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Submission + - Introducing students to rigor 2

An anonymous reader writes: As an engineer who studied in Asia for most of my life, my first exposure to real mathematics was when I arrived at graduate school in the United States. While I did take and enjoy some basic courses in mathematics (like real and functional analysis, measure theory and probability), I had a tough time because I found myself having to train myself in making rigorous proofs/arguments, compared to the engineering approach. I also found that training invaluable in helping me in other aspects of my life (including my engineering job). Now that I am back in my home country with children of my own, I see that the curriculum and approach in mathematics hasn't really changed. Rather than getting them used to thinking and making concrete arguments, they are taught formulae and most of their homework and exams focus on number crunching. So I'd like to ask slashdotters: What books/activities would you recommend for students in the 5th-12th grades (or even earlier) that might get them to appreciate rigor and critical thinking?
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Introducing students to rigor

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  • I cannot speak to the topic from a college level, except for a few textbooks I know about lying around in this house. From a high school perspective, rigor and proof go hand in hand: no ambiguity, clear simple steps that are well defined.
    Geometry, and geometric proofs: Euclidean Geometry, any high-school level textbook, preferably using only two color illustrations, and the ones from before 1990 seem to be much cooler and better at making you think.
    If you don't know the basics of geometric proofs, and bu
  • You must have a different definition of engineer than any I am used to. Perhaps you think "engineer" is appropriate shorthand for "software engineer"?

    Engineer as a standalone job description involves mathematics every semester of college and you better have had it in high school before that. How you could get to graduate school, as an engineer, without having studied any mathematics, is beyond me.

All laws are simulations of reality. -- John C. Lilly