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Am I the only one too dumb or too overwhelmed to make this curriculum work?

Background: ODS has been using AoPS curriculum for years.  He thrived on BA, having requested "hard math" after a couple levels of RS.  His need for my help was minimal.  I was worried that PreAlg would be a difficult transition, but he LOVED it.  I started to worry, though, because when he needed my help, I couldn't remember my high school math well enough to help him; I usually had to start reading the solution until he went, "Oh, I get it!  You can stop now," and finished the problem on his own.  

He's now in Intro to Alg.  Some chapters have been a breeze; some chapters seem impossible for him to wrap his mind around.  And it's as if some days are better than others.  (He was working through chapter 10 this week, and it's like every other day he couldn't remember how quadratics worked.)  I'm not sure if that's adolescence or ADHD or this being the wrong math program for him.  

The other weird thing is that he seems to do fine with Alcumus.  I had forgotten about it until he had a chapter he just wasn't understanding.  I sent him to do Alcumus in the middle of the chapter for extra practice, and he had no issue.  But when he returned to the book, he was stuck again.

Part of the problem is that his mind does not work at all like mine does, so I have a hard time explaining things to him.  DH calls him an intuitive learner.  He's definitely not visual or auditory (doesn't learn from watching or hearing explanations--the videos never help when he's confused), so he just has to...click with the material on his own, from what I can figure.  Sometimes if I talk for long enough, something gets through, but I never know what's going to help him understand.  And the other problem is that I don't have the time or energy to work the whole book with him, as I know many parents do.  I only have three kids, but I can't spend an hour a day glued to ODS's side, since the others need my input/guidance as well.  And I know some parents pass the math off to a spouse, but DH didn't go as far as I did in math (and said his education wasn't as rigorous as mine anyway).  I did fine in math (made it through one semester of college calc before relievedly checking off the math requirement with "Teaching Elementary Math" classes), but I feel completely dumb when I try AoPS problems.  I'm really more of a humanities gal.

I've considered online classes, but the AoPS classes I can find are waaay out of my budget range.  ODS is seriously disheartened at the thought that he might not be able to continue his beloved AoPS, and I feel like I'm failing him because I can't teach it effectively.  Did anyone else face the same issues?  I'd welcome any advice, experience, or sympathy. 🙂  Thanks for slogging through this long post!

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I would venture to say that most people who use AOPS face these issues, and there’s a very small subset of people who can easily make this curriculum work.  They are very proud of it though (rightfully so!) so you will hear about it a lot. Count the posters 🙂 

If it failed, people are less likely to admit but I’ve received the fair share of PMs over this. anyway around  mid Algebra is also when we got off that merry-go-round. The experience was exactly like yours: very uneven in terms of difficulty and the way I’d work something out was not at all the way DS would work it out. dH also tried it (and he’s more mathy than I am) and he would not touch it again . And yes, DS usually would do better in alcumus. He also tool C&P there and recently I had to ask for his records while assembling his transcript. mostly green and blue and yet...DS remembered no C&P at all. I mean nothing sunk. We are the only ones with this particular experience so I’m fairly sure it’s user error.  For full disclosure, DD is in beast. She does it mostly independently through a class. The moment I have to get involved in any material manner is the moment she stops doing beast. I am more hands on with her other math curriculum because I like that one better 🙂

 

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My DS11 is working through AoPS Intro to Algebra as well. He did BA3-5 (2 wasn't out yet) and then AoPS pre-alg last year. He just finished chapter 7 today, and it was *hard* for him. I think it's partly that his brain has finally come up to it's working level (he was flying through curriculum before, and suddenly he's truly being challenged) and partly because he's in 'growing-boy brain fog' phase. Some days he thinks the problems are hard, some days they are easy, and some days they are just fine. We are just moving at his pace. Some days I sit with him for a long time to help, and some days he doesn't need me at all. But, I have three others I need to help, so I understand the need to be able to have him work independently most of the time!

I will say that, even though I have a math degree and teach (remedial) college math, I'm not always sure exactly how to start problems right away in that book. I will usually read the solution to myself and then ask him leading questions to get him to better understand the question, and then he can go from there.

Have you had him look for help in the AoPS forums? I was thinking that my DS11 might start looking there first, if I'm working with one of his brothers. I'm not sure if it would be better than just reading the solution manual himself, though.

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We had a very similar experience. My oldest is very mathy - he started AOPS prealg when he was 8. It took him 18 months, and though it was not a walk in the park, and he took breaks to review on Alcumus, he did successfully make it through. 

Then he did AOPS algebra, but got stuck in chapter 10. It just wasn’t clicking. At first I tried to have him review on Alcumus for a few weeks, but that didn’t help. Then I took him through the topics on Khan and in Math Mammoth, and then had him try chapter 10 again. Nope. Finally we abandoned the book. Dis worked through Chuckles the Rocket Dog and finished the algebra topic in Alcumus. 

We didn’t even consider the AOPS book for geometry. DS is using a Great Courses class supplemented with Alcumus. He is working through the AOPS C&P book (concurrently with geometry). 

Next year DS will be using Foerster Algebra 2. If he wants to, he may supplement with Alcumus, but he may choose to be done with AOPS. 

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DD also had trouble with AOPS Intro to Algebra. She got through the first half of the book on her own, but we switched to AOPS Online for the 2nd half of the book (Intro to Alg B).

I, like you, have trouble keeping up with the math. DD has found the online forum helpful for getting help on difficult questions. You may need to explore the forum with your child and teach them how to write and effective question. (I found that DD at first wrote questions that made sense to her but were quite vague for someone else). DD eventually got the hang of how to word her questions effectively.  

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Thanks, everyone.  I'm encouraged to hear that some of our troubles are shared by others.  It's interesting to hear that two of our most frustrating chapters--7 and 10--are also ones that others have struggled with.  At least I don't feel like his difficulty must be all my fault somehow.  I'll have him try using the online forum as a resource to help him when he struggles, but knowing that others have jumped ship is reassuring for both of us, as we may ultimately go that direction.

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For us, we needed to do ch. 10-13 again because the first pass through was pretty rough. We just took as long as it took the second pass through and just keep at Aclumus until he passed. And, yes, there were many days of frustration, but he made it through and I survived (haha). It is tremendously helpful to hear where others have hit the proverbial wall because up until this point PA and Algebra was pretty smooth for him. As I reflect on what was going on, I think it was difficult because he has reached a point where he really wants to be independent, and he clearly needed help. The idea of being forced to slow is way down and work a problem at a time and check in to make sure he is on the right track has been frustrating to him. AOPS is so tricky in how the problems build off each other because if your solution is incorrect, continuing on without knowing this just compounds things since you usually needed to learn something from that problem in order to solve the next one. On this second pass through, he felt a lot more confident. That being said, we decided that we will finish working through the text and do the 5 chapters of the Intermediate Algebra to cover what would be covered in Algebra II and go with WTMA for AOPS Geometry in the fall. 

Plan B is to look at Foerster using Math WIthout Borders lectures and worked solutions.

 

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I've posted elsewhere that my kid likes to cover everything through both AoPS and Life of Fred.  AoPS is weird to me because on one hand it's so much more challenging that you'd think they'd be able to do very complicated things...and they can...but at the same time I think my kid sometimes got so wrapped up in the complexity that they'd miss the simple stuff.  I've wondered if it comes from problems that are super tricky and are only reasonably solvable if you use one particular approach.  On one hand, it's great training to actually study problems before jumping in, but they almost forget how to solve easy problems.  My kid thinks seeing the material twice, through 2 wildly different lenses (highly complicated vs 'no more complicated than it needs to be') is very helpful.  

My kid loved number theory and enjoyed C&P and overall has probably benefitted from using AoPS, but I'm not sure that it was the best option.  It's not what I chose with my younger child, who has no frustration tolerance at all.  🙂  

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14 hours ago, eternallytired said:

Thanks, everyone.  I'm encouraged to hear that some of our troubles are shared by others.  It's interesting to hear that two of our most frustrating chapters--7 and 10--are also ones that others have struggled with.  At least I don't feel like his difficulty must be all my fault somehow.  I'll have him try using the online forum as a resource to help him when he struggles, but knowing that others have jumped ship is reassuring for both of us, as we may ultimately go that direction.

What specifically is he struggling with? 🙂 Is there any way I can troubleshoot what he's getting stuck on? 

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16 hours ago, Noreen Claire said:

Have you had him look for help in the AoPS forums? I was thinking that my DS11 might start looking there first, if I'm working with one of his brothers. I'm not sure if it would be better than just reading the solution manual himself, though.

The forums ought to be better than reading the solution manual, since sometimes people can guide you to a solution. A class is the easiest way to get more guidance, though. 

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1 hour ago, Not_a_Number said:

The forums ought to be better than reading the solution manual, since sometimes people can guide you to a solution. A class is the easiest way to get more guidance, though. 

My DS makes fun of AoPS forums - he says when you ask a question the response is usually - Have you tried reading the problem? 😂  His response - what do you think I have been doing here for the entire week? 😂😂😂😂 I think sometimes you are stuck because you don’t “see” something and it’s hard to give a hint without giving away the answer, hence the “help” doesn’t always materialize. 

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14 minutes ago, Roadrunner said:

My DS makes fun of AoPS forums - he says when you ask a question the response is usually - Have you tried reading the problem? 😂  His response - what do you think I have been doing here for the entire week? 😂😂😂😂 I think sometimes you are stuck because you don’t “see” something and it’s hard to give a hint without giving away the answer, hence the “help” doesn’t always materialize. 

I wouldn't know about the open forums, but on my class forums, there are TONS of threads that help kids out, and usually there's a decent number of kids per class who use them extensively. 

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9 minutes ago, Not_a_Number said:

I wouldn't know about the open forums, but on my class forums, there are TONS of threads that help kids out, and usually there's a decent number of kids per class who use them extensively. 

I was making a joke. Class forums are very helpful, most of the time. 😉

And yes, these books and classes can be crazy hard. My DS said one time a kid complained on a class forum that even his mathematician father couldn’t solve something. That tells me ton of kids have either super strong support at home or maybe even tutors. 

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Just now, Roadrunner said:

I was making a joke. Class forums are very helpful, most of the time. 😉

And yes, these books and classes can be crazy hard. My DS said one time a kid complained on a class forum that even his mathematician father couldn’t solve something. That tells me ton of kids have either super strong support at home or maybe even tutors. 

Well, mathematicians aren't magic, lol -- half of them haven't seen the elementary stuff in 20 years, except for the classes they teach. I don't think DH remembers half the geometry theorems even in the Intro to Geometry class...

I haven't found the classes to be ridiculously hard as much as insufficiently scaffolded. A lot of times, they expect you to do hard problem-solving with concepts you haven't quite internalized, and that's a recipe for a lot of frustration. 

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Just now, Not_a_Number said:

 

I haven't found the classes to be ridiculously hard as much as insufficiently scaffolded. A lot of times, they expect you to do hard problem-solving with concepts you haven't quite internalized, and that's a recipe for a lot of frustration. 

This is hard for a parent to know this and have enough knowledge to scaffold. 

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2 hours ago, Not_a_Number said:

The forums ought to be better than reading the solution manual, since sometimes people can guide you to a solution. A class is the easiest way to get more guidance, though. 

What do you suggest if the classes a) look to be too fast-paced and b) are beyond budget range?  It's taken him all year to get to the end of chapter ten, and it looks like the online classes cover that in one semester.  I'm not sure he'd learn it well at that pace.  (He's ADHD and tends to be a slow, methodical worker anyway.)  Besides, if we wanted to afford AoPS online, we'd have to cut expenses elsewhere, and I'm not willing to suggest that he give up his beloved piano lessons or taekwondo for the sake of math.  (If AoPS were the ONLY option, then I do think that math would take precedence over musical or physical development--especially because he LOVES math--but since they're not the only option, I can't justify having him eliminate his co-curricular enrichment activities that I see as very beneficial to him.)

I've been pondering the forums, but I'm not sure if they'd help.  Once in a while he'll have a question like, "Why doesn't this method work to solve the problem?" which I think could be answered, but what do you do when half of the time you don't even know where to begin?  Since the problems usually build on the steps they used in the exercises in the first half of the chapter, I try to prompt him to think of how he could apply those.  But sometimes he and I look at a solution and think, "Where on earth did that come from?"  I suppose that for most chapters he has been doing fine, but this chapter (10) and chapter 7 have been such doozies that I'm questioning whether he's going to overall understand enough to thrive in further math.  And I keep reading how PreA and Alg are foundational to upper-level success, so I don't want to push onward if I feel like he's not truly solid.  Nor do I think that I'm going to be any good at helping in the future, so I see my problems compounding in the coming years.  He's only 12 now; I've got several years before I can count on DE to help me out.

My biggest dilemma is that AoPS, overall, works for the way this kid's mind works.  He likes the discovery method, he likes being asked to look at things in creative ways.  Math is one area where he THRIVES on challenge and doesn't mind working on something for a long time.  He said if he has to switch to another curriculum, he doesn't want it to be straightforward.  So I certainly don't want to ask him to settle for something that's not going to stretch him.  (And it's not that I don't think an excellent education can't be had elsewhere.  DD is likely going to be doing Foerster next year, but she adores MM.  For her, Foerster will be perfect.  I don't think it would meet ODS's needs, though.)

Has anyone tried Elements of Mathematics: Foundations lately?  I looked it up after seeing it referenced in another AoPS-related post and it looks really cool, but most of the chatter about it was from 2012-2014 or so.  I realize that ODS would have to start at the beginning of the program, re-covering PreA and Alg, but I'm not opposed to a second pass from a new perspective if it'll mean he'll have an even stronger foundation in math and he'll get to keep the challenge that he loves.  Maybe I should start a new thread on that...

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2 hours ago, Not_a_Number said:

What specifically is he struggling with? 🙂 Is there any way I can troubleshoot what he's getting stuck on? 

I second this. If there is something that comes up in Chapter 10 that is hard for him to solve please post here.

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I'm really curious what is so difficult about chapter 10 because I don't remember having these issues with my kids.  Looking at the TOC and my copy of the text, chapter 10 covers:

  1. quadratic formula
  2. factoring quadratics
  3. Vieta's (which is basically how you factor quadratics)

This is all bread and butter stuff which your student will be using on and off in math through high school.  What specifically is giving him trouble?  

Is your student having issues with 10.5, the starred section?  Remember starred sections are more challenging, and definitely skippable if you are short on time. 

If you decide to use the forums to answer your questions, I would try these:  https://artofproblemsolving.com/community/c69_aops_online_books that are specific to the textbooks themselves.  The Middle School and High School Math forums are populated with kids mostly interested in contests.  

You can also post questions here!  Some of us really enjoy those kinds of threads.  (I'm not a mathematician or even a math major, but I get these problems because I did math contests in high school.)

 

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3 hours ago, Not_a_Number said:

What specifically is he struggling with? 🙂 Is there any way I can troubleshoot what he's getting stuck on? 

 

23 minutes ago, mathnerd said:

I second this. If there is something that comes up in Chapter 10 that is hard for him to solve please post here.

Somehow I missed Not_a_Number's original post until mathnerd's quote.  Thanks for the offer of help!  Here's one that stumped us this week:

Problem 10.29: In this problem, we write the expression 6r^2-7rs+2s^2+23r-13s+21 in the form (Ar+Bs+C)Dr+Es+F), for some constants A, B, C, D, E, and F.  We expanded the problem just fine for a, but b and c have us scratching our heads.  They tell you to break out all the terms that have no "s" and factor them and then pull out all the factors with no "r" and factor them--but the 21 is used both times.  How can you use the 21 twice in factoring?

Sometimes it seems like it's just a matter of him not fully internalizing whatever shortcut/method the section is trying to teach--but shouldn't there be a way to solve each problem without using one special method?  I like the idea that he's learning different ways to attack problems; I don't like the idea of a curriculum where, yet again, there's only one right way to find a solution.  And, FWIW, he has zero interest in math competitions.  He hates time pressure and competition, he just loves problem solving and math.

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3 hours ago, Not_a_Number said:

I wouldn't know about the open forums, but on my class forums, there are TONS of threads that help kids out, and usually there's a decent number of kids per class who use them extensively. 

DS11 took a pre-algebra 2 course last year (I needed him to be held accountable to someone else for a while) and the class forum was useless. Mostly just kids posting "I have no idea how to solve this problem," over and over. No one ever offered help. 

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2 hours ago, eternallytired said:

 

Somehow I missed Not_a_Number's original post until mathnerd's quote.  Thanks for the offer of help!  Here's one that stumped us this week:

Problem 10.29: In this problem, we write the expression 6r^2-7rs+2s^2+23r-13s+21 in the form (Ar+Bs+C)(Dr+Es+F), for some constants A, B, C, D, E, and F.  We expanded the problem just fine for a, but b and c have us scratching our heads.  They tell you to break out all the terms that have no "s" and factor them and then pull out all the factors with no "r" and factor them--but the 21 is used both times.  How can you use the 21 twice in factoring?

OK, I think I see how do this in a pretty way. If you let s = 0, you get the equation

 

(Ar + C)(Dr + F)=  6r^2-23r+21. 

 

And if you let r = 0, you get the equation 

 

(Bs + C)(Es + F) = 2s^2-13s+21.

 

Is that the step you guys were having trouble with? Do you want me to keep going or see if you can make some headway from here? Do you want me to explain what I did? 

 

2 hours ago, eternallytired said:

Sometimes it seems like it's just a matter of him not fully internalizing whatever shortcut/method the section is trying to teach--but shouldn't there be a way to solve each problem without using one special method?  I like the idea that he's learning different ways to attack problems; I don't like the idea of a curriculum where, yet again, there's only one right way to find a solution.

I've seen problems that require one very special method, but at least the problem you listed above isn't like that. I think the tricky thing here is to realize you can set some of the variables to 0 to make things nicer. 

I've actually how done this in three different ways (I wrote you up the pretty one, since some of mine were ugly), and all of them contains some real thought and interesting observations. None of them were tricky in a silly way. 

 

2 hours ago, eternallytired said:

 And, FWIW, he has zero interest in math competitions.  He hates time pressure and competition, he just loves problem solving and math.

You know, you can always do math contest math without doing the actual contests. Higher level contests aren't really about about the time pressure, anyway... they are much more about the problem solving. They are no AMCs. 

For some context to what I mean... the USAMO and the IMO (the highest level math olympiads) are 4.5 hours for 3 problems. Even if you get really psyched out by time pressure, like me, 4.5 hours of thought for 3 problems feels pretty luxurious. And as you can imagine, with that kind of timing, the problems require ingenuity and serious problem-solving. 

DH used to do the Math Talent Search, which is math contest style problems without the time pressure. I did something similar in Canada. 

Anyway, I do think there's no need to write off that kind of math -- they often require more creativity than standard math. The timing factor isn't the point. 

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Just now, Noreen Claire said:

DS11 took a pre-algebra 2 course last year (I needed him to be held accountable to someone else for a while) and the class forum was useless. Mostly just kids posting "I have no idea how to solve this problem," over and over. No one ever offered help. 

Really?? On the official AoPS website? OK, that's bizarre. Usually, there are more people than I like trying to help the kids and answering the questions. There are office hours and everything. 

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3 hours ago, eternallytired said:

What do you suggest if the classes a) look to be too fast-paced and b) are beyond budget range?  It's taken him all year to get to the end of chapter ten, and it looks like the online classes cover that in one semester.  I'm not sure he'd learn it well at that pace.  (He's ADHD and tends to be a slow, methodical worker anyway.)  Besides, if we wanted to afford AoPS online, we'd have to cut expenses elsewhere, and I'm not willing to suggest that he give up his beloved piano lessons or taekwondo for the sake of math.  (If AoPS were the ONLY option, then I do think that math would take precedence over musical or physical development--especially because he LOVES math--but since they're not the only option, I can't justify having him eliminate his co-curricular enrichment activities that I see as very beneficial to him.)

Well, I'm happy to help troubleshoot on here! I do think the classes are fast-paced, although I also think that having the kids be accountable to an outside teacher can be useful. He would also get actual feedback on his writing problems, which is pretty invaluable, especially if someone makes sure that he actually reads the feedback and engages with it. 

 

3 hours ago, eternallytired said:

My biggest dilemma is that AoPS, overall, works for the way this kid's mind works.  He likes the discovery method, he likes being asked to look at things in creative ways.  Math is one area where he THRIVES on challenge and doesn't mind working on something for a long time.  He said if he has to switch to another curriculum, he doesn't want it to be straightforward.  So I certainly don't want to ask him to settle for something that's not going to stretch him. 

Then I'd stick to it. I do think this is the kind of thing that AoPS is good for. (Disclaimer: I teach classes there. I'm not a paid advertiser, though, and I probably spend more time grumping about them than selling people on them.) 

 

3 hours ago, eternallytired said:

I realize that ODS would have to start at the beginning of the program, re-covering PreA and Alg, but I'm not opposed to a second pass from a new perspective if it'll mean he'll have an even stronger foundation in math and he'll get to keep the challenge that he loves.  Maybe I should start a new thread on that..

Oh, I dunno. After a while, covering the SAME material over and over again just gets boring and tedious. And you do revisit certain concepts in later classes, which will, in fact, reinforce them. The question is whether anyone's keeping track of what concepts he's struggling with and which one he isn't? I'd make sure you were on top of what he understands and he doesn't, so that you can help him out with gaps if they occur. It's very hard to avoid gaps, but I don't think seeing things over and over is a great idea. (If this program is totally and utterly different, then I withdraw my objection. But if it's basically the same material, my comment stands.) 

Has he done the "fun" AoPS classes like Intro to C&P and and Intro to NT? Those can be a good way to reinforce algebraic ideas, too. Algebra does come up all over the place... as long as you're mindful of it, you can see the same ideas from different angles instead of mostly from the same angle, and I think that's beneficial. 

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4 minutes ago, Not_a_Number said:

There are office hours and everything. 

Huh. This is news to me. We must have missed that.

 

3 hours ago, eternallytired said:

I suppose that for most chapters he has been doing fine, but this chapter (10) and chapter 7 have been such doozies that I'm questioning whether he's going to overall understand enough to thrive in further math. 

This makes me feel better! Glad to know if wasn't just DS11.

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2 minutes ago, Noreen Claire said:

Huh. This is news to me. We must have missed that.

Yeah, every day... during class time, I think? But I won't swear to that. 

I just taught a Prealgebra 2, and I peeked at my message board -- most questions were answered quite quickly. People answer more in the evening, I think? That's when office hours are, too. 

ETA: in some classes, I try to be very on the ball about answering myself. This time, I was swamped, so I was very on top of the precalc I was running (I wrote the online version, so I'm attached to it), but I'm embarrassed to say I wasn't on top of the prealgebra and it was mostly Halpers answering. 

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Honestly, I would try an alternative. AoPS just gets harder and the jump from Into level books to Intermediate is significant.

What I find problematic is finding a teacher friendly. To me that means detailed solutions (not just answers at the end of the book). Otherwise if we are stuck, we have no idea how to get unstuck. I really wish I knew more math to not find myself in that situation. 
I hope you find a solid alternative. People swear by Foerster. 

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27 minutes ago, Not_a_Number said:

Yeah, every day... during class time, I think? But I won't swear to that. 

I just taught a Prealgebra 2, and I peeked at my message board -- most questions were answered quite quickly. People answer more in the evening, I think? That's when office hours are, too. 

ETA: in some classes, I try to be very on the ball about answering myself. This time, I was swamped, so I was very on top of the precalc I was running (I wrote the online version, so I'm attached to it), but I'm embarrassed to say I wasn't on top of the prealgebra and it was mostly Halpers answering. 

I think long time ago there were no dedicated office hours. Board was there and help was there as well but maybe not as much (?). My kids have been using them for eight years I think and I can’t remember when official office hours emerged. 

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Just now, Roadrunner said:

I think long time ago there were no dedicated office hours. Board was there and help was there as well but maybe not as much (?). My kids have been using them for eight years I think and I can’t remember when official office hours emerged. 

Yeah, that's a new thing, but like... a few years new, not a few months. 

I've been there for 6 years myself 🙂 . So I've seen things come and go. The current excitement is the new classroom! 

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1 hour ago, Noreen Claire said:

DS11 took a pre-algebra 2 course last year (I needed him to be held accountable to someone else for a while) and the class forum was useless. Mostly just kids posting "I have no idea how to solve this problem," over and over. No one ever offered help. 

Office Hours were there last year when my son took a class. Though he did not use them, AOPS teachers are there every day with immediate help. I guess that there are dedicated instructors to help students in each session of a class. So, if your son were to take an online class and he was stuck, he could log into his account during office hours (evenings usually) and there will be a banner on his page in a bright color that says "Office Hours ...." and "Click to join" or some such message. Our instructor and the AOPS weekly emails that we got posted often about the office hours and encouraged students to make use of it.

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2 hours ago, Not_a_Number said:

OK, I think I see how do this in a pretty way. If you let s = 0, you get the equation

(Ar + C)(Dr + F)=  6r^2-23r+21. 

And if you let r = 0, you get the equation 

(Bs + C)(Es + F) = 2s^2-13s+21.

Is that the step you guys were having trouble with? Do you want me to keep going or see if you can make some headway from here? Do you want me to explain what I did? 

Thank you!  That totally makes sense to me.  The solution in the book said, "Try simplifying the problem by looking at the terms that do not have 's' in them."  Once we factored that, they had us do the same to the ones without 'r' in them.  But they never explicitly stated that we are thereby assuming the other term to be zero--and I certainly didn't make that connection in my head, so I couldn't figure out how we could just ignore the other half for a while and then reuse the 21.  

Oddly, this post won't let me type below the second quote, so I'll have to comment here.  The numbers go in order of the parts I've bolded.

1. I keep hearing about people whose kids work for 2-3 hours a day to keep up with the online classes, and I really don't want to do that to my kid yet at 6th grade.  I think that having to dedicate so much time to it daily (sacrificing free time) would kill his love of math.  He already doesn't think he has enough time in the day to do everything he wants to do!  I would totally love to have outside input for him, though, since I've felt inadequate to teach him for a couple years already, but besides the pacing/time commitment there's the prohibitive cost--so I really shouldn't keep rehashing it because it can't happen anyway.

2. I'm not always sure what he gets well and what he doesn't--partly because I understand very little of it well.  (I think I'm getting progressively stupider each year.  It's depressing.)  Also, his comprehension seems to vary widely from day to day, which also throws me off.  I'm not sure if that's the ADHD or adolescence or what.  In short, I'm overwhelmed.  While sometimes the explanations make sense to me, sometimes they just make my brain hurt.  I've never been a mathy person (nor has DH), so ODS has really outpaced what I can teach.  I need some other way of making sure he's getting a solid understanding.

3. EMF is supposedly a totally different approach to math, which is about the only reason I'd be okay with redoing essentially two levels of work.  The posts I was reading where people were considering it at roughly the same place we are in AoPS got the response that it would be worth doing, that a majority of the material would be new or so vastly different in approach that it would still be worthwhile and engaging.  But again, almost all of the in-depth discussions I can find (not just an offhand reference) are a good 5+ years old.

4. The C&P and NT are recommended after Intro to Alg A, so he hasn't done either of them yet.  I think he'd definitely enjoy the topics, though I've also heard mixed things about their difficulty levels and level of dryness.  This was another reason EMF looked interesting--it introduced those topics pretty early on.  But maybe I just try to plod through the Chapter 13 mark that ends Intro A and take a break with one of those.

2 hours ago, Not_a_Number said:

Well, I'm happy to help troubleshoot on here! I do think the classes are fast-paced, although I also think that having the kids be accountable to an outside teacher can be useful. He would also get actual feedback on his writing problems, which is pretty invaluable, especially if someone makes sure that he actually reads the feedback and engages with it. 

Then I'd stick to it. I do think this is the kind of thing that AoPS is good for. (Disclaimer: I teach classes there. I'm not a paid advertiser, though, and I probably spend more time grumping about them than selling people on them.) 

Oh, I dunno. After a while, covering the SAME material over and over again just gets boring and tedious. And you do revisit certain concepts in later classes, which will, in fact, reinforce them. The question is whether anyone's keeping track of what concepts he's struggling with and which one he isn't? I'd make sure you were on top of what he understands and he doesn't, so that you can help him out with gaps if they occur. It's very hard to avoid gaps, but I don't think seeing things over and over is a great idea. (If this program is totally and utterly different, then I withdraw my objection. But if it's basically the same material, my comment stands.) 

Has he done the "fun" AoPS classes like Intro to C&P and and Intro to NT? Those can be a good way to reinforce algebraic ideas, too. Algebra does come up all over the place... as long as you're mindful of it, you can see the same ideas from different angles instead of mostly from the same angle, and I think that's beneficial. 

 

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@eternallytired Have you considered the other AOPS classes out there? Like WTMA or Royal Fireworks? I'm planning to get my kid through what WTMA covers for Algebra II according to their syllabus to do Geometry in the Fall. 

If you are looking at WTMA, they indicated that they were able to rotate through waiting lists if you got on one for February as they are committed to adding sections to meet need. Many of their AOPS sections are full. 

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8 hours ago, eternallytired said:

 

Problem 10.29: In this problem, we write the expression 6r^2-7rs+2s^2+23r-13s+21 in the form (Ar+Bs+C)Dr+Es+F), for some constants A, B, C, D, E, and F.  We expanded the problem just fine for a, but b and c have us scratching our heads.  They tell you to break out all the terms that have no "s" and factor them and then pull out all the factors with no "r" and factor them--but the 21 is used both times.  How can you use the 21 twice in factoring?

 

Yes, in my copy of the book, Problem 10.29 is in the starred section, 10.5*.  I don't sweat the starred problems too much.  We definitely work through all the problems, but I never had my kids  solve the introductory problems on their own.  We use the introductory problems to illustrate the concepts being taught, so we work through them together.  And that's not even the starred sections, that's every section.  Then I have my kids do the Exercises at the end of each section and the Review and Challenge Problems independently. 

Take a look again at the instructions on page (iii).  "If you can't solve some of the problems, that's OK, because they will all be fully solved as you read the section."  

ETA:  The complete step by step solution to Problem 10.29 is on pp. 315-316.

Edited by daijobu
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We quit and shifted to Saxon last year which was a good decision for us (but maybe not for a dyslexic kid that loves maths).  We’re playing around with counting and probability for AOPS for now but if it doesn’t work we will shift quickly. Classes aren’t in my budget and we aren’t looking at a math career so I just need to tick the boxes really.  Also I get what you mean about some problems being really challenging and others kind of over simple. 

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8 hours ago, eternallytired said:

Thank you!  That totally makes sense to me.  The solution in the book said, "Try simplifying the problem by looking at the terms that do not have 's' in them."  Once we factored that, they had us do the same to the ones without 'r' in them.  But they never explicitly stated that we are thereby assuming the other term to be zero--and I certainly didn't make that connection in my head, so I couldn't figure out how we could just ignore the other half for a while and then reuse the 21.  

You can also think of this purely algebraically by matching coefficients. I did that first -- like, I expanded things out and got equations like 

AD = 6. 

You can also put those together into polynomial equations, but I think what I wrote above is clearer. 

 

8 hours ago, eternallytired said:

Oddly, this post won't let me type below the second quote, so I'll have to comment here.  The numbers go in order of the parts I've bolded.

1. I keep hearing about people whose kids work for 2-3 hours a day to keep up with the online classes, and I really don't want to do that to my kid yet at 6th grade.  I think that having to dedicate so much time to it daily (sacrificing free time) would kill his love of math.  He already doesn't think he has enough time in the day to do everything he wants to do!  I would totally love to have outside input for him, though, since I've felt inadequate to teach him for a couple years already, but besides the pacing/time commitment there's the prohibitive cost--so I really shouldn't keep rehashing it because it can't happen anyway.

Hmmmm. I'm curious if that's really standard or not. I'm pretty sure most of the kids in my classes weren't spending quite that much time on it, and if anything, half of them procrastinated and did things at the last minute 😛 . 

Might be interesting to get a good sample of posters and see how long kids spent on it. 

 

8 hours ago, eternallytired said:

2. I'm not always sure what he gets well and what he doesn't--partly because I understand very little of it well.  (I think I'm getting progressively stupider each year.  It's depressing.)  Also, his comprehension seems to vary widely from day to day, which also throws me off.  I'm not sure if that's the ADHD or adolescence or what.  In short, I'm overwhelmed.  While sometimes the explanations make sense to me, sometimes they just make my brain hurt.  I've never been a mathy person (nor has DH), so ODS has really outpaced what I can teach.  I need some other way of making sure he's getting a solid understanding.

I totally get it. I think in this case, the options are either classes, a tutor, or learning the material well yourself.

I'm always happy to troubleshoot, though, if you go with the last option 🙂. I love math and I love teaching. 

 

8 hours ago, eternallytired said:

3. EMF is supposedly a totally different approach to math, which is about the only reason I'd be okay with redoing essentially two levels of work.  The posts I was reading where people were considering it at roughly the same place we are in AoPS got the response that it would be worth doing, that a majority of the material would be new or so vastly different in approach that it would still be worthwhile and engaging.  But again, almost all of the in-depth discussions I can find (not just an offhand reference) are a good 5+ years old.

I don't know a ton about it. I'd be curious if any of the mathier posters have tried it 🙂 . 

 

8 hours ago, eternallytired said:

4. The C&P and NT are recommended after Intro to Alg A, so he hasn't done either of them yet.  I think he'd definitely enjoy the topics, though I've also heard mixed things about their difficulty levels and level of dryness.  This was another reason EMF looked interesting--it introduced those topics pretty early on.  But maybe I just try to plod through the Chapter 13 mark that ends Intro A and take a break with one of those.

You're pretty close to being ready for the next courses, anyway! In my experience, C&P is fun and not that hard, especially if you don't rush through it. 

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11 hours ago, calbear said:

@eternallytired Have you considered the other AOPS classes out there? Like WTMA or Royal Fireworks? I'm planning to get my kid through what WTMA covers for Algebra II according to their syllabus to do Geometry in the Fall. 

If you are looking at WTMA, they indicated that they were able to rotate through waiting lists if you got on one for February as they are committed to adding sections to meet need. Many of their AOPS sections are full. 

Correct me if I'm wrong, but I think both WTMA and RFWP classes are still in the $400/semester range, which is the main thing that eliminates them as an option.  I might be able to scrape together $200/semester, but there's no way I can do $400 unless I eliminate other things in our curriculum.  Since this is not the only math option available, I really don't want to get rid of other things I think are important.

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10 hours ago, daijobu said:

Yes, in my copy of the book, Problem 10.29 is in the starred section, 10.5*.  I don't sweat the starred problems too much.  We definitely work through all the problems, but I never had my kids  solve the introductory problems on their own.  We use the introductory problems to illustrate the concepts being taught, so we work through them together.  And that's not even the starred sections, that's every section.  Then I have my kids do the Exercises at the end of each section and the Review and Challenge Problems independently. 

Take a look again at the instructions on page (iii).  "If you can't solve some of the problems, that's OK, because they will all be fully solved as you read the section."  

ETA:  The complete step by step solution to Problem 10.29 is on pp. 315-316.

I do generally work through the introductory problems with him.  The problem was that even the explanation for that particular problem didn't make sense to either of us.  I quoted the explanation above; Not_a_Number clarified the point that what they were doing was setting first r and then s equal to zero, which wasn't stated (and I'm too dense to make that connection at this point in my life).  I suggested that we could skip the section because it is starred, but DS really doesn't like skipping.  He wants to understand it all--which I hate to discourage.

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Just now, eternallytired said:

I do generally work through the introductory problems with him.  The problem was that even the explanation for that particular problem didn't make sense to either of us.  I quoted the explanation above; Not_a_Number clarified the point that what they were doing was setting first r and then s equal to zero, which wasn't stated (and I'm too dense to make that connection at this point in my life).  I suggested that we could skip the section because it is starred, but DS really doesn't like skipping.  He wants to understand it all--which I hate to discourage.

I think the easy solution is just to tag me when you guys are stuck 😉 . In my not-so-humble opinion, I can generally explain things better than those books, at least if you get me a few chances. 

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1 minute ago, Not_a_Number said:

I think the easy solution is just to tag me when you guys are stuck 😉 . In my not-so-humble opinion, I can generally explain things better than those books, at least if you get me a few chances. 

That's so kind of you! I don't want to take advantage of you as some sort of free tutor, though.  Maybe if we just need occasional clarification, I'll bump you.  Thank so much!

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14 minutes ago, eternallytired said:

That's so kind of you! I don't want to take advantage of you as some sort of free tutor, though.  Maybe if we just need occasional clarification, I'll bump you.  Thank so much!

I really, really, really don't mind. Honestly. In fact, I would like it. I spend tons of time on this forum. I like chatting about math. I like DOING math questions. 

Like, the main thing I did in high school was math. I did tons and tons of math contests for fun. I spent time in the summers at math camps  (yes, really 😛) and participating in math olympiads.  I teach for AoPS now and I thoroughly enjoy it. 

You won't take advantage of me at ALL if you tag me on here when you have a question. I'll answer when I have the chance, and I'll enjoy doing so. And if you don't believe me, ask other people on here whether I enjoy talking about math or not and see what they say 😉 . 

Edited by Not_a_Number
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  • 6 months later...
On 2/13/2021 at 8:18 PM, Not_a_Number said:

OK, I think I see how do this in a pretty way. If you let s = 0, you get the equation

 

(Ar + C)(Dr + F)=  6r^2-23r+21. 

 

And if you let r = 0, you get the equation 

 

(Bs + C)(Es + F) = 2s^2-13s+21.

 

On 2/14/2021 at 1:47 PM, Not_a_Number said:

Plus, you can think of it as a public service 😉 . If you guys are stuck, you may very well not be the only one. Someone else might appreciate having a questions answered on here! 

Who knows while looking for more reviews on the online classes I came across this problem that we were also stuck🤣. The "let's assume s=0" just makes a lot more sense. Thanks Not_a_Number! 

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