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    #159547 - 06/08/13 10:15 AM Re: Finishing school maths when not ready for college [Re: 22B]
    ColinsMum Offline
    Member

    Registered: 09/19/08
    Posts: 1898
    Loc: Scotland
    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.

    You've had some good answers while I was away, but here's mine anyway. We've mostly used past papers from maths competitions. Early on the ones which are multiple choice worked much better than anything where he had to "show his working"; that's less of an issue now, and ymmv anyway. The three families of UK contests we've used are:

    The Mathematical Association's Primary Maths Challenge, aimed at children up to the age of 11. A few papers are available here (February is the follow-on round, so harder than November) and there are also books, usefully sorted into challenge levels, e.g. this.

    The UKMT ones - very usefully wide range, starting from the Junior Maths Challenge, aimed at children up to 13. One of each paper available from their website here, and again you can buy collections. The mentoring scheme papers, here, are also worth knowing about (perhaps for the future more than now, or if not I'm seriously impressed!)

    The Scottish Mathematical Council ones, see here. In the actual competitions, these require full written solutions.

    School have used scholarship papers (for entry to senior schools at 13, e.g. these or these) too. Unfortunately the ones that are on the web are the exception.

    Originally Posted By: 22B
    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?

    Interesting question, not least because it isn't something I've been in the habit of thinking about at all!

    I suppose I suck it and see. I can think of three occasions when he's worked at something that, with hindsight, he wasn't ready for:

    - Probably the first time I ever saw him have what looked like conceptual difficulty with something was when, at 7, he came to a section on cumulative frequency graphs in the textbook he was working through in class. He had trouble getting what it was they were showing and how. He could do the questions mechanically, but didn't like it and made weird mistakes. I helped him through the material in the book's (short) section as best I could, and didn't linger, because it really felt like something he wasn't ready to learn yet, rather than like something where he was having trouble that would be productive to work on. This - and especially the fact that I don't really understand what the problem was (given that he has had no problem with any other kind of graph or data handling) - is probably why I've been holding off on him doing more stats, actually.

    - That same year he did the (now defunct) ALEKS course on high school chemistry. He'd been desperate to do this for a while, and I'd insisted on his getting at least to the end of ALEKS's grade 6 maths before he did so. I hadn't realised, though, how far the course would take him, or I might have tried harder to put him off starting it! It started fully appropriate, but got much harder towards the end. I did suggest fairly forcefully that he stop and come back when he was older. He insisted on finishing the course, but there was a lot that didn't stick. (He's now doing their introductory college chemistry, which has a lot of the same material, and it's a different story entirely.)

    - The other thing he'd been very keen on learning for years before I let him at it was calculus. (I had a short thread here, actually.) I subscribed to the eIMACS course and put it on the list of things I let him pick from to do on the bus (we have a long bus journey together to school in the mornings and that's where he gets most of his mathematical input from me!) He started it with great enthusiasm and did a chapter on limits (that was useful, I think) and one or two chapters on differentiation, but just gradually asked for it less and less often. The year's subscription lapsed without his getting to integration and I didn't renew it. In this case, it wasn't really that anything was hard - it was more that he'd satisfied his curiosity, perhaps. I didn't attempt to keep him interested, because I thought it'd go better after he had more trigonometry, anyway.

    [ETA and to answer the later question about eIMACS, I thought this course was OK, but not great. Understandably, not many of the exercises were automatically graded, so he definitely needed someone there to check he was understanding; well, there are answers available, but since other correct answers are possible, that's of limited use. Pedagogically it was not bad, but there was a fair bit of "in the AP exam you can expect" to be ignored.]

    I suppose my general attitude is that he has time, and it's fine to be guided by his interest. If he isn't ready for something, he can leave it for later, no problem, or if he wants to have a go anyway but it doesn't stick, he can do it again later, equally no problem.

    With DS I wouldn't, incidentally, have picked proofs as an area to delay for mathematical maturity reasons - he's been very interested in proof, and proof theory, for a long time (there's a resource I would love to recommend, but can't till it's finished and published!). Writing proofs longhand has been another matter as until recently handwriting was a problem; I did have to push back against a teacher who wanted him to focus strongly on "showing his working" for this reason.

    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.

    As kcab said, Language Proof and Logic - for the software (more than just Tarski's World here, though that's good), more than for the book, which obviously isn't written to be appealing to children and isn't particularly so to DS. And this other resource that I can't point you at yet!

    HTH!


    Edited by ColinsMum (06/08/13 10:23 AM)
    Edit Reason: add opinion of eIMACS
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    #159550 - 06/08/13 11:05 AM Re: Finishing school maths when not ready for college [Re: ColinsMum]
    ColinsMum Offline
    Member

    Registered: 09/19/08
    Posts: 1898
    Loc: Scotland
    PS the other resource I'd strongly advise considering is Descartes' Cove. It's not cheap, the graphics are dated and there are mistakes (mostly where the communication between the graphics people and the maths people went wrong so diagrams intended to be explanatory are misleading) but DS loved it and learned a lot from it.
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    #159664 - 06/09/13 10:01 PM Re: Finishing school maths when not ready for college [Re: ColinsMum]
    22B Offline
    Member

    Registered: 02/10/13
    Posts: 1228
    ColinsMum, Thanks for all the sources of problems. That's very useful. We really haven't tried this, but we need to. DS7 does edutain himself with lots of maths stuff on the internet, but he hasn't really been exposed to a lot of challenging problems.

    As for "mathematical maturity", I guess your right that it's okay to have some false starts when they're way ahead anyway, although I wouldn't want a false start to happen in his school courses. If a competition or AoPS course doesn't work out, it's not the end of the world. Better to try, as long as it's not so traumatic that it instills fear in trying very difficult things (aka "perfectionism").


    Originally Posted By: ColinsMum
    [ETA and to answer the later question about eIMACS, I thought this course was OK, but not great. Understandably, not many of the exercises were automatically graded, so he definitely needed someone there to check he was understanding; well, there are answers available, but since other correct answers are possible, that's of limited use. Pedagogically it was not bad, but there was a fair bit of "in the AP exam you can expect" to be ignored.]


    FWIW I think software can be pretty sophisticated at recognizing equivalent answers.

    Originally Posted By: ColinsMum

    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.

    As kcab said, Language Proof and Logic - for the software (more than just Tarski's World here, though that's good), more than for the book, which obviously isn't written to be appealing to children and isn't particularly so to DS. And this other resource that I can't point you at yet!


    Is the software appealing to 7yo children. I'm looking for the most extremely elementary parts of set theory and logic (and maybe graph theory) just to be aware that these topics exist at all, because they're just not in his courses at all.


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    #159666 - 06/10/13 03:04 AM Re: Finishing school maths when not ready for college [Re: 22B]
    ColinsMum Offline
    Member

    Registered: 09/19/08
    Posts: 1898
    Loc: Scotland
    Originally Posted By: 22B
    Better to try, as long as it's not so traumatic that it instills fear in trying very difficult things (aka "perfectionism").

    FWIW, I think perfectionism is more easily instilled (was in me!) by never trying things that are too hard. But you the parent have to really, really believe it's OK to try and not succeed yet, and I take the point that this is lower stakes at home than at school (though I don't have virtual school experience and that must be interestingly different).

    Originally Posted By: 22B
    FWIW I think software can be pretty sophisticated at recognizing equivalent answers.

    Can be, sure - that's why I wrote "understandably" not "inevitably". It's still hard work to make it that sophisticated, though.

    Originally Posted By: 22B
    Is the software appealing to 7yo children. I'm looking for the most extremely elementary parts of set theory and logic (and maybe graph theory) just to be aware that these topics exist at all, because they're just not in his courses at all.

    It was to ours - not wildly so, but enough that it saw a fair bit of use over a year or so - but of course ymmv. He used to like, for example, making a set of sentences in this interface and challenging me to build a world that satisfied them all, and vice versa.
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    #161659 - 07/05/13 10:13 AM Re: Finishing school maths when not ready for college [Re: ColinsMum]
    ohmathmom Offline
    Member

    Registered: 03/27/13
    Posts: 161
    Loc: Ohio
    Have you considered math competitions? Even if DS doesn't want to compete, you may be able to find out about math enrichment opportunities in the UK. Try contacting someone at the UK Mathematics Trust: http://www.mathcomp.leeds.ac.uk/about-us/.

    Another option is Art of Problem Solving. In addition to courses, they have communities that might keep DS active in interesting math until he's ready for University: http://www.artofproblemsolving.com/

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    #161663 - 07/05/13 12:52 PM Re: Finishing school maths when not ready for college [Re: ohmathmom]
    ColinsMum Offline
    Member

    Registered: 09/19/08
    Posts: 1898
    Loc: Scotland
    Originally Posted By: ohmathmom
    Have you considered math competitions? Even if DS doesn't want to compete, you may be able to find out about math enrichment opportunities in the UK. Try contacting someone at the UK Mathematics Trust: http://www.mathcomp.leeds.ac.uk/about-us/.

    Yes! He's doing very nicely at these, thank you :-)

    Originally Posted By: ohmathmom
    Another option is Art of Problem Solving. In addition to courses, they have communities that might keep DS active in interesting math until he's ready for University: http://www.artofproblemsolving.com/

    Also already in the mix. He's actually a couple of weeks into his first taught AOPS course now, and I'll post more about that when we both have a better idea about how it's going.

    Thanks anyway :-)
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    #162840 - 07/23/13 11:48 PM Re: Finishing school maths when not ready for college [Re: ColinsMum]
    22B Offline
    Member

    Registered: 02/10/13
    Posts: 1228
    Originally Posted By: ColinsMum

    Originally Posted By: 22B
    One concern is I was wondering if taking university courses (while officially being a seconday school student) could disqualify you from competing in certain maths competitions.

    This is a valid concern, I think, and the rules are quite likely to change given the fluidity of the current situation, so it's one to watch. For the IMO at present,
    Originally Posted By: IMO
    Contestants must not have formally enrolled at a university or any other equivalent post-secondary
    institution, and they must have been born less than twenty years before the day of the second Contest
    paper.

    Unfortunately, "formally enrolled" is not further defined, though some countries (Canada turned up on my google) elucidate this as meaning enrolled on a degree-granting programme.


    In another thread
    http://giftedissues.davidsongifted.org/B...html#Post162766
    this link was posted
    http://www.oregonlive.com/news/index.ssf/2009/03/eugene_high_school_student_win.html
    Originally Posted By: linked article
    Larson is a member of his school's math, chemistry and programming clubs. He won the silver medal at the International Math Olympiad in 2007, and since his freshman year he has taken all his math classes at the University of Oregon .

    Here "freshman" means 1st year high school -- 9th grade.
    So that's one data point that someone can take university maths courses and still go in the IMO.
    http://www.imo-official.org/participant_r.aspx?id=15882

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    #163429 - 08/01/13 12:48 AM Re: Finishing school maths when not ready for college [Re: ColinsMum]
    matmum Offline
    Member

    Registered: 11/06/09
    Posts: 195
    Loc: Australia
    DS finished his Extension 1 and 2 Higher School Certificate maths in Year 9 and it wasn't going to be an option that he go three years with no maths.

    I spoke with the school and they acknowledged that it wasn't a suitable outcome so the Principal approached the local university and arrangements were made for him to enrol as a external student in a BSc. The agreement was he would concentrate on completing only mathematics units initially and as time progressed branch out as he desired.

    He started with one unit per semester and attended residential schools where appicable.

    As he completed further school subjects ahead of time he picked up more university units. By this time he was driving so he pretty much spent the last two years of school splitting his time between school and attending lectures on campus.

    His enrolment at university did not affect his entering mathematics competitions here although he did lose interest in them so rarely entered.

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    #163430 - 08/01/13 02:33 AM Re: Finishing school maths when not ready for college [Re: ColinsMum]
    squishys
    Unregistered


    That's great to know, matmum! Australia seems a bit behind the mark when it comes to gifted education... Your son is lucky to have a supportive school. May I ask which state you are in?

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    #163431 - 08/01/13 02:51 AM Re: Finishing school maths when not ready for college [Re: ColinsMum]
    matmum Offline
    Member

    Registered: 11/06/09
    Posts: 195
    Loc: Australia
    Hey squishys,

    We are in Northern NSW. My son attends UNE (University of New England). He was interviewed in 2008 and commenced in 2009. There was also another lad there from QLD doing a BSc majoring in Mathematics and he was 12y/o.

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