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Earliest Age someone has successfully started AoPS?


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DS is done with elementary math in one of our three ongoing math curriculums. Having done one, the other two should fly by even faster. He is done with LOF, on 5a with Singapore and working through Beast as they come but has only done one chapter in 4 so far. He is not even remotely ready for Aops PA. He just doesn't even come close to the maturity needed to tackle it yet, but it is the curriculum that I am aiming for. I am trying to figure out how many years I need to plan for slowing him down. I can't put off Pre-A forever, but I am trying to figure out how long I need to space things out. Maybe I cut math back to 20 min. a day and if he doesn't get much done-- all well-- that will just help slow us a bit. I'm thinking that at most SM will take us four months to finish 5 and 6 and Beast might be another four. At which point DS won't even be 7.5 yet. But that seems way too young to start Aops, as does 8. Nine seems more manageable. But that is 1.5 years to fill with ???? Two other pre-a programs (LOF, JA)?? At which point it just seems crazy to continue with running three consecutive math curriculums.

So I'm just wondering the youngest age to start Aops successfully with "average" very non-average kids? Can I really hold off an extra 1.5 years till nine?

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There's always other problem solving e.g. the elementary and middle school math olympiad books, Moscow Puzzles, math hand in hand with science through the TOPS Science books, Martin Gardner books (Aha Insight, Aha Gotcha) etc. DS started with AoPS when he was 8 years and 5 months-ish or so, but he did the Intro to Counting and Probability book first and the class (there was no Pre A then), then a couple of chapters of Intro to Number Theory before he hit 9. Your DS could also start gently with Alcumus if he is into online problem solving.

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We started at eight.  It worked well, or as well as the first initial chapters go.  There was no way we were going to get through the curriculum in a year.  We went really slowly, put it away for long stretches, pulled it out again.  I think you should start early and just let your son know that anytime he is fet up, it can go away.  Anytime he is really starting to have meltdowns, you take a week or two off.  By letting my son decide to stop he felt more in control and was much more willing to pull it out.  I will preface this by saying, he knew up front that math was never going away totally, just for a bit till he felt more comfortable tackling it.

 

I think we only made it through the first four chapters that first year.  When the emotions died down, then he flew through it.  He is all set and ready to go this coming year.  Openly asked to begin Geometry.  Really felt victorious at the end of last year.  Very much so a slow and steady wins the race game with AoPS, at least in our experience.

 

 

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My DS is 6 (almost 7) and we started one month ago. I do not let him loose on AoPS. I work through the chapters with him - basically hand holding. We are also working on SM CWP, MEP worksheets and Zaccaro on the side (mostly for review). DS finished grade 5 material in one online course and in one textbook based curriculum sometime last year and I got tired of asking him to repeat more of the same stuff. So, I had him do dragonbox, some Critical Thinking Company Balance Builder kind of stuff and some whiteboard based algebra for a few months and finally started AOPS PA recently. He is also very strong in his math facts and we spent a while on drilling those as well.

 

AOPS is slow going for us - we stop and discuss in more detail what some of the explanations mean. We are in chapter 2 now, and we will not be making any dramatic change in pace until my DS turns 8.

 

IRL, I met several kids in a local gifted school offering radical acceleration where 60% of 3rd graders were doing pre algebra (using Saxon PA). They were all around 7-8 years old.

I think that if you can preview some of the pre algebra stuff informally, and if your child is strong in his math facts, then you can start AOPS PA and go at a slow and steady speed right away.

 

Good luck.

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PreA wasn't out when older ds started AoPS.  He started Intro Algebra at just 9 and worked on it *completely* independently.  It took him almost 3 years to finish including every single challenger.  It is definitely a different approach than most take, and definitely one that I did not plan or really even condone.  But it was the path that my boy *had* to take.  He would not let me help him, ever.  And he would cry day after day, until finally in desperation I hid the book.  But somehow it was this fight, this battling for understanding that forged his math talent. 

 

I don't really have any sage advice for you.  But thought that an additional experience might be helpful.

 

Ruth in NZ

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We started AOPS PA at 8. DD was ready, math-wise, at 7, but wouldn't have been ready emotionally (I thought, anyway), so we spent a year on LOF and Key to Algebra. She spent from August-Nivember on the first four chapters, took a month break, and then came back and soared through the rest of the book. We just started AOPS algebra, and that's going pretty smoothly.

 

I don't regret the 2 year PA plan here-I think she needed the time to grow up. I can't imagine her handling those first couple of chapters of AOPS PA at 7. However, she's not, primarily, a math kid. If she were into math the way she's into science, I could see AOPS having worked earlier.

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It would be interesting to know the details of those using AoPS with younger students. Doing the main lessons, but skipping the challenge problems or working through all the problems on a white board together is a different scenario than a student doing all the problems -including challenge problems- independently. Not that there is one right way, but details do help others to have a better understanding and more realistic expectations. 

 

I sometimes worry that now it's not only about getting to calculus quickly, it's about getting there quickly while using AoPS, even if that means not using it to the fullest.

 

Again, not that there is one right path. Everyone has different children and different goals. My point is that there are many ways to use AoPS, and I find it most helpful when specifics are given.

 

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We had a lot of tears and frustration last year. The funny thing, though, is that it usually wasn't the challengers that got her, but problems earlier in the chapter. She understood that the challengers were supposed to be hard, supposed to trip her up, so it bothered her less. I noticed the same phenomenon with starred problems-often she'd have an easier time working through them than a non-starred problem earlier on. It got better as the year went on, and I think a big part of it was simply realizing that AOPS is supposed to be hard and that it's normal to not get every problem right up front.

 

I do think that part of that is because if she was struggling with the regular problems, we'd sit on that section for awhile before moving to the challengers, though. If I'd handed her the challengers from the exponents before we'd beaten those suckers into the ground, I have a feeling we would STILL be on that chapter, with daily meltdowns at the sight of the book!!

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Yes-one major reason I held off a year was so she could get used to writing out math, and LOF was good training because the author ( who DD idolizes) explicitly tells the reader to write out the problems.

 

There is one exception. When they asked for "explain why" initially, I would let her explain it in words to me and write it for her at first, and then let her figure out what was important and write out the steps, because she'd tend to brain dump. I wanted her to start approximating a proof form, not a several page narrative that rambles and winds. She got much better at that through the year. So far, she's been able to skip the dictation step this year, but she's still on the review section, so it's more a case of remembering what she figured out last year than truly explaining from scratch.

 

I'm expecting to hit some slow spots in Algebra, and I'm rather expecting to spend 2 years on it, like we did for PA. I'm also planning to do number theory and C/P before going to AOPS geometry, because DD has really struggled with geometry in the past, so I'm thinking more maturation and time to grow before reaching it would be good. She may surprise me, though. It wouldn't be the first time.

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My kids started around 7.5 years old. My older wrote everything and did everything but he did not copy the questions. My younger wrote everything but I ask him to skip the challenge questions and he did those after finishing all the chapters as a end of book review.

 

After doing the prealgebra book, they were faster with the intro to algebra book. Before prealgebra we did math contest problems for fun since kids weren't interested in competitions. Their favorite subject is science all along.

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I started at 9 with my son, and he would not have been emotionally ready before that.

 

We do the book as intended - All problems, exercises, review, and challenging problems. I use the program to slow my son down, and it has worked for that. We're spending at least 1.5 years on Prealgebra. I plan to use another program for Algebra, then do Algebra again with AoPS. I think by the end of that, my son would only be maybe a year ahead of a typical advanced public school sequence. Granted, AoPS Algebra may go faster than I expect after doing another Algebra course. We'll see.

 

I held my son's hand through the first 2 chapters of PA, but he's been on his own since chapter 3. If he needs more practice, I pull out Dolciani for some basic drill.

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As from above, my son started at eight. We took two years for PreA, but there were long stretches of no math. I held his hand for the first two chapters of PreA going very slowly. It was an emotional grind and an important confidence builder, not a math issue. By the third chapter, I had him work on the whiteboard to write out the problems with discussion and then the exercises independently. By chapter four, he was doing the problems and exercises independently and then I would pick one at random for him to have to explain/teach to me. At that point it was all independent. The only chapter he did not do the challenge problems for was exponents. It was a brutal one for him that we are going to cycle back through this year. The lights were on, but they were flickering. I didn't want to crush him.

 

I am involved when he does not completely understand the wording or exactly what they are asking for with a proof. He will also sometimes come up with his proof in long winded garble and not know exactly how to write it out so I ask him questions to help him narrow down what he is saying. He will sometimes want me to help him with how to show his work as well. As a visual spacial kid, his way is often involving shapes or not the standard algebra.

 

He has chapter tests that I create from the review questions, including the challenge questions and definitions from the chapter. I make a study guide by splitting the review into half study guide, half test. Each review takes one week for him to go back and read/study/ask questions then he takes the test. He gets one day for those ten to fifteen problems. Exponents took two days, where we drew a line for which problems were completed the second day.

 

Mostly the thing he learned that first difficult year was to know when he really gets something. Now he can differentiate if he gets it and should move on, or if he needs to linger longer to understand. Before, he would just read the words and plow through. When he got to the problems/exercises he would then panic because he did not understand. Now he understands the need to move purposefully. It allows him to work independently, because he can check himself.

 

ETA: I mis-used a version to, and just could not let it stand.

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This is all interesting and helpful for me to think through how I want to use Aops. Do I want a lot I hand holding, or more independence? I need to start on the book myself so I know just the level that it is asking for and then I will know better when DS will be ready for it. Thanks for all your thoughtful replies. I am quite floored that ashleysf's 6.? Yr old is staring on Aops, not that there aren't really really mathy kids that could do it, but just that they could possibly be ready for the format and the emotional struggle of being challenged. I know my DS has at least a year or two before he reaches that stage. He still freaks out just seeing a starred problem in Beast, no matter how hard or easy it is for him-- just the star sends him into panic, and not out of experience as we have only hand picked out a few Beast chapters so far.

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Now that we're done with Pre-A, all I have to add is that it seems to be easier in the later chapters because the child has adapted to the format and is a bit older. I've seen a huge difference when we started at 7 and now (we just finished during the summer after the online class). There is a huge adjustment from working in a work text to copying problems, from many practice problems to just a handful, from not having to think as hard to thinking that your brain cells are getting killed off by AOPS (DD's words, not mine). I'm glad we're moving on since AOPS Pre-A was way too intense to justify just a Pre-A label.

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A quick note about what we are doing -- we started the introductory Algebra, Number Theory and Counting/Prob. books when A. was 8.  We cycle, there is a good deal of explicit teaching, I pick challenge problems as I deem appropriate.  I just need to keep him engaged with math and used to working hard as he matures, and this is working.  He didn't engage with other stuff I tried. 

 

ETA: I think that how one ought to use AoPS must depend a great deal on the child & the parent too.  A. is the sort of accelerated that qualifies, in terms of how much active management and intervention/support/intense parenting he requires, as "special needs".  Math normalizes him.  He does not thrive when bored, so I have to keep him challenged, but he doesn't "like" math so he won't just sit and do it on his own.  He is a systematic and analytical/abstract thinker.  Other programs, including upper-level Math U See and Singapore DM, failed to engage him -- he didn't ever get excited about the work or perk up.  With AoPS Intermediate level materials, he works slowly and he requires a great deal of teaching support and he is totally demoralized by some of the challenge problems so I don't make him do those.  On the other hand, he is learning excellent maths, is being emotionally stabilized, and is engaged -- he gets excited sometimes. 

 

Also I require do-the-next-thing materials for this child, because parenting him takes so much of my energy and creativity, and it prevents me struggling to get him to do something that's supposed to be "fun": we just do the work we have.  I wouldn't be doing this with N., and won't need to (heaven willing and the creek don't rise!).

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It would be interesting to know the details of those using AoPS with younger students. Doing the main lessons, but skipping the challenge problems or working through all the problems on a white board together is a different scenario than a student doing all the problems -including challenge problems- independently. Not that there is one right way, but details do help others to have a better understanding and more realistic expectations. 

 

I sometimes worry that now it's not only about getting to calculus quickly, it's about getting there quickly while using AoPS, even if that means not using it to the fullest.

 

Again, not that there is one right path. Everyone has different children and different goals. My point is that there are many ways to use AoPS, and I find it most helpful when specifics are given.

 

... your post is why I typed out the ETA above.  I agree that rushing isn't a good idea.  In our case, I am happy to go slowly, but I need the child engaged and challenged.  We may come back and do the challenge problems before moving to the advanced level. 

 

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I think another question should be "earliest age someone has finished AOPS", except that defining "finishing" is hard. That is, it's not so much starting at 7 that's a concern if you don't mind that it takes until 9 to finish because your child needs that extra time to absorb the concepts or needs more repetition. I suspect my DD would have finished AOPS PA at about the same time if we'd started straight out with it after 5B-it just might have required more breaks and more additional material. It's simply that she did the additional material first. I'll be interested in seeing what happens with AOPS Intro Algebra. (DD studies snakes...I study DD).

 

I do think that sometimes there's a "hurry up and wait" with these kids.I've seen it with biology for my DD-she got to a level that truly challenged her, but now, she seems pretty content to sit on that level of content and absorb and connect. Which sometimes gets frustrated (I'm sorry, but there really isn't that much difference between the parts of plants and animal cells that she learned at age 5-6 and the ones that she's spending a huge amount of time on in Campbell's bio-but apparently, it's just really, really engaging). Her mentor says that she's making connections that are beyond what a lot of college undergrads make, so obviously, she's still drawing content from what seems like more of the same, but I don't pretend to understand it.

 

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It would be interesting to know the details of those using AoPS with younger students. Doing the main lessons, but skipping the challenge problems or working through all the problems on a white board together is a different scenario than a student doing all the problems -including challenge problems- independently. Not that there is one right way, but details do help others to have a better understanding and more realistic expectations. 

 

I sometimes worry that now it's not only about getting to calculus quickly, it's about getting there quickly while using AoPS, even if that means not using it to the fullest.

 

Again, not that there is one right path. Everyone has different children and different goals. My point is that there are many ways to use AoPS, and I find it most helpful when specifics are given.

 

DS is seeing some of this in his AoPS classes.  There are definitely some very young and very advanced kids who have accelerated through the material without developing the problem solving skills and the 'math maturity' that allows for insight into tough problems.  I just went and asked him how you develop this math maturity that everyone talks about, and he said 'experience.'  So I asked him, if you peak at the solutions for the challengers is that still experience?  -- because you would have seen more problems in the same amount of time than if you struggle over just 1 problems for hours and hours.  And he said that it is the struggle that counts. Peaking is ok, but only after you have really fought for it.  So I asked him, 'how long is long enough to struggle?', but he had no answer to that one.  Last year, the kids at the Math Olympiad training camp were constantly talking about how you develop the insight.  All of them could always understand the answer even to incredibly complicated problems, but often could not get it themselves. 

 

It seems to me that you could start kids off young and hold their hand for a while and then slowly transition them to more independent work.  But you really have to give them enough time and encouragement to struggle with the hard problems.  There were days in the Intro Algebra book that my ds would take a full 2 hours for a challenger, and there would be 15 challengers in a section.  I guess you can see how it could take 3 years to finish the book.  But what is so great about starting young is that you have *time*, lots and lots of time for your kid to develop the ability and desire to struggle.  There is just no hurry. During those 3 long years I did feel a bit of :toetap05: , but ds wanted to do it *his* way and needed me to get out of the way!  At this point, he is the kid that helps all the other kids. He is the kid that solves the really tough proofs that no one else can solve.  He is also the kid that never gives up. I do think it is a personality thing, but I also think that having the luxury in the past to master the material at his own pace has been critical to his current success.

 

I will also say that Kathy in Richmond said that Advanced Geometry in particular requires a lot of math maturity, and told me that a lot of that is just age.  DS will be taking Olympiad Geometry starting in October, so we will see if he is just too young to handle it.  He will be studying intermediate geometry full time for 2 months to prepare.  Apparently, one of the kids told my ds that he only figured out 7 problems during the entire 3 months class. :huh:

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It would be interesting to know the details of those using AoPS with younger students. Doing the main lessons, but skipping the challenge problems or working through all the problems on a white board together is a different scenario than a student doing all the problems -including challenge problems- independently. Not that there is one right way, but details do help others to have a better understanding and more realistic expectations. 

 

I sometimes worry that now it's not only about getting to calculus quickly, it's about getting there quickly while using AoPS, even if that means not using it to the fullest.

 

Again, not that there is one right path. Everyone has different children and different goals. My point is that there are many ways to use AoPS, and I find it most helpful when specifics are given.

I gave this an "invisible like" earlier today, but it merits repeating.

 

There's so much good material packed into AoPS. That's the real gift of the curriculum, and those challengers. No hurry needed; in fact, the kids I've seen go furthest in the long run are the ones who took their time and attempted most or all of those challengers and starred sections. If you start young, take it easy and travel at your kids' pace.

 

One of the reasons that I removed myself from Epsilon camp was the pressure to have these young 8-10 year old kids complete a formal algebra 1 course like AoPS before attending. It wasn't that they couldn't - they certainly could! But was it the optimal path? I don't think so, at least in the vast majority of cases. There are always exceptions, and I certainly met a few. But overall, I believe that math is best learned by thinking deeply, and that takes time, lots of time, and struggle.

 

When I first read lewelma's post a couple of years ago about how her son was wrestling with the alg 1 book on his own initiative and attempting every single problem, I knew he'd go far. :001_smile: On the other hand, when kids tell me that they've "breezed" through and finished a book like AoPS problem solving vol 2, I scratch my head. I'm not sure how anyone could really feel they've ever completed it. At least for me, I revisit it every now and then and always find new stuff to learn and topics I haven't yet mastered.

 

Our story with AoPS has been different from everyone's above, mostly because the books weren't written (except the two classic problem solving texts) in time for my two kids. But there were online classes available then at the intermediate and olympiad levels. Ds worked on the olympiad classes at 15 and up, and dd started with intermediate classes around 12/13. Back then, without Alcumus or textbook problems, they "only" were assigned a midterm and a final problem set in addition to the weekly problems on the classroom boards. I credit the hours they spent thinking hard over those problem sets in making the necessary connections in their minds to bring them up to the next level of mathematical thinking. AoPS classes and math camps were the key ingredients that gave my son the ability to attend the US math olympiad training camp (it certainly wasn't a result of studying past AMC tests, LOL; that rarely happened here). And he was a kid who didn't hit algebra 1 till grade 6 when I brought him home from public school.

 

DS is seeing some of this in his AoPS classes.  There are definitely some very young and very advanced kids who have accelerated through the material without developing the problem solving skills and the 'math maturity' that allows for insight into tough problems.

True. You should hear the stories dd relates now that she works there... And the calls from parents who want them progressing even faster... :sad:

 

I just went and asked him how you develop this math maturity that everyone talks about, and he said 'experience.'  So I asked him, if you peak at the solutions for the challengers is that still experience?  -- because you would have seen more problems in the same amount of time than if you struggle over just 1 problems for hours and hours.  And he said that it is the struggle that counts. Peaking is ok, but only after you have really fought for it.  So I asked him, 'how long is long enough to struggle?', but he had no answer to that one.  Last year, the kids at the Math Olympiad training camp were constantly talking about how you develop the insight.  All of them could always understand the answer even to incredibly complicated problems, but often could not get it themselves.

I think that the struggles and deep thinking and the years of experience are what allow the mind to make connections. And connections are the root of creativity in problem solving.

 

One of dd's math club teammates here in VA was a USAMO winner (top dozen kids) back in high school. He was a public schooler downtown at the Governor's School, so we guessed that his schedule was busy enough that he hadn't had much time to study for the AMCs. So we asked him why he thought he did so well on those hard proof problems. He said it was simply applying to Mathcamp that spring. He'd had to take the entry quiz, which is a set of eight extremely difficult and open-ended math problems. The deep and extensive thinking he'd had to do on just a few tough problems helped his mind grow by leaps and bounds. (he definitely said it wasn't because of his high school's 'gifted' math, which involved accelerating them through the local uni's math sequence) He now works at AoPS a couple of desks down from dd. :)

 

I will also say that Kathy in Richmond said that Advanced Geometry in particular requires a lot of math maturity, and told me that a lot of that is just age.  DS will be taking Olympiad Geometry starting in October, so we will see if he is just too young to handle it.  He will be studying intermediate geometry full time for 2 months to prepare.  Apparently, one of the kids told my ds that he only figured out 7 problems during the entire 3 months class. :huh:

I wish, wish, wish that AoPS would develop an online *intermediate* geometry course! But they are already overbooked...

 

Good luck to your son, Ruth! My kids enjoyed Olympiad Geometry at age 16, but I bet if anyone could do it earlier, it would be your boy. And I've definitely heard of kids who took that particular class twice, hoping to get more out of it the second time around. It was the only AoPS course where I personally threw my hands in the air because I couldn't keep up...I don't have the VSL talents that my kids have (they get that from their dad!)

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Math maturity may be the key over mental maturity.  Arithmetic skills really don't translate to AoPS.  You need to have a feeling for the language to really succeed.

 

DS7 is doing AoPS Prealgebra, and through the first few chapters, doing great, even on the challenges.  He is a bit slow because he has the focus of a seven year old, but he is persistent and has a solid foundation in arithmetic theory already.  He has needed a couple of hints, but that's all.

 

We will see how things go with the later chapters, but the first few haven't been a problem.

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There is a mathematical maturity/mental maturity pas de deux. On the continuum there will be the extraordinarily rare child who has the right combo of mathematical maturity/mental maturity to excel far beyond the norm.  Sho Yano is one example. If I'm not mistaken, by age 18 he had received his PhD in Molecular Genetics and Cell Biology from the University of Chicago. He received his MD at 21.

 

From there we continue along the continuum through the various mixes...

 

There are times when the mathematical maturity is near its max for two closely performing students, so the mental maturity will be what determines the difference. There will also be instances when mental maturity will allow a child to outpace another who has more mathematical maturity, but less in the way of overall maturity. It makes boards like this tricky. We don't actually see the children, so it's hard to truly understand the different mixes of traits we're comparing. Sometimes even when seeing the child, it can be hard to remember all the factors that are contributing to the end result.

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If your child really enjoys working on math and understands it, let him go at his own speed. That's ideal.

 

My son didn't start AoPS until about 6th/7th grade but he went through a lot of it fairly quickly working in fits and spurts. He has always attended a B&M school but worked on math whenever he had free time because it was, and still is, his favorite subject.

 

In high school he has worked through different areas of math with some excellent and dedicated teachers and local professors. He is lucky in that regard.

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One of the reasons that I removed myself from Epsilon camp was the pressure to have these young 8-10 year old kids complete a formal algebra 1 course like AoPS before attending. It wasn't that they couldn't - they certainly could! But was it the optimal path? I don't think so, at least in the vast majority of cases. There are always exceptions, and I certainly met a few. But overall, I believe that math is best learned by thinking deeply, and that takes time, lots of time, and struggle.

This is very interesting and sad. I hope you find a way to use your talents and enthusiasm to help other young mathematicians.

 

True. You should hear the stories dd relates now that she works there... And the calls from parents who want them progressing even faster... :sad:

DS knows who they are. These kids even talk about their parents pushing them to take the WOOT in 6th grade, and ds is the one helping them to solve almost every single problem in Algebra 3. So they end up with all blue bars. Yes, they have learned a lot, but not nearly enough and then they just progress further. DS at first was really frustrated with all these really young kids, but now he is feeling sad for them that they feel this pressure to just go further, faster, and without the depth and mathematical maturity needed to truly succeed.

 

I think that the struggles and deep thinking and the years of experience are what allow the mind to make connections. And connections are the root of creativity in problem solving.

Very well said. There is also a serious need for persistence and for a lack of fear of failure. I think some kids fear disappointing their parents as much as fear of their own personal failure, so all of us need to be very very careful.

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