AoPS question

[Just Robyn]

I'm looking ahead and looking at AoPS. Right now I'm thinking about my oldest who is not particularly mathy. I'm wondering if anyone can comment on whether the following possible sequence is thorough "enough". Ideally, I would love to see him doing the pre-algebra book in 6th grade, but if his math education ends up looking like the following, is that going to look bad or incomplete to most?

 

Grade 7 - pre-algebra

Grade 8 - start intro to algebra

Grade 9 - finish intro to algebra; do counting/probability or number theory if we finish early

Grade 10 - geometry

Grade 11 - intermediate algebra

Grade 12 - pre-calc

 

I guess I feel like most people here want their child to do calculus in grade 12, but is doing pre-calc in grade 12 considered behind or lacking?

[regentrude]

The sequence looks fine to me. Calculus in 12th is nice, but not necessary- solid algebra skills are way more important for college success. Please keep in mind that AoPS covers way more than the traditional high school course.

This brings me to the question that puzzles me: why do you want to choose AoPS for a child which you describe as "not particularly mathy"? This is a curriculum for kids who are good at, and excited about, math and who want to go above and beyond. It is great for a student with a particularly strong interest in math. Are you sure your child is motivated to work more, and harder, at math than would be necessary for any other standard curriculum?

Just something to ponder - we love the program and I do not want to dissuade you. But it is not the right program for every student.

 

 

I'm looking ahead and looking at AoPS. Right now I'm thinking about my oldest who is not particularly mathy. I'm wondering if anyone can comment on whether the following possible sequence is thorough "enough". Ideally, I would love to see him doing the pre-algebra book in 6th grade, but if his math education ends up looking like the following, is that going to look bad or incomplete to most?

 

Grade 7 - pre-algebra

Grade 8 - start intro to algebra

Grade 9 - finish intro to algebra; do counting/probability or number theory if we finish early

Grade 10 - geometry

Grade 11 - intermediate algebra

Grade 12 - pre-calc

 

I guess I feel like most people here want their child to do calculus in grade 12, but is doing pre-calc in grade 12 considered behind or lacking?

[Just Robyn]

The sequence looks fine to me. Calculus in 12th is nice, but not necessary- solid algebra skills are way more important for college success. Please keep in mind that AoPS covers way more than the traditional high school course.

This brings me to the question that puzzles me: why do you want to choose AoPS for a child which you describe as "not particularly mathy"? This is a curriculum for kids who are good at, and excited about, math and who want to go above and beyond. It is great for a student with a particularly strong interest in math. Are you sure your child is motivated to work more, and harder, at math than would be necessary for any other standard curriculum?

Just something to ponder - we love the program and I do not want to dissuade you. But it is not the right program for every student.

 

I feel that a lot of very capable students are not offered higher level learning materials and opportunities just because they are not gifted and/or a particular subject is not their strongest. I think this is a mistake which keeps a lot of students thinking that subjects are boring, not because they're too advanced in the subject to find the "normal" material interesting because they've already learned it, which may be the case for some students advanced in a particular subject, but because the material that is more interesting is usually more advanced material. It is my belief that if given the chance to study the more interesting material, many students would be motivated to advance their skills. Some students, mathy students, naturally love and advance through math. Some students need to be shown what's so cool about it; they may be stronger in LA, but are still capable of a meatier math program.

 

Compare this to the MCT materials that were created for gifted students. These materials are amazing and are being used successfully by many non-gifted students on these boards who would possibly never be introduced to the beauty of LA if required to use only standard Daily Language Review, K12, WWE, types of materials due to not being gifted. (We use all of these too; I'm not trying to say K12, WWE etc. are not good for their purposes.) I would not doubt that MCT is successfully used not only by non-gifted students, but by students who are stronger in math than LA.

 

ETA: My thoughts were that if he gets through pre-calc with AoPS, it might be better than getting through calc with a different program - better for his opinion of and understanding of the math he does cover. Worded another way - cover less math, but do it more thoroughly and in a more interesting way.

Edited October 1, 2011 by crstarlette

[wapiti]

I feel that a lot of very capable students are not offered higher level learning materials and opportunities just because they are not gifted and/or a particular subject is not their strongest. I think this is a mistake which keeps a lot of students thinking that subjects are boring, not because they're too advanced in the subject to find the "normal" material interesting because they've already learned it, which may be the case for some students advanced in a particular subject, but because the material that is more interesting is usually more advanced material. It is my belief that if given the chance to study the more interesting material, many students would be motivated to advance their skills. Some students, mathy students, naturally love and advance through math. Some students need to be shown what's so cool about it; they may be stronger in LA, but are still capable of a meatier math program.

 

Compare this to the MCT materials that were created for gifted students. These materials are amazing and are being used successfully by many non-gifted students on these boards who would possibly never be introduced to the beauty of LA if required to use only standard Daily Language Review, K12, WWE, types of materials due to not being gifted. (We use all of these too; I'm not trying to say K12, WWE etc. are not good for their purposes.) I would not doubt that MCT is successfully used not only by non-gifted students, but by students who are stronger in math than LA.

 

ETA: My thoughts were that if he gets through pre-calc with AoPS, it might be better than getting through calc with a different program - better for his opinion of and understanding of the math he does cover. Worded another way - cover less math, but do it more thoroughly and in a more interesting way.

 

This line of thinking has been on my mind (i.e., whether some "non-mathy" students are non-mathy because they haven't had opportunities with the right curriculum, or simply because elementary math and secondary math are different; do some math curricula ensure that a non-mathy student remains non-mathy?), particularly since the thread the other day. This is the reason I have very mixed feelings about tracking when it comes to exposure to specific teaching and materials. And I was just thinking out loud on this morning's Lockhart's Lament thread on the general board about the difference between fuzzy math (which was applied to average students) and AoPS math, and wondering what would happen if the AoPS approach were applied to more general students.

 

If the AoPS books specifically would be "too challenging" for an average student, I wonder whether the same approach could be used in books yet to be written (by Rusczyk ;), although that would not seem to be a goal of his at the moment). Or, whether such average students could, say, avoid the challenge problems but still get the benefit of the teaching, to an extent that may be superior to the same students using a different curriculum. Clearly there's no one-size-fits-all math curriculum, but I can imagine that somewhere there may be students who would greatly benefit from this approach, and that perhaps those students may be more numerous than one would have otherwise guessed. When I look at how the lesson problems are sequenced in a particular lesson, the genius in it makes me giddy.

 

Then there's a learning style issue, though someplace in the preface, Rusczyk suggests that students who don't do well with the discovery approach could use the book in a more traditional way, I assume by reading through the problem solutions.

 

Also, after a rough day yesterday, late last night I was watching some of the more recently posted Prealgebra videos (for relaxation and enjoyment? :lol:; actually I do think I laughed - he was quite animated - he really puts his heart into it) and before I knew it, I was googling, and came upon an article where the difference between the "problems" and the "exercises" was being discussed by Rusczyk (I think :tongue_smilie:; it was late). If I have time later, I'll try to find the link. It presented some food for thought.

 

I'm doing way too much thinking out loud here and I better get to work cleaning up the house before the mess-makers return from the playground...

[Beth in SW WA]

Also, after a rough day yesterday, late last night I was watching some of the more recently posted Prealgebra videos (for relaxation and enjoyment? :lol:; actually I do think I laughed - he was quite animated - he really puts his heart into it) and before I knew it,

 

I love Richard!! He is so delightful to watch. His energy and passion are contagious. How I would have appreciated alg more with him as my teacher.

[JenC3]

This line of thinking has been on my mind (i.e., whether some "non-mathy" students are non-mathy because they haven't had opportunities with the right curriculum, or simply because elementary math and secondary math are different; do some math curricula ensure that a non-mathy student remains non-mathy?), particularly since the thread the other day. This is the reason I have very mixed feelings about tracking when it comes to exposure to specific teaching and materials. And I was just thinking out loud on this morning's Lockhart's Lament thread on the general board about the difference between fuzzy math (which was applied to average students) and AoPS math, and wondering what would happen if the AoPS approach were applied to more general students.

 

:iagree:

 

I read Lockharts's book last year and it really changed the way I felt about math education, more so than Liping Ma. I can't say how excited I am about Beast Academy, really I think about it everyday and WISH I hadn't been on vaca the week the samples were offered:(

 

My dd just turned 8 last week and is I think an average math student. As far as problem solving, she is excellent. She understands concepts, fractions were a "duh, mom." She is VERY mechanical. She is not quick with arithmetic and is learning multiplication at a fair rate I think. Anyway, I think foundational math is kind of boring to her. She hates the rows of problems. When I do math labs/review with say 5-10 problems, she gets great scores. Right now we are using TT4 and MM 3 as our spines. By using TT4 I can get another math lesson in her each day and she does not complain one bit...if it were 2 MM3 lessons there would be an uproar. We also do LoF everyday as well. It's below her ability at this point, but fun and she at one point will be challenged more by it.

 

We have 60+ books in our math library as well as lots of math games. My dd and ds learned to play chess in the past 2 weeks and they are crazy for it.

 

Now just because she isn't jumping for joy and asking for more math one might advise me not to use AoPS, but I think slow and steady cultivation of math is as important as high-level reading. I can't imagine accepting that my dd will not be able to read and discuss great literature as a teen. but that's because she will have been conditioned to understand it. The same goes for math. I'm so thrilled we will be able to start AoPS materials this summer. DD would only be going in 3rd according to the PS cutoff here so it will be perfect.

 

I think many kids can benefit from the AoPS style. My best teachers were the hard ones, the classes I got stressed about I did the best in.

Edited October 1, 2011 by JenC3

[8filltheheart]

I feel that a lot of very capable students are not offered higher level learning materials and opportunities just because they are not gifted and/or a particular subject is not their strongest. I think this is a mistake which keeps a lot of students thinking that subjects are boring, not because they're too advanced in the subject to find the "normal" material interesting because they've already learned it, which may be the case for some students advanced in a particular subject, but because the material that is more interesting is usually more advanced material. It is my belief that if given the chance to study the more interesting material, many students would be motivated to advance their skills. Some students, mathy students, naturally love and advance through math. Some students need to be shown what's so cool about it; they may be stronger in LA, but are still capable of a meatier math program.

 

Compare this to the MCT materials that were created for gifted students. These materials are amazing and are being used successfully by many non-gifted students on these boards who would possibly never be introduced to the beauty of LA if required to use only standard Daily Language Review, K12, WWE, types of materials due to not being gifted. (We use all of these too; I'm not trying to say K12, WWE etc. are not good for their purposes.) I would not doubt that MCT is successfully used not only by non-gifted students, but by students who are stronger in math than LA.

 

ETA: My thoughts were that if he gets through pre-calc with AoPS, it might be better than getting through calc with a different program - better for his opinion of and understanding of the math he does cover. Worded another way - cover less math, but do it more thoroughly and in a more interesting way.

 

I personally do not believe that the comparison of MCT to AoPS is a good analogy. There is nothing about MCT's materials that are inaccessible to the general population. There is nothing that requires students to spend hrs pondering what is being taught in order to get the full grasp of the concepts. MCT is pretty straight-forward/direct instruction. While his vocab program is engaging and his writing program emphasizes stylistic pts, there is nothing difficult about anything that he teaches.

 

AoPS will work well with kids that like the discovery approach and like thinking about math. But, I agree w/Regentrude in that I don't think it will be a math program that all students will want to use, even good math students. Unlike MCT, there are lots of concepts that are incredibly difficult in the AoPS texts and it will capture the attention of those kids that want to engage in concepts that way; and it will probably overwhelm students that don't.

 

I own almost all of the AoPS books.....and I am unsure if any of my other kids will use them or not. Regardless of being a huge fan of the books, I know that they will not be a good fit for all kids. I am going to have to simply wait and see whether they are or aren't. Conversely, I could use MCT materials w/any of my kids.

Edited October 1, 2011 by 8FillTheHeart

[8filltheheart]

This line of thinking has been on my mind (i.e., whether some "non-mathy" students are non-mathy because they haven't had opportunities with the right curriculum, or simply because elementary math and secondary math are different; do some math curricula ensure that a non-mathy student remains non-mathy?), particularly since the thread the other day. This is the reason I have very mixed feelings about tracking when it comes to exposure to specific teaching and materials. And I was just thinking out loud on this morning's Lockhart's Lament thread on the general board about the difference between fuzzy math (which was applied to average students) and AoPS math, and wondering what would happen if the AoPS approach were applied to more general students.

 

:iagree:

 

I read Lockharts's book last year and it really changed the way I felt about math education, more so than Liping Ma. I can't say how excited I am about Beast Academy, really I think about it everyday and WISH I hadn't been on vaca the week the samples were offered:(

 

My dd just turned 8 last week and is I think an average math student. As far as problem solving, she is excellent. She understands concepts, fractions were a "duh, mom." She is VERY mechanical. She is not quick with arithmetic and is learning multiplication at a fair rate I think. Anyway, I think foundational math is kind of boring to her. She hates the rows of problems. When I do math labs/review with say 5-10 problems, she gets great scores. Right now we are using TT4 and MM 3 as our spines. By using TT4 I can get another math lesson in her each day and she does not complain one bit...if it were 2 MM3 lessons there would be an uproar. We also do LoF everyday as well. It's below her ability at this point, but fun and she at one point will be challenged more by it.

 

We have 60+ books in our math library as well as lots of math games. My dd and ds learned to play chess in the past 2 weeks and they are crazy for it.

 

Now just because she isn't jumping for joy and asking for more math one might advise me not to use AoPS, but I think slow and steady cultivation of math is as important as high-level reading. I can't imagine accepting that my dd will not be able to read and discuss great literature as a teen. but that's because she will have been conditioned to understand it. The same goes for math. I'm so thrilled we will be able to start AoPS materials this summer. DD would only be going in 3rd according to the PS cutoff here so it will be perfect.

 

I think many kids can benefit from the AoPS style. My best teachers were the hard ones, the classes I got stressed about I did the best in.

 

I don't think anyone is encouraging people to not use AoPS. From my perspective it is not simply about difficulty level or even understanding math. It is all about how the material is taught. I do not believe that it is a program that will be accessible to all math students, even good math students. There is a lot more to it than that.

 

But.....you won't know until you get there and give it a try. But if students aren't thriving w/it, it doesn't mean they aren't solid math students. They may simply need direct instruction.

[ChandlerMom]

I think it is good to challenge all students. Where AoPS is a bit different though is that it seems to assume the learner wants to be challenged (for lack of a better way of putting it). It starts off with problems to work before explaining the concepts. It then uses the problems to explain the concepts. Then there are a very small number of problems to try. Then at the end there are challenge problems. The approach might be frustrating and there might not be enough practice problems for the core concepts for some students. I'm only referring to my limited experience with pre-algebra.

 

I can imagine working around that (don't start off by doing the problems and add in more problems). But if that is necessary then maybe there is something better out there.

 

I just started with the book. In the first section one of the problems they start off with asks the student to add the numbers 1 through 20. My son literally sat down and attempted to add them one at a time (in his head). Midway he was frustrated and gave up. So then when he read the explanation on how to do it without literally adding up the numbers it was like a little light bulb went on in his head. By the next section of pre problems he was already trying to imagine ways to solve problems without doing it the "long and difficult way". Would all students do that? I'm not sure. Some might prefer something a little more straightforward.

 

Again, we only just started so I'll have to see how it goes.

 

See, that is exactly the challenge that makes my dd love AoPS preA -- we talk about doing things SMART rather than HARD. She gets this deliciously wicked smile when she sees some "sneaky" way to solve the problem.

 

In the example of adding 1 to 20, the two preceding worked problems required the student to think about the order of addition to make it easier (making 10s). If your child is younger or not as "mathy" I recommend reading ahead through the lesson and reviewing each lesson problem as the kid does them (at least at first), so you can make sure they "see" the trick in the earlier problems. They really DO telegraph and build thru the example problems, but if a kid toughed thru the previous examples they won't be prepared for the next.

[Beth in SW WA]

I can't imagine accepting that my dd will not be able to read and discuss great literature as a teen. but that's because she will have been conditioned to understand it. The same goes for math. I'm so thrilled we will be able to start AoPS materials this summer. DD would only be going in 3rd according to the PS cutoff here so it will be perfect.

 

 

That's the spirit! I look forward to reading your progress reports. :)

[JenC3]

What I like about AoPS is the joy of it. My dh would have been crazy for AoPS. He hates math because it was always so boring to him. He has math genes, his mother is a math professor, yet she is more about method, IMO.

 

8fill the heart, do you think using Beast Academy can groom kids for AoPS later on?

 

Btw, my dd is loves problem solving, she adores thinking about the steps to make or figure something out. She invented a pulley without knowing what one was a few years ago, she constructs lots of 3D projects unbidden, etc. I don't what to short change her because she doesn't jump up and down about number bonds like I do.

[JenC3]

That's the spirit! I look forward to reading your progress reports. :)

Thanks!

[regentrude]

I feel that a lot of very capable students are not offered higher level learning materials and opportunities just because they are not gifted and/or a particular subject is not their strongest. I think this is a mistake which keeps a lot of students thinking that subjects are boring, not because they're too advanced in the subject to find the "normal" material interesting because they've already learned it, which may be the case for some students advanced in a particular subject, but because the material that is more interesting is usually more advanced material. It is my belief that if given the chance to study the more interesting material, many students would be motivated to advance their skills. .

 

That's all correct.

Go ahead and use AoPS and see what you think.

My concern is that not every student is motivated to use a discovery approach, is willing to puzzle out the problems before looking at the answers, is willing to work for several hours on a single algebra problem until he gets the answer, is willing to spend more time and do more and harder math than his peers.

If you say yes to all of these for your student, then this is the program for him. It is a great program, and if you can "sell" it to your kid, fantastic. It's just my experience that the student really has to love math already to go through all of this and find it enjoyable.

[wapiti]

From my perspective it is not simply about difficulty level or even understanding math. It is all about how the material is taught. I do not believe that it is a program that will be accessible to all math students, even good math students. There is a lot more to it than that.

 

But.....you won't know until you get there and give it a try. But if students aren't thriving w/it, it doesn't mean they aren't solid math students. They may simply need direct instruction.

 

8 (or anyone else), do you have any thoughts on Rusczyk's suggestion that traditional learners could still learn the traditional way with his books, I assume by reading through the solutions as a method of direct instruction? Do you think that would not be direct enough for such students? Or might there be a formatting issue? I vaguely recall that one of your dc preferred Foerster - was Foerster clearer? Obviously the effect of trying to use AoPS a direct method wouldn't be quite the same; we haven't tried that but I'm just wondering. So far in the Prealgebra, the solution section seems quite explicit in terms of teaching, though I don't know whether that's always the case. My dd is a person who, in language arts at least, struggles with inference and does better with explicit instruction, so I am on the lookout for difficulties with the discovery aspect. So far, so good though.

 

Along those lines, sometimes I wonder whether, just like with some of the WTM LA methods (narration, etc. - I'm harking back to some old Nan threads), what may be hard for a particular student about learning problem solving with AoPS may be just the reason to practice it, or at least some of it, if there were a way to walk the fine line balancing that with the frustration level.

 

More thinking out loud (y'all tired of me yet, lol): I wonder to what extent the discovery problems simply provide extra training in "problem-solving," or whether the discovery method teaches some aspect of problem-solving that is less accessible by direct instruction. There's a chapter at the end of the Prealgebra book entirely about problem-solving, which of course I haven't gotten around to reading :tongue_smilie: and probably includes lots of direct instruction, but it also seems to me that every lesson is about problem-solving, i.e., deciding how to approach a type of problem you haven't seen before.

 

My concern is that not every student is motivated to use a discovery approach, is willing to puzzle out the problems before looking at the answers, is willing to work for several hours on a single algebra problem until he gets the answer, is willing to spend more time and do more and harder math than his peers.

If you say yes to all of these for your student, then this is the program for him. It is a great program, and if you can "sell" it to your kid, fantastic. It's just my experience that the student really has to love math already to go through all of this and find it enjoyable.

 

Certainly tears and hating math/hating a math curriculum would be reasons to avoid a curriculum, but I don't know whether it has to be one or the other with AoPS. Are you saying that you think AoPS is a love/hate curriculum? ETA, thinking more, I think you're saying that if the student doesn't love it, they'll never get through it - correct?

Edited October 1, 2011 by wapiti

[regentrude]

More thinking out loud (y'all tired of me yet, lol): I wonder to what extent the discovery problems simply provide extra training in "problem-solving," or whether the discovery method teaches some aspect of problem-solving that is less accessible by direct instruction.

 

IMO, the discovery achieves something that is way beyond offering extra problem solving practice: it encourages the student to play around with math, to explore concepts he has not been previously thought, to treat problems as puzzles. It is a completely different thing to solve an unknown problem with a self-discovered method than to practice solving a few more problems with a method that has been presented and explained by somebody else.

With a discovery approach, the student himself extends previously known concepts to new scenarios and generalizes/synthesizes information in a way that can not be replicated by direct instruction.

 

Are you saying that you think AoPS is a love/hate curriculum? ETA, thinking more, I think you're saying that if the student doesn't love it, they'll never get through it - correct?

No, I am not saying it is love/hate. I am saying that if I had a student with little love for math, I would not make him spend that much extra time and effort to go above and beyond the necessary (but rather settle for solid mastery of the traditional curriculum). I save the above-and-beyond for the subjects my kids are excited about, not the ones where I would have to push and shove to get it accomplished. Just my personal opinion, of course. I am sure one can make a student who does not love it get through the books... only it's not something I would want to do. Edited October 1, 2011 by regentrude

[FairProspects]

But.....you won't know until you get there and give it a try. But if students aren't thriving w/it, it doesn't mean they aren't solid math students. They may simply need direct instruction.

 

8, could you or someone else give me some examples of a curriculum that is more direct instruction focused so I can compare samples of the two?

[Just Robyn]

8 (or anyone else), do you have any thoughts on Rusczyk's suggestion that traditional learners could still learn the traditional way with his books, I assume by reading through the solutions as a method of direct instruction? Do you think that would not be direct enough for such students? Or might there be a formatting issue? I vaguely recall that one of your dc preferred Foerster - was Foerster clearer? Obviously the effect of trying to use AoPS a direct method wouldn't be quite the same; we haven't tried that but I'm just wondering. So far in the Prealgebra, the solution section seems quite explicit in terms of teaching, though I don't know whether that's always the case. My dd is a person who, in language arts at least, struggles with inference and does better with explicit instruction, so I am on the lookout for difficulties with the discovery aspect. So far, so good though.

 

Along those lines, sometimes I wonder whether, just like with some of the WTM LA methods (narration, etc. - I'm harking back to some old Nan threads), what may be hard for a particular student about learning problem solving with AoPS may be just the reason to practice it, or at least some of it, if there were a way to walk the fine line balancing that with the frustration level.

 

More thinking out loud (y'all tired of me yet, lol): I wonder to what extent the discovery problems simply provide extra training in "problem-solving," or whether the discovery method teaches some aspect of problem-solving that is less accessible by direct instruction. There's a chapter at the end of the Prealgebra book entirely about problem-solving, which of course I haven't gotten around to reading :tongue_smilie: and probably includes lots of direct instruction, but it also seems to me that every lesson is about problem-solving, i.e., deciding how to approach a type of problem you haven't seen before.

 

 

 

Certainly tears and hating math/hating a math curriculum would be reasons to avoid a curriculum, but I don't know whether it has to be one or the other with AoPS. Are you saying that you think AoPS is a love/hate curriculum? ETA, thinking more, I think you're saying that if the student doesn't love it, they'll never get through it - correct?

 

Regarding this - I get that the discovery method is not gonna work for all students, but wouldn't working through discovery with them, even as a supplemental thing done twice a week, help them understand what math can be and stretch their mind in some way? If AoPS isn't going to work with your child as their main program, couldn't you still pull it out and use it? Also, wouldn't the illustrations in the book be helpful to most students, even if it is something they read through once they already understand the concepts? Possibly it is something that could be read through (in part, if it is too much) a year behind explicit instruction.

[wapiti]

Regarding this - I get that the discovery method is not gonna work for all students, but wouldn't working through discovery with them, even as a supplemental thing done twice a week, help them understand what math can be and stretch their mind in some way? If AoPS isn't going to work with your child as their main program, couldn't you still pull it out and use it? Also, wouldn't the illustrations in the book be helpful to most students, even if it is something they read through once they already understand the concepts? Possibly it is something that could be read through (in part, if it is too much) a year behind explicit instruction.

 

I think therein lies the problem - the discovery method is not going to work if one already knows what is being discovered. And, it's hard to imagine AoPS being used as a supplement. However, I have thought about it the other way around - suppose, for example, you supplemented with something more direct after going through the discovery lesson on a particular topic, if the student did not get a firm grasp on the concept via discovery or otherwise struggled. The other possibility might be, as you suggest, to do less discovery, alternating with direct instruction on some lessons. On the one hand, I think there might be degrees to which one could "go lighter" on the discovery aspect, but on the other hand, I wonder whether that may water down the benefits too much; and like anything else, a lot might depend on the particular kid. Logistically, it would seem to me that rather than combining AoPS with something else, it might be easier to go straight through AoPS, and use the solutions to the lesson problems as direct instruction only when you feel you must.

Edited October 1, 2011 by wapiti

[regentrude]

but wouldn't working through discovery with them, even as a supplemental thing done twice a week, help them understand what math can be and stretch their mind in some way? If AoPS isn't going to work with your child as their main program, couldn't you still pull it out and use it?

 

Yes, you can certainly use AoPS as a supplement.

There was recently a thread where several users mentioned that this caused the program to sort of "flop" because once you have been told, you can't discover anymore, and so the program did not work as well and was not inspiring for the student. (Search for the thread, it was in the last few weeks)

 

Also, wouldn't the illustrations in the book be helpful to most students, even if it is something they read through once they already understand the concepts? Possibly it is something that could be read through (in part, if it is too much) a year behind explicit instruction.

I don't know the pre-algebra book; in the other books there are very few illustrations.

As far as reading through: I found that reading through a math book does absolutely nothing unless one works the problems. There is very little general text - mostly problem solutions are discussed and generalized. So, reading the book is not helpful; the student has to work through the problems in order to get any benefit. Which, of course, can be done even if the student has gone through another program before - it just loses the joy of discovery.

[wapiti]

IMO, the discovery achieves something that is way beyond offering extra problem solving practice: it encourages the student to play around with math, to explore concepts he has not been previously thought, to treat problems as puzzles. It is a completely different thing to solve an unknown problem with a self-discovered method than to practice solving a few more problems with a method that has been presented and explained by somebody else.

With a discovery approach, the student himself extends previously known concepts to new scenarios and generalizes/synthesizes information in a way that can not be replicated by direct instruction.

This confirms what I have rolling around in my head.

 

No, I am not saying it is love/hate. I am saying that if I had a student with little love for math, I would not make him spend that much extra time and effort to go above and beyond the necessary (but rather settle for solid mastery of the traditional curriculum). I save the above-and-beyond for the subjects my kids are excited about, not the ones where I would have to push and shove to get it accomplished. Just my personal opinion, of course. I am sure one can make a student who does not love it get through the books... only it's not something I would want to do.

 

Thanks for fleshing this out!

[lewelma]

I am currently trying to catch up with my ds in the AoPS Intro Algebra book. And I have been avoiding the discovery approach and just reading the instruction portion of the book as a way to save time, and then doing the exercises. Boy is this ANNOYING! If you are not doing discovery, they way he instructs is just wordy, and you keep thinking "get to the point, just tell me what to do." I keep wanting to skim, but then I can't figure out what he is talking about, and I have to go back and read more carefully. Point being: I would NOT recommend doing this book with a non-discovery approach. Instead, I would use a standard book, and then work through some of the challenge problem in AoPS to supplement something like Forresters. I don't know how easy this would be to do, but it is an idea.

 

Also, let me be clear (and I don't mean to be mean or rude or anything else): AoPS is NOT algebra like any of us learned it. It is training for the Math Competitions. Instead of comparing it to MCT, I would compare it more to NaNoWriMo. There is no way that my Mathy son would write 50,000 words in a month, and I would not set him up for failure by trying. Think carefully before you over challenge a child. AoPS is HARD for me, and I was a math teacher in High School and have a PhD in a mathematical science.

 

Smart kids can successfully learn math and learn to solve problems without using AoPS (I did). My other ds(7) is likely to do Foresters because it will fit him better. He is advanced by 3 yeas, but that does not mean that AoPS will fit him.

 

Please, please don't jump on the wagon unless you want your children to do discovery math using a book that trains kids for the competitions.

 

Please no flaming, this is only meant to be very clear and useful to those who are on the fence.

 

Ruth in NZ

 

 

(I have not seen the PreAlgebra program so I can't speak to it. )

[JenC3]

What I find the most exciting about AoPS is the voice of the text. I can hear someone actually talking to me who ENJOYS math, who CARES if I understand it, and by sheer brilliant simple instruction BELIEVES I will understand it. Now this is with the pre-algebra book. I haven't looked at the other books except Beast samples. The math books I had in highschool were B-O-R-I-N-G...my teachers were terrible and seemed likely to dislike either all of us or their subject matter.

 

I really feel the text and teacher make all the difference in what the student likes/dislikes.

[Just Robyn]

What I find the most exciting about AoPS is the voice of the text. I can hear someone actually talking to me who ENJOYS math, who CARES if I understand it, and by sheer brilliant simple instruction BELIEVES I will understand it. Now this is with the pre-algebra book. I haven't looked at the other books except Beast samples. The math books I had in highschool were B-O-R-I-N-G...my teachers were terrible and seemed likely to dislike either all of us or their subject matter.

 

I really feel the text and teacher make all the difference in what the student likes/dislikes.

 

This is what I am attracted to too. It looks to be a book with the goal of showing a student how cool math is (even if that isn't the main goal). I too have only looked at the pre-algebra samples, so I guess I'll look at some of the higher level samples and see if they give me the same feeling.

 

If there is a program with the same feel but with direct instruction, :bigear:.

[JenC3]

I am currently trying to catch up with my ds in the AoPS Intro Algebra book. And I have been avoiding the discovery approach and just reading the instruction portion of the book as a way to save time, and then doing the exercises. Boy is this ANNOYING! If you are not doing discovery, they way he instructs is just wordy, and you keep thinking "get to the point, just tell me what to do." I keep wanting to skim, but then I can't figure out what he is talking about, and I have to go back and read more carefully. Point being: I would NOT recommend doing this book with a non-discovery approach. Instead, I would use a standard book, and then work through some of the challenge problem in AoPS to supplement something like Forresters. I don't know how easy this would be to do, but it is an idea.

 

Also, let me be clear (and I don't mean to be mean or rude or anything else): AoPS is NOT algebra like any of us learned it. It is training for the Math Competitions. Instead of comparing it to MCT, I would compare it more to NaNoWriMo. There is no way that my Mathy son would write 50,000 words in a month, and I would not set him up for failure by trying. Think carefully before you over challenge a child. AoPS is HARD for me, and I was a math teacher in High School and have a PhD in a mathematical science.

 

Smart kids can successfully learn math and learn to solve problems without using AoPS (I did). My other ds(7) is likely to do Foresters because it will fit him better. He is advanced by 3 yeas, but that does not mean that AoPS will fit him.

 

Please, please don't jump on the wagon unless you want your children to do discovery math using a book that trains kids for the competitions.

 

Please no flaming, this is only meant to be very clear and useful to those who are on the fence.

 

Ruth in NZ

 

 

(I have not seen the PreAlgebra program so I can't speak to it. )

 

Thanks! I think this is important to think about. I'm planning on using Beast through Pre-Algebra, but depending on how my dd develops I may switch after. My ds is using Rightstart along with Essentials, but I will switch him to Beast after RSB at 6.5-7 when I hope 2nd grade will be done. It all depends on them how far we go.

[8filltheheart]

IMO, the discovery achieves something that is way beyond offering extra problem solving practice: it encourages the student to play around with math, to explore concepts he has not been previously thought, to treat problems as puzzles. It is a completely different thing to solve an unknown problem with a self-discovered method than to practice solving a few more problems with a method that has been presented and explained by somebody else.

With a discovery approach, the student himself extends previously known concepts to new scenarios and generalizes/synthesizes information in a way that can not be replicated by direct instruction.

 

No, I am not saying it is love/hate. I am saying that if I had a student with little love for math, I would not make him spend that much extra time and effort to go above and beyond the necessary (but rather settle for solid mastery of the traditional curriculum). I save the above-and-beyond for the subjects my kids are excited about, not the ones where I would have to push and shove to get it accomplished. Just my personal opinion, of course. I am sure one can make a student who does not love it get through the books... only it's not something I would want to do.

 

:iagree: with this.

 

The reality of high school is that days are long and full of lots of work. In my mind it boils down to a cost/benefit analysis and would working through hrs of math necessarily be to the student's benefit. Not every student needs to understand math to this degree.

 

I have pondered the scenario a lot of what our oldest would have done w/a program like AoPS. I didn't know about it back then. He thinks about math very much like youngest ds, so I can see it would have benefited him. BUT, not doing AoPS certainly hasn't hurt or hampered him in any way. He never made below a high A in any math or engineering class he ever took. He graduated near the top of his class. So....it even being well-prepared for chemical engineering doesn't require an AoPS level of understanding of math.

 

The difference in my mind is if it would have changed what he would have pursued. For example, youngest ds is planning on pursuing a phD. He wants to be a theoretical physicist of some sort. The way he thinks about things has been nurtured and developed even beyond his norm by AoPS. I think hitting AoPS during those vital yrs of 13-15 was also important. Ds had major mental "growth" during those ages. (None of my kids have ever experienced "puberty brain-fog" but tend to really develop mental acuity during those yrs....this ds more than all the others and I think the hrs spent thinking about math solutions was a major influence.)

 

7th grade dd is just as good at math as her older brothers. She, however, does not think about math like they do. She does not solve problems uniquely or derive proofs for formulas by simply looking at them. She is very methodical and deliberate and defines and computes. She takes direct-instruction and understands it and uses it. Could she learn math via AoPS? I'm sure she could if I forced the issue. However, she doesn't like math. She loves biology and ornithology. I'm just not seeing a reason to implement AoPS w/her. She can use the extra time she is not spending on math delving into the subjects that really interest her (which a future in math and engineering definitely are not.)

 

I'm not sure if that helps anyone or not.

Edited October 1, 2011 by 8FillTheHeart

[8filltheheart]

I am currently trying to catch up with my ds in the AoPS Intro Algebra book. And I have been avoiding the discovery approach and just reading the instruction portion of the book as a way to save time, and then doing the exercises. Boy is this ANNOYING! If you are not doing discovery, they way he instructs is just wordy, and you keep thinking "get to the point, just tell me what to do." I keep wanting to skim, but then I can't figure out what he is talking about, and I have to go back and read more carefully. Point being: I would NOT recommend doing this book with a non-discovery approach. Instead, I would use a standard book, and then work through some of the challenge problem in AoPS to supplement something like Forresters. I don't know how easy this would be to do, but it is an idea.

 

Also, let me be clear (and I don't mean to be mean or rude or anything else): AoPS is NOT algebra like any of us learned it. It is training for the Math Competitions. Instead of comparing it to MCT, I would compare it more to NaNoWriMo. There is no way that my Mathy son would write 50,000 words in a month, and I would not set him up for failure by trying. Think carefully before you over challenge a child. AoPS is HARD for me, and I was a math teacher in High School and have a PhD in a mathematical science.

 

Smart kids can successfully learn math and learn to solve problems without using AoPS (I did). My other ds(7) is likely to do Foresters because it will fit him better. He is advanced by 3 yeas, but that does not mean that AoPS will fit him.

 

Please, please don't jump on the wagon unless you want your children to do discovery math using a book that trains kids for the competitions.

 

Please no flaming, this is only meant to be very clear and useful to those who are on the fence.

 

Ruth in NZ

 

 

(I have not seen the PreAlgebra program so I can't speak to it. )

 

:iagree: completely. I don't think there is adequate understanding of just how difficult the problems in the texts actually are. ;)

[JenC3]

7th grade dd is just as good at math as her older brothers. She, however, does not think about math like they do. She does not solve problems uniquely or derive proofs for formulas by simply looking at them. She is very methodical and deliberate and defines and computes. She takes direct-instruction and understands it and uses it. Could she learn math via AoPS? I'm sure she could if I forced the issue. However, she doesn't like math. She loves biology and ornithology. I'm just not seeing a reason to implement AoPS w/her. She can use the extra time she is not spending on math delving into the subjects that really interest her (which a future in math and engineering definitely are not.)

 

I am all for this if that's the way she develops. My dd has engineers and doctors in her line. My dh (english) and my bil (neuroscientist) both hold PhD's, my mil (math), fil (engineering) and other bil (english) all have MA's. She has already said she wants a PhD. Who knows, but I do want her to have the best chance to develop. She's also a whiz at LA, but I don't know yet which way she'll go. I do think upper levels will depend on her interest.

[NittanyJen]

I don't think anyone is encouraging people to not use AoPS. From my perspective it is not simply about difficulty level or even understanding math. It is all about how the material is taught. I do not believe that it is a program that will be accessible to all math students, even good math students. There is a lot more to it than that.

 

But.....you won't know until you get there and give it a try. But if students aren't thriving w/it, it doesn't mean they aren't solid math students. They may simply need direct instruction.

 

:iagree:

 

There are many, many excellent math programs out there that will provide a challenge for a good student. AoPS is getting a lot of play right now because they just put out their new pre-algebra book, promo'd their upcoming Beast Academy series, and are the shiny new thing on the block. They represent one good choice among many, but as with any curriculum, the approach won't fit all, and using AoPS won't necessarily make your kid better than anyone else's. That is their marketing materials talking ;)

 

What will make your child the best he can be at math is finding the instructional style that is best suite to his learning style from among the many good choices available-- something that sparks that, "Oh, now I get it!" moment is worth more than 200 WTM reviews :)

[regentrude]

What I find the most exciting about AoPS is the voice of the text. I can hear someone actually talking to me who ENJOYS math, who CARES if I understand it, and by sheer brilliant simple instruction BELIEVES I will understand it. ...

I really feel the text and teacher make all the difference in what the student likes/dislikes.

 

Yes, that is a major appeal to us too. The book radiates joy. Very different form the boring, dry "math is good for you and useful, that's why you must do it" approach of some other texts I have seen.

[TKDmom]

This is what I am attracted to too. It looks to be a book with the goal of showing a student how cool math is (even if that isn't the main goal). I too have only looked at the pre-algebra samples, so I guess I'll look at some of the higher level samples and see if they give me the same feeling.

 

If there is a program with the same feel but with direct instruction, :bigear:.

 

How would Life of Fred fit in here? I'm hoping there are people here who have experience with both AoPS and LoF.

 

My dd(10) is about halfway through Fractions. She loves it because it makes her giggle, but I don't have enough experience with the series to know how rigorous it is, or what the teaching style is (on the surface it's just a goofy story with some math problems thrown in at the end.) I get the impression that AoPS is more about the intrinsic joy of math and LoF is more about making math fun (if that even makes any sense. I need to go to bed...)

Edited October 2, 2011 by bonniebeth4

[Beth in SW WA]

Yes, that is a major appeal to us too. The book radiates joy. Very different form the boring, dry "math is good for you and useful, that's why you must do it" approach of some other texts I have seen.

 

:iagree:

 

I'm already using Richard's terminology with dd. "Isolate, isolate, isolate." I stole a few other zingers from his videos. He's too fun. He has inspired me in my own math journey.

 

Tonight at dinner I asked dd to figure out 1/4 divided by 3 by using a pizza cutter on our Papa Murphy's pizza. It only took a minute. It would never have occurred to me to experiment with fractions the way we have been doing lately. (She can do it on paper but it was fun for her to prove it in the real world.)

 

We've been doing easy alg equations tonight that she says are 'simple'. She knows the 'golden rule of algebra' (not an aops term) and now she is learning how to isolate (5x=20) by dividing. Granted, the problems are very basic. Solving for x & y is still fun.

 

Now Abi hasn't seen the book (nor will she for some time, if ever). The point is that I am enjoying the book and Richard's style of teaching. Maybe that's all it will be for some families. Mom or Dad may have a new vision for math. Simple & sweet.

 

My older dc used CD alg and we took the straightforward approach. No bells & whistles and it worked out great. I wasn't jazzed about alg when my kids were in elementary school. This time I am. Maybe this next time around we'll attack alg a bit differently.

 

I'm not a math phd like others who I admire here. I tolerated college alg. At this stage of my life I love reading about this topic. And learning. I'm cuddled in a blanket fighting a cold today and reading, reading, reading..... :)

 

Carry on. I'm just a fly on the wall. :)

[JenC3]

I'm not a math phd like others who I admire here. I tolerated college alg. At this stage of my life I love reading about this topic. And learning. I'm cuddled in a blanket fighting a cold today and reading, reading, reading..... :)

 

This is exactly me! My dh thinks I'm a bit nutty, but I want to also be an example so I have to learn math in a deeper way, latin...

[boscopup]

I'd suggest researching other curricula to have a backup plan in case AoPS doesn't work out. I too am planning to give it a try. My son IS mathy, though I don't know for sure if AoPS will fit him. Sometimes he seems like discovery would be the way to go (afterall, he usually teaches himself math before I get there :tongue_smilie:), but at the same time, sometimes he seems to do better with just telling him how to do it. He's only 7 though, so I really can't say what he'll be like when he gets to high school level problem solving, and he'll be hitting it young too, so he may not even be ready for AoPS when we get to prealgebra (likely age 9 or maybe 10). I have a backup plan for Algebra already (I think Foerster's would probably fit him well if the discovery approach doesn't work out), and I'm researching prealgebra options. I just looked at the Prentice-Hall prealgebra sample, and it uses algebra tiles and such to explain stuff. I never had that as a kid. :confused: The text looked interesting to me. It's not AoPS, for sure, but it appears to explain the concepts decently, and the layout is appealing.

 

Honestly, I don't think I'd even be looking at AoPS if my kid didn't love math. It's not at all like MCT. I think LOF is closer to being the math equivalent of MCT.

[JenC3]

Boscopup,

 

Like I said, I'm planning on using Beast through Pre-Algebra, after that, who knows? My mil teaches college math so she's my back up for Algebra. I'm sure if by then dd does not have a bent for it, we will move on. If Beast were not coming out at a perfect time and my dd did not display other types of math interest...I'd not be considering it.

 

BTW, MCT has not impressed me or dh, at least not island level. LoF is okay. I mostly read it b/c the kids like it.

Edited October 2, 2011 by JenC3

[Kathy in Richmond]

Regarding this - I get that the discovery method is not gonna work for all students, but wouldn't working through discovery with them, even as a supplemental thing done twice a week, help them understand what math can be and stretch their mind in some way? If AoPS isn't going to work with your child as their main program, couldn't you still pull it out and use it? Also, wouldn't the illustrations in the book be helpful to most students, even if it is something they read through once they already understand the concepts? Possibly it is something that could be read through (in part, if it is too much) a year behind explicit instruction.

 

I am currently trying to catch up with my ds in the AoPS Intro Algebra book. And I have been avoiding the discovery approach and just reading the instruction portion of the book as a way to save time, and then doing the exercises. Boy is this ANNOYING! If you are not doing discovery, they way he instructs is just wordy, and you keep thinking "get to the point, just tell me what to do." I keep wanting to skim, but then I can't figure out what he is talking about, and I have to go back and read more carefully. Point being: I would NOT recommend doing this book with a non-discovery approach. Instead, I would use a standard book, and then work through some of the challenge problem in AoPS to supplement something like Forresters. I don't know how easy this would be to do, but it is an idea.

 

I'm trying to imagine how to use AoPS as a supplement. Just reading through it wouldn't work well IMHO; the texts are definitely meant to be used with a pencil and paper in hand. And that takes a lot of time.

 

Just dipping into AoPS once a week or so, using another curriculum as primary...I'm not sure what you'd get out of it. You could do so if you don't mind moving slowly and orderly (& there's nothing at all wrong with that approach). But dipping into the texts randomly (so that they lined up with the primary text) might prove frustrating because AoPS texts build on concepts previously covered, & that list is much, much broader for AoPS than other texts. So you might pick out a trig problem, only to find that your student should have already seen complex numbers or worked with some trig concepts not covered in her primary text.

 

I would say that supplementing with AoPS by using it *after* the student has studied with another text might be the best bet. I'd pull tougher problems out of AoPS as a challenge. But be forewarned that a lot of the problem sets (especially starred problems and challenge sets) are REALLY tough.

 

Finally, there aren't many illustrations or diagrams in the upper levels (I haven't seen the prealgebra yet); you could do better elsewhere for that.

 

What I find the most exciting about AoPS is the voice of the text. I can hear someone actually talking to me who ENJOYS math, who CARES if I understand it, and by sheer brilliant simple instruction BELIEVES I will understand it.

 

Yes, this is what is absolutely wonderful! Their love for math shines through. You'll be able to see that in your child's face if the fit is right for him. :)

 

The reality of high school is that days are long and full of lots of work. In my mind it boils down to a cost/benefit analysis and would working through hrs of math necessarily be to the student's benefit. Not every student needs to understand math to this degree.

 

Exactly. We all juggle; time is too short in high school to devote hours and hours to something the student doesn't absolutely love. That doesn't mean not to try AoPS; it also doesn't mean you're not successful at math if you choose something else.

 

Last year, I tutored two siblings in precalculus. We used AoPS precalculus for one and Foerster precalculus for the other. The AoPS user absolutely adored math and wanted to think about it all the time. His sister is a very capable math student, on the level of the honors math students I tutor from the local high schools, but without a big love for math. She needed something substantial, but more straightforward. Their learning styles differed as well. The brother (like me & my kids) wanted to figure math out for himself and find the patterns and formulas and theorems. He is frustrated by direct instruction. Sort of a right-brained, wants first to see the forest & not the trees type. The sister, however, thrives on direct instruction. Foerster provided those trees for her and then populated the forest. Each student did well with his or her approach, and the sister certainly wasn't shortchanged.

 

I don't think there is adequate understanding of just how difficult the problems in the texts actually are.

 

Also, let me be clear (and I don't mean to be mean or rude or anything else): AoPS is NOT algebra like any of us learned it. It is training for the Math Competitions. Instead of comparing it to MCT, I would compare it more to NaNoWriMo. There is no way that my Mathy son would write 50,000 words in a month, and I would not set him up for failure by trying. Think carefully before you over challenge a child. AoPS is HARD for me, and I was a math teacher in High School and have a PhD in a mathematical science.

 

:iagree:I have a PhD in applied math, and I'm constantly learning new things from the AoPS materials and problems. So.much.fun. :D

 

Yes, they've pulled problems from various math competitions (w/permissions granted) to use in the AoPS texts. These aren't going to be easy for anyone usually. They’re worthwhile, though; the “use simple concepts on really hard problems†that AoPS promotes. [in later levels (intermediate alg & precalulus), some of these problems might be AIME competition problems, or even higher level. The AIME is taken by roughly the top 10,000 kids in the US, & the avg score is about 3 out of 15. Not easy is an understatement.]

 

AoPS precalculus is one intense course. Even after a year, my student and I hadn't completed the whole text. The problems were just that good & meaty. Rusczyk covers topics that you won't see in other precalculus books - more trig and triangle theorems (the only trig text I’ve seen that's comparable is Gelfand's), more complex numbers (instead of stopping with DeMoivre's theorem, he delves deeply into roots of unity and the geometry of the complex plane), and even includes an introduction to linear algebra (linear dependence, transformations, vector geometry..)

 

Here's one side-by-side example comparison of the two texts:

I taught matrices with both AoPS and Foerster. In AoPS, the approach is to view matrices as representations of linear transformations with respect to a specific basis in Euclidean space. In Foerster, a matrix is defined as, say, a 2x3 array of numbers. He shows how they operate on vectors, but without the underlying idea of linear transformations, vector spaces, etc, that a mathematician wants to see. Foerster tells how to find the inverse of a 2x2 matrix (and says to use calculators for the 3x3 case) and he shows how to use inverse matrices to solve systems of equations. Very handy. AoPS, on the other hand, gives a nice mathematical treatment of determinants & then has the kids derive the formula for inverse matrices for both 2x2 and 3x3 cases. Then AoPS goes further to generalize to the nxn case, all while setting the matrix math firmly in linear algebra where it belongs. While Foerester's approach is completely appropriate for high school kids, AoPS is the right approach for the future mathematician.

 

What to do if AoPS doesn’t turn out to be the right choice for your child, but you still want the flavor of discovery?

One idea would be to use Foerster’s text along with his “Explorations†sheets. For Precalculus, they’re found in one of the supplemental teacher books that you can purchase. He has several Explorations for each chapter in precalculus (I’m assuming his other texts have something similar? Maybe someone else knows?) Their purpose is to give the student a taste of guided discovery. AoPS is more like throwing you in the deep end of the pool, sink or swim. Foerster teaches the strokes in the shallow end first: his explorations are guided & step-by-step, but still utilize the discovery approach. And they are fun; I used them with my student last year. She liked them & enjoyed the discovery process now and then. And she still had the detailed exposition of Foerster’s text.

 

Another idea is to try some of the Key Curriculum Press offerings. Their Discovering Algebra and Discovering Geometry texts are based on the (duh!) discovery approach. I’ve only used the geometry book and like it with certain students – it comes with plenty of teacher supplemental helps. It’s short on proofs, but does address them at the end of the text.

 

P.S. I'm not trying to be discouraging. I love reading all the success stories and even struggles & doubts about your adventures with AoPS. I absolutely am one of the biggest fans of AoPS around. I think it is closest to the ideal math education out there right now. And I think that lots of kids could succeed in it given enough time, appropriate guidance, the right attitude toward hard work, and a fit for the unique presentation. It's just that I've used most of the upper levels & I see where it's going & what it takes to get through. Be prepared to spend lots of time and energy, and be prepared to let go if your child ever gets to the point where he has more frustration than joy. It’s not going to be the right curriculum for everyone or even for most.

[Aquinas Academy]

When I first discovered AoPS I believed it was the perfect math text. DD 12 (now 15) started Intro to Alg. and within a few weeks I was sure I'd use AoPS with all my children. The rigour, excitment, and joy contained in the books made them completely perfect. Here, I thought, was the curriculum to beat all curricula. I had two years of blissful AoPS love, then disaster struck.

My second daughter, 12 at the time, hated AoPS. I let her skip all the challenge problems and she still hated it. Some days weren't too bad, but far too often math resulted in tears. "I can't do this! I'm no good at math!" She'd done SM all the way to 6B and, while she certainly wasn't a math lover, she did well enough. But AoPS was just too much.

I finally got the message that AoPS wasn't the all-perfect curriculum I had thought, and switched DD 13 to Singapore's NEM, which is also a challenging math text. The difference has been extraordinary. NEM challenges DD at a level within her capabilities. It makes her think, not cry. She doesn't love math, but she does it without fuss and even admits that it can be kind of intriguing. We are very happy with the switch to NEM.

But I'm not nearly as anti-AoPS as it may sound. DD 15 is doing Intermediate Algebra, her fifth AoPS book, now. She (and I) have been thrilled with how well AoPS works for her; the discovery approach could not have been a better fit. She relishes the challenge and has come to love math so much more than I think she would have with any other curriculum. It's currently 11:40 on a Saturday night and DD, of her own choice, is working on an AoPS problem. How her brain can function so well at this hour is beyond me. :001_huh:

Anyway, all this rambling to say, it really (really, really) depends on the child. Don't set your heart on AoPS. It's not for everyone, and that's okay. Not everyone needs to use the most challenging curriculum on the market. From the AoPS website: The Art of Problem Solving curriculum is designed for high-performing math students in grades 6-12. I hate to break it to you, but it's mathematically impossible for everyone to be in the top of the class. ;) Your child might be perfectly bright and still not be at AoPS level. That does not mean that he/she is doomed. I am all for pushing children, but only as far as they are capable. The problems in AoPS are not just hard, they are at a level that might be incomprehensible for those of us who are used to the formulaic problems in standard high school math texts.

Like others have said, I'm not wanting to discourage. I'm just offering the some words of warning from someone who's used AoPS very succesfully with one child and found it to be a disaster with another. :)

[JenC3]

Again, my sights are not set for dd or any of my other children to use AoPS beyond elementary and pre-algebra. Now, we may go further, who knows, but I want their start to be dynamic. They both got really excited by the Guide samples. My dc love math story books, we have an extensive library. They love math games, logic puzzles, strategy, etc. My goal is to cultivate a love/joy of math just like we have done with reading. I believe making math a priority and providing engaging math texts can make this happen.

[wapiti]

I am currently trying to catch up with my ds in the AoPS Intro Algebra book. And I have been avoiding the discovery approach and just reading the instruction portion of the book as a way to save time, and then doing the exercises. Boy is this ANNOYING! If you are not doing discovery, they way he instructs is just wordy, and you keep thinking "get to the point, just tell me what to do." I keep wanting to skim, but then I can't figure out what he is talking about, and I have to go back and read more carefully. Point being: I would NOT recommend doing this book with a non-discovery approach. Instead, I would use a standard book, and then work through some of the challenge problem in AoPS to supplement something like Forresters. I don't know how easy this would be to do, but it is an idea

 

I think I see what you mean about your experience with using AoPS as direct instruction - very useful info - thanks!

 

I'm not sure if that helps anyone or not.

 

Well it helps me, as usual. You are ever a font of wisdom, and your thoughts and experiences are heard and much appreciated :)

 

Yes, that is a major appeal to us too. The book radiates joy. Very different form the boring, dry "math is good for you and useful, that's why you must do it" approach of some other texts I have seen.

 

Yes, *sigh*. Looking at books and teaching/learning with them are two different things of course, but in terms of visceral appeal to me personally, AoPS next to other books is like a piece of yummy chocolate next to a graham cracker.

 

Here's one side-by-side example comparison of the two texts:

I taught matrices with both AoPS and Foerster. In AoPS, the approach is to view matrices as representations of linear transformations with respect to a specific basis in Euclidean space. In Foerster, a matrix is defined as, say, a 2x3 array of numbers. He shows how they operate on vectors, but without the underlying idea of linear transformations, vector spaces, etc, that a mathematician wants to see. Foerster tells how to find the inverse of a 2x2 matrix (and says to use calculators for the 3x3 case) and he shows how to use inverse matrices to solve systems of equations. Very handy. AoPS, on the other hand, gives a nice mathematical treatment of determinants & then has the kids derive the formula for inverse matrices for both 2x2 and 3x3 cases. Then AoPS goes further to generalize to the nxn case, all while setting the matrix math firmly in linear algebra where it belongs. While Foerester's approach is completely appropriate for high school kids, AoPS is the right approach for the future mathematician.

 

 

Thank you for this detailed comparison, and for all your other thoughts! Yet again, I have to save this. I need to put your posts in a word document.

 

I finally got the message that AoPS wasn't the all-perfect curriculum I had thought, and switched DD 13 to Singapore's NEM, which is also a challenging math text. The difference has been extraordinary.

 

Thanks for sharing your experiences! Very helpful!

 

I know I'm not alone when I say that reading about other's experiences with AoPS and other secondary math curricula is invaluable! And, it always helps to be reminded of the importance of staying flexible in our choices. We're taking things one day at a time with AoPS Prealgebra; it's certainly an adjustment, and comes at a time for dd to begin to develop some maturity with her work anyway (writing it down, for starters ;)). My hope is that she'll learn a lot from this book even if she ends up using something else for algebra, or even if we use another prealgebra down the road. This IS an experiment, but not one that will be a waste of time (which she has plenty of right now anyway). She's still learning lots, and I'm hoping she'll slowly be converted over to the AoPS way of thinking - she's very attracted to hard problems even when she can't do them - it's like a dare, though she has a bad habit of flipping to the back of the book and looking at problems she has no hope of solving. Dd: "Mommy, I need help!" me: "well let's see--" dd: "NO! DON'T tell me... wait WAIT!" LOL.

 

Come to think of it, I'm seeing her do something similar with Alcumus - she would prefer to jump to a harder topic than the topics/levels she's supposed to be working through (which are sufficiently challenging already). I wonder if that way she doesn't feel as bad if she doesn't get it right, or if it's extra-exciting when she does. hmmmm....

[melmichigan]

The pre-algebra book covers more topics than other pre-algebra books, but it's still totally appropriate as a pre-algebra book (if that makes any sense..LOL). Meaning you can go onto algebra in another series and be prepared.

 

I looked at this last night. My DD finished Chapter 2 in AoPS Prealgebra last week. The last portions on negative and zero exponents are addressed in Jacobs Algebra Chapter 8 just before the Midterm Review, and not at the same level of problems.

[brownie]

hmmm...so AOPS is good for kids who like the forest and not the trees? DS11 is this kind of thinker. He is doing Saxon Alg1/2 right now but I was thinking of repeating pre-alg with AOPS next year. He hates the details (and shows it every day by forgetting commas, labels, and adding wrong) but send him to Math Olympiad and he hardly makes a mistake...I can't figure out what to do with him. He's making me crazy! The review chapters in Saxon are making us bonkers...it's as if he tries to find new ways to make dumb mistakes. The easier it gets, the worse it seems to get, but I thought with the harder problems in AOPS that he would have a hard time managing the necessity of the details.

brownie