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    #159129 - 06/04/13 05:42 AM Re: Finishing school maths when not ready for college [Re: ColinsMum]
    squishys
    Unregistered


    I don't share info too freely, but some people notice. By 'people' I meant more like my friends and family.

    I have considered PAC, but I'll probably go with Glenunga International (since we are atheists). It's a toss up between the rich kids or the smart kids. I have no idea. I'll start researching it more in a few years.

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    #159183 - 06/04/13 11:52 AM Re: Finishing school maths when not ready for college [Re: ColinsMum]
    aquinas Offline
    Member

    Registered: 11/02/12
    Posts: 2499
    I've been following this thread and wanted to thank all the posters who've contributed to the discussion. This is one of the most informative threads I've seen on the forum!
    _________________________
    What is to give light must endure burning.

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    #159192 - 06/04/13 12:50 PM Re: Finishing school maths when not ready for college [Re: 22B]
    kcab Offline
    Member

    Registered: 10/02/07
    Posts: 1603
    Loc: Sparta, apparently
    Originally Posted By: 22B
    ColinsMum, could you recommend some sources of problems in addition to Alcumus. We've almost never had DS7 solving (non-routine) problems at all, yet, as we were just getting him through the basic K-5 maths so he'd have some basic knowledge, but now he desperately needs to be challenged.

    Another question, what's your approach to assessing "mathematical maturity" and readiness for certain mathematical activities? For example, I haven't mentioned at all to DS7 about theorems and proofs, since he's not ready for that. He can understand and explain things, but I'm just happy for him to think about things without worrying about rigor at this time. Know what I mean? What other stages of "mathematical maturity" should I be thinking about?

    Another question, anyone know of a good resource (especially online) for learning very basic logic (and, or, not, quantifiers) and the same for set theory. These topics are totally absent from the school curriculum, so this void needs to be filled.
    Not the person addressed, but thought I'd give the info I have while bumping the question up again.

    In addition to the suggestions for sources of non-routine problems already made, you could try NRICH math. Another resource that could be useful is IMACS or eIMACS. (Have had (good) experience with IMACS classes, but none with on-line.) This would also be an answer for your question on basic logic and set theory. Math circles could be good, if there is one locally and it works out for you.

    And I'm sure there are things I'm not thinking of right at the minute.

    My recollection is that in the past, ColinsMum has recommended Tarski's world for logic. I'm hoping she'll say more again here since I'm not sure if that is still her recommendation and I'd like to know too.
    _________________________
    kcab

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    #159317 - 06/05/13 02:05 PM Re: Finishing school maths when not ready for college [Re: kcab]
    arlen1 Offline
    Member

    Registered: 11/20/12
    Posts: 113
    Originally Posted By: 22B
    Another question, anyone know of a good resource (especially online) for learning very basic logic (and, or, not, quantifiers) and the same for set theory. These topics are totally absent from the school curriculum, so this void needs to be filled.

    Logic puzzle books by Raymond M. Smullyan have been widely popular among 'mathy' children for decades. Try:
    - "What Is the Name of This Book?"
    - "The Lady or the Tiger?".

    Smullyan, 94, is "an American mathematician, concert pianist, logician, Taoist philosopher, and magician". Here is his picture and his story (in his own words, lower on the page): http://mysite.verizon.net/vzeeaya7/raymondsmullyan/ .

    Also consider books by "fellow polymath" Martin Gardner.

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    #159323 - 06/05/13 02:23 PM Re: Finishing school maths when not ready for college [Re: kcab]
    arlen1 Offline
    Member

    Registered: 11/20/12
    Posts: 113
    Originally Posted By: 22B
    Another question, what's your approach to assessing "mathematical maturity" and readiness for certain mathematical activities?

    Pre/post-tests (online) for AOPS books and courses would be useful for this.

    Originally Posted By: 22B
    For example, I haven't mentioned at all to DS7 about theorems and proofs, since he's not ready for that. He can understand and explain things, but I'm just happy for him to think about things without worrying about rigor at this time. Know what I mean? What other stages of "mathematical maturity" should I be thinking about?

    AOPS "Prealgebra" book asks students to construct proofs (AFAIR, distributive property, etc.) at the very beginning.

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    #159423 - 06/06/13 07:06 PM Re: Finishing school maths when not ready for college [Re: arlen1]
    22B Offline
    Member

    Registered: 02/10/13
    Posts: 1228
    kcab and arlen1, thanks for the references.

    Has anyone tried eIMACS?

    -------------------------------------

    To the Australians, this may be of interest
    http://www.amt.edu.au/
    http://www.amt.edu.au/mcya.html
    http://www.amt.edu.au/amcfact.html


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    #159427 - 06/06/13 09:09 PM Re: Finishing school maths when not ready for college [Re: ColinsMum]
    squishys
    Unregistered


    Thanks for that, 22B. I think my son will be very interested.

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    #159433 - 06/06/13 11:52 PM Re: Finishing school maths when not ready for college [Re: 22B]
    kaibab Offline
    Member

    Registered: 08/24/10
    Posts: 99
    Loc: USA
    Originally Posted By: 22B
    kcab and arlen1, thanks for the references.

    Has anyone tried eIMACS?




    Yes -- for the computer science U course. It was ok, but DS found it tedious and repetitive. There were lots of "exercises" to do.

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    #159463 - 06/07/13 09:15 AM Re: Finishing school maths when not ready for college [Re: ColinsMum]
    HowlerKarma Offline
    Member

    Registered: 02/05/11
    Posts: 5181
    Good to know, kaibab.
    _________________________
    Schrödinger's cat walks into a bar. And doesn't.

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    #159535 - 06/08/13 07:56 AM Re: Finishing school maths when not ready for college [Re: HowlerKarma]
    ColinsMum Offline
    Member

    Registered: 09/19/08
    Posts: 1898
    Loc: Scotland
    [back from a week away and catching up]

    Topically, here's an article about Alex Thorne, who has just finished a master's degree in maths in parallel with being at school for other subjects. Depressingly, "His mother [...] had to sit in on the lectures with him because of his age", i.e., it's yet another case where the solution only worked because his mother was available during the day to make it work, i.e. didn't have a typical career or gave it up.
    _________________________
    Email: my username, followed by 2, at google's mail

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