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oscilatorium

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  1. Yup, reminds me of this. https://www.maa.org/external_archive/devlin/LockhartsLament.pdf He perfectly explains what many of us felt but couldn't put into words. I cried the first time I read it, realizing how many kids suffer through math class in schools.
  2. When you say she has no trouble with proofs, does that mean she can understand it and explain it well? Can she also write down the logical steps of the proof in a paragraph? If so, is it only the 2-column format that's troubling her? Many bright kids are averse to the 2-column format of proofs taught in geometry and prefer the more natural paragraph form used everywhere else outside of geometry class because it's more expressive and less constraining. You say she is bad at algebra, but what about her arithmetic/calculation skills? Can she quickly multiply small numbers and do small computations pretty easily? If she is visual she might be able to see/manipulate some of the smaller steps in her head without having to write down every intermediate step, as is normally stressed in school. Additionally, is she comfortable with negative numbers and fractions and can think about them visually/intuitively (i.e. on the number line)? Assuming she has no weak spots with arithmetic and doesn't make a lot of computation errors, I don't see why she should have much trouble with algebra. Unless she doesn't really have the intuition in place for how to solve/manipulate simple equations (e.g. one variable linear equations), and is just blindly applying rules learned in school. Given her good logic and VSL ability, she should be able to learn how to solve simple equations intuitively (i.e. think of them visually as balance scales, and visually understand how operations would impact them). For most kids all that is too much; it's easier just to remember and apply the rules, but for her it might be a lot more beneficial to "see" certain steps in her head since she can more easily do that than others. I don't think memory is an issue, it's possible that unless she understands something really well conceptually, she will not remember it long term, even with practice. Her ability to derive stuff is a great thing and suggests that she is naturally using reasoning/logic. This might mean that she cannot pick up something that is partially picked up in her mind, unless she sees/gets the whole picture and how all the pieces fit in. I know I was like this when I was little. I was slow at learning new things well (I could easily pick up simple rules and blindly follow them and was quite good at arithmetic and calculation) but without practice I would forget stuff after a while and would need to re-read, re-derive how the rules worked. I always thought it was a memory thing, but later as I grew older I realized that my "forgetfulness" was not really a memory issue (I could remember all kinds of very specific stuff from the past that was memorable), my issue was that I could not remember stuff that I hadn't fully understood well. In her case it might be that she doesn't really see the reasoning/logic behind certain rules that still feel arbitrary to her, so after a while she forgets them.
  3. If your son finds most of the problems easy, just have him do all the Challenge problems and see if that's still the case. If he still finds those easy (especially the latter half/starred problems), then he could be ready for Intro to Algebra... but it really depends what point in the book you are at, as there are many types of topics.
  4. I think many boys get to play video games from an early age. They find it fun and the idea of beating the game (i.e. winning) is really appealing. That attitude of completion or finishing something can translate in positive ways to school and sports, etc. It was definitely true for me when I was in elementary/middle school, whereas my sisters did not really find video games as entrancing to anywhere near the same level as I. I think you'll notice that girls that tend to play video games tend to have more competitive personalities, but there are not many girls that do that because it's generally not socially acceptable for girls to play video games during the K-12 years. So girls don't get that environment early on, unless they're the tomboy type and/or if it's promoted as a family activity and everyone does it. My guess is this translates sort of negatively in that they don't respond as well to competitive pressure in later years (middle and high school), so wouldn't get the same level of excitement from competitions. Hopefully that seems to be slowly changing in terms of marketing and toys, (tech geekiness is in, and Barbie slowly fading out). Yeah from what I understand, in Mathcounts, there are very small differences between many kids that just don't make it past Chapter round in competitive states, vs kids that make the national team for their state. Probably not in all cases, but there is no doubt that Mathcounts is at the high levels is primarily a speed competition and there are just way too many kids that could solve all the problems if they had more time, but not within the allotted time. Mathcounts is fantastic of course for initial exposure as they have many neat problems and the team aspect is fun, but at later stages it's way too high pressure (countdown round is ridiculous in my opinion, besides providing some entertainment for the audience at the expense of the 12 kids who have to be up at the podium). For Olympiad level, I think the differences in ability are much more marked, that is the top scorers/winners/honorable mentions have a much stronger sense of problem solving, intutiton, imagination, and experience, than the lower scorers on the USAMO. Time is no longer an issue (9 hrs for 6 problems), so it's all about finding a way to crack very difficult problems; the complete opposite of Mathcounts. I can imagine a math circle is only as good as the teacher leading it and how they plan/organize the problems/lesson around the particular audience. They should have a good ability to judge the level of skillset of the kids in attendance and adapt as necessary. I have not participated in one, but would love to start one at some point in time. What particularly struck me was the wonderful problems in some of the math circle books that I have seen, as well as the many tips for how to elegantly present them and explain them in such a way as to promote thinking through exploration, rather than just focus on calculation (as many of the mathcounts and other lower level competitions problems too much focus on). I'm currently reading a math circle book for middle-schoolers (linked below) and the quality of the problems absolutely blew me away, I would probably put it above even AoPS in terms of stimulating creative thinking. There is not too much math introduced, but lots of reasoning, logic, and argument and a good level of informal proofs (focused on explanations and good reasoning, rather than mathematical symbolism). The problems are of very high quality, and many have very creative, imaginative solutions that are explained thoroughly. The topics choice is simply wonderful and each topic has its own lesson along with a problem set to go with it so it's perfect for an adventurous parent to work through with their own kids, or with a small group of kids. http://www.amazon.com/Anna-Burago-Mathematical-Circle-Diaries/dp/B00DJY9MOE
  5. Agree, would love to see to see more girls on the US IMO team, as we had a couple in the past. Unfortunately it's so hyper competitive to make that 6 person team that it takes more than just talent. One needs sheer will and and huge competitive desire; I would even guess that some people who were on the IMO teams had to sacrifice many other activities/grades in school to focus almost exclusively on math, and high school boys for whatever reason tend to thrive more in that type of pressured environment. I agree that math circles are amazing but hard to find, and in a good area are even very hard to get into. We desperately need more passionate folks across the whole country to step up and volunteer to host them; the demand is definitely there and many bright kids really need this type of environment as school does not even come close. But other than circles, I think we have a tremendous amount of opportunities online. The AOPS website of course is amazing, but even beyond it, you can find almost every past competition exam and its solutions by just googling (i was able to find almost all of the Mathcounts and AMC materials for free, and even managed to find a pdf of one AoPS book). Not to mention the # of high quality MOOC's that are popping up everywhere (not all of them are great, but some are absolutely fantastic, on par with the best classes given at top colleges). And almost all of it for free, or with minimal cost. So I think the material is there, the real problem is one of awareness, but that is also slowly going up. Sites such as these really give fantastic perspectives to parents as to what is really out there, and there are many interesting blogs focused on high quality education that guide readers where to find valuable material and opportunities. I personally know many parents concerned about their kids education, but found after talking to them that they didn't really know about many of these opportunities; so we all just need to spread the word how it is very possible to get a really high quality education and enrichment material if school doesn't provide it. Agree that most kids don't start out mathy, but become so through their exposure. My personal belief is that most kids can be really good at math (after all it is just logic), but they've just never been taught to think mathematically in school. By the time they get exposure to problem solving, or reasoning about any multi-step problem, they find the barrier of entry really high and are conditioned to give up if they can't get anywhere after 5 minutes of trying. Then they're subconsciously taught to tell themselves that they're just not good enough; that someone else who can do it in < 5 mins is better than them. These days this starts in early middle school (even in elementary school), and it is often too late, if they haven't been exposed to reasoning,and doing games/puzzles from an early age. Most of the kids that participate in math competitions are no more gifted than the kids in normal math classes; they've just had the opportunities and training for that type of thinking from an earlier age and have had years to practice (some have been involved in some sort of math events/competitions even since early elementary school), so of course they appear "geniuses" to other kids. We need to teach kids that math is no different than a sport, it takes deliberate practice over a long period of time to get good at it. What's fantastic is that almost anyone can do it as there is no genetic barrier unlike in some sports. I know there are efforts out there that focus not necessarily on identifying mathy kids, but kids who have generally good thinking/reasoning skills and/or display a lot of effort/curiosity to learn, and thus would be well suited to take advantage of high quality resources. BEAM (http://www.beammath.org/), originally started by AOPS, comes to mind. Once there is enough awareness in the general population that elementary school years are critical in building general problem solving skills, (and that almost all schools do not do nearly enough in that area), and if kids get the right exposure early on, they will then have a pretty easy transition to many of the activities that the "genius" or mathy kids do in middle school.
  6. Yes I've seen the descriptions. I'm sure the 12 week class is very good as review, but I don't think it would really help cement the many topics on the AIME for someone learning many of them for the first time. I think the intermediate classes/books are much more thorough and go deep in the particular area and I believe the concepts really stick better on a slower schedule. I do think the AIME class would be very useful to take prior to the exam to refresh the topics and problem solving needed, (but self studying from past tests would also be very similar, and free). I took the advanced amc/mathcounts aops course out of curiosity a while back and found it very good, but it covered one major topic per week which is way too quick and is great as a review, but not enough time for any depth and proofs of results.
  7. Yes her and the parents goal is to get to the USA(J)MO and she plans on devoting 7-8 hrs a week for the next year (outside of school class). Given what I've seen from her in the past year, she is talented and capable of reaching that level if she puts enough effort in (she took the AMC 10 the first time this year as a 7th grader and qualified for the AIME, but did not do much on the AIME (naturally expected, as she doesn't know trig/advanced algebra, and other precalc topics). I explained to her parents that it will take many hours of problem solving to pass the AIME (i.e it will not be enough just to study old practice tests 1-2 months before the exam and accumulate all the concepts needed to pass the AIME, which is what she did when passing the AMC 10). Her mom mentioned her starting to try the online EPGY algebra course, but I told her it wouldn't be near her level and would not help with her goal of reaching the olympiad. So far I have not found any other class other than the AOPS intermediate classes for deep problem solving integrated into an actual curriculum and told her mom it's the only practical choice to challenge her, if she wants to make it by 8th or 9th grade.
  8. Yes, she has no problem with the pretest for the class. In her case she has not taken the Intro B algebra class but she has enough experience with competition math from mathcounts/amc10 that I believe she can do fine in the Intermediate class. E.g. even though she hasn't seen logarithms and some aspects of series/sequences/functions, I'm not too concerned, as the Intermediate course teaches it from the ground up, though at a faster pace than in the Intro courses. So I think the Intro B Algebra class isn't essential and could be skipped if someone has a good enough problem solving base; (e.g. if they could do most of problems on an amc 10 test). Logs/sequences/series/functions are taught from the beginning in the intermediate class without any prior knowledge but a faster and deeper level, so having the mathematical maturity/problem solving experience would help in picking it up at that quick pace. If on the other hand he's not very comfortable solving/factoring things like quadratics, or simple inequalities, and/or not been exposed to significant problem solving with prior aops classes, then the Intermediate course would be too much and I'd say to continue with Intro B.
  9. I would try to figure out what motivates him to do so many math problems if he doesn't love it. If he isn't forced into doing it, then what drives him to work so hard in math without love? (even though he is really smart, I'm sure he still has to put a lot of effort to work every problem in an aops curriculum), so something is driving him. Coursera and edX have some really great and enjoyable CS courses if that's something he'd find interesting. With a strong discrete math background he could easily pick them up. But I definitely wouldn't push anything, you can never run out of math learning. I would just show him lots of exciting options to explore, and maybe his interest will pick up more. MIT OCW has great courses, if he enjoys self learning. Also 6.041x (probability theory) on edX is fantastic; I have never seen such amazing explanations.
  10. Correct, the AOPS book goes way beyond what is known as Algebra 2 in high school, both in problem depth and coverage of topics. So I think ample problem solving skill, some mathematical maturity, and a good understanding of basic algebra (up to quadratics/factoring) should be a good prerequisite for taking it and doing well in it.
  11. Yes they are quite prepared; a lot of middle school competition problem solving experience and qualified to take the AIME exam earlier this year. Long term goal is to pass the AIME exam, so I think AOPS is probably the best choice (maybe the only choice) for an appropriate curriculum that will both prepare her well for math competitions and cover all Algebra 2 curriculum at the same time. I was looking for any curriculum alternatives to AOPS aimed at her level, but I am not having luck finding much else.
  12. Hi, I am tutoring a gifted student who will be starting to take an intermediate algebra course. They are looking into the Stanford's EPGY Intermediate Algebra course online program versus Art of Problem Solving's Intermediate Algebra course. I would like to know how the two compare to each other. I have looked at the AOPS course table of contents and I also own the book and can see that the material goes beyond any typical honors algebra 2 curriculum. However I am having trouble finding much information about the EPGY course table of contents (it seems they use the text Intermediate Algebra by Lial/Hornsby/McGinnis), I saw this book's table of contents on Amazon and it appears to be a standard curriculum. Could someone who knows more about the EPGY Intermediate Algebra course comment on the challenge level? Just from seeing the TOC of the book, I am guessing the course will mirror that curriculum and it does not appear to be as challenging as AOPS. Note, the student is gifted middle schooler and has math competition experience (MathCounts/AMC/AIME), so I am definitely recommending AOPS, but wanted to know whether I am not missing anything in the EPGY program.
  13. Soo true... I made that mistake when i discovered Alcumus; it was around 10-11pm and I made and account and started doing them quickly in my head, then they got a bit harder but I couldn't stop since I realized I was on a streak, then I started getting tired but they gave me quests, and the problems simultaneously got more fun (number theory, geometry, etc), so I kept going way past midnight... Long story short, it was not a fun day at work the next day, but totally worth it!
  14. I agree, for computer science, the Counting/Probability material is extremely useful to learn as early as possible in order to have a leg up in today's challenging CS college curriculums. If they will go into CS, it's imperative they learn this stuff asap, because in my experience being able to 'count' properly (i.e. combinatorics) takes a couple of passes before it really registers in the brain, so doing this book at the earliest possible age will provide the greatest benefit later. To me counting, and probability to a lesser degree, seemed quite murky the first time I wrapped my head around them, and I felt I only really understood the concepts well, when I had seen them 2 or 3 times, unlike the standard algebra/geometry/calc stuff. Number Theory is beautiful but not as applicable as the other book; definitely great for a math major, but in my opinion probably less important in terms of overall applicability. Wonderful stuff to know for high school competition math contests, though.
  15. Thanks for this hadn't heard of it; I'll read up on it. A good set of word problems would be a bonus to have.
  16. Thanks, I checked this out and looks pretty comprehensive. I don't think my student will have time for a full course since she's already taking algebra in school, and although she knows it all, she wants to compete so she'll be spending about half her time contest problem solving and the other half with geometry. Also it's a bit pricey since it's a full structured course and I don't think the parents will want to budget for it. The Jacobs book looks great though, it seems to be the book of choice for many people here.
  17. Wow thank-you, I just checked out the review of Geometry: Guided Inquiry (calling it GGI for now), and the sample pages and it looks wonderful! I love the interesting questions posed in each chapter opening and the fun aspect to solving the problems. I never knew something like this existed for geometry!! That said, did you guys feel that the problems presented in GGI are too easy on average for a smart student? How does it compare to AoPS geometry? I can see that they have the same exciting tone, and problem solving through exploration approach, but I'm wondering how the material overlaps between the two books (i.e. what's missing in one vs the other). I think I have the Jacobs geometry book; I bought it at a thrift store a few months back, but it must be a 1st edition since it says it's from 1974. I had quickly gazed through it and it looks pretty interesting.
  18. Thanks quark, I had already read those other threads as well, and there seem to be a few good suggestions that are popular among users here. I've also seen the massive collection of competition problems from AoPS, and I know that will help her a lot. I had already found AMC problems + sols from the last 13 years posted elsewhere online and printed them out in pdf for her, so she has a full binder worth of stuff to solve, so I think she is set for now in terms of problem solving material. I've only had a 2 hr session with her so far, but it was extremely productive and I was impressed by her ability to focus and solve problems the whole time without any breaks. It's clear to me that she will go far if she keeps up this pace/effort. I know her mom told me she had won some sort of math competition in the past, but I'm not sure what it was exactly, as it was before 6th grade, so must have been something aimed at K-5 kids. I will find out more next week. For now I have decided to stick with AoPS geometry and have picked a bunch of geometry problems from the first chapter (angle chasing), to start her out. I did them myself and found them pretty easy, so I'm hoping the geometry book will actually get harder as we move to deeper topics. I've also given her a set of fun exponent manipulation problems to see how she does on them (most were from the challenge section of the AoPS pre-algebra book, exponent chapter; I worked these myself before picking them and some were tough; many were from MathCounts, and they all involved some tricky manipulations, so they're definitely competition material worthy).
  19. That's true. When I first discovered the AoPS site earlier this year, I wasn't really impressed with their book samples posted on their site; it was only when I decided to order a book and started reading it from the beginning and doing the problems that I realized how well it flowed, and how logically connected with great explanations it had.
  20. Thanks everyone, I have started a new topic on this in the Accelerated Learning board.
  21. I'm currently looking at geometry books for tutoring a gifted sixth grader, and her mom had the Abeka geometry book handy and gave it to me to evaluate. I have looked through it briefly, and I noticed that it is very wordy, talks about some things in a way that you don't find in other texts (confusing in my opinion), and it just seems very very dry in general (2 column proofs, and not enough exciting problems, like in the typical AoPS books), and just proof after proof. On the other hand, I already have the AoPS geometry book and I've started reading it from the beginning, and it's absolutely delightful; i.e explains things wonderfully well, the problems are connected, and fun but challenging at the same time. So my gut strongly tells me to go with AoPS book, which her mom has as well. Regarding her abilities: I gave her a diagnostic exam in algebra 1, and she is quite talented; (she can easily solve quadratics, find roots, etc), has good number sense and pretty good problem solving ability, even managing to solve a few of the problems that I gave to her from the AoPS algebra 1 book. (She is taking an algebra 1 honors course in school, but she is bored and works on her own half the class). However, she admitted that she doesn't really enjoy geometry (I think probably it's the proofs she doesn't like), but loves algebra. Also, I'm not sure whether her mom had her do any AoPS material before, (I think her mom said she had done algebra somewhere else), but it's apparent to me that she loves math and loves solving problems, so AoPS would be a natural choice here, in my opinion. The last thing I want to do is bog her down with boredom, and I'm pretty sure AoPS geometry will keep things exciting. Based on the AoPS prerequisite of having a strong algebra background, I think she'd be a good fit. Her mom would like her to focus 50/50 on geometry/AMC 8 math competition, and I know that she will also be able to start MathCounts at some point as well, which is the most challenging competition for middle school and they have a strong team at her middle school. Her mom's geometry goal would be for her to test out of geometry next year (7th grade), and take algebra 2 instead at her school. In terms of fulfilling these goals, my thoughts are that AoPS makes sense because it continues to sharpen her problem solving ability which will help her for her middle school competitions (especiall MathCounts), and also will hopefully make geometry feel more fun for her than other geometry texts. Also she doesn't have to finish the whole geometry book; I understand there is more than enough in there to be able to place out of her geometry class next year. Would love to hear feedback from veterans on this site!
  22. I'm currently looking at geometry books for tutoring a gifted sixth grader, and her mom had the Abeka book handy and gave it to me to evaluate. I have looked through it briefly, and I noticed the exact same things you said; it is very wordy, talks about some things in a way that you don't find in other texts (confusing in my opinion), and it just seems very very dry in general (2 column proofs, and not enough exciting problems, like in the typical AoPS), and just proof after proof. On the other hand, I already have the AoPS geometry book and I've started reading it from the beginning, and it's absolutely delightful; i.e explains things wonderfully well, the problems are connected, and fun but challenging at the same time. So my gut strongly tells me to go with AoPS curriculum. I gave her the diagnostic exam in algebra, and she is quite talented; (she can easily solve quadratics), has good number sense and pretty good problem solving ability, even managing to solve a few problems that I gave to her from the AoPS algebra 1 book. However, she admitted that she doesn't really like geometry, but loves algebra. I'm not sure whether her mom had her do any AoPS material before, (I recall not, I think she mentioned she had her algebra somewhere else), but it's apparent that she loves math and loves solving problems, so AoPS would be a natural choice here. The last thing I want to do is bog her down with boredom, and I'm pretty sure AoPS geometry will keep things exciting. Would love to hear feedback from veterans on this site!
  23. I poked around the net a bit and apparently their calc text is even harder than the precalc (if that's possible), some of the problems are taken from the Putnam, which is the most prestigious math college competition in the US. It's a surprisingly small book; only about 300 pages, not like the standard 1000 page calc tomes, but the problems are much harder than standard stuff. So after taking AoPS pre-calc any normal calculus class (AP AB or BC, etc) should be a breeze for your daughter, while on the other hand AoPS calc will be really hard unless she's won high school math competitions. More below: http://talk.collegeconfidential.com/college-admissions/1132444-has-anyone-taken-aops-calculus.html
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