S/o of 'hard' math & AOPS discussions . . .

[Chrysalis Academy]

Ok, here is the question I really want to ask: what would you do to prepare a young dc for AOPS, or another equally challenging (if such a thing exists) problem-solving math curriculum?

 

Not so much preparing in terms of math knowledge - we are using Math Mammoth, and every day I love and appreciate this program more. I feel confident that when dd completes MM 6 she will have the conceptual and computational skills to move on with confidence and success. The growth in conceptual understanding that she has made in just 4 months is phenomenal.

 

More in terms of problem-solving *skills* which I am convinced are partly a result of innate personality traits and partly a result of training and developing good habits. Personality I can't do much about. She is good at math, but she is more of a big picture thinker, likes analyzing and making connections, loves evaluating and synthesizing. Not so into the details. Not a perfectionist. She wouldn't sit around and do logic puzzles for fun, she would rather read a book or cut and tape all the cardboard boxes in my office into an elaborate townhouse for all of the dolls she has made by hand from old pillow stuffing, socks, and cloth rags.

 

The habits/training I am working on - every day. It isn't supposed to be easy, if it is easy we are going too slow or working below your level. I do not want or expect you to get the final answer immediately, I want to see you work through the problem and take logical steps. I want to see you look at your answer before you tell me you are done, and make sure it makes logical sense given the problem/numbers you started out with. Stuff like that, and lots of encouragement that it is ok to make mistakes. "Try again, Fail again, Fail Better" is on our wall.

 

Anyway, given all that, do you think there is anything (else) I could do to help this child learn to embrace problem solving, and be ready for the kind of brain-stretching conceptual challenges that something like AoPS would throw at her? I really want this for her - "this" meaning not necessarily AoPS, but the determination and ability - and confidence - to take on tough problems, work at them, and feel good about the process, not just "success" measured in % correct.

[regentrude]

Ok, here is the question I really want to ask: what would you do to prepare a young dc for AOPS, or another equally challenging (if such a thing exists) problem-solving math curriculum?

 

 

 

We did nothing.

My kids were in public school through 5th/6th grade and were not challenged at all. DD went right from public school 6th grade into AoPS Intro to Algebra without problem. DS did an ultra-quick run through Saxon8/7 during second half of 5th grade and then moved to AoPS Intro to Algebra.

I see no need for any specific preparation.

Btw, neither likes logic games or puzzles of any kind.

[Spetzi]

I agree that problem solving is a life skill and is often ignored in many curricula. We use a lot of "living math" books so problems are seen as part of life. We like Zaccarro's books like Challenge Math. My son used Life of Fred and moved right into AoPS.

 

There is a Yahoogroup for Living Math and she has a great website: http://livingmath.net/

 

The suggested book stretch and challenge the kids to think outside the box.

[quark]

nm

Edited March 13, 2012 by quark

[Crimson Wife]

Beast Academy when the full program becomes available

 

Singapore with the Intensive Practice books

 

MEP

 

Edward Zaccaro's Challenge Math series

 

Royal Firework Press' Problemoids book

 

Though you may find that your child does not like the "discovery" method, in which case AOPS would not be a good "fit" :glare:

[Julie of KY]

Make sure they have a solid foundation. If they can do problems by plugging in numbers, but don't really understand, then they need to work on it more.

 

Exposure to hard problems that make the student think.

 

Don't rush. Some students can breeze through a lot math - make sure they are challenged and they can go as fast as they are ready to go.

 

Take it more slowly with students that need to go slower. Don't be afraid to set aside a hard topic and come back to it later - sometimes it just needs to gel.

[Chrysalis Academy]

Beast Academy when the full program becomes available

 

Singapore with the Intensive Practice books

 

MEP

 

Edward Zaccaro's Challenge Math series

 

Royal Firework Press' Problemoids book

 

Though you may find that your child does not like the "discovery" method, in which case AOPS would not be a good "fit" :glare:

 

I guess this is what worries me, a bit. (I ordered AoPS PreAlgebra for myself, btw, so when it arrives I will be able to read it and have a better grasp of the discovery method, and thus ask more intelligent questions!)

 

Can someone help me understand the distinction between the discovery method, as used by AoPS, and problem-solving skills in general? I get that AoPS seems to "suit" only a subset of students, but I think problem solving is really critical, whether you are tempermentally wired that way or not. I guess I'm wondering what you would do for your student to hone and develop their problem-solving skills, even if the discovery method of AoPS is not a good fit.

[regentrude]

Can someone help me understand the distinction between the discovery method, as used by AoPS, and problem-solving skills in general? I get that AoPS seems to "suit" only a subset of students,

 

I do not think the subset is limited by the discovery method, but more by the level of difficulty AoPS poses. Sure, some kids can not learn well with a discovery based approach, but IMO opinion this is not the critical limitator for AoPS suitability - rather the level of interest in math and the willingness to engage for hours in a math problem. Not all kids have this.

 

Problem solving and discovery approach do not really have anything to do with each other per se. Very linear thinkers who need a concept presented before they can understand it will, if they are taught well and understand the concept, not just memorize procedures, also be able to acquire problem solving skills.

If I had a student who did not do well with the discovery method, I(would make sure to include plenty of problems that require the student to think (and not just reproduce a drilled procedure) AFTER the concept has been introduced in a linear fashion. you can still practice creative problem solving even if the student did not arrive at the concept through his own discovery, but has been presented with it. It is just essential that the "why" question is thoroughly answered and that the instruction does not just focus on algorithms.

[Chrysalis Academy]

This makes sense. Would something like Zaccaro's challenge math offer this kind of creative-problem solving practice without relying on the discovery method? Or something else?

[NittanyJen]

My son self-directed using Life of Fred (Fractions, Decimals & Percents, and started Pre-Algebra w/ Biology just ahead of starting to use AoPS as a supplement, but working the sections in order, doing all the problems). The only intervention from me during Fred has been (he continues Fred, now in PreAw/Economics) checking the bridge tests.

 

That work prepared him just fine for the type of work in AoPS PreA, since it emphasizes understanding and creative problem solving, and he has had zero problems so far (up through chapter 4).

 

The only intervention I have begun is to add a new section to his notebook for "starred thoughts," where he is to write down the exclamation point notes in AoPS and general rules he encounters in Fred; this is a tab-separated section from the work section of his notebook (lined paper here, graph paper in the work section). He grumps a bit, but I think that moving into algebra and doing proofs, having this stuff cemented in by writing it down will help (excuse the tortured sentence).

[FairProspects]

...IMO opinion this is not the critical limitator for AoPS suitability - rather the level of interest in math and the willingness to engage for hours in a math problem. Not all kids have this.

 

:iagree:I think this is it. I have heard from a number of homeschooled teens I know who are fantastic at math that they just don't have the desire to spend that much time (sometimes days) solving a math problem when they also have other interests.

[Crimson Wife]

Very linear thinkers who need a concept presented before they can understand it will, if they are taught well and understand the concept, not just memorize procedures, also be able to acquire problem solving skills.

 

:iagree::iagree::iagree:

My oldest DD is a quick learner but not intuitively "mathy". She HATES when Singapore makes a conceptual leap (which is why I have supplemented with Math Mammoth). She is very much an auditory-sequential thinker and wants things explained to her step-by-step-by-step. Asking her to figure math out for herself by puzzling over tricky problems? :svengo:

 

She likes the Singapore IP books and the Zacarro Challenge Math ones but those both come after she has been taught the basic concept.

[Chrysalis Academy]

:iagree::iagree::iagree:

My oldest DD is a quick learner but not intuitively "mathy". She HATES when Singapore makes a conceptual leap (which is why I have supplemented with Math Mammoth). She is very much an auditory-sequential thinker and wants things explained to her step-by-step-by-step. Asking her to figure math out for herself by puzzling over tricky problems? :svengo:

 

She likes the Singapore IP books and the Zacarro Challenge Math ones but those both come after she has been taught the basic concept.

 

Yeah, I don't see my dd being thrilled with being asked to spend hours puzzling over tricky problems that might not be solvable at all. She is good at math, and she likes it, but she doesn't live and breathe math. There are lots of things she would choose to do with her time instead. And that's fine. I just want her to develop strong problem-solving skills, and I do think attitude has a lot to do with it.

 

Hmmm. Lots of food for thought in all of your responses, which I appreciate very much. I will be happy to get my copy of AoPS and check it out for myself. I also decided to spring for Beast, as my younger will use it eventually, and my older hasn't done Geometry yet to speak of (we've not done that chapter in MM, and she didn't really cover it in ps) so I thought that would be a great intro to the Beast world for her. She is unfortunately too old to fully benefit from the program, I think, but I may be surprised. I'm also planning on having her start LOF Fractions independently, in the next couple of weeks. She has loved LOF so far. I will keep Zaccaro and Problemoids on the back burner, too, and monitor the co-development of strong conceptual understanding of math and the grit and determination needed to solve tough problems, in math and in life. I hope. :D

[cfn10]

Interesting thread since I too just bought the PreAlgebra books. I like the idea of Discovery because I want my children to learn to search for answers and succeed and fail. I have concerns regarding the long descriptions I have seen on the sample pages. I understand that is necessary but I am unsure if it will fit well with them. We will see.

[Roadrunner]

I do not think the subset is limited by the discovery method, but more by the level of difficulty AoPS poses.

 

Do you think (or anybody else who used this program) sample pages for Intro to Algebra and Intermediate Algebra do justice to this program? I am asking because after reading so many posts about AoPS and feeling quite a lot of fear, I sat my husband down last night and had him solve almost all of it (loooong story :tongue_smilie: especially considering my oldest is 7). He breezed through and then asked in puzzlement what exactly was suppose to be "beyond normal". I know he is not an average guy (has engineering degree) and very bright in math, but he is still "normal" (not like one of my friends who doesn't even need a math class). Sure he used to sleep with math problems all around his bed, but he hasn't done math for 20 years. Yesterday was a release of my fears. But then I keep thinking the samples are nothing like what's in other pages.

[regentrude]

Do you think (or anybody else who used this program) sample pages for Intro to Algebra and Intermediate Algebra do justice to this program?

 

I just looked at the three Intro to Algebra samples and yes, these are representative for the program.

Of course your husband with an engineering degree who has been taught this math before would, and should, breeze through the problems! But he is not the target audience - the target audience is a 6th grader who sees this material for the first time and is in the process of discovering the concepts. To this student, the problems will appear entirely differently than to your DH. After all, algebra 1 is pretty trivial once one has mastered it, and - unless one has experience teaching - it is sometimes hard to understand why a student would have difficulties with certain concepts.

 

I will say that the challenge problems can be quite challenging even to a math savy adult.

[Roadrunner]

I just looked at the three Intro to Algebra samples and yes, these are representative for the program.

Of course your husband with an engineering degree who has been taught this math before would, and should, breeze through the problems! But he is not the target audience - the target audience is a 6th grader who sees this material for the first time and is in the process of discovering the concepts. To this student, the problems will appear entirely differently than to your DH. After all, algebra 1 is pretty trivial once one has mastered it, and - unless one has experience teaching - it is sometimes hard to understand why a student would have difficulties with certain concepts.

 

I will say that the challenge problems can be quite challenging even to a math savy adult.

 

Thanks you! I know, but his assessment was that dedicated "normal" (my kids are mathy and ahead, but I don't think there is anything spectacular about them) child should be able to work through it. That helps take the fear of the program away :) .

[cfn10]

When I was in college the math prof would hand out the test answers as soon as the exam was over. He believed that immediately after taking the test would be when students were most interested in the solutions. Curious if aops is similar.

[regentrude]

When I was in college the math prof would hand out the test answers as soon as the exam was over. He believed that immediately after taking the test would be when students were most interested in the solutions. Curious if aops is similar.

 

:confused:

No matter what book I use, I always go over the answers immediately after give a test. Not sure what this has to do with AoPS specifically.

[cfn10]

I meant regarding teaching structure. If one places a problem on the board and says "Solve based on your previous knowledge" then students may be more interested in how the answer was achieved than if teacher begins with the lesson.

 

Example: Add the numbers 1+2+3...to 10. (I took this from an AoPS video and modified it:001_smile:.)

 

I do agree with you---always go over test results immediately after test. I went to traditional school though so many teachers did not do that and sometimes the answer was not something that could be looked up by a student i.e. math/physics problem.

[Gratia271]

If I had a student who did not do well with the discovery method, I(would make sure to include plenty of problems that require the student to think (and not just reproduce a drilled procedure) AFTER the concept has been introduced in a linear fashion. you can still practice creative problem solving even if the student did not arrive at the concept through his own discovery, but has been presented with it. It is just essential that the "why" question is thoroughly answered and that the instruction does not just focus on algorithms.

 

:iagree: This is crucial in order to advance in higher level mathematics.

[ElizaG]

Ok, here is the question I really want to ask: what would you do to prepare a young dc for AOPS, or another equally challenging (if such a thing exists) problem-solving math curriculum?

 

Not so much preparing in terms of math knowledge (...)

More in terms of problem-solving *skills* which I am convinced are partly a result of innate personality traits and partly a result of training and developing good habits. (...) I really want this for her - "this" meaning not necessarily AoPS, but the determination and ability - and confidence - to take on tough problems, work at them, and feel good about the process, not just "success" measured in % correct.

 

I agree that problem solving is a life skill and is often ignored in many curricula. We use a lot of "living math" books so problems are seen as part of life. We like Zaccarro's books like Challenge Math. My son used Life of Fred and moved right into AoPS.

Maybe I am being dense this morning, but given that taking on and solving tough problems is a "part of life," why all the emphasis on using curriculum to teach it? :001_huh:

 

I was expecting more answers along the lines of helping the child through difficult everyday situations (keeping the level of assistance low enough that there will be some frustration), or thinking out loud when we have to solve problems ourselves. Just doing hard things in general. That seems to be the biggest confidence builder around here.

[regentrude]

Maybe I am being dense this morning, but given that taking on and solving tough problems is a "part of life," why all the emphasis on using curriculum to teach it? :001_huh:

Just how many hard problems does a young child growing up in a stable family have to solve?

I was expecting more answers along the lines of helping the child through difficult everyday situations .

 

What are these? Honestly, my kids do not encounter truly difficult situations that require a lot of analytical thinking in their daily lives. They do encounter situations where they need patience and perseverance (in music, sports), but actual problem solving?

[ElizaG]

Just how many hard problems does a young child growing up in a stable family have to solve? (...)

 

What are these? Honestly, my kids do not encounter truly difficult situations that require a lot of analytical thinking in their daily lives. They do encounter situations where they need patience and perseverance (in music, sports), but actual problem solving?

I don't necessarily go out of my way to make things tough for them, but we've always been generally oriented toward Montessori philosophy, where children are helped to do things for themselves, and for others, as much as they are able. Given that they're all fairly intense and have many interests (which is typical of bright children, from what I've read), these things often are hard. Maybe it also helps that we have a large family and do a lot of things together. Sharing of resources, conflict resolution, scheduling... believe me, my analytical skills are given a workout at times. And that's before even getting to any of their own special projects such as crafts, gardening, building a treehouse, figuring out how to convince me to let them keep some exotic animal, and (in the case of my eldest) plotting world domination. ;)

 

I would also challenge the notion that problem solving always involves a high degree of analysis. Sometimes just accepting part of a situation as unsolved for now, detaching and looking at it a different way, etc., can be steps toward the solution. It's my understanding that AoPS does require this degree of involvement, and that this aspect is a big turn-off for some more faint-hearted or routine-minded students. Thus the OP's question.

[boscopup]

What are these? Honestly, my kids do not encounter truly difficult situations that require a lot of analytical thinking in their daily lives. They do encounter situations where they need patience and perseverance (in music, sports), but actual problem solving?

 

The hardest problem my son usually has to solve at home is: He wants to carry 4 science books to the van. He gets to the door of the house and can't open it. His hands are too full. What can he do?

 

And seriously, that is a challenge for him. :tongue_smilie: Thankfully, he does better at math problem solving. Real life problem solving is a different ball of wax for him, apparently. :glare: My newest saying for him is, "Solve your problem! Think!" ;)

[Chrysalis Academy]

I just read the Problem-solving chapter from Teach Like Your Hair Is On Fire. I know what we are going to be talking about on Monday morning . . . along with some of the "star" problems from BA! :lol:

 

This is a very interesting discussion, and I'm grateful to all who are sharing their thoughts and experience.

Edited March 18, 2012 by rroberts707
Grammar!

[ElizaG]

The hardest problem my son usually has to solve at home is: He wants to carry 4 science books to the van. He gets to the door of the house and can't open it. His hands are too full. What can he do?

 

And seriously, that is a challenge for him. :tongue_smilie: Thankfully, he does better at math problem solving. Real life problem solving is a different ball of wax for him, apparently. :glare: My newest saying for him is, "Solve your problem! Think!" ;)

He's learned the basic procedure of how to get stuff out to the car, and can plug in the items for simple problems, but lacks deeper conceptual understanding. ;)

[boscopup]

He's learned the basic procedure of how to get stuff out to the car, and can plug in the items for simple problems, but lacks deeper conceptual understanding. ;)

 

Exactly! Now what curriculum teaches deeper conceptual understanding of how to open a door?!? :lurk5:

 

:lol:

[8filltheheart]

Just how many hard problems does a young child growing up in a stable family have to solve?

 

 

What are these? Honestly, my kids do not encounter truly difficult situations that require a lot of analytical thinking in their daily lives. They do encounter situations where they need patience and perseverance (in music, sports), but actual problem solving?

 

:confused: My kids encounter situations requiring problem-solving skills daily. Really. When they play w/construction kits (Legos, electrical kits, brick/mortar kits, etc) withOUT plans, the construction process itself is a problem-solving situation. (FWIW, while having pre-fab plans/kits might build cool designs, my kids have always preferred self-designing (and me, too b/c of the learning process).

 

Setting up games like "Little City" when they have to design their "market," what they are going to charge, how are they going entice customers.......problem-solving.

 

Playing on the playground and rigging up pulleys and lifts....problem-solving.

 

Designing ways to turn off their bedroom light w/o getting out of bed....problem-solving.

 

Figuring out how to beat me in a strategy-game.....definitely problem-solving.

 

Problem-solving occurs in multiple (and sometime, unnoticed) ways.

 

But, I do agree w/your OP in this thread. We didn't do anything special to prepare for AoPS other than our lifestyle and a solid regular ole math background.

[ElizaG]

:confused: My kids encounter situations requiring problem-solving skills daily. Really. When they play w/construction kits (Legos, electrical kits, brick/mortar kits, etc) withOUT plans, the construction process itself is a problem-solving situation. (...) Problem-solving occurs in multiple (and sometime, unnoticed) ways.

 

But, I do agree w/your OP in this thread. We didn't do anything special to prepare for AoPS other than our lifestyle and a solid regular ole math background.

It's been a while since I looked at the AoPS web site, but I'm pretty sure that this was what they recommended, too. Something like, "If your child is below 6th grade, please come back in a few years. In the meantime, just have them do basic elementary math and go fly a kite. Literally." :)

 

Looking through this article on Dealing With Hard Problems, every step in it could be applied to building a kite, or setting up a dog-walking business, or even doing a jigsaw puzzle.

 

DH, who loves to watch our babies, just pointed out that problem-solving starts in infancy. This reminded me of the reason why Maria Montessori was against pacifiers. It's because she believed that even though it could take a while for a baby to learn to suck his thumb -- and there was bound to be some frustration during those early weeks -- getting that little hand in there was the little one's first experience of problem-solving, and it was a powerful triumph.

 

(We do sometimes use pacifiers anyway, because my analytical skills tell me that I need some sleep. I guess we can blame it on me if they don't grow up to solve all the world's problems... :auto:)

[StephanieZ]

I think Singapore (TEXT & WKBK +/- IP +/- CWP) is a great foundation. I also think Miquon is lovely. I like to use both.

 

My dc used SM (Text, Wkbk, + a bit of IP) as well as Miquon and are very well prepared for AoPS. I highly recommend this combo.

 

I have not seen the new AoPS elem. math books, or the RFWP books, or many of the other wonderful resources out there. I'd be tempted to explore them if I still had a child in need of them. Oh, so many good things to explore!

 

FWIW, I do not find that SM makes conceptual leaps. I find that the texts walk through each step very carefully, and when you use it as designed (Text/WkBk), I've never had a moment's hesitation for a concept. Ever. With 3 dc. I doubt I've had to spend more than 5-10 teaching hours per year per child on average for SM, and my kids spent a minimal (under 2 hrs/wk) time on math and sped through the books.

 

(Granted, we are a mathy family, and granted they do Miquon also, so have additional math exposure.) If one did not use the Text/WkBk combo as designed, I am sure you'd have gobs of conceptual leaps, b/c you've essentially SKIPPED ALL THE CONCEPTUAL TEACHING!

 

I think Miquon is a great teacher of problem solving b/c for the most part, it leads the child to explore ideas and to figure out ways to solve problems independently. It definitely encourages independence and problem solving, and even has the child make up their own problems. (Again, used as designed, as a child-led program, per the accompanying teacher's texts.)

 

Also, FWIW, I don't think that AoPS math need require a child to struggle for hours on problems. My dc who are using it have not done that. If they are doing an online class, then they will have to commit more time than typical just to keep up as the classes move fairly quickly. However, even taking the online classes, my dc are spending maybe 5-8 hrs/wk on math at most, and neither would cheerfully struggle for hours on a problem. Maybe 10 minutes. But more than that, and they get irritated, ask for help, or move on. I think a willingness to struggle on a problem for an extended period of time would be both a function of personality and maturity. . . but is not an imperative trait to benefit from AoPS.

[StephanieZ]

It's been a while since I looked at the AoPS web site, but I'm pretty sure that this was what they recommended, too. Something like, "If your child is below 6th grade, please come back in a few years. In the meantime, just have them do basic elementary math and go fly a kite. Literally." :)

 

I'd be surprised to read this. Please provide a linky if you can.

 

It isn't consistent with my experience. :)

 

Richard Rusczyk is my dd9's PreAlgebra teacher, and he and the moderators have been exceedingly welcoming and in no way discouraging the youngest students from signing up for or participating in the classes. In fact, I get the distinct impression that they welcome the opportunity to nurture mathy-ness in very young minds. :) I know another boy (now 16) who used AoPS for Algebra and other online classes at least 5 years ago, as he is extremely accelerated and gifted, and I know that even then they were very supportive of his particpation in the AoPS community and classes.

 

Now, I WOULD have imagined a statement like that referring to if your child had not mastered MATH through 6th grade level. But, that is a VERY different thing from being past 6th grade AGE.

[Tattarrattat]

Just curious, for those who have kids taking AoPS classes, do you usually let the instructor or classmates know your kid's age or rather keep it private? I usually remind my kid not to mention his age. Just wonder what others normally do?

[boscopup]

I'd be surprised to read this. Please provide a linky if you can.

 

:iagree:

 

In fact, if you click on the recommendations for "Highly Advanced Elementary", it pops up the prealgebra, intro to algebra, number theory, counting & probability, and intro to geometry books.

 

Also, when I emailed AoPS last year to ask about their prealgebra book being after 5th or 6th grade Singapore (he said after 5th grade), I also asked about younger students like 8 or 9 year olds, and he suggested trying the prealgebra book after Singapore 5, and if it's too much, go back to Singapore 6.

 

So yeah, I'd be pretty surprised to see anything like what Eleanor said. I looked around the website and couldn't find it either. Perhaps she's confusing AoPS with LoF. I know the LoF author has made comments about how boys shouldn't do algebra until they have hair on their underarms. :rolleyes:

[8filltheheart]

 

Now, I WOULD have imagined a statement like that referring to if your child had not mastered MATH through 6th grade level. But, that is a VERY different thing from being past 6th grade AGE.

 

I agree that the comment would be directed toward math level, not age, but I am assuming that is what Eleanor meant. (And keep in mind that the pre-alg bk and Beast Academy are new.)

 

But as far as the the rest of Eleanor's comment (go fly a kite).....that is what Richard Rusczyk does suggest:

 

In his slides that accompany this talk http://mathprize.atfoundation.org/archive/2009/rusczyk, he includes a slide which says:

 

Keys to Developing Strong Problem Solving Skills in the Early Years

•Read (picture of boy pulling a wagon full of books)

•Play (picture of a kite flying)

(Link to slides: http://mathprize.atfoundation.org/archive/2009/rusczyk.pdf )

[boscopup]

In his slides that accompany this talk http://mathprize.atfoundation.org/archive/2009/rusczyk, he includes a slide which says:

 

Keys to Developing Strong Problem Solving Skills in the Early Years

•Read (picture of boy pulling a wagon full of books)

•Play (picture of a kite flying)

(Link to slides: http://mathprize.atfoundation.org/archive/2009/rusczyk.pdf )

 

 

Thanks! I'll have to watch that lecture later... probably while working more Alcumus problems. :lol:

[8filltheheart]

I think Singapore (TEXT & WKBK +/- IP +/- CWP) is a great foundation. I also think Miquon is lovely. I like to use both.

 

My dc used SM (Text, Wkbk, + a bit of IP) as well as Miquon and are very well prepared for AoPS. I highly recommend this combo.

 

I have not seen the new AoPS elem. math books, or the RFWP books, or many of the other wonderful resources out there. I'd be tempted to explore them if I still had a child in need of them. Oh, so many good things to explore!

 

FWIW, I do not find that SM makes conceptual leaps. I find that the texts walk through each step very carefully, and when you use it as designed (Text/WkBk), I've never had a moment's hesitation for a concept. Ever. With 3 dc. I doubt I've had to spend more than 5-10 teaching hours per year per child on average for SM, and my kids spent a minimal (under 2 hrs/wk) time on math and sped through the books.

 

(Granted, we are a mathy family, and granted they do Miquon also, so have additional math exposure.) If one did not use the Text/WkBk combo as designed, I am sure you'd have gobs of conceptual leaps, b/c you've essentially SKIPPED ALL THE CONCEPTUAL TEACHING!

 

I think Miquon is a great teacher of problem solving b/c for the most part, it leads the child to explore ideas and to figure out ways to solve problems independently. It definitely encourages independence and problem solving, and even has the child make up their own problems. (Again, used as designed, as a child-led program, per the accompanying teacher's texts.)

 

Also, FWIW, I don't think that AoPS math need require a child to struggle for hours on problems. My dc who are using it have not done that. If they are doing an online class, then they will have to commit more time than typical just to keep up as the classes move fairly quickly. However, even taking the online classes, my dc are spending maybe 5-8 hrs/wk on math at most, and neither would cheerfully struggle for hours on a problem. Maybe 10 minutes. But more than that, and they get irritated, ask for help, or move on. I think a willingness to struggle on a problem for an extended period of time would be both a function of personality and maturity. . . but is not an imperative trait to benefit from AoPS.

 

 

My experience w/AoPS is that my dd is spending only minutes/WEEK on alg for the online class. (and I do mean minutes. She has completed every weeks' complete set of challenge problems in under 30 mins total for all.) However, she has already taken alg and has not encountered anything new that she didn't already know from Foerster.

 

I do not believe that my dd's experience reflects what she will encounter at the upper levels and w/new material. I believe ds's experience is the norm. And when she continues w/the upper level courses she is going to have to either be prepared to spend hrs or switch curriculum.

 

B/c, ds, who started at the alg 3 level and all the material was new.....he does spend literal hrs on problems. He is a very strong math student. (and I know from others that have taken these level courses in the past that his experience is the norm at this level, not only unusual, but what the founders of AoPS want!)

 

You find a math problem in a book, or maybe on a contest, or maybe your teacher tells you the problem. You work on it for a half-hour. Then another half-hour. It bugs you and bugs you because you know that other kid who wins all the trophies knows how to do the problem. You want to win the trophies, too, but that's not why you spend another half-hour on the problem. You want to know the answer. More than just the answer, you want to know how to do the problem.

 

Finally, you give up and look up the answer. The solution mostly makes sense, but you're not entirely satisfied. You may not even know why you're not satisfied. You're not satisfied because the solution didn't answer the most important question...

How would I have thought of that?

 

The creators of this site were this student once. We were the kids who wanted to win the trophies. We worked hard and became the kids who won the trophies. The trophies are in attics now. The problem-solving skills, the love of mathematics, and the friendships forged with peers with similar interests remain. We've applied the skills we've developed through mathematics to a variety of fields in college, then in the professional world.

 

Now we've returned to our starting point - the student in a room, chewing on a pencil, staring at a question, giving up, reading the answer, and thinking. . .

How would I have thought of that?

 

This time you are the student. We are building this site for you, to provide a resource you can turn to.

You're stuck on a problem, so you write friends on our Forum. You hang out in our Math Jams. You take an online class. You pick up a book. You don't give up. You learn how to think of the solution. You solve the problem. Then you think...

 

Next problem.

http://www.artofproblemsolving.com/Company/index.php

[fractalgal]

Ok, here is the question I really want to ask: what would you do to prepare a young dc for AOPS, or another equally challenging (if such a thing exists) problem-solving math curriculum?

 

 

If you are asking above and beyond math curricula, I think it helps to let children solve their own problems from the time they are very little...as long as they are in no danger.

 

Also, when children are doing hard, frustrating math problems and they make mistakes, make them fix them. I sometimes give my daughter the same problem five times until she solves it. If she has been working on it for awhile I will sometimes point out where she is going wrong, and give her another way of thinking of it. But I do not tell her the answer. She will usually figure it out after awhile. Then she feels proud of herself.

 

It helps in math to have that 'never give up' attitude. ;)

[Halcyon]

If you are asking above and beyond math curricula, I think it helps to let children solve their own problems from the time they are very little...as long as they are in no danger.

 

Also, when children are doing hard, frustrating math problems and they make mistakes, make them fix them. I sometimes give my daughter the same problem five times until she solves it. If she has been working on it for awhile I will sometimes point out where she is going wrong, and give her another way of thinking of it. But I do not tell her the answer. She will usually figure it out after awhile. Then she feels proud of herself.

 

It helps in math to have that 'never give up' attitude. ;)

 

I agree. When my older encounters a problem that he cannot solve, I might give a suggestion for another approach, or I might have him put it away til the next day. I will then have him tackle it again. When he finally does get it, I often bring a similar problem back the following week and see if he has retained/understood how to solve the problem. If not, rinse and repeat. :001_smile:

[ElizaG]

I agree that the comment would be directed toward math level, not age, but I am assuming that is what Eleanor meant. (And keep in mind that the pre-alg bk and Beast Academy are new.)

Yes, I did mean 6th grade level. Sorry I wasn't clear. :) Thanks for posting. (I think that slide show must have been one of the things I looked at back then!)

Edited March 19, 2012 by Eleanor

[StephanieZ]

My experience w/AoPS is that my dd is spending only minutes/WEEK on alg for the online class. (and I do mean minutes. She has completed every weeks' complete set of challenge problems in under 30 mins total for all.) However, she has already taken alg and has not encountered anything new that she didn't already know from Foerster.

 

I do not believe that my dd's experience reflects what she will encounter at the upper levels and w/new material. I believe ds's experience is the norm. And when she continues w/the upper level courses she is going to have to either be prepared to spend hrs or switch curriculum.

 

B/c, ds, who started at the alg 3 level and all the material was new.....he does spend literal hrs on problems. He is a very strong math student. (and I know from others that have taken these level courses in the past that his experience is the norm at this level, not only unusual, but what the founders of AoPS want!)

 

 

http://www.artofproblemsolving.com/Company/index.php

 

This makes perfect sense to me . . . that at an advanced level (alg 3, etc) a longer attention span would be expected for the student. PreAlg and Alg1 so far have not required lengthy problem solving, but even Intro C&P would indeed require longer -- as it was new material to my son and it required new thinking skills and approaches -- so he might have spent 30 min on some problems, but at age 12, he wasn't patient enough to spend longer than that, and I didn't push him to struggle longer. As the kids mature, their patience grows, and the expectations for the more advanced courses would be greater. I can't see any child in PreAlg struggling for more than 5-10 min on a problem without benefitting from assistance.

[regentrude]

This makes perfect sense to me . . . that at an advanced level (alg 3, etc) a longer attention span would be expected for the student. PreAlg and Alg1 so far have not required lengthy problem solving,

 

Now I am curious: how fast did your kid solve the linear optimization problem with farmer Fred who wants to plant his acres in corn and soy beans in Intro to Algebra?

For us, this was the longest problem so far from any of the four books we have used (we are in precalculus). If I remember correctly, it took close to two hours.

[8filltheheart]

Now I am curious: how fast did your kid solve the linear optimization problem with farmer Fred who wants to plant his acres in corn and soy beans in Intro to Algebra?

For us, this was the longest problem so far from any of the four books we have used (we are in precalculus). If I remember correctly, it took close to two hours.

 

This is the only reason why I didn't drop the class for dd. So far it has been extremely easy for her and nothing but complete review. I am assuming that the further into the class she gets that the difficulty is going to crank up.

 

I want it to! But, in the meantime, I am satisfied b/c she now says she is enjoying how they discuss topics vs. the end of last yr when I tried AoPS and she emphatically stated she detested it. ;)

 

Frog in the water and all. I'm hoping that she doesn't notice the heat and gets hooked. :D

 

BTW, StephanieZ, if you haven't listened to RR's talk that I linked, I highly recommend it. He lays out the case for long hours of problem-solving struggles.

[Chrysalis Academy]

I just watched the AoPS lecture 8 linked to. . . . Wow. My head is spinning. I'm glad to see we're on the right track, with reading and playing ;). Lots and lots to think about. Put this together with all I've been thinking of since reading the classical education /circe how-to thread, and listening to a bunch of those lectures yesterday (8, you really inspired me over there, too) and my brain is completely. frozen. just now.

 

I think a radical re-evaluation is in order . . . luckily after less than 5 months, none of our ruts are that deep! :D

 

If you haven't watched that video, do. Really.

 

And continuing gratitude for the sharing and the inspiration. :bigear:

[Beth in SW WA]

In his slides that accompany this talk http://mathprize.atfoundation.org/archive/2009/rusczyk,

 

Thanks for the link, 8. Watching now....

[Crimson Wife]

FWIW, I do not find that SM makes conceptual leaps. I find that the texts walk through each step very carefully, and when you use it as designed (Text/WkBk), I've never had a moment's hesitation for a concept. Ever. With 3 dc. I doubt I've had to spend more than 5-10 teaching hours per year per child on average for SM, and my kids spent a minimal (under 2 hrs/wk) time on math and sped through the books.

 

(Granted, we are a mathy family, and granted they do Miquon also, so have additional math exposure.) If one did not use the Text/WkBk combo as designed, I am sure you'd have gobs of conceptual leaps, b/c you've essentially SKIPPED ALL THE CONCEPTUAL TEACHING!

 

The workbook does not have any additional teaching, and that's the only thing that we skip in favor of IP and CWP.

 

The issues we have had with conceptual leaps have been where the textbook jumps from point A to D without first taking the child through points B & C. Math Mammoth is far more incremental. Multi-digit multiplication, long division, and fractions were the topics where we had the biggest problems with conceptual leaps in Singapore.

[daijobu]

Sorry, I'm late to the discussion, but I didn't see anyone mention MOEMS. Look at their bookstore at moems.org. Their books of old exams have lots of good math problems with detailed solutions in the back. Good luck!

[KirstenH]

Is there an article somewhere that says basically the same thing as the video? I really can't listen to someone talk for an hour, especially when the quality's not great.

[wapiti]

Is there an article somewhere that says basically the same thing as the video? I really can't listen to someone talk for an hour, especially when the quality's not great.

 

The first half of this article includes a bit of what the video discusses, and of course there are the problem solving articles here and here, and the Calculus Trap.

 

but, I think the video is worth listening to. I've listened to it more than once. One day I should outline it...

 

ETA, one of the key problem-solving points in the video is the importance of using simple tools to solve harder and harder problems rather than learning more complex tools to solve simple problems. I'm sure I didn't word that quite right, but I think it's relatively early on in the video, certainly in the first half.

Edited April 15, 2012 by wapiti

[forty-two]

Is there an article somewhere that says basically the same thing as the video? I really can't listen to someone talk for an hour, especially when the quality's not great.

 

I know this is an old thread, but here's the transcript for the video: http://mathprize.atfoundation.org/archive/2009/Rusczyk_Problem_Solving_Presentation_at_Math_Prize_for_Girls_2009.pdf

 

Agree with pp - it's very much worth reading/watching :yes. (And worth bumping this thread for ;).)