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# AoPS Alternative Usage Question

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Ok, I've have been wondering something about AoPS for quite some time now. How might some families use it in the non-traditional sense? In other words you use it as supplimental, non-Discovery, or partial discovery, etc... The reason I ask is that although I like the texts quite a bit, I'm just not sure it will work for my kids in its traditional way (Discovery) as a spine or not.

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I just got the Intro to Algebra today and am reviewing over it. So far I really like how it reads and flows, like a work of art almost. In the 'How to Use' section the author mentions something which strikes me and I've heard few discuss here. That is the two approaches one can take with the book. I'll provide the quote for those who haven't seen it:

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"We hope that teachers will find that their stronger students will discover most of the material in this book on their own working through the problems. Other students may learn better from a more traditional approach of first seeing the new material, then working the problems. Teachers have the flexibility to use either approach when teaching from the book." -- Richard Rusczyk

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This speaks to two teaching approaches, neither necessarily being more valid than the other depending on the child. Yet I hear very few AoPS fans trying any other approach than Discovery. The thing that strikes me as odd is that even the greatest fans admit that AoPS's approach (singular) may not work for all of their children. So they may end up using something more traditionally written like Foerster or Dolciani (my childhood Algebra text). However this also begs the question if a more traditional approach was ever tried using the same AoPS text before switching to something else? One could possibly show the short video lesson 'first' for example, before trying to work the initial problems. I know its not necessarily discovery in that case. But if it works best in that order then why not? I guess I'm just seeing more AoPS usage options outside the standard box. Does this make any sense at all? In fact I've already used the AoPS videos and sample Pre-Algebra text on linear equations with ds11 while using another Pre-A spine (TabletClass). We found that chapter to be a great resource as we also did Khan Academy. It was that experience with the text that put me over the top in making a decision to buy Intro to Algebra. So I wonder who else may use it in alternative ways, finding value in the excellent texts as they really are?

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First of all, I have tried to use it in a direct teaching manner for myself personally (later chapters in Intro Algebra are nothing I have seen before). I read the problems and learn from them and then do the exercises. There seem to be 2 problems with this. 1) The text is wordy. I keep thinking " get to the point." It is written for the discovery approach, not for direct teaching, which honestly makes it really annoying. 2) If you have not put the brain power to the discovery method, then there don't seem to be enough exercises. The exercises are "lite" because the student has discovered the material for himself which counts for quite a few exercises, if you see what I mean.

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I don't know if you have seen this post that I made on the accelerated-learners board. It was written for a very young student, but it still presents what I see as the main argument to use AoPS as written. However, I will say that my younger student might benefit from some direct teaching. So obviously, my ideas as to what is the "best" still depends on the student. If my younger son *can* use the discovery approach, then I will encourage him to use it even if this means that he needs to delay a year to gain maturity. I would rather he does AoPS as written as an older student than adapting it to a direct teaching method for a younger student. Obviously, how you use the text depends on your goals for your child and on his personal abilities and goals in life. My kids are keen on STEM majors, which informs my choices for them.

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I would suggest that the "best" way to use AoPS is to use it as written. This means the discovery approach and with the student working independently and using the text as a teacher. I don't want to get into an argument because I know that there are a lot of people using it in other ways including direct teaching (which I am likely to do with my younger who is not as mathy). However, given that your student is an incredibly strong math student, he would benefit greatly by the struggle, confusion, and frustration that goes along with using AoPS as written. Real mathematical problems (I mean in the real world as a job) are never clearly written, and are not laid out so that the approach is obvious. People in math related jobs try many different approaches before finding one that works. In fact, I have spent more than 3 months going down the wrong mathematical path, and eventually had to give up and try a new approach. I have had to get 6 math textbooks out of the library, lay them out on the floor all turned to the same topic, and read and compare all the different descriptions to try to understand. I have struggled my way through nonlinear probabilistic chaos papers in Economics journals hoping that I could apply the ideas to ecological systems. I fought for every mathematical equation that I ever published. This is reality, and this is what using AoPS as written will teach your child to do.

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My point: I would be careful of starting the AoPS sequence too early, because your ds will not have the verbal skills to work through the books independently. He can learn the material with your help and guidance, but then you lose half of what the program is teaching. It teaches math but also it teaching the true process of doing math.

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Given his strong skills I would suggest you do all the hardest problems in SM5 IP and CWP, and then switch to PreA. Start by helping, but by the second half of the book see if he can work through the book independently. Slow him down by making him do ALL the challengers. If he cannot do a challenger, then tell him to think about it and come back to it tomorrow. Make him struggle and fight for every answer. It seems like a waste of time compared to just teaching him the material, but you are after the true process, not just the math. After struggling through the entire Intro Algebra book by himself over 2.5 years, my son is now so good at problem solving that he has quit doing the review problems at the end of the chapter and is only doing the challengers. And geometry is supposed to be the hardest of the intro books. The AoPS way works! Don't short change it by starting too early.

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HTH,

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Ruth in NZ

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This is a really interesting question to me, too, although dd is not quite there yet. I *love* the AoPS approach, and I'm learning so much from the (PreAlgebra!) book, that I really, really want to use it with her, but at this point she's not ready for full-discovery - I am working hard to teach her to struggle and grapple with math problems, and she's getting a lot better at it, but she's not ready to jump in completely independently yet. But I think the systematic explanations of the foundations of arithmetic is just unmatched, and I don't want her to miss it. I have thought of doing a different Pre-A, and then AoPS via discovery, but then I wonder if 2 years of Pre-A is overkill, and if it wouldn't be better to spend 2 years of Algebra (something else, then AoPS)?

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I guess I'll know when the time comes. I'm a planner, but it seems clear to me that you can't plan too far ahead in math, because progress is definitely not linear, especially with puberty hormones kicking in! Some days she flies through her lessons so effortlessly I think we'll be in Calculus by 10th grade, and sometimes she looks at the problems like she's never seen a number before. :tongue_smilie:

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Right now, I'm making the conscious effort to *not* accelerate, but to go for deeper, broader coverage, to try and avoid the swiss-cheese effect. We're working on fractions & decimals using MM, Zaccaro, LOF, and by golly by the end of 5th grade we will have it *down*! So she might be ready for a more intense Pre-A after all that. I hope so, because I really, really like AoPS. . .

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...

My point: I would be careful of starting the AoPS sequence too early, because your ds will not have the verbal skills to work through the books independently. He can learn the material with your help and guidance, but then you lose half of what the program is teaching. It teaches math but also it teaching the true process of doing math.

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Given his strong skills I would suggest you do all the hardest problems in SM5 IP and CWP, and then switch to PreA. Start by helping, but by the second half of the book see if he can work through the book independently. Slow him down by making him do ALL the challengers. If he cannot do a challenger, then tell him to think about it and come back to it tomorrow. Make him struggle and fight for every answer. It seems like a waste of time compared to just teaching him the material, but you are after the true process, not just the math. After struggling through the entire Intro Algebra book by himself over 2.5 years, my son is now so good at problem solving that he has quit doing the review problems at the end of the chapter and is only doing the challengers. And geometry is supposed to be the hardest of the intro books. The AoPS way works! Don't short change it by starting too early.

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HTH,

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Ruth in NZ

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Ruth, Thanks for your input and well thought out rationale for using AoPS in its traditional sense. I definately see value in the Discovery approach as I also experience more of these types of problems in my own workplace (software engineering). However I'm just not sure its the best approach for every student, hence the question. This is more about the *other* students who Discovery does not work well for which Richard Rusczyk also acknowledges. Does that mean just use something else entirely at that point? Or still integrate AoPS material into their education process, just in a different way.

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I really like the point you made about about not starting AoPS too early. Its seems like with more and more bright, early learners there is the tendancy to think why not just throw the hardest thing at them since they're bright/gifted anyway? And while they may be ready for some abstract thought, jumping into the deep end of AoPS Discovery can overwhelm very quickly. This is especially true when frustration and stuggle are intentionally built right into the teaching method. Handling that frustration along with totally new abstract reasoning is a lot for many children, young and older alike. That is one of the reasons I didn't use AoPS Pre-A for my son, at least as the spine. I just didn't feel he was ready for it in terms on his maturity level. Yet he can do abstract reasoning with traditional instruction and in fact enjoyed using AoPS in part. However I am considering Discovery with him after he has more algebraic reasoning under his belt. But if discovery doesn't work I still want to utilize the text as a great resource which I think that it is. With my girls it may never work. Only time will tell.

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My younger child is one of the "other" students you refer to, so I'll discuss my plans for him.

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My goal for my younger is to initially use AoPS with direct teaching, and slowly over the year transition my son into the discovery learning approach. This transition might look like this: 1) direct teaching 2) guided discovery 3) direct teaching difficult problems and discovery method the easy problems 4) discovery method with lengthy overview in the beginning by me 5) independently discovery method. If he hates the discovery approach, I plan to do a traditional text for a year and wait for maturity and then try again. I really believe that older children do better with these texts. And I refuse to give up on the approach, just because my child is young. After all this, if the discovery method is just not to be, then I would use a traditional text and perhaps have him work through some of the starred review problems or challengers in AoPS in additional to a different text. But honestly, I doubt I would do this. There are a lot of good algebra texts out there and typically they have some very nice challengers. I would embrace a program that I know my child loves and appreciates, and steer clear of the grass is greener syndrome.

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You have not commented on *my* experience with AoPS. And I stand by it. The explanations are WORDY if used for direct teaching and the exercises are too few. Obviously, I am not a child, but I would think that these 2 problems would be accentuated in children. Some of the sections in AoPS Intro Algebra could be set out in about 1 page, and AoPS takes 12 pages. I just want to know *how* to do the problems so I can go practice on the exercises. And I have to wade through so much text. Often I find myself skipping over stuff I think looks like extra, only to find out I needed it. But then when I get to the exercises, there are just not enough of them. Because I have not struggled through the discovery aspect, I need to spend more time on practice. And there are not enough there. It. is. just. frustrating. Personally, I would have hated this series as a kid, and I went into mathematical modelling as a career!

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Ruth in NZ

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Hi Derek,

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I tried something sort of like that w/our dd. I tried using the AoPS alg text w/her after finishing MUS's alg/geo book. Even though she was familiar w/the content in the beginning of the text, she still did not like how it was presented. She could do the problems, but she didn't feel like how she had to get to the pt helped her understanding of alg any better.

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After completing Foersters (which she finished in about 2/3 of the following school yr), I enrolled her in AoPS alg 1 online course just to give it one more try. (She is just as strong of a math student as her brother, but she doesn't love math like he does.) Anyway, she finished the course w/very little difficulty (only a few of the challenge problems challenged her in a way that I would say required more than just a little mental exertion.) At the end, she just plain out said that she didn't like the way they teach and that she even going through it when she understood what they were teaching was unappealing and not helping her understand it any better than she already did.

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So......take this as simply one student's experience vs. anothers.......I personally believe the strength in the AoPS texts is learning the material via the methodology. Direct method teaching just doesn't produce the same impact and AoPS used via the direct method doesn't seem to produce the same impact either. B/c while I can absolutely state that my dd is as strong of a math student as my ds, she is not his equal in deductively arriving in the same place. Ds can prove just about anything that he uses mathematically (and does all the time for his advanced classes) It is the deductive reasoning that is fostered via the AoPS approach. Direct teaching mutes that skill to a certain extent. At least that is what I see in my own kids.

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ETA: FWIW, I did not attempt to start AoPS too early by any stretch of the imagination. ;)

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HTH

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My younger child is one of the "other" students you refer to, so I'll discuss my plans for him.

Â

My goal for my younger is to initially use AoPS with direct teaching, and slowly over the year transition my son into the discovery learning approach. This transition might look like this: 1) direct teaching 2) guided discovery 3) direct teaching difficult problems and discovery method the easy problems 4) discovery method with lengthy overview in the beginning by me 5) independently discovery method. If he hates the discovery approach, I plan to do a traditional text for a year and wait for maturity and then try again. I really believe that older children do better with these texts. And I refuse to give up on the approach, just because my child is young. After all this, if the discovery method is just not to be, then I would use a traditional text and perhaps have him work through some of the starred review problems or challengers in AoPS in additional to a different text. But honestly, I doubt I would do this. There are a lot of good algebra texts out there and typically they have some very nice challengers. I would embrace a program that I know my child loves and appreciates, and steer clear of the grass is greener syndrome.

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This is an interesting way to introduce or ease into this whole new way of discovery learning. I may consider this approach vs. all at once or not at all. I agree that there are a lot of other really solid traditional programs available. Personally I really like Dolciani and Foerster which I also have copies of to compare.

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You have not commented on *my* experience with AoPS. And I stand by it. The explanations are WORDY if used for direct teaching and the exercises are too few. Obviously, I am not a child, but I would think that these 2 problems would be accentuated in children. Some of the sections in AoPS Intro Algebra could be set out in about 1 page, and AoPS takes 12 pages. I just want to know *how* to do the problems so I can go practice on the exercises. And I have to wade through so much text. Often I find myself skipping over stuff I think looks like extra, only to find out I needed it. But then when I get to the exercises, there are just not enough of them. Because I have not struggled through the discovery aspect, I need to spend more time on practice. And there are not enough there. It. is. just. frustrating. Personally, I would have hated this series as a kid, and I went into mathematical modelling as a career!

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Ruth in NZ

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Althought quite removed from a child's level of mathimatical reasoning :tongue_smilie: you make some valid points regarding your experience and frustrations with the AoPS writing style. I find your last sentance revealing in a number of ways. First, even as a mathematical modeller you would have hated this Discovery approach as a child. Yet now you see so many of its benefits. Obviously you did fine in math without it. And many other STEM students will do well using direct instruction.

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I haven't heard of as many using AoPS with the direct instruction approach. But the ways you described above easying into discovery with your youngest does address the variation I am referring to. I just don't see it necessarily as all or nothing with AoPS. For example even if we use Dolciani as the spine I would like to use some of the AoPS problems and explanations of certain subject areas simply because I like them and they are well done. The videos are another great teaching tool which align directly with the text as well. Sometimes when a child hits a wall in understanding its nice to present things in a different light. AoPS's section on Linear Equations was great example of this and supplimental for ds11. The wordiness in that case was a welcomed perspective which 'added' to the instruction he had received from his spine program (TabletClass). Also for the kids going to ps who use AoPS as extracurricular many times along with their primary texts this information is at least partially introduced to them. A Russian coworker of mine has his son doing weekend Russian math which also uses a discovery approach along side his High School coursework. From what I've heard there are quite a number of PSers in the AoPS classes. This is more like parallel integration.

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I find your last sentance revealing in a number of ways. First, even as a mathematical modeller you would have hated this Discovery approach as a child. Yet now you see so many of its benefits. Obviously you did fine in math without it. And many other STEM students will do well using direct instruction.

I have no problem with direct instruction. I would just use a direct instruction textbook if that is the method I would be using with my child. I think that a student needs to be able to use his textbook to learn independently. I good math student should not wait around to be taught. There has to be some passion and interest and desire to self-teach. I am not a hands off type of homeschooler; however, I do think that you put your child at a disadvantage if you choose a text that can only be accessed with the help of a teacher. When I was in school, I always worked ahead and did my homework in class so I did not have to bring it home. I could only do this because I was using Jacobs (a direct instruction text) and I was a kid who learned from direct instruction. As I said, discovery would have killed my love of math. My older boy is the opposite. He cannot learn from direct instruction. It MUST be discovery. And when he used a direct instruction text (singapore) he turned it into a discovery curriculum by refusing any direct teaching. This speaks to the importance of working with your student's style of learning.

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However, and this is a big however, I had to learn the discovery method eventually to have a STEM career. And it was a shock to my system when I realized in university that I did not know how to do it. I was a plug and chug type, and now needed to be more intuitive with answering difficult questions. The first physics class I *ever* took, was calculus-based physics for engineers at Duke University. Talk about sinking. I tried to continue with my plug and chug methodology by memorizing the entire physics text book and every single type of problem in it. But boy oh boy did that take a lot of time. I did well in the class, but realized then and there that I needed a new approach.

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If a student can handle the discovery method, I think it is superior. But not all kids can, for whatever reason. As I said, I don't think I could have. So clearly you do not need to use AoPS to succeed in math, but IMHO eventually you will need the methodological skills it teaches if you plan to go into certain STEM careers.

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So I think there are 2 different issues:

1) Should you encourage your student to develop the ability to learn through discovery?

2) If you are planning on using a direct instruction method, should you choose to use AoPS?

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Hope this clarifies my thinking and helps you in some way,

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Ruth in NZ

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I am glad to see that RR acknowledge that there is a place for direct instruction with AOPS. I have a young, bright daughter who I think would totally fail if using AOPS as designed - at least right now. Yet, she is (at the ripe old age of 9) leaning toward science careers. I want to do my best to prepare her. It is hard to know which direction to go, but it seems like using AOPS w/ direct instruction would be a good middle ground. However, I'm not really seeing anybody post who has actually btdt and felt that AOPS w/o discovery was a good way to go.

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Anyway, I hope y'all keep talking so I can continue to be a fly on the wall....

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Hi Derek,

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I tried something sort of like that w/our dd. I tried using the AoPS alg text w/her after finishing MUS's alg/geo book. Even though she was familiar w/the content in the beginning of the text, she still did not like how it was presented. She could do the problems, but she didn't feel like how she had to get to the pt helped her understanding of alg any better.

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After completing Foersters (which she finished in about 2/3 of the following school yr), I enrolled her in AoPS alg 1 online course just to give it one more try. (She is just as strong of a math student as her brother, but she doesn't love math like he does.) Anyway, she finished the course w/very little difficulty (only a few of the challenge problems challenged her in a way that I would say required more than just a little mental exertion.) At the end, she just plain out said that she didn't like the way they teach and that she even going through it when she understood what they were teaching was unappealing and not helping her understand it any better than she already did.

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So......take this as simply one student's experience vs. anothers.......I personally believe the strength in the AoPS texts is learning the material via the methodology. Direct method teaching just doesn't produce the same impact and AoPS used via the direct method doesn't seem to produce the same impact either. B/c while I can absolutely state that my dd is as strong of a math student as my ds, she is not his equal in deductively arriving in the same place. Ds can prove just about anything that he uses mathematically (and does all the time for his advanced classes) It is the deductive reasoning that is fostered via the AoPS approach. Direct teaching mutes that skill to a certain extent. At least that is what I see in my own kids.

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ETA: FWIW, I did not attempt to start AoPS too early by any stretch of the imagination. ;)

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HTH

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8Fill, as always this is a very thoughtful and helpful post. I really do enjoy hearing the different experiences your children had with AoPS, especially this dd. It was very clear that AoPS wasn't for her in hindsight, though maybe not so much earlier on. She was able to complete a challenging class without too much trouble. Yet it didn't do much for her. I guess like many other bright kids, direct instruction is best for her.

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This also makes one ponder the benefit of taking an AoPS course following another challenging class in the same subject matter. I could see starting with an easier Algebra then possibly attempting AoPS in a second year. For my son I'd like to spread Algebra 1 over two years including something rigorous in the mix. If we stick with TabletClass into Algebra 1 it is rather meaty. So I'll have to think about how to integrate something else in such as AoPS, either sequentially or more in parallel. I'm starting to consider the interweaving idea more, though I know its not for everyone as its extra work. But I don't mind using more than one thing at a time and actually enjoy the variety as I think my son does. I could even stagger the content. I'll have to think on that a bit more.

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Its interesting how you notice the difference in your ds and dd's deductive abilities. I wonder if there is also a difference in their computational skills? Do you think that even though AoPS seems to work on fewer problems than other texts the depth of the problems combined with wrestling with the content (discovering it) makes up for this?

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So I think there are 2 different issues:

1) Should you encourage your student to develop the ability to learn through discovery?

2) If you are planning on using a direct instruction method, should you choose to use AoPS?

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Thank you for setting out this distinction. To the first question, I'd add "and when"

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However, I'm not really seeing anybody post who has actually btdt and felt that AOPS w/o discovery was a good way to go.

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FWIW, my ds is halfway done with the Prealgebra book and, on occasion, I have had him watch the videos before doing the lesson problems. Sometimes that takes the edge off of the difficulty of working through the lesson problems, though he still needs to work through the lesson problems to really understand and pay attention to what the lesson is teaching. Once or twice I tried to teach an AoPS lesson only directly, but it doesn't seem to work very well for ds - it usually goes in one ear and out the other. This is also the reason that, while we have used other sources like Dolciani a little bit, we always seem to find ourselves back with AoPS.

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What seems to work best for my ds at the moment might be termed a combination style, working on the lesson problems together, either on paper or on the white board. This usually involves ds screeching "I need help!" and me sitting with him, asking questions, trying not to give too much away unless necessary. Ds is young and of limited patience sometimes, though I'd like to develop that more because ironically his talent lies in slow, deep thinking. I do feel like I'm seeing improvement in this area. The wordy-ness of the lesson problem solutions hasn't been much of an issue, since I go through that with him and point out anything we didn't hit on while working on the lesson problems, plus special notes, key concepts, etc. If he were older, I'd be hoping for much more independence.

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Generally, he's more interested in working independently on problems in Alcumus than in the book. Right now, I'm having him work in Alcumus through the first half of the Prealgebra book topics (until the bar for each topic "turns green") as review before moving on to the second half of the book. As we get further along into the second half of the book (which seemed less steep for my dd than the first half), I'm hoping to let him struggle for longer periods.

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IMO, there is still another significant aspect of AoPS in addition to the discovery method and hard problems. It has to do with how the problems are set up, not simply to practice a calculation but to think about how to best use the concepts as tools to solve them "the smart way." I'm not saying this quite correctly... Also, they often are less tedious than the problems in other texts even when they are harder, which makes them "easier" and more fun.

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There is of course the discovery aspect of it, but it's not the only aspect. I don't know that some kids are quite ready for that self teaching "discovery" method, but the problems aren't like anything I've seen. They flicked a switch in my brain and I think they did for my son (despite the fact he never used it on his own). So there is also that aspect of the challenge. A lot of books don't challenge. They present a topic and you practice predictable problems. Maybe at the end they throw in a challenge problem or two.

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When he moans about it, I tell my son math training is like weight training. You don't strengthen your muscles with finger bends. You have to do something harder than that.

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That said, I didn't enjoy using it to teach from.

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Wendy,

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Thanks for sharing both your pain and successes with AoPS. I like your analogy in comparing tough problems to weight lifting. I also enjoy the challenging aspect of the questions along with the thorough examples and explanations provided. It sounds like you had a hard time teaching from the text more directly. Did you use the videos to suppliment the book as well?

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When I had my son go through the chapter on linear equations I had him listen the lesson first, then read through the text on his own and try the problems. This approach worked pretty good for him in working through the material himself. He is used to working on his math independently which is the approach we took with him and our dds pretty early on. We've never taught from a book but rather looked for programs which lent themselves toward independence. And that is something I think AoPS does as well.

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I have no problem with direct instruction. I would just use a direct instruction textbook if that is the method I would be using with my child. I think that a student needs to be able to use his textbook to learn independently. I good math student should not wait around to be taught. There has to be some passion and interest and desire to self-teach. I am not a hands off type of homeschooler; however, I do think that you put your child at a disadvantage if you choose a text that can only be accessed with the help of a teacher. When I was in school, I always worked ahead and did my homework in class so I did not have to bring it home. I could only do this because I was using Jacobs (a direct instruction text) and I was a kid who learned from direct instruction. As I said, discovery would have killed my love of math. My older boy is the opposite. He cannot learn from direct instruction. It MUST be discovery. And when he used a direct instruction text (singapore) he turned it into a discovery curriculum by refusing any direct teaching. This speaks to the importance of working with your student's style of learning.

Â

However, and this is a big however, I had to learn the discovery method eventually to have a STEM career. And it was a shock to my system when I realized in university that I did not know how to do it. I was a plug and chug type, and now needed to be more intuitive with answering difficult questions. The first physics class I *ever* took, was calculus-based physics for engineers at Duke University. Talk about sinking. I tried to continue with my plug and chug methodology by memorizing the entire physics text book and every single type of problem in it. But boy oh boy did that take a lot of time. I did well in the class, but realized then and there that I needed a new approach.

Â

If a student can handle the discovery method, I think it is superior. But not all kids can, for whatever reason. As I said, I don't think I could have. So clearly you do not need to use AoPS to succeed in math, but IMHO eventually you will need the methodological skills it teaches if you plan to go into certain STEM careers.

Â

So I think there are 2 different issues:

1) Should you encourage your student to develop the ability to learn through discovery?

2) If you are planning on using a direct instruction method, should you choose to use AoPS?

Â

Hope this clarifies my thinking and helps you in some way,

Â

Ruth in NZ

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This does help Ruth. To your first point regarding working independently I wholeheartedly agree. That is a philosophy we adopted pretty early on in our homeschooling with math especially. We actually started with the Robinson approach which emphasizes self-learning. He is also a scientist and a number his children went on to do the same after he homeschooled all six of them by himself. Robinson used Saxon primarily which lends itself toward independent learning. He also emphasizes the importance in allowing students to wrestle with difficult problems vs. helping them right away. Although we never followed his approach strickly we did like some of his ideologies regarding learning and discovery. The funny thing was although a scientist he didn't believe students should even study science until they had finished Calculus. Math was his big thing until then, which they did a lot of and usually finished early. But that's another story.

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I think learning via discovery can happen in other ways beyond AoPS. Though it was obviously designed to facilitate that thought process. My idea of using AoPS in a modified way is probably different than what some have in mind when we talk about direct instruction. I would never attempt to teach from the book, ever. But rather I would have ds go through it himself. The only difference might be whether to have him listen to the lesson first and possibly read some of the lesson before working the problems. That is different from direct instruction in the more traditional sense (e.g. parent teaching lesson from the book, then child working problems). I could see how trying to do that would be difficult since the text is written to the student with self-learning in mind.

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Well, Derek, because of this discussion, I actually went and got my AoPS prealgebra book off the shelf and looked through it. Hummmmm. It is clearly a "no go" for my younger. I think it is very esoteric.

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My older worked for a full year to get through the first 5 chapters in AoPS intro Algebra independently. He was adamant that he did not want help and he was successful in making the AoPS program his own. So, I got to thinking, if I want my younger to be able to do the discovery method, how can I mimic my older's experience. What struck me is that my older read through 150 pages of Intro algebra in his first year (prealgebra was not out), wheras my younger is looking at 500+ pages in his first year of AoPS if we use prealgebra. Originally, I was thinking of using prealgebra to introduce him to working through discovery independently, by slowly walking him through what is expected and how to do it. But now, I'm thinking that my older's success had to do with the fact that he had fewer pages to get through. There is a big difference between 150 and 550 pages. So, if I want to teach my younger how to do the discovery method, I'm thinking that perhaps moving very slowly through the intro algebra book is the answer. Its the speed that's the problem, because that means more pages. It is simply overwhelming. If I want him to have success with discovery and independence, there needs to be less to get through.

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I think that your next big thread to start is how Intro Algebra users are teaching their students to use this wonderful curriculum. We will be ready by August (I think) to start the process. He will be starting as a direct-instruction type kid and I will be guiding him into the discovery method. My personal goal (which may not be shared by all) is to train him to be independent and use the discovery method, and I would be happy to discuss successes and failures with other hive members.

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Ruth in NZ

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Its interesting how you notice the difference in your ds and dd's deductive abilities. I wonder if there is also a difference in their computational skills? Do you think that even though AoPS seems to work on fewer problems than other texts the depth of the problems combined with wrestling with the content (discovering it) makes up for this?

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I would say there is not a difference in their computational skills. Simply put, they are both very good at math.

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Let me try to clarify what I mean by deductive abilities. Give both of them word problems and if they possess the mathematical tools to solve the problem (as in it requires typical alg 1 skills and that is the math they have taken), then both will normally be able to solve the problem. They might take different approaches, (one might be more elegant than the other and that is not to imply that ds's approach is always more elegant), but generally speaking, if they know the formula/process, etc, both will be able to work it out. This applies to completely unique scenario type problems----I am not referring to plug and chug work.

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However, let's say they are given a problem and they have not been introduced to some of the math tools used to solve the problem. Here is the difference. I'm not quite sure how to articulate it so that you can understand what I mean, but here goes. Ds can build "mathematical proofs" to get to where he needs to go (within obvious limits!!) I guess the simplest analogy would be that ds turns to mathematical theory and where it might be going. His understanding of theory allows him to see not only the tools he possesses, but how they work together to draw the paths that are a short distance ahead. Dd, otoh, is a master user of the tools she possesses. However, she doesn't automatically realize deductively how those tools might actually work together ahead of where she already is.

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That is probably clear as mud. But, it is an important difference. ;) Sorry I just stink at explaining what I am thinking. The ability to do what ds does has meant for him that when he has encountered high level math or physics problems on a test, and he doesn't know a formula or something specific, he just spends a few minutes proving the formula with his smaller tools. He doesn't need as much explanation into "why" things mathematically work via formulas/processes b/c he is always proving them to himself first along the way (that is the way AoPS teaches, especially at the higher levels and keep in mind that ds never used Alcumus or watched videos b/c they didn't exist for his classes.) B/c he has lived math proving everything along the way, the way he looks at its structure/use/interaction is different and he can not only be builder but the architect as well (again, w/in the obvious limits of what he has learned)

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Dd, otoh, can build awesomely w/her tools. But she is much more reliant upon someone somewhere along the way providing the blue print. (FWIW, I do NOT want to give the impression that I am discussing conceptual understanding of math processes, b/c I am NOT. Dd has full conceptual understanding of what she does. What I am attempting to describe goes beyond conceptual understanding to deductive proofs.)

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No idea if any of that makes sense to someone who hasn't gone through the books or watched kids interact w/higher level materials, but the difference is obvious to me looking at them work.

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My older worked for a full year to get through the first 5 chapters in AoPS intro Algebra independently. He was adamant that he did not want help and he was successful in making the AoPS program his own. So, I got to thinking, if I want my younger to be able to do the discovery method, how can I mimic my older's experience. What struck me is that my older read through 150 pages of Intro algebra in his first year (prealgebra was not out), wheras my younger is looking at 500+ pages in his first year of AoPS if we use prealgebra.

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Everything you said made a lot sense to me but this make me scratch my head.

sure Algebra has 150+ pages and PreA has 500+ pages. However, majority of PreA is Covered during the 5/6 grade material, right? I found many similar question when I compare the PreA to SM 5/6. So, sure it is 500+ pages, but there should be very little to "discover"

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DS is also very young. He probably fall in many people's category to be too early to use the AOPS Algebra. I have to admit that he does not always read the wordy explanation in the problem set. He only reads when he stuck in excerise. We are into chapter 8 now and so far as far as I can tell, The problem set did a fantastic job to lead you through the thinking process to get the concept. For example, We were working on slope yesterday. The 1st question the hopsalot bunny hops 1 on the right and 2 to the up and plot what he hops on the cartesian plane.. I hardly think you need to read the explanation for that. Then it tell you to plot points based on a equation on the grid. again, hardely think you need to read through explantion on that. 3rd problem is to plot points of another equation and what is relation between the difference of Y to difference to x. still not really need a explanation. then it tell you that is the defination of slop on next problem. The next one asked if I remeber right is when the slope is 0 and when it is undefined. DS has to think on this a bit. I have to ask him to pay attention on that slope equation. He gets it in probably 5-10 mins, still didn't read the explanation. To be all honest, I think for this one, it will kill the fun if he just read the explanation. Next problem ask 2 slops if they are greater than 1 or less than 1. He gets it quickly but I made him to read through the explanation. So 6 problems, he only read 1 explanation. That is what I found in AOPS, that 6 problems lead you through how to identify the slop. and most of time, he only reads explanation for 1 question. When we do excercise on Friday, our next afterschool section, I expect he will forget the slope equation. And he will complaint and I will ask him to go back to problem section to figure out. It is pretty much how we worked through the last 8 chapters. We don't always read the explanation, and we don't see it always needed.

Again there are sections very very hard for him. no doubt , he cried couple times (he is young) when we went through 7.4: rate. so we didn't do ANY end of chapter challenging question on chapter 7 because I know based on how he handle the excerise in 7.4, this won't be pretty.. So, I guess what I am getting into is, I don't see a reason why wordy explanation stops u using AOPS. I think AOPS did a great job lead you through problems with questions to understand concept. And the other point I want to make is to be flexible. if you see your kid struggle in certain section. Skip it, circle it back later won't hurt anybody. In DS's case. we also do NEM as review. And when we hits rate again, we sure will give that challenge section another try.

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My older worked for a full year to get through the first 5 chapters in AoPS intro Algebra independently. He was adamant that he did not want help and he was successful in making the AoPS program his own. So, I got to thinking, if I want my younger to be able to do the discovery method, how can I mimic my older's experience. What struck me is that my older read through 150 pages of Intro algebra in his first year (prealgebra was not out), wheras my younger is looking at 500+ pages in his first year of AoPS if we use prealgebra. Originally, I was thinking of using prealgebra to introduce him to working through discovery independently, by slowly walking him through what is expected and how to do it. But now, I'm thinking that my older's success had to do with the fact that he had fewer pages to get through. There is a big difference between 150 and 550 pages. So, if I want to teach my younger how to do the discovery method, I'm thinking that perhaps moving very slowly through the intro algebra book is the answer. Its the speed that's the problem, because that means more pages. It is simply overwhelming. If I want him to have success with discovery and independence, there needs to be less to get through.

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Hmm... I'm actually really glad I had dd work through the Pre-A book before tackling Algebra, even though I'm not sure she did it completely "right" and not sure all of it stuck as well as it would've if she had.

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She did Singapore through 6A, then enrolled in the AoPS Pre-A online class. She worked through the teaching problems in the book, participated in the classes, and did all of the Alcumus and Challenge problems. What she did not do regularly, I think, was really read through all of the solutions to the teaching problems, to get the teaching that's in that part of the book. So that was way less than 500 pages of reading. :001_rolleyes: While she did all of those problems, I did often sit next to her (at her request) to ask questions to guide her to see which problem-solving method she should use (once she had that down, she was good). She used the calculator on the computer whenever I wasn't looking. :glare:

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While she got an A and A- in those two classes, and they were quite complimentary on her written explanations (which I never helped her with at all) I still thought she needed to go way slower in the Algebra text, and I wanted to make sure she worked things in the right order to really get the most benefit. For example, during the class she'd often do the challenge problems before doing the text or Alcumus - which is probably why she needed me to come guide her, as she was doing the hard stuff before the problems leading her to show how to do them.

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So now we're nearing the end of Chapter 3 of Algebra. I started by sitting with her while she worked the teaching problems on a white board, but she's now doing those independently (at her request). We then go over them and read through the solutions together, which she is a bit resistant to, but at least then I know she's gotten it done. Then I assign the end of section problems. I usually assign just the harder ones at this point (where it's still a lot of review from Pre-A), and I'm also going to have her do all the Alcumus problems on each topic (she likes working on the computer, so this is a nice mix of written and computer. And written I can make sure she doesn't use the calculator). I assign a selection of the Review and Challenge problems. She has yet to ask to see the videos. I think they're great, but for some reason she's not so bullish on them. I'm hoping to use them more (after teaching problems, before practice exercises) as the material gets harder.

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But... while I'm not sure she did the Pre-A book as completely and correctly as I'd have liked, I think the fact that a lot of what's of the beginning of the Alg book is now review for her has really helped her confidence, and made it much quicker to get through. We could well slow down once we get to completely new material, but the familiarity with the process she got from the Pre-A book I think has been really helpful. I think she may just finally be internalizing some of the lessons (that crazy radical? Yes, you should factor it to look for perfect squares. No, not punch it into the calculator. :glare: :glare: :glare: ).

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All, thanks for your great input! I am still going through the replies and thinking about them.

Today I got a response from the author regarding this question with some clarification on recommended AoPS uses:

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Greetings,

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I'm not a huge fan of labels like "discovery approach", since terms like these are typically ill-defined and loosely-used, but I suspect that people are referring to the fact that we give students the option of trying to solve problems before explaining to them how to solve the problems. We do so by presenting all of the problems that will be covered in a section before presenting the solutions to those problems. However, students who would prefer a more traditional approach can simply skip straight to the presentation of the solutions and the ensuing discussion in the text. So, the books can be used either as what people call a "discovery" approach, or in a more traditional "read the material first, then try some problems" approach. The "discovery" approach will help students develop more general (not math-specific) problem-solving skills that will be essential to success down the road (and arguably may be more important than the math skills), but some younger students may really struggle with it and need to get a little more mature before taking it on.

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Sincerely,

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Richard (Rusczyk)

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One of the keys here for me is that the more direct approach still has the the student going through the textbook as it was writtent toward them. Of course this is not to say that other approaches couldn't also be adapted if a young learner for example wasn't ready for the language yet. But I think having the student go through on their own would be the easiest way to teach it.

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Well, Derek, because of this discussion, I actually went and got my AoPS prealgebra book off the shelf and looked through it. Hummmmm. It is clearly a "no go" for my younger. I think it is very esoteric.

Â

My older worked for a full year to get through the first 5 chapters in AoPS intro Algebra independently. He was adamant that he did not want help and he was successful in making the AoPS program his own. So, I got to thinking, if I want my younger to be able to do the discovery method, how can I mimic my older's experience. What struck me is that my older read through 150 pages of Intro algebra in his first year (prealgebra was not out), wheras my younger is looking at 500+ pages in his first year of AoPS if we use prealgebra. Originally, I was thinking of using prealgebra to introduce him to working through discovery independently, by slowly walking him through what is expected and how to do it. But now, I'm thinking that my older's success had to do with the fact that he had fewer pages to get through. There is a big difference between 150 and 550 pages. So, if I want to teach my younger how to do the discovery method, I'm thinking that perhaps moving very slowly through the intro algebra book is the answer. Its the speed that's the problem, because that means more pages. It is simply overwhelming. If I want him to have success with discovery and independence, there needs to be less to get through.

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I think that your next big thread to start is how Intro Algebra users are teaching their students to use this wonderful curriculum. We will be ready by August (I think) to start the process. He will be starting as a direct-instruction type kid and I will be guiding him into the discovery method. My personal goal (which may not be shared by all) is to train him to be independent and use the discovery method, and I would be happy to discuss successes and failures with other hive members.

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Ruth in NZ

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Ruth, this sounds like the same conclusion I arrived at with my d11s earlier this year when evaluating AoPS Pre-Algebra. In reviewing the samples online and considering his maturity and math level it was just too much. However, now that he is well into Pre-A this year in another program (TabletClass) and learning a ton of new abstract skills I see his overall maturity and confidence rising. At some point in the future I can imagine him attempting AoPS Discovery to some degree at least. That includes reading through the lessons independently and working the problems.

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This also goes back to an earlier point you made about a child being *ready* vs. possibly too young. Maybe for some Pre-Algebra *is* too early, yet by the time they are a bit older, more mature, Algebra may not be so bad. This of course also depends of their Pre-A preparation. But this worked fine for many kids including 8Fill's who didn't even have AoPS Pre-A at the time. RR seems to think maturity can also play a role in Discovery readiness. See his email I quoted above.

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You mentioned you may take your dd through AoPS Intro to Algebra next year. She still seems very young. Yet I guess if you adapted it where you somehow teach her then do the problems at least initially it could work. I would be interested in hearing your experiences. If we start ds11 it won't be until later next school year. And I'm still looking at what that mix would be. He's really thriving in TabletClass Pre-A right now. So we will probably continue with that as well.

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Let me try to clarify what I mean by deductive abilities. [snip] That is probably clear as mud. But, it is an important difference.

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This is an awesome distinction! Thanks for spending the time to write it out.

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Ruth in NZ

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One more thing I forgot to Mentioned. RR replied in a follow-up email that younger kids sometimes go through the same AoPS material *twice*. The first could be more direct instruction/non-discovery with the second time being discovery. In thinking this over I could also imagine the first time being *another* program such as for Pre-A or Algebra, then following with AoPS in the same subject area. This was actually my initial thought for an Algebra 1, option year 2. However now I'm considering a hybrid approach also which consists of parallel integration or weaving in of two separate programs, over an extended period of course.

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For kids beginning Intro Algebra at a young age of say, pre-12, there is a lot of social and emotional development happening at the same time. I'm seeing my son developing into a preteen (ouch) and wanting even more independence. AoPS is playing nicely into this. We didn't start off with any "discovery method" in mind. I found out what that was when I chanced upon the hive when desperately googling for advice (he got stuck quickly at chapter 1). My original MO about 3 months ago was to to run through the beginning explanation with him. But by now, he doesn't want me involved and I can see that he likes reading the explanations -not every one, but those where he has a different method or where he got wrong.

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I'm rapidly arriving at this conclusion: for anyone interested in getting their child on to this book, do start when you see fit at the appropriate math level. Then, present it according to your child's *frustration* level. Ie, if he's likely to get very frustrated, you might want to do more on your part to ease the pain. Help him to deal with it by reading it together, or just read it to him. If or when he's able to tolerate a higher level, do less. Because the book takes anywhere from a year plus to over two years to complete, the chances of your child gradually growing into it is high. I'm listening to SWB's audio and she makes a good point - separate the various elements. Eg, math level, frustration level, and the stress of learning a new mode of learning. The less one infringes on the other, the higher the chances of success with the subject.

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Good luck, and remember that time is on your side.

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One more thing I forgot to Mentioned. RR replied in a follow-up email that younger kids sometimes go through the same AoPS material *twice*. The first could be more direct instruction/non-discovery with the second time being discovery.

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This is key. It's easy to think that if discovery is going to happen at all, it has to happen the first time a student encounters a topic, but this is completely untrue. I actually find that discoveries are *more* likely to occur on repeat "visits" regardless of the method used for the initial introduction. I find this to be true both in my teaching and in my own studies as a math major. So I don't think it's necessary to come down quite so hard as some do when it comes to using materials with both the discovery and direct teaching methods, especially with younger students. Modelling the discovery method in the early years by working together (being careful to be fairly Socratic and to not do all the "driving"), seems an ideal way to introduce the mathematical thought process to young students. If we were talking about late middle or high school students working on the upper levels, there would be excellent cause for requiring independence, but elementary students working several years above grade level have a long time and many levels ahead of them in which to gradually increase independence.

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... It's easy to think that if discovery is going to happen at all, it has to happen the first time a student encounters a topic, but this is completely untrue. I actually find that discoveries are *more* likely to occur on repeat "visits" regardless of the method used for the initial introduction...

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:iagree:

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RR replied in a follow-up email that younger kids sometimes go through the same AoPS material *twice*.

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My older watched the videos a few months before I bought the pre-algebra book. So in a way he is going through the same material twice. He just turn 8 and we can spend as long as he want on pre-algebra.

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So, I got to thinking, if I want my younger to be able to do the discovery method, how can I mimic my older's experience. What struck me is that my older read through 150 pages of Intro algebra in his first year (prealgebra was not out), wheras my younger is looking at 500+ pages in his first year of AoPS if we use prealgebra. Originally, I was thinking of using prealgebra to introduce him to working through discovery independently, by slowly walking him through what is expected and how to do it. But now, I'm thinking that my older's success had to do with the fact that he had fewer pages to get through. There is a big difference between 150 and 550 pages. So, if I want to teach my younger how to do the discovery method, I'm thinking that perhaps moving very slowly through the intro algebra book is the answer. Its the speed that's the problem, because that means more pages. It is simply overwhelming. If I want him to have success with discovery and independence, there needs to be less to get through.

Everything you said made a lot sense to me but this make me scratch my head.

sure Algebra has 150+ pages and PreA has 500+ pages. However, majority of PreA is Covered during the 5/6 grade material, right? I found many similar question when I compare the PreA to SM 5/6. So, sure it is 500+ pages, but there should be very little to "discover"

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I think I missed a step in my explanation. Let me try again. My younger son is a good math student but not naturally a discovery type kid. I would like to try to slowly convert him. It seems to me, to use AoPS successfully he needs to develop 2 skills: the willingness to struggle through the discovery method and the ability to read the text. I am actually much more concerned about the second.

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When I looked at the PreA book, I was just overwhelmed with the text, and I was sure that my ds would be too. I am concerned that if his first experience with the discovery method is with the PreA book, that he will fail and will never want to try discovery again, even though it is actually the reading that will be the problem. And I think that he will have little interest in me reading that much text *to* him. What that leaves me with is my reading the text earlier and teaching him directly (paraphrasing the text), and then having him work through the problems and exercises. I think it will give him the wrong impression of what AoPS is all about. He likes to be independent in math and if he is reliant on me to read the text, I think he will become very frustrated. He is a stubborn kid, if he does not like something, I doubt I will have a second chance.

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So instead I think that we will go with an alternative PreA book (like first part of Jacobs) and then start the discovery method with AoPS Algebra, but just moving very slowly. As a pp mentioned, The first 5 chapters of AoPS Intro Algebra covers a lot of the same topics as PreA, just in a more concise manner. So if I want my ds to try to develop the ability to read the book himself, it seems that fewer pages would equate to more success even if the problems are harder because he would have completed a different PreA program.

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Hope that makes more sense,

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Ruth in NZ

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Ruth, this sounds like the same conclusion I arrived at with my d11s earlier this year when evaluating AoPS Pre-Algebra. In reviewing the samples online and considering his maturity and math level it was just too much. However, now that he is well into Pre-A this year in another program (TabletClass) and learning a ton of new abstract skills I see his overall maturity and confidence rising. At some point in the future I can imagine him attempting AoPS Discovery to some degree at least. That includes reading through the lessons independently and working the problems.

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Interesting. I did not keep up with either the PreA or Algebra fence straddler threads, so I did not know what you had finally decided. I just bought the AoPS PreA book because I had all the others. My older did not use PreA because it was not out yet. So, when I finally went to really look at it, I was very surprised. I think I expected that the reading level in addition to the math would be at a lower lever than Intro Algebra. But this is definitely not true.

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Ruth in NZ

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So instead I think that we will go with an alternative PreA book (like first part of Jacobs) and then start the discovery method with AoPS Algebra, but just moving very slowly. As a pp mentioned, The first 5 chapters of AoPS Intro Algebra covers a lot of the same topics as PreA, just in a more concise manner. So if I want my ds to try to develop the ability to read the book himself, it seems that fewer pages would equate to more success even if the problems are harder because he would have completed a different PreA program.

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Hope that makes more sense,

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Ruth in NZ

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Ruth, I was going to recommend the same thing. There is a time and a place for everything and sometimes its better to conquer one hill at a time. Mukmuk made an excellent point speaking to this very thing:

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I'm listening to SWB's audio and she makes a good point - separate the various elements. Eg, math level, frustration level, and the stress of learning a new mode of learning. The less one infringes on the other, the higher the chances of success with the subject.

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In starting with one of the elements first (e.g. comprehending algebraic reasoning) its takes something very difficult (AoPS Discovery Pre-A) and simplfies it somewhat. This is also very much the way us math geeks solve more complex problems through breaking things down into their simpler parts. It makes perfect sense to me. The other *big* factor in this equation is the rapidly developing brain. So as one part advances - understanding abstract math, other parts begin to catch up - reading comprehension and reasoning skills. Of course this could be done using AoPS twice or another program first then AoPS. It really depends more I think on the indivdual child at that point in terms of what may work best, first. I do think two seperate programs can compliment each other well in certain cases. 8Fill for example used MUS Algebra 1 to prep her kids for AoPS Intro to Algebra which seemed to provide a good mental bridge for them.

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I'm really enjoying the collaborative thought and discussion on this topic. So many good points are brought forth as we each consider the best approaches to take for our unqiue children. I think we all want the same thing, and that is for them to succeed in whatever they do. If by chance its AoPS then what will facilitate the success of their unique journey from point A to point Z? In many cases, especially with young ones, its ok to take non-linear or non-traditional paths to get there.

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I do think two seperate programs can compliment each other well in certain cases. 8Fill for example used MUS Algebra 1 to prep her kids for AoPS Intro to Algebra which seemed to provide a good mental bridge for them.

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Just thought I would clarify that the above is not what I do. ;)

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All 5 of my older kids have used MUS's alg/geo as a pre-alg/pre-geo program. All of them have followed MUS with Foerster. I did not discover AoPS until our 4th child had already finished MUS alg/geo, Foerster alg 1. Houghton Mifflin's geo (Chalkdust), and was in the middle of Foerster alg 2. He started AoPS w/counting and probability while finishing alg 2. His first "sequential" AoPS course was AoPS alg 3 (intermediate alg).

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Since our dd (#5) is similar to her brother, when she finished MUS alg (pre-alg in our home), I asked her if she wanted to try AoPS alg and she said yes. However, it did not take long for her to say she didn't like the approach. (I think it was through chpt 3?? I can't remember exactly now.) She did not have problems w/the math, just the way things were approached. We switched to Foerster. She was finished w/Foerster sometime around Feb. (again, I don't remember exactly) Anyway, I asked her if she wanted to do one of AoPS online courses and take the alg 1 b/c she would finish around the end of the school yr and she could just give AoPS one more try and it shouldn't be difficult b/c it would be her 3rd time through alg 1.

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Well, she had zero difficulty w/the math, but her view of the approach remained the same.......she just really does not like the texts. So, there you go. This is the view pt of a strong math student that didn't struggle with the work and just flat out doesn't like it.

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I don't know if knowing how to solve the problems prior to using the text diminished its appeal (b/c she would approach the material with full knowledge of where it was going) or what. I just know it is a complete flop with her. She has absolutely no desire to pursue anything related to math, so I'm perfectly content in sticking w/Foerster.

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While my previous post about the distinctions in my kids is accurate......the big picture is that not everyone needs to be able to deductively prove math at high levels. For ds who wants to major in theoretical aspects of physics......it is definitely a good tool. For dd, who at this pt is more interested in foreign languages and linguistics, it isn't a need. Even our oldest as a engineer didn't "need" the AoPS approach (Foerster was great preparation for him).

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Honestly, from my POV, it AoPS fits the student, run with it. If it doesn't, I would not exert a lot of effort trying to make it fit.

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This is key. It's easy to think that if discovery is going to happen at all, it has to happen the first time a student encounters a topic, but this is completely untrue. I actually find that discoveries are *more* likely to occur on repeat "visits" regardless of the method used for the initial introduction. I find this to be true both in my teaching and in my own studies as a math major. So I don't think it's necessary to come down quite so hard as some do when it comes to using materials with both the discovery and direct teaching methods, especially with younger students. Modelling the discovery method in the early years by working together (being careful to be fairly Socratic and to not do all the "driving"), seems an ideal way to introduce the mathematical thought process to young students. If we were talking about late middle or high school students working on the upper levels, there would be excellent cause for requiring independence, but elementary students working several years above grade level have a long time and many levels ahead of them in which to gradually increase independence.

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I can't tell you how helpful this, in particular, is to me. From reading posts on this Forum, I was getting the impression that "The Discovery Method" was the key to AoPS, and if you don't do it this way (i.e. have AoPS be your child's first exposure to X topic via discovery) then you might as well not use it at all. This was frustrating, because I can see that my dd will be ready for more advanced/challenging math, conceptually, before she is ready to wrestle with thie level of problem entirely independently. What I'm reading now confirms my own intuition that much - so much - can still be gained by going through AoPS, either later after concepts have been introduced in other ways, or with another method than pure discovery.

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So thanks for starting this thread and thanks to all who have posted!

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I can't tell you how helpful this, in particular, is to me. From reading posts on this Forum, I was getting the impression that "The Discovery Method" was the key to AoPS, and if you don't do it this way (i.e. have AoPS be your child's first exposure to X topic via discovery) then you might as well not use it at all. This was frustrating, because I can see that my dd will be ready for more advanced/challenging math, conceptually, before she is ready to wrestle with thie level of problem entirely independently. What I'm reading now confirms my own intuition that much - so much - can still be gained by going through AoPS, either later after concepts have been introduced in other ways, or with another method than pure discovery.

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So thanks for starting this thread and thanks to all who have posted!

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I agree Rose, that is actually the reason I started the thread. I felt frustrated by the portrayal of a 'one size fits all' approach which doesn't, even if you like *some* aspects of AoPS. So hearing these different experiences along with clearification from the author has helped me gain a wider understanding of AoPS uses.

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Just thought I would clarify that the above is not what I do. ;)

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All 5 of my older kids have used MUS's alg/geo as a pre-alg/pre-geo program. All of them have followed MUS with Foerster. I did not discover AoPS until our 4th child had already finished MUS alg/geo, Foerster alg 1. Houghton Mifflin's geo (Chalkdust), and was in the middle of Foerster alg 2. He started AoPS w/counting and probability while finishing alg 2. His first "sequential" AoPS course was AoPS alg 3 (intermediate alg).

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Since our dd (#5) is similar to her brother, when she finished MUS alg (pre-alg in our home), I asked her if she wanted to try AoPS alg and she said yes. However, it did not take long for her to say she didn't like the approach. (I think it was through chpt 3?? I can't remember exactly now.) She did not have problems w/the math, just the way things were approached. We switched to Foerster. She was finished w/Foerster sometime around Feb. (again, I don't remember exactly) Anyway, I asked her if she wanted to do one of AoPS online courses and take the alg 1 b/c she would finish around the end of the school yr and she could just give AoPS one more try and it shouldn't be difficult b/c it would be her 3rd time through alg 1.

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Well, she had zero difficulty w/the math, but her view of the approach remained the same.......she just really does not like the texts. So, there you go. This is the view pt of a strong math student that didn't struggle with the work and just flat out doesn't like it.

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I don't know if knowing how to solve the problems prior to using the text diminished its appeal (b/c she would approach the material with full knowledge of where it was going) or what. I just know it is a complete flop with her. She has absolutely no desire to pursue anything related to math, so I'm perfectly content in sticking w/Foerster.

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While my previous post about the distinctions in my kids is accurate......the big picture is that not everyone needs to be able to deductively prove math at high levels. For ds who wants to major in theoretical aspects of physics......it is definitely a good tool. For dd, who at this pt is more interested in foreign languages and linguistics, it isn't a need. Even our oldest as a engineer didn't "need" the AoPS approach (Foerster was great preparation for him).

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Honestly, from my POV, it AoPS fits the student, run with it. If it doesn't, I would not exert a lot of effort trying to make it fit.

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Woops, sorry 8Fill! I guess I have a hard time keeping all your kiddos' math paths straight. :tongue_smilie: I knew you used MUS as Pre-A and that some used AoPS which you've discussed in this thread (dd & ds). I guess I was a bit fuzzy on the rest.

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You do make a good point for all the AoPS interested parents reading this thread. There should no guilt or shame in using another fine program when AoPS is simply not a good fit. Keeping that in mind is liberating, especially if/when that is the discovery. There can be the impression that if one does not use AoPS they are only settling for second best or less. And as caring parents we obviously want the *best* for our children.

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I think what interests many parents also is the *way* in which AoPS is introduced, and if that way at least partially influences outcome.

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I can't tell you how helpful this, in particular, is to me. From reading posts on this Forum, I was getting the impression that "The Discovery Method" was the key to AoPS, and if you don't do it this way (i.e. have AoPS be your child's first exposure to X topic via discovery) then you might as well not use it at all. This was frustrating, because I can see that my dd will be ready for more advanced/challenging math, conceptually, before she is ready to wrestle with thie level of problem entirely independently. What I'm reading now confirms my own intuition that much - so much - can still be gained by going through AoPS, either later after concepts have been introduced in other ways, or with another method than pure discovery.

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Rose, I am very sorry if I have been one of the ones that has discouraged you. Sometimes I just don't have time to write out all the subtleties of an argument. You should just hop a plane, and we could have a nice long chat face to face! :001_smile:

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There are obviously many ways to use AoPS. But the way I am using it (as in me personally) is really the worst IMHO. I am not a discovery learner and I am very mathy. I plan to work my way through all the books over 5 years by reading the text first and then doing the problems. As RR said, you can definitely do this. But it is really annoying. Really. There are just many other textbooks out there that would be so much more efficient for a direct-instruction, self learner to get through high school math. I have used many, many math textbooks in my day (well, mostly statistics) independently, without a teacher. I basically got a masters in Statistics through self study so that I would have the tools to do my population dynamics modelling research. So, I know, without a doubt, that I can learn new material quicker and less painfully than with the AoPS approach.

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When I go looking for a math curriculum for my kids, I prefer to stick with a single series if I can. Just a bit more continuity. Fewer gaps etc. So if you plan to use AoPS with direct instruction, I would suggest you think about some long term plans. These are the long-term options I see for using AoPS with direct instruction:

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1) You teach them all the way through High School and not have them read the book. This would be like what happens in most high school math classes; students are taught in class and do homework but never read the textbook. The negatives being the lack of independence and passion that develops when a student self-studies. Also, you will have to be up on the material to act as full teacher.

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2) If your student is going to self-study but retain a direct instruction style, he will have to read the text first and then go back and do the problems. As I have stated, there are better texts out there for this approach.

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3) You are going to use direct instruction just temporarily while training, modelling, waiting for maturity, etc. You are going try to convert your kid from a direct-instruction type to a discovery type (like I will try to do with my younger). And then he will use the texts as written - in the discovery style.

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I am sure there are some blending of these approaches possible. But as I see it, these are the big 3.

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So if you have a direct instruction kid, there are many questions to consider (all of which I am asking about my younger). Will you be satisfied with #1 or #2 if #3 fails? Or would you switch textbooks? How long will you keep trying #3? Will your efforts at #3 turn your child off of math? Obviously, the answers to these questions will vary for each family depending on too many factors to count. But these are questions that you need to consider before heading down this path (and I am in the same boat).

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As I have said, I do believe that the discovery method is superior to direct instruction. I think it creates a very strong mathematical thinker. My older is a perfect example of this. However, and this is a big however, you do NOT need it in high school to succeed in a STEM career. And I will be very very careful with my younger to make sure that I do not turn him off math in my effort to change the way he approaches learning math. He does not need AoPS. He does need passion and confidence.

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HTH,

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Ruth in NZ

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...

When I go looking for a math curriculum for my kids, I prefer to stick with a single series if I can. Just a bit more continuity. Fewer gaps etc. So if you plan to use AoPS with direct instruction, I would suggest you think about some long term plans. These are the long-term options I see for using AoPS with direct instruction:

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1) You teach them all the way through High School and not have them read the book. This would be like what happens in most high school math classes; students are taught in class and do homework but never read the textbook. The negatives being the lack of independence and passion that develops when a student self-studies. Also, you will have to be up on the material to act as full teacher.

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2) If your student is going to self-study but retain a direct instruction style, he will have to read the text first and then go back and do the problems. As I have stated, there are better texts out there for this approach.

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3) You are going to use direct instruction just temporarily while training, modelling, waiting for maturity, etc. You are going try to convert your kid from a direct-instruction type to a discovery type (like I will try to do with my younger). And then they will use the texts as written - in the discovery style.

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So if you have a direct instruction kid, there are many questions to consider (all of which I am asking about my younger). Will you be satisfied with #1 or #2 if #3 fails? Or would you switch textbooks? How long will you keep trying #3? Will your efforts at #3 turn your child off of math? Obviously, the answers to these questions will vary for each family depending on too many factors to count. But these are questions that you need to consider before heading down this path (and I am in the same boat).

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As I have said, I do believe that the discovery method is superior to direct instruction. I think it creates a very strong mathematical thinker. My older is a perfect example of this. However, and this is a big however, you do NOT need it in high school to succeed in a STEM career. And I will be very very careful with my younger to make sure that I do not turn him off math in my effort to change the way he approaches learning math. He does not need AoPS. He does need passion and confidence.

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HTH,

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Ruth in NZ

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I would hazard a wild guess that no one does #1, ever (all the way through High School). It just sounds too crazy, like trying to fit a round peg in a square hole, over and over and over. Why do that?

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I think most will probably use a combination of these approaches in varying degrees initially to try to introduce the program and find a fit. #2 would be less common longer term, unless one uses AoPS as a supplimental. In that case I think it can work.

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I also think there are more than these three options. For example, one could watch the videos first, then go through the book including wrestling with the intial problems *before* reading the text. I'm not saying this pattern is recommended. However if that works for some kids who are struggling too much without the instruction, why not?

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For our children I do not feel compelled to use only one program, especially all throughout High School. I view courses and their associated curriculum at this level as more independent (Algebra, Geometry, Trig, Calculus, etc...). I don't think I ever used the same author twice while in High School or in College for math or even science. And I never found that a stubbling block in any way. In fact I think there can be some advantages such as looking at things from a different prespective, being challenged in a different way when facing similar or related subject matter, etc... But that's just my perspective based on my own experiences. Maybe if you had all the same author throughout HS or possibly during some college courses you discovered a benefit? I am also considering dual enrollment once at the High School level. So for example our kids could take AoPS or any other curriculum for Algebra and Geometry, then a college course in Algebra II or Pre-Calc. Many HS families I know do that (dual enrollment) very successfully. AoPS could even continue as extracurricular if time and desire permits.

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Rose, I am very sorry if I have been one of the ones that has discouraged you. Sometimes I just don't have time to write out all the subtleties of an argument. You should just hop a plane, and we could have a nice long chat face to face! :001_smile:

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I would love that!!!! Math and Science with Ruth, over a nice cup of tea . . .

snip

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As I have said, I do believe that the discovery method is superior to direct instruction. I think it creates a very strong mathematical thinker. My older is a perfect example of this. However, and this is a big however, you do NOT need it in high school to succeed in a STEM career. And I will be very very careful with my younger to make sure that I do not turn him off math in my effort to change the way he approaches learning math. He does not need AoPS. He does need passion and confidence.

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HTH,

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Ruth in NZ

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This is what it all boils down to, doesn't it? Keeping one's eye on the prize: To not be attached to any one curriculum/method, but to give your child what s/he needs to develop passion and confidence so that s/he can become whatever s/he chooses. I don't want lack of math skill/ability/confidence to close doors to my dd. I also don't want to make her hate or dread math, so that she chooses not to pursue a field she would love and be well suited for.

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My biggest goal for her, and the biggest thing we are working on right now, is the ability to persist and persevere in solving tough problems. Today she worked on Zaccaro, and spent over an hour doing 9 problems - but she stuck with it, she persisted, her attitude stayed great, she didn't devolve into tears and start calling herself stupid, and she got it done - and I felt better about what she'd accomplished, in terms of character development, than any day of success with math/computation would have made me feel.

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Lots of paths to the same destination. I appreciate how you laid it out on this post. I don't know if *I'm* up to #1!! I think #3 is our goal, but #2 would be a perfectly respectable place to end up, and if that is the case I will be looking for advice about more straightforward curricula for self-teaching, no doubt!

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For our children I do not feel compelled to use only one program, especially all throughout High School. I view courses and their associated curriculum at this level as more independent (Algebra, Geometry, Trig, Calculus, etc...).

I don't think I ever used the same author twice while in High School or in College for math or even science. And I never found that a stubbling block in any way. If fact I think there can be some advantages such as looking at things from a different prespective, being challenged in a different way when facing similar or related subject matter, etc... But that's just my perspective based on my own experiences. Maybe if you had all the same author throughout HS or possibly during some college courses you discovered a benefit?

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A few comments:

1. There is a good reason not to use the same author for science - because you want a textbook written by somebody who is an expert in his field. The author of a great biology text would not be qualified to write a decent physics text, and vice versa.

2. In math, the issue is not so much that one wants to keep the same author (if that were the case, AoPS would not fit the bill, as the books of the series have different authors), but rather that one wants a program that has no gaps. The goal of using materials from the same series is to ensure that the student has the prerequisites from the preceding volumes to be successful in the next one - something that is much harder to do if you switch series. Since math builds organically on itself, this is a unique requirement not present in other subjects. You can still learn Renaissance history of you have gaps in Ancients, but you can not study precalculus if you have gaps in algebra.

(As an aside, the compartmentalization of math into neat packages labeled "algebra" and "precalculus" is a unique US phenomenon - elsewhere it would simply be "math", with a more organic approach.)

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I agree that there are advantages in using different approaches. But the most important ingredient for success to me seems to be that the student has mastered the material that poses the prerequisite for his current textbook, something easier accomplished if one follows the same series, because the books are coordinated to be used in sequence.

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Btw, if one is taught by a teacher who possesses subject expertise, it is pretty irrelevant what book is used, if the teacher is good. I have not the slightest idea who the authors of my high school textbooks were, but I also did not have to learn the material by studying from the books: I had a teacher who taught me.

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I would hazard a wild guess that no one does #1, ever (all the way through High School). It just sounds too crazy, like trying to fit a round peg in a square hole, over and over and over. Why do that?

I really do see it as an option. If you are a math teacher, you just teach the material, and then the kids do the problems in class, and the exercises for homework. In my experience as a math teacher, I saw very few kids that ever read a textbook. They just waited for the teacher to explain the material. When I hear that high schools are using AoPS, I am guessing that a lot of them are doing this. The discovery method takes time, and I think that a lot of schools are under increasing time pressure for teaching the curriculum. Direct instruction is efficient.

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#2 would be less common longer term, unless one uses AoPS as a supplimental. In that case I think it can work.
Yes it does work. It is just inefficient as a base curriculum, and reading through the entire text book as a supplement would be a pretty impressive feat.

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I also think there are more than these three options.
Ah, I just am making the big cuts, not the subcuts. Shortened they are:

1) Either you learn the material from a source or you discover it yourself

2) If you learn the material from a source, it could be through text or orally

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For example, one could watch the videos first, then go through the book including wrestling with the intial problems *before* reading the text. I'm not saying this pattern is recommended. However if that works for some kids who are struggling too much without the instruction, why not?

Derek, I don't know anything about the videos. Looks like I should look into them. I think that videos first sounds like a wonderful idea for students needing a little extra help. What I don't like is reading the text which is the answer to the problems, and then doing the exercises. It is just not efficient.

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For our children I do not feel compelled to use only one program, especially all throughout High School.

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ahhhh, but it just so easy. :001_smile: I love the idea of having math all set out. And I do think that the AoPS books build on themselves. My son is using algebra concepts he learned in Intro Algebra in the geometry book. And he is using problem solving techniques previously learned also. It would be interesting to hear from others how easy it is to jump into AoPS at a later date. I'm sure it depends on the kid. My older skipped PreA with no trouble, but would you want to go into intermediate algebra without doing AoPS's Intro algebra? not sure. I am also in a different situation here in NZ because my children must take the Cambridge math exams to gain university entrance, and there is a set curriculum with set books. I am very hopeful that working through AoPS will be overkill, but my younger might just use the cambridge math books if AoPS is a no go. I simply forgot the differences in the educational practices between the countries. NZ has a standardized curriculum for all 5 years of high school, so typically you choose 1 series of books and work through them. They build quite tidily on each other.

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Still, I am a long term planner. And I have found that sometimes people need to be reminded to consider the big picture. I have definitely appreciated that same advice from other more seasoned homeschoolers.

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Ruth in NZ

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I really do see it as an option. If you are a math teacher, you just teach the material, and then the kids do the problems in class, and the exercises for homework. In my experience as a math teacher, I saw very few kids that ever read a textbook. They just waited for the teacher to explain the material. When I hear that high schools are using AoPS, I am guessing that a lot of them are doing this. The discovery method takes time, and I think that a lot of schools are under increasing time pressure for teaching the curriculum. Direct instruction is efficient.

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I was actually thinking more terms of homeschoolers vs the public/private school teachers. I think it would be interesting to hear if teachers using AoPS would try to keep the focus discovery based like the online classes or make them more direct instruction.

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Yes it does work. It is just inefficient as a base curriculum, and reading through the entire text book as a supplement would be a pretty impressive feat.

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Ah, I just am making the big cuts, not the subcuts. Shortened they are:

1) Either you learn the material from a source or you discover it yourself

2) If you learn the material from a source, it could be through text or orally

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Ok, I understand. I have heard of kids using AoPS in addition to their regular pubilc/private school workbooks. Some take the courses as extracurricular activities. I think many at this level are really into math, think math clubs, competitions, etc... My coworker's son is like that. I'm not sure any of my kids would ever be that driven. Though I could still see using AoPS as supplimental to gain another perspective and for added challenge.

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Derek, I don't know anything about the videos. Looks like I should look into them. I think that videos first sounds like a wonderful idea for students needing a little extra help. What I don't like is reading the text which is the answer to the problems, and then doing the exercises. It is just not efficient.

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I'm quite surprised you haven't watched the videos yet since they are so darn good! RR is a great instructor and I think kids can relate to his upbeat presentational style, more than most. Sal Khan is another naturally gifted math teacher. Though their styles are quite different. The videos were one of the things that initially drew me in to AoPS to want to learn more. They only go through Algebra right now Though he has plans to produce Geometry in the future.

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ahhhh, but it just so easy. :001_smile: I love the idea of having math all set out. And I do think that the AoPS books build on themselves. My son is using algebra concepts he learned in Intro Algebra in the geometry book. And he is using problem solving techniques previously learned also. It would be interesting to hear from others how easy it is to jump into AoPS at a later date. I'm sure it depends on the kid. My older skipped PreA with no trouble, but would you want to go into intermediate algebra without doing AoPS's Intro algebra? not sure. I am also in a different situation here in NZ because my children must take the Cambridge math exams to gain university entrance, and there is a set curriculum with set books. I am very hopeful that working through AoPS will be overkill, but my younger might just use the cambridge math books if AoPS is a no go. I simply forgot the differences in the educational practices between the countries. NZ has a standardized curriculum for all 5 years of high school, so typically you choose 1 series of books and work through them. They build quite tidily on each other.

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Still, I am a long term planner. And I have found that sometimes people need to be reminded to consider the big picture. I have definitely appreciated that same advice from other more seasoned homeschoolers.

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Ruth in NZ

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Sorry, I sort of overlooked that you are in an entirely different country! :tongue_smilie: I guess that does change a few things in relation to university enrollment and quite a bit else I would imagine. It sounds like NZ has a standardized test based on their standardized curriculum. In that case that is a consideration as well.

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Why did I not know there were videos?!? This may be a game-changer for younger students.

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I'm quite surprised you haven't watched the videos yet since they are so darn good!

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My older would consider it cheating to watch any videos. :001_smile: And I have only started to look into what to do with my younger! Off to go find some videos.....

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Here is the link to Intro to Algebra videos: http://www.artofprob...pe=introalgebra

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I haven't seem any official usage statement regarding these. But I think most who want the fullest discovery experience start with the book, do the chapter's initial challenge problems, wrestle with them, then watch the video lesson after. Though I could see how watching them first would be a good way to go for someone needing a little jump start. Also using the videos could substitute at least in part with you trying to create your own lessons from scratch, especially since they are designed to align with the book already. That's not saying you wouldn't have to do some supportive teaching. But I think it could minimize some of the frustration in terms of lesson plan design.

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A few comments:

1. There is a good reason not to use the same author for science - because you want a textbook written by somebody who is an expert in his field. The author of a great biology text would not be qualified to write a decent physics text, and vice versa.

2. In math, the issue is not so much that one wants to keep the same author (if that were the case, AoPS would not fit the bill, as the books of the series have different authors), but rather that one wants a program that has no gaps. The goal of using materials from the same series is to ensure that the student has the prerequisites from the preceding volumes to be successful in the next one - something that is much harder to do if you switch series. Since math builds organically on itself, this is a unique requirement not present in other subjects. You can still learn Renaissance history of you have gaps in Ancients, but you can not study precalculus if you have gaps in algebra.

(As an aside, the compartmentalization of math into neat packages labeled "algebra" and "precalculus" is a unique US phenomenon - elsewhere it would simply be "math", with a more organic approach.)

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I agree that there are advantages in using different approaches. But the most important ingredient for success to me seems to be that the student has mastered the material that poses the prerequisite for his current textbook, something easier accomplished if one follows the same series, because the books are coordinated to be used in sequence.

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Btw, if one is taught by a teacher who possesses subject expertise, it is pretty irrelevant what book is used, if the teacher is good. I have not the slightest idea who the authors of my high school textbooks were, but I also did not have to learn the material by studying from the books: I had a teacher who taught me.

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These are good points Regentrude. I think that as long as parents/teachers are aware of the potential scope and sequence differences from one program to the next it shouldn't be too much of an issue. I always examine these carefully when making curriculum decisions. However I can see how it would be easier to stay with only one program - all Saxon, MUS, TT, AoPS, etc... You really wouldn't even have to think about the transition from one year to the next.

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I also know what you mean about being taught by a teacher with subject matter expertise. I had two excellent math teachers whom I will never forget, one who taught Algebra and the other Calculus. Yet I coudn't remember the texts they used. It was only after performing a search for various quality Algebra books that I realized I had used Dolciani. The texts didn't teach me, the teacher did. But that is also the way those books were designed, more as student workbooks to be supplimented by direct classroom instruction. That is also why I wouldn't use Dolciani or Foerster alone for independent learning. Although other programs such as Saxon, TT, AoPS, TabletClass, etc... are designed to be done independently. I actually think that my son's current teacher, John Zimmerman of TabletClass, is really good at explaining algebraic concepts to him. I know parents can do this also. But for me I like letting these well regarded teachers provide the lecture portion. That's also why I like the AoPS videos.

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My older would consider it cheating to watch any videos. :001_smile: And I have only started to look into what to do with my younger! Off to go find some videos.....

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Dd has refused to watch any of the algebra videos this year. She enjoys RR's style----she just wants to learn it by herself (well, with my help if she gets stuck badly).

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Here is the link to Intro to Algebra videos: http://www.artofprob...pe=introalgebra

I haven't seem any official usage statement regarding these. But I think most who want the fullest discovery experience start with the book, do the chapter's initial challenge problems, wrestle with them, then watch the video lesson after. Though I could see how watching them first would be a good way to go for someone needing a little jump start. Also using the videos could substitute at least in part with you trying to create your own lessons from scratch, especially since they are designed to align with the book already. That's not saying you wouldn't have to do some supportive teaching. But I think it could minimize some of the frustration in terms of lesson plan design.

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We used many of the prealgebra videos last year------if those videos were up when we were at the relevant sections (they put the videos up in chunks last year). Dd would do all the introductory problems, read the explanations, and watch the videos. Then she'd do the end-of-section exercises.

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It got to the point that she was rolling her eyes while watching the videos. She said she felt like she was back in a classroom having to listen to the teacher explain things to the kids who didn't "get it" as quickly as she did. I didn't make her watch the videos once she started the algebra book in the spring.

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Why did I not know there were videos?!? This may be a game-changer for younger students.

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Yes, the videos are awesome. My daughter works through the textbook, watches the videos and uses Alcumus for review. Do you know about Alcumus? If you create an account, you can have Alcumus "follow the book". So, Alcumus gives problems to your student that correspond to the order of topics in the textbook. Also, there are Quests. If they answer a certain number correctly, they can earn like a "virtual badge" for their account. My kid works through the section in the textbook, watches the videos that correspond to the topics and then she uses Alcumus for extra review problems. When she completes a topic, she stops Alcumus and moves on in the textbook.

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I'm sorry if this has already been brought this up (I just skimmed the thread), but the problems in the textbook are really unusual (to me). The math is more like finding patterns...using the "rules" to solve number puzzles... That's the best I can explain it. I'm working through the book at the same time as my daughter. If I didn't, there's no way I would be able to help her if she got stuck. It's very different from how we learned math in ps. Just to let you know - look at the sample problems before you buy it to make sure it's right for your student.

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I'm sorry if this has already been brought this up (I just skimmed the thread), but the problems in the textbook are really unusual (to me). The math is more like finding patterns...using the "rules" to solve number puzzles... It's very different from how we learned math in ps. Just to let you know - look at the sample problems before you buy it to make sure it's right for your student.

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But that is exactly what math is: finding patterns and relationships.

What passes as "math" in school often does not go beyond straight computation - but actual mathematics is all about patterns and puzzles, not about computing a number.

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But that is exactly what math is: finding patterns and relationships.

What passes as "math" in school often does not go beyond straight computation - but actual mathematics is all about patterns and puzzles, not about computing a number.

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Exactly.

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Yes, the videos are awesome. My daughter works through the textbook, watches the videos and uses Alcumus for review. Do you know about Alcumus? If you create an account, you can have Alcumus "follow the book". So, Alcumus gives problems to your student that correspond to the order of topics in the textbook. Also, there are Quests. If they answer a certain number correctly, they can earn like a "virtual badge" for their account. My kid works through the section in the textbook, watches the videos that correspond to the topics and then she uses Alcumus for extra review problems. When she completes a topic, she stops Alcumus and moves on in the textbook...

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Thanks for this ellaboration on Alcumus usage. I didn't know there was a 'follow the book' feature. The time we tried it over a year ago we used it in kind of a random fashion which quickly frustrated my ds at the time. Of course we went on later to discovery that it challenges and frustrates by design. :tongue_smilie: Yet if it could be aligned with a current lesson it would probably frustrate ds11 less now.

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