Another 'how to use AoPS' question.

[Pen]

We just recently started the AoPS adventure with Intro to Algebra.  In the how to use this book part if says, "You should think hard about a problem before deciding to give up and look at the solution."

 

For how long?   An hour?  months?   Over time gaps away from desk while doing other things?  Stopping the program till the one problem is done, or going on to easier ones while it percolates at back of mind?

 

What have you / your child found best?

 

My purpose with it is in large part learning how to problem solve and think and not be intimidated by difficult questions.

[regentrude]

 

We just recently started the AoPS adventure with Intro to Algebra.  In the how to use this book part if says, "You should think hard about a problem before deciding to give up and look at the solution."

 

For how long?   An hour?  months?   Over time gaps away from desk while doing other things?  Stopping the program till the one problem is done, or going on to easier ones while it percolates at back of mind?

 

What have you / your child found best?

 

 

For the problems at the beginning of the section, I expect my kids to think maybe up to half an hour. They are usually rather straightforward and not that time consuming, because the questioning guides them in the right direction. If they have not figured out the answer then, they look at the explanation in the chapter and continue.

Now, some of the challenge problems at the end of the chapter do take an hour of thinking, or more. And for some, stepping away and doing something else is a good strategy (I recently went to get a haircut while pondering a geometry proof, and while the hairdresser was messing with my head, the solution came to me, LOL). Sometimes even putting away the problem for weeks.

When my son gets stuck on a hard problem, he usually puts it away and tells me in the afternoon. Sometimes we then sit together and talk through the problem, or I may give him a slight hint.

 

I assign some of the challenge problems after we had just worked through the chapter. Some of the other we do as part of the semester review before the exam. Sometimes sitting on the concepts and revisiting them a few weeks later makes it easier.

We have had road blocks where it was beneficial to skip and come back later.

[StephanieZ]

I'd say somewhere between 10 minutes and an hour, depending on the kid. 

 

 

[quark]

Son uses AoPS as a supplement. He mostly chooses the review and challenge questions. What I do is to let it percolate (and he moves on), and I pencil the question number on a later chapter's page. So say for example, if he's stuck on something in chapter 9, I will pencil that question number on top of the review problems section of chapter 10. This reminds him/ me that he needs to go back to the question in chapter 9 at some point while working on chapter 10's review and challenge questions. If he still doesn't get it by the time he finishes chapter 10, despite trying hard, he checks the solutions and rechecks all his steps.

[Pen]

I think I'll incorporate all ideas above.  Thanks.

 

[StephanieZ]

FWIW, my dd16 is finishing up AoPS PreCalc, and it is not unusual for her to spend more than 2 hours on a tricky challenge set problem. I'd wager that she's spent 4 or 5 hours on some of them. Of course they don't all take terribly long time periods, and no one is forcing her to spend such insane effort on single problems, but she always wants to be "in the blue" (the A+ zone) on her class report, lol. It sure goes to show that as kids mature, under the right AoPS circumstances, they can happily spend large periods of times struggling! 

[Luckymama]

FWIW, my dd16 is finishing up AoPS PreCalc, and it is not unusual for her to spend more than 2 hours on a tricky challenge set problem. I'd wager that she's spent 4 or 5 hours on some of them. Of course they don't all take terribly long time periods, and no one is forcing her to spend such insane effort on single problems, but she always wants to be "in the blue" (the A+ zone) on her class report, lol. It sure goes to show that as kids mature, under the right AoPS circumstances, they can happily spend large periods of times struggling!

Dd is taking the AoPS online geometry class. She has spent up to 3 hours on a challenge set problem. There have been problems that she just could not get, as well (which is great---she shouldn't be able to get everything correct with an AoPS class!).

 

Getting "in the blue" is a Very Powerful Motivator for dd :D

[kohlby]

Agree that it depends on the child.  My 10 year old starts to get very frustrated after 15 minutes stuck on one problem.  But when he first started Intro to Alg last year at 9, he would get frustrated immediately if he didn't know how to do it.  He had to be reprogrammed to learn that it's okay to struggle.  The problem sets take different amounts of time.  If he gets stuck and is starting to get frustrated to the point that he can't think straight, then I come in and ask him some questions or give him some hints and help guide him.  A 16 year old may be more willing to spend an hour or more on just one problem, but my child isn't there yet.  He has spent up to 2 hours on a problem set before, but it's usually 30-90 minutes.  The total time spent isn't the issue with him, it's how much time of that is spent stuck.  If he gets stuck and I guide him through, then he gets less stuck on the next problems.  If he skips that problem to go back, then he has trouble relaxing his brain to focus since he's still bothered by the other problem.

[Pen]

...  He had to be reprogrammed to learn that it's okay to struggle.  ... The total time spent isn't the issue with him, it's how much time of that is spent stuck.  If he gets stuck and I guide him through, then he gets less stuck on the next problems.  If he skips that problem to go back, then he has trouble relaxing his brain to focus since he's still bothered by the other problem.

 

 

How did you do this: "reprogrammed to learn that it's okay to struggle"?

 

Thank you for pointing out the potential problem with skipping and then going back.  I think my ds also has that issue.  Do you think it is possible to learn to move past that as with learning that it is okay to struggle?

[Luckymama]

How did you do this: "reprogrammed to learn that it's okay to struggle"?

 

I don't know if you have the time or ability or interest, but I sometimes do the problems at the same time as dd, at the other end of the table. She sees me try one way, then another, then a third, until I reach a solution. She hears me sighing and erasing :lol: At first, dd would shut down after her first attempt left her stuck. Then she'd try two ways. Now she'll try three or four ways before throwing down her pencil.

 

I call that success :D

 

(My background is in academic chemistry. I should have been a math major. When I'm a grown-up I want to be a math and science tutor.)

[kohlby]

I explained struggling like using your muscles.  If you exercise more than you're used to, then it's hard and your muscles may get tired.  But they get bigger as a result.  I explained that though he did learn with MUS, he didn't learn as much as he does with AoPS since he's now challenged.  I also explained a study I had seen about math ability.  It showed that people who were willing to struggle with math to get it ended up better at math - that it wasn't so much what they went in knowing but them not giving up.  That idea - that smartness doesn't mean knowing the answers - really helped.  I think gifted kids sometimes struggle with that more.  They know they're advanced and think that means they're supposed to know how to everything.  I made sure to change the focus to the struggle.  I also told him that it was okay to get the problems wrong - that I cared more about the process than the answer.  When going through his work, I made sure to point out what he did right in the thought process - or if he did something wrong other than a careless error, I pointed out why I understood why he did that but why it didn't work.  He's also seen me work alongside him jump into a problem to only go down the wrong path and have to try something else.  At the start, I had to sit by his side and lead him through the process.  I had to ask him what to do next and give him ideas - and sometimes tell him, but it was a step here and there, not the whole problem.

 

He now works mostly by himself with AoPS.  He actually reached that point within a few months.  I made sure to check up on him since there were some times that I had to tell him to go jump on his pogo stick if he was getting too frustrated.  The idea was to teach him to relax his brain when he started getting too stressed to think clearly.  Me coming in and stepping him through a problem or showing him what parts of the process he got correct was also helpful.  He now normally refuses to go jump on the pogo stick - he wants to get the problems done first.  But a simple few minutes of me showing him where he went wrong and where he went right gets him back on track.  Also, I assigned all the challenge problems for quite a while.  That was his least favorite day so we switched it to him picking so many of them.  It might be picking 6 out of 8 or 9, but it gave him the control and now the challenge problem day is one of his favorite days.

 

Another thing that was helpful was not assigning him too many problems if they were of the wrestling sort.  The Intro to Alg book will end up taking him about 1.5 years by the time we're done.  I've heard of it taking 2 years for some.  And 1 year for others.  We didn't do the online classes since I worried that would be too fast paced.  I wanted him to feel that he had as much time as needed, so there was plenty of time for wrestling.  We also don't do our maths by certain years.  From the start, first grade, we've simply gone forward and started the next one when one ended.  That's how he ended up so far ahead without skipping.  With an advance student, it's also easy to point that out - that they're so far ahead that they have more than enough time to move slowly.  That we could spend years on Algebra and he still wouldn't be behind the public school kids. 

 

He did have a rocky start due to having to change mindset.  But I knew there was victory when about a month in he said, "I'm glad I'm homeschooled because that means I can be challenged in math." He was still getting frustrated a lot at that point and I was still having to help lead him through the process.  At only 9 years old, he had learned to recognize that the challenge is a good thing.  Switching to AoPS was worth it for the math, of course, but it was worth it for him to learn that lesson as well.

[Dmmetler]

How long should it take a DC to do a section? I'm trying to keep math to an hour right now, and for DD, it appears that means that it takes about 2 days to get through a single section of AOPS. Which is fine, I guess-she's learning, understanding, and making steady progress, but at the same time, I'm used to going through multiple math books in a single year, so to be entering the 3rd week without finishing chapter 2 yet is a little disconcerting.

 

 

[regentrude]

How long should it take a DC to do a section? I'm trying to keep math to an hour right now, and for DD, it appears that means that it takes about 2 days to get through a single section of AOPS. Which is fine, I guess-she's learning, understanding, and making steady progress, but at the same time, I'm used to going through multiple math books in a single year, so to be entering the 3rd week without finishing chapter 2 yet is a little disconcerting.

 

I do not think there is a "should" - I have two kids who are both "mathy" and have vastly different working speeds and focus.

My DS never got through one section in one day. He needs at least two, one for the problems, and one for the exercises, often more.

I require one hour of math; we will be done when we are done.

 

But I never had the notion that we would be using more than one math book, as AoPS is plenty for the entire school year (and the algebra book can easily be plenty for two years).

Just to give you perspective: we spent an entire school year on 13 chapters. But: those 13 chapters constitute a complete algebra 1 course that is more rigorous than other one year high school courses. So, I see 2-3 weeks per chapter to be a reasonable speed. (my very ambitious and focused DD covered the entire book in her 7th grade school year plus summer, but I would not expect this from most kids)

[wapiti]

How long should it take a DC to do a section? I'm trying to keep math to an hour right now, and for DD, it appears that means that it takes about 2 days to get through a single section of AOPS. Which is fine, I guess-she's learning, understanding, and making steady progress, but at the same time, I'm used to going through multiple math books in a single year, so to be entering the 3rd week without finishing chapter 2 yet is a little disconcerting.

 

Some sections are longer, some are shorter.  Same with the chapters - different lengths.  Besides, chapter 2 (you are in the prealgebra?) is a bit challenging.  Take your time - it's an important one - as many weeks as it takes.  If she gets bored with exponents, you can shuffle a bit and come back to it (e.g., chapter 3 is easy relative to ch 2).

 

AoPS is typically slow-going even with a much older kiddo.  For a student as young as yours (8 or 9?), slow is to be expected.  In particular, my kids found chapters 2 and 5 to be the most difficult, and they picked up the pace in the second half of the book, where the lessons and chapters are shorter and a bit more even in length.  I'd expect the prealgebra text to last the school year at the very least.

[quark]

When you have a hardworking, bright/ gifted child starting to slow down in math (after starting to use a high quality higher level book) and still doing it willingly most of the time, I think it's finally that true indication of hitting the right challenge level. It's no longer just about starting a book and finishing it within a year. It's no longer about leaping from level to level like you probably did with Singapore Math or Math Mammoth or whatever resources were used at the elementary level. They finally have to slow down, grind those mental gears, really think and be willing to contemplate different approaches. It's super valuable, especially when they don't really need to be rushing through the high school progression just yet. A part of me envies that kiddo gets to experience this process and grow so much from it. I didn't have this as a child and I rue the lost opportunity. I can pick it up again but I am so much slower now in mental stamina and enthusiasm than I was before.

 

Point being, it *will* be disconcerting at first but it's probably the right thing for your kiddo. The disconcerting part comes from being conditioned over and over again by the traditional school mentality to learn something within a given year when not everyone can or should learn that way. It will be disconcerting but you'll get used to it eventually! :) If it continues to be disconcerting, have her take a breather (if she will agree, mine won't) and work on a stack of math circle or contest problems for a while, just for your peace of mind. :p

[boscopup]

How long should it take a DC to do a section? I'm trying to keep math to an hour right now, and for DD, it appears that means that it takes about 2 days to get through a single section of AOPS. Which is fine, I guess-she's learning, understanding, and making steady progress, but at the same time, I'm used to going through multiple math books in a single year, so to be entering the 3rd week without finishing chapter 2 yet is a little disconcerting.

 

It is quite different, isn't it?!? :) We're doing the Prealgebra book, and I am expecting it to possibly take us 2 years (we're also supplementing with other things so it's not all challenge all the time, plus I have a basic arithmetic strand going to keep things from falling out of his 9 year old brain). We usually do the problems one day, exercises the next day. The review takes a couple days, and the challenge takes 2-3 days. We're in the middle of Chapter 2 right now, and again, I'm supplementing with other things as needed. We don't do AoPS every day. This week, we'll only do it once, because I'm using some Dolciani Prealgebra to practice exponents more. He still needs drill, and Dolciani has plenty! :lol:

 

We're not used to a book taking a full year either, but I just remind myself that we're waaaaay ahead, so we can take as long as we want without worrying about the time. ;) If we were doing AoPS every day with no supplements, we'd be done in a year, but at the rate we've been taking it, it will probably be a little less than 2 years. And when he's done, he'll have a very solid understanding of prealgebra skills - both conceptually and procedurally, and should be automatic with those skills. At that point, I'll be quite confident to move him to algebra.

[kohlby]

There are days that take over an hour for my son, and days that take 30 minutes.  We didn't do the Pre-Algebra, but started with the Intro to Alg.  I agree to tell your child that it could take two years and that moving more slowly is a GOOD thing since it means they're at the right level now.  Alg I takes a year in public school, as does Alg II.  So Intro to Alg taking two years makes sense - and it's much more advanced than what the public schools do.  We're now on the second half of Intro to Alg and he does problems one day and exercises another.  In the first half, it depended on the section.  The review problems take 1-2 days depending on the chapter. The challenge problems take one day.  There are chapters that we could do these in two days, but I've found he does best if we limit it to one day and reduce the number instead.  Then he does Alcumus for one day before we move on to the next chapter.  If I don't feel that he's learned it well enough, then he does Alcumus more.  Alcumus explains the problems really well and is an excellent learning tool.  We didn't do any formal math until first grade.  Before AoPS, my son went through 3.5 levels of math in first grade.  In second grade, he went through 2+  levels.  In third grade, he did 2 more levels, which actually meant finishing up one, doing Pre-Alg, and doing half of  Alg I.  In 4th grade, we switched curriculums to AoPS and started with Alg I since the other program wasn't challenging him appropriately and was boring him (and me).  The first half of AoPS Intro to Alg took him about 3/4 of a year.  He took a break with Number theory, which took half a year, and is now doing the second half of the book, which I expect to take most of this year. 

 

 

 

 

[oscilatorium]

FWIW, my dd16 is finishing up AoPS PreCalc, and it is not unusual for her to spend more than 2 hours on a tricky challenge set problem. I'd wager that she's spent 4 or 5 hours on some of them. Of course they don't all take terribly long time periods, and no one is forcing her to spend such insane effort on single problems, but she always wants to be "in the blue" (the A+ zone) on her class report, lol. It sure goes to show that as kids mature, under the right AoPS circumstances, they can happily spend large periods of times struggling! 

 

I recently got their PreCalc book; it's probably by far the hardest one in terms of the sheer difficulty of many of their problems (I would think it likely surpasses their calculus book in difficulty). Many problems from it are from high level competitions (AIME, and even beyond, to National and International contests), so you can view this book as probably a AoPS culmination of sorts. So I think it'd be perfectly normal for your daughter to struggle on some of them for long periods of time, as long as she enjoys figuring out the challenge of solving them. If she can do some of these hard problems in this particular book, her thinking goes way beyond the standard curriculums, even in college.

[StephanieZ]

I recently got their PreCalc book; it's probably by far the hardest one in terms of the sheer difficulty of many of their problems (I would think it likely surpasses their calculus book in difficulty). Many problems from it are from high level competitions (AIME, and even beyond, to National and International contests), so you can view this book as probably a AoPS culmination of sorts. So I think it'd be perfectly normal for your daughter to struggle on some of them for long periods of time, as long as she enjoys figuring out the challenge of solving them. If she can do some of these hard problems in this particular book, her thinking goes way beyond the standard curriculums, even in college.

Well, that is awesome to hear! She loves these hard problems, but I have to admit I'd be delighted if Calculus is a bit less time consuming! I guess we will find out in about a month when she wraps up precalc and moves on to Calc!

[oscilatorium]

Well, that is awesome to hear! She loves these hard problems, but I have to admit I'd be delighted if Calculus is a bit less time consuming! I guess we will find out in about a month when she wraps up precalc and moves on to Calc!

 

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

[8filltheheart]

Well, that is awesome to hear! She loves these hard problems, but I have to admit I'd be delighted if Calculus is a bit less time consuming! I guess we will find out in about a month when she wraps up precalc and moves on to Calc!

  

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

Stephanie, the cal class is fabulous. Just a heads up that if your dd is planning on the bc exam in may that starting sometime around Feb or Mar, she might want to start working on mastering the bc format. Ds needed a lot of practice on the calculator section since AoPS doesn't really spend time on those kinds of problems. The other thing that he had to work on was how to write the FRQ in the format AP wants for scoring.

 

He started off in a traditional cal class and hated it. He dropped it and went back to AoPS. I was a little panicky in late April second guessing if we had made the right decision. But, he says it was one of the best decisions he ever made. Just knowing ahead of time that there is zero test prep in the course allows you to factor it in.

[lewelma]

My ds(13) just took 10.5 hours to solve a problem and write his proof.  It was not in AoPS, but rather on the NZ math olympiad exam.  However, AoPS trained him to *want* to work that hard and to not be afraid of putting something away and trying again later.

 

Ruth in NZ