstore/pspdf/mcl-5-prev.pdf

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  • $\begingroup$ You might consider to expand your question to contain a bit more information on the book and why it is good. $\endgroup$
    – quid
    Commented Jan 7, 2015 at 13:16
  • $\begingroup$ Seriously? Polya for 5-12 year olds? $\endgroup$
    – Eric
    Commented Mar 17, 2015 at 7:55
  • $\begingroup$ The book is for the teacher, not the child. And yes, that particular book is appropriate for your purpose. Think instead of patttern matching. $\endgroup$
    – Arthur B.
    Commented Mar 17, 2015 at 11:26

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