what a brave new world. when i was a high school student back in the early 60's (1960's that is), as far as i know, no one took it more than once. and there were no prep classes i knew of. i just got up early one morning, drove to the other side of town, and took it once and that was it. i may be wrong, but i think making a habit of studying in school for your whole career, taking 4 years of high school math and english, and continually learning new words is more important than taking it over and over. of course anyone can have a bad day, so if the taker thinks he/she had such a day, maybe taking it twice is a good idea. i agree that taking it to see what it is like, is not as wise as just buying a $20 book of old tests and taking some of them. Also, since i was on the math team, i got a lot of test taking practice in competitions, without specifically thinking about preparing for the SAT. Forgive me if these old memories are irrelevant today.

On the hopeful side of this topic, I found the brilliant children I had the pleasure of mentoring from epsilon camp this summer, to be extremely considerate of and patient, even gentle, with each other, even though there were many occasions on which some saw through problems much more quickly than others. They generously helped each other, thanked each other, and honestly acknowledged their own errors. I often tried to take a lesson from them for my own style of responding. Maybe something is changing in these new generations from the way I grew up. A lot of them are home schooled, by the way, and some attend public schools which seem to genuinely accommodate and perhaps celebrate the gifted.

this thread reminds me of the time i visited a famous and brilliant man in my field and asked him a math question. he started writing a computation on a piece of paper that i thought i understood but that did not seem to deal with my problem fully, and then he stopped abruptly. I assumed he was stuck, and remarked that it was all right as i didn't really need the answer anyway. he said nothing, but gave me a slightly lingering look, so i asked if i might have the piece of paper he had written on. an hour later, after studying his computation intently alone in my office, i realized he had completely solved my problem. i was struck by two things, one was the power of his methods, and two was his restraint at not saying a single word to insult my lack of comprehension. i realized this man had worked long and hard to try more successfully to communicate with the world of average minds, and my respect for him only increased.

yes, they are probably negotiating the location and terms of use. i thought they were pretty happy at seattle pacific this past summer and had just assumed they would likely return there, but i have no information from the organizers.

well i found this statement there; that's all i know: "The application season for new students begins in the latter part of November by which time the important details of the camp including location, dates, admission criteria, and fees will have been posted."

Of course clarity in writing is an important goal. I would suggest to that end reading the short (and cheap) classic work, The Elements of Style: http://www.amazon.com/Elements-Style-Fourth-William-Strunk/dp/020530902X/ref=sr_1_1?s=books&ie=UTF8&qid=1413226760&sr=1-1&keywords=the+elements+of+style

For me the cartoons in Jacobs are fun. I found AOPS rather dry and unappealing. I remember more about the jacobs geometry than the algebra, but i love stuff like the caveman professor from BC where he asks the students if anyone knows the Pythagorean theorem and the girl answers yes, and states it perfectly. His response is "you may go clap the erasers." (Makes me remember the way I felt sometimes when starting out, I am embarrassed to say, when I had students much better than me, and I was hoping to appear important and knowledgable. I even once stammered in shock to such a brilliant student "what are you doing in the class?", since she knew apparently more than I did. She was from Spain, but later when she gave a lecture to the Italian students she spoke Italian. At first I prided myself on my good Italian comprehension since I was understanding the lecture perfectly, until I realized she was also writing it out on the board in English, apparently just for me!) I also like in the section of jacobs on the volume of a sphere where he shows a picture of the world's biggest ball of string that someone has collected. It's just so light hearted. The downside is the price nowadays that it is out of print. A used copy for my son, who is now tutoring, cost over $75 last week! I only paid about $17.50 for the copy I gave away a few years ago. For my son's use, I made him a present of Jacobs' Elementary Algebra, Jacobs' Geometry (1st edition), Euclid's Elements (the Green Lion edition paperback), Euler's Elements of Algebra, and Hartshorne's Geometry: Euclid and Beyond. This seemed to me like a compendium of outstanding materials on those two high school subjects.

well...i think so, but i'm not sure....

i wanted to get A's, and I did, but that only required studying literally the night before the test. in class i slept with my head on the desk, and i never read anything. so i learned almost nothing, could not write well nor read intelligently, and had no interest in academics.

yes. my experience with jacobs was having my 11 or 12 year old son read it for a half hour or an hour each sunday afternoon. and do some problems. he finished half the book and won something like the state math counts (?) competition with a perfect paper afterwards. jacobs is so clear and fun almost any age math gifted kid might do it, especially if you monitor it at first to see if it is appropriate.

A propos of nothing: in 1954 when I skipped 6th grade, the only skill taught there was multiplying and dividing fractions as I recall. So to prepare for skipping 6th grade I spent a few minutes one afternoon practicing multiplying fractions, the tops and the bottoms separately, and then turning fractions upside down before multiplying them. Afterwards I was a top student again in 7th grade math that fall and apparently hadn't missed anything. Oh, you meant how long per day - I thought you meant how long total. So I meant that in the ancient past, I spent about 30 minutes total for the whole year's worth of material.

By the way, this year epsilon camp started a sister progem: del;ta camp for 6-7 year olds. I met a few of those amazing kids yesterday. It was such a trip when a supremely confident 7 year old girl plops down opposite me and asks energetically, "and what's YOUR name?" making me feel as accepted as if i were another 7 year old.

Here are this year's forum topics, some repetitions of last year: I was kind of blown away this year because last year's students were back with even more enthusiasm and knowledge and I had trouble keeping up. (Less calculus, more geometry and topology.) returning students: determined orders of all rotation groups of the 5 regular solids. classified all finite subgroups of 3 dimensional rotations, without knowing they are rotation groups of regular solids to begin with, by classifying their action on “polesâ€. classified all compact triangulated surfaces, oriented or not, and their representation using cross caps and handles. showed homeomorphism of sphere with either three cross caps or with one cross cap and one handle. including discussion of how to define an orientation of a triangulated surface by giving compatible orderings of vertices. discussed euler characteristics of surfaces, mainly by triangulating but also briefly by “morse theoryâ€. determined the effect on the euler characteristic of adding a handle or cross cap to a surface. classified all plane euclidean isometries, and determined the possible translation subgroups and associated quotient or “point groups†of all discrete subgroups of plane isometries. discussed slightly the orbifolds resulting from modding out the plane by a discrete subgroup of isometries. new students: solved quadratic and (reduced) cubic equations by “cardano’s formula†determined which primes are sums of 2 squares, using factorization by Gaussian integers, modular arithmetic. including discussion of unique factorization of gaussian integers. tangent lines, “Descartes’ rule of signsâ€.

i try to work problems together with my charges and share that i myself make lots of mistakes. I hope this gives the impression that i am not opposed to mistakes. especially when they get something right that i get wrong i emphasize this fact and praise them enormously. i always admit openly at once that i made a mistake when i really have, which is often, so i have no need to fake it. the connesction with the OP's question is that fear of making mistakes is linked with the fear of the difficult.

"what is mathematics"? or "principles of mathematics", are books that have so much material that they will last her for years, or decades. http://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192/ref=sr_1_1?s=books&ie=UTF8&qid=1398221237&sr=1-1&keywords=what+is+mathematics http://www.amazon.com/PRINCIPLES-MATHEMATICS-CLETUS-BARNETT-ALLENDOERFER/dp/B000W6JYMM/ref=sr_1_1?s=books&ie=UTF8&qid=1398221294&sr=1-1&keywords=principles+of+mathematics%2C+allendoerfer

1st arithmetic, then algebra.

i have taught many children math at many levels, from 3rd grade through post graduate professional research instruction. I have learned over several decades not to stipulate what the next level should be. Until a child reaches adulthood, I suggest just following his/her interests. There is no topic or level of topic that is required for a young child. I can lay out a program that goes "deeper" in the sense of more fundamental, or more theoretical, but these levels are only of importance to a preprofessional young adult. For a child, there is no good reason to go deeper, if that is not what the child is engaged by. i apologize if this is not of use to you. fun topics: complex numbers, topology, number theory, advanced plane geometry, 3 dimensional geometry, spherical geometry,......

I think one thing I did that worked out well was to introduce my kids to lots of good movies and tv shows. The samurai trilogy, the miracle worker, oliver twist (with W.C.Fields as Mr.Micawber), Great Expectations (with Alec Guinness), Sugar cane alley (by Euzhdan Palcy), The count of monte cristo (the 1934 version with Robert Donat), the jungle book (Walt Disney version with Phil Harris), the maltese falcon, casablanca, african queen, bad day at black rock (with spencer tracy), children of paradise (with jean louis barrault), foreign correspondent, north by northwest, the seven samurai, ivan the terrible (by eisenstein), singin' in the rain, star wars, dr, strangelove, dr. who, ferris bueller's day off, real genius, breaking away, buck rogers, sid caesar, sound of music, chariots of fire, henry the fifth (kenneth branagh), maverick (the tv western), ....... one child became a fine arts and film major, the other has had a life long love of movies. I do not recommend any of these specific movies to you or your children, as they require prior screening for suitability, but they give an idea of the diversity of films we watched together at various ages.

i already have about 250-300 math books, so i am not getting any more this year. i am trying to give some away. i have already given quite a few away to colleagues students and some to the undergraduate library. of course every now and then i am still tempted to acquire more. but better to read some more of those i already have.

I am a retired college professor and have taught college calculus for 40 years. I have some experience with AP courses in high school through my children and through advising/teaching advanced high school classes, and from perusing the available AP exam booklets. My experience may be out of date by now to some extent. The situation is a little complicated and I suggest you interview the people who would teach both classes for a better idea what the courses will be like. Personally as a college professor I disliked AP courses because I felt they did a poor job of preparing students for college, but simultaneously pretended to be a good substitute for those college courses. Traditionally, it was my impression that AP courses were test oriented, and lacked proper emphasis on concepts. Former AP students who took my college classes seemed not to know any more than other students, nor to do any better. The BC curriculum did have slightly more emphasis on theory/proof than the weaker AB curriculum. However it is not that simple. Due to the huge success of AP courses as political phenomenon, colleges are swamped by students who have taken AP courses and we have had to make accommodations: i.e. even though the AP students do not usually know what we would want them to, we are still obliged politically (i.e. for financial reasons) to offer them exemption or credit for our classes anyway. So we tend to accommodate more those students who want to avoid paying for our superior classes, rather than the students who want to learn from them. Unfortunately we have also adjusted by gradually weakening the quality of our own classes to make them palatable to students expecting their high school preparation to have prepared them well. Thus it may be that some college classes you will find are in fact no better than high school AP classes. A key problem is the need for gifted and advanced students to be taught in advanced or honors level classes. An AP high school class is by definition an honors class in high school, but a regular college calculus class is not. So by dual enrolling but taking a regular college class you, as an honors student, are enrolling in a non honors class. In general it is my opinion that this is not good for your intellectual development. I.e. just the fact that it is a college class will not make it challenging to a gifted student. Thus the course many people recommend is to go ahead and take the high school AP class, preferably BC level if that is appropriate, and then in college, do not try to exempt the college calculus sequence on this basis. Rather use the AP preparation as preparation to take an honors level college calculus class. But take a beginning honors level class. I.e. take calculus from the beginning, but at a honors level, in a challenging class oriented towards gifted students. See for example the discussion of math 2400 on the UGA math dept website, where there are 2 or 3 different levels of calculus classes offered. http://www.math.uga.edu/~curr/LowerDivision.html Here is a similar page of discussion from Univ of Chicago: http://www.math.uchicago.edu/undergraduate/faq.shtml This advice will not work however unless the people teaching it have the same perspective that I am proposing. So it is crucial to consult with everyone and raise all the issues that matter to you. Do you want mainly to save money by taking as few classes as possible? Do you want as impressive a looking vita as possible? or do you want to just learn at as high a level as appropriate for you, and not be bored in a non honors class? good luck!

Your friend meant well, and was possibly correct about an average 10 year old, but certainly not about all, and apparently not about yours. Just to give you some counterexamples, when I taught epsilon camp in summer 2011, I believe the age requirement was that only students under age of 11 could enroll, and the prerequisite for enrollment was algebra up through quadratic equations. We enrolled 28 students. In 2013, I conducted the online pre-camp program for first time campers, some much younger than 10, and we began with quadratic equations, moving on through ideas of differential calculus, which we did carefully and in detail, from various historical perspectives. This was a small group of 5-10 very bright very young students. Here are links to the notes we covered in 2013 from my web page, and to the epsilon camp page with the description of prerequisite material. http://www.math.uga.edu/~roy/epsilon13.pdf http://www.epsiloncamp.org/who_is_eligible.php I hasten to add, these are very exceptional 8- 10 year olds, and only a handful worked through that online algebra and calculus material, but we are talking about unusual students here, namely yours. I suspect there is almost no fundamental math concept at all that anyone can reliably say is entirely inaccessible to someone just based on that person's age. So comments like the ones made by your friend are just statistical remarks which are mostly true, or mostly true in her experience, but have little relevance to your situation, in my opinion. What may be true, is that if she tried teaching those concepts to a typical class of 10 year olds, she would likely have an unsuccessful class. I am guilty myself of making similarly sweeping remarks of the following sort: students who have used calculators so thoroughly, that they have missed grappling with basic arithmetic operations, like multiplication and raising to powers, are probably unable to comprehend algebra. This however has nothing to do with age, but with background. In this case I am also extrapolating from my teaching experience with average classes, and I could be wrong here too, in individual cases. By the way, you say your son is "zooming through the material", but what does that mean? Is he doing the problem sets correctly or just reading the text easily? If he is consistently working both routine and challenging problems correctly, then I would say he is understanding the material, but not otherwise. (My perspective is that of a college math teacher.)

Decades ago, I bought some of his books for our children and one had such a test in it. It had off the wall questions like: "how many uses can you think of for an old rusted car?" I recall one of his ways of scoring creativity of responses was simply how many answers one could generate. It may have been in this book: http://www.amazon.com/Search-Satori-Creativity-Paul-Torrance/dp/0930222040/ref=sr_1_3?s=books&ie=UTF8&qid=1385934973&sr=1-3&keywords=paul+torrance One of our children took an IQ test given by one of Paul's students and it had a creativity component. One question was simply for the child to say as many different words as possible in 30 seconds after being given the go signal. Without waiting for the signal, the child began immediately counting rapidly: "0ne, two, three, four, five, six, seven, eight, nine, ten,.." and then cracked up laughing, at having so easily outwitted the question. Then he continued with a few desultory responses like " cat, pig, dog,...." but he had lost interest in the question. As I recall he got a zero score on the question for not waiting for the signal to begin, but his creativity assessment from the tester was quite high.

I was a math teacher for over 40 years. Although I often inflicted lectures on them, none of my bright students really liked to be told anything. they always preferred me to pose a problem for them to do on their own. Then they would allow me to slip in small tidbits of information in between that would help them do the problems. Thus the most successful style of teaching for motivated kids was: 1) pose an interesting problem. 2) ask them how to solve it, and let them brainstorm for a while. 3) either clarify their solutions if they are adequate, or make a few guided suggestions leading to the solution you have in mind. 4) sum up what has been learned.

i am interested to hear that my guess, increased use of typed or computer based math is in use with many. it makes me think of the young man with a cognitive disability in one of my classes, who could never write normally or at normal speed, even as an adult. his computer skill however was far above average and he eventually obtained a Bill and Melinda Gates fellowship to Cambridge based upon it.

i found these free placement tests for singapore math: http://www.singaporemath.com/Placement_Test_s/86.htm