Any suggestions for a math sequence that's advanced but not AOPS?

[pgr]

I've searched and researched and asked but I still keep hitting a wall. My 13yo flew through and really liked SM when he was younger, and more recently also flew through and *loved* Jousting Armadillos, but has balked at AOPS Pre-algebra. He's crawled through (clawed through?) a small handful of chapters over the course of a year, with some Jacobs sprinkled in. I feel he's definitely capable of the actual math (and does understand and perform the computations) but the format seems to freak him out and he just feels overwhelmed. We're at the point that just pushing through is getting counterproductive. 

Any suggestions for a strong math sequence that's not AOPS? FWIW, I've also tried Dolciani, but that didn't work. Nor does online coursework. I feel like Goldilocks here but math is important enough that I really want to get it right. 

[bensonduck]

We really like Foerster’s here. 

[Not_a_Number]

40 minutes ago, pgr said:

I've searched and researched and asked but I still keep hitting a wall. My 13yo flew through and really liked SM when he was younger, and more recently also flew through and *loved* Jousting Armadillos, but has balked at AOPS Pre-algebra. He's crawled through (clawed through?) a small handful of chapters over the course of a year, with some Jacobs sprinkled in. I feel he's definitely capable of the actual math (and does understand and perform the computations) but the format seems to freak him out and he just feels overwhelmed. We're at the point that just pushing through is getting counterproductive. 

Any suggestions for a strong math sequence that's not AOPS? FWIW, I've also tried Dolciani, but that didn't work. Nor does online coursework. I feel like Goldilocks here but math is important enough that I really want to get it right. 

Any idea what was going wrong with AoPS? 

[mathnerd]

Could you explain how he has tried working with Dolciani and AOPS. Is he self-directed and struggling with the language and text heavy pages or is a parent directing the learning by teaching each chapter or is it in between? I am guessing that he has not yet adjusted to the high school textbook format.

[kokotg]

Mine didn't like AOPS pre-algebra, either. We went straight from Singapore 6B to Jacobs Algebra and Geometry, then Foersters for Algebra 2 and Trig. My husband's a calculus teacher, so they've used his/his school's materials for that. That worked very well with my oldest--perfect scores on everything math-related, and he's now a math major. My next kid is much less mathy, but just got a 4 on Calc AB after this sequence, so it's worked out well for him, too. 

[wendyroo]

Since my kids use Math Mammoth for elementary math, we continue and use MM7 which is pre-algebra. My oldest went through AOPS pre-algebra, but I doubt I will subject any of my other kids to that. My second son is going through Dolciani pre-algebra along with Zaccaro's Problem Solving Genius and Real World Algebra. (Prior to this all my kids go through the Hands on Equations word problem book.)

I like Foerster for algebra 1 and 2. For geometry I like Math without Borders...actually, I just like the out-of-print textbook that they provide as part of that course: Geometry: A Guided Inquiry. I like that text better than others I have looked at.

As supplements I LOVE the math Great Courses by James Tanton - so conceptual and visual and deep.

[Momto6inIN]

For my oldest DS who was/is advanced in math, we used Video Text Algebra and Geometry and he completed both programs in 2 years. (I think the official sequence calls for 3.5ish years.) It's not in AoPS's league as far as rigor goes, but it is a strong and solid conceptual program with short 15 min instructional videos that I was able to watch alongside him and then have enough of the gist of it to help with any problems.

For my other kids who are good at math, but not advanced, Video Text was a strong program for them as well, but they did it more slowly than 1st DS.

After VT my oldest did just fine with self studying AoPS books for PreCalc and Calc and Counting & Probability/Number Theory, but if AoPS is not your kid's style, there are plenty of other Precalc and Calc options, or by then he could possibly take CC courses. AoPS is a good program, and it was amazing for my oldest, but it's not "the best" for a variety of kids.

[Not_a_Number]

1 hour ago, wendyroo said:

My oldest went through AOPS pre-algebra, but I doubt I will subject any of my other kids to that.

I don’t get the AoPS pre-algebra book, to be honest. It doesn’t do what I want it to, somehow.

That being said, I think the topics in Intro to NT and Intro to C&P are hard to find good coverage of otherwise, and all the books are good as repositories of problems.

[8filltheheart]

Another Foerster fan. Derek Owens might be another option.

[pgr]

3 hours ago, mathnerd said:

Could you explain how he has tried working with Dolciani and AOPS. Is he self-directed and struggling with the language and text heavy pages or is a parent directing the learning by teaching each chapter or is it in between? I am guessing that he has not yet adjusted to the high school textbook format.

 

3 hours ago, Not_a_Number said:

Any idea what was going wrong with AoPS? 

It intimidates him. He's very self-directed in general (really, he resists any parent directed teaching of math), but with AOPS I think he feels like the explanations are less of an "aha!!" moment (as they were for his older sister) and more of a "duh, you didn't figure out the super clever way to do it, ya ding-dong" moment. He's been leery of AOPS since his sister started the pre-algebra book. Even Beast Academy, which he liked, made him "feel like an idiot" at times. I don't think it's a matter of the language or the text - he's worked through other text heavy materials without any issue. I think it's a preconceived mindset that he's not going to grasp concepts immediately and therefore it's not even worth trying as he's "already failed". 

As for Dolciani, he just really didn't like the text at all. The little he completed was through clenched teeth and it didn't feel like he was internalizing any of it. 

To be fair, he's my most sensitive kid. He's very bright and his personality is fairly mature, but if a curriculum doesn't fit him, there will be a LOT of resistance to working through it and, I've learned, there will be very little learning. 

[wendyroo]

2 hours ago, Not_a_Number said:

That being said, I think the topics in Intro to NT and Intro to C&P are hard to find good coverage of otherwise, and all the books are good as repositories of problems.

I have such mixed feelings about this.

Peter did work through AOPS Counting and Probability this past year. And I think it was good conceptual material that isn't often covered at this level.

OTOH, he hated it. He LOVES math; he thinks and breathes and adores math, and yet he dreaded that AOPS book. And now he says that math is "bland" and "confusing". When I asked him what additional subject he wanted to add to his schedule this week (we are ramping up to the full fall lineup), he chose history over math. Huh? He hates history and has almost always delighted in the whole plethora of math resources we have used.

The last time he was down in the dumps about math was when he finished AOPS pre-algebra and started AOPS algebra. It got so severe then that I switched him to a different algebra. This time, though, we soldiered on because there wasn't another good C&P resource. But I'm not sure I made the right choice. He is just so turned off and disheartened by math right now, and I lay most of the blame on the AOPS style of textbook.

I do think they are a good repository of problems, but I can just use Alcumus for that. That is what we did for Geometry. I chose a couple strong, interesting, conceptual, but straight-forward, explicitly taught geometry resources. Throughout the year I also had him work through the Alcumus geometry sections to ensure that he was tackling more challenging, rigorous problems that forced him to integrate concepts and think outside the box.

[pgr]

Thank you so much for all the suggestions! I'm going to go look at Foerster again; I think I checked it out for DD, but AOPS has been a good fit for her so I didn't pursue it further. I'd forgotten about it... 

I've also order Crocodiles and Coconuts, so there's that, right? :) 

[Not_a_Number]

Just now, wendyroo said:

I have such mixed feelings about this.

Peter did work through AOPS Counting and Probability this past year. And I think it was good conceptual material that isn't often covered at this level.

OTOH, he hated it. He LOVES math; he thinks and breathes and adores math, and yet he dreaded that AOPS book. And now he says that math is "bland" and "confusing". When I asked him what additional subject he wanted to add to his schedule this week (we are ramping up to the full fall lineup), he chose history over math. Huh? He hates history and has almost always delighted in the whole plethora of math resources we have used.

The last time he was down in the dumps about math was when he finished AOPS pre-algebra and started AOPS algebra. It got so severe then that I switched him to a different algebra. This time, though, we soldiered on because there wasn't another good C&P resource. But I'm not sure I made the right choice. He is just so turned off and disheartened by math right now, and I lay most of the blame on the AOPS style of textbook.

I do think they are a good repository of problems, but I can just use Alcumus for that. That is what we did for Geometry. I chose a couple strong, interesting, conceptual, but straight-forward, explicitly taught geometry resources. Throughout the year I also had him work through the Alcumus geometry sections to ensure that he was tackling more challenging, rigorous problems that forced him to integrate concepts and think outside the box.

Ugh. That sounds really unfortunate. I'm sorry Peter disliked it so much 😕 . It's a little easy for me to talk, because I do NOT use AoPS as a curriculum. I teach the material myself, then I throw some problems at my kid. And at that point, it's kind of nice to have a repository of problems, instead of having to hunt around a variety of contests before I find the ones appropriate for a topic. I can make up my own problems (and usually do), but sometimes having someone else come up with the 200th "fun algebra" problem is a relief. 

Is the discovery thing that's making him feel quite this disheartened? Or is it the pacing? When I've taught Intro to C&P online, I remember feeling like there were some fundamentals we went over FAR too quickly... I wasn't sure if that'd happen with the book or not. 

[kokotg]

3 minutes ago, pgr said:

 

It intimidates him. He's very self-directed in general (really, he resists any parent directed teaching of math), but with AOPS I think he feels like the explanations are less of an "aha!!" moment (as they were for his older sister) and more of a "duh, you didn't figure out the super clever way to do it, ya ding-dong" moment. He's been leery of AOPS since his sister started the pre-algebra book. Even Beast Academy, which he liked, made him "feel like an idiot" at times. I don't think it's a matter of the language or the text - he's worked through other text heavy materials without any issue. I think it's a preconceived mindset that he's not going to grasp concepts immediately and therefore it's not even worth trying as he's "already failed". 

As for Dolciani, he just really didn't like the text at all. The little he completed was through clenched teeth and it didn't feel like he was internalizing any of it. 

To be fair, he's my most sensitive kid. He's very bright and his personality is fairly mature, but if a curriculum doesn't fit him, there will be a LOT of resistance to working through it and, I've learned, there will be very little learning. 

Yes--it was a bad fit for my super perfectionist oldest because he was used to math being easy; being SUPPOSED to struggle to answer all the questions did not work for him. My youngest is my other mathy kid, and I'm hoping he'll fare better with AOPS because he'll get there through Beast Academy, so he'll be used to it. 

[Not_a_Number]

5 minutes ago, pgr said:

It intimidates him. He's very self-directed in general (really, he resists any parent directed teaching of math), but with AOPS I think he feels like the explanations are less of an "aha!!" moment (as they were for his older sister) and more of a "duh, you didn't figure out the super clever way to do it, ya ding-dong" moment. He's been leery of AOPS since his sister started the pre-algebra book. Even Beast Academy, which he liked, made him "feel like an idiot" at times. I don't think it's a matter of the language or the text - he's worked through other text heavy materials without any issue. I think it's a preconceived mindset that he's not going to grasp concepts immediately and therefore it's not even worth trying as he's "already failed". 

As for Dolciani, he just really didn't like the text at all. The little he completed was through clenched teeth and it didn't feel like he was internalizing any of it. 

To be fair, he's my most sensitive kid. He's very bright and his personality is fairly mature, but if a curriculum doesn't fit him, there will be a LOT of resistance to working through it and, I've learned, there will be very little learning. 

You're right, that really doesn't sound like a fit to me. I think AoPS works best for kids who kind of LIKE being stuck on problems and having "ah-ha!" moments, as you say. 

I've heard quite a few people recommend Foerster on here. I don't use curriculum, so I don't have a suggestion... I just wanted to chime in since I have quite a lot of AoPS experience (I've taught most of the lasses online.) 

[pgr]

3 minutes ago, wendyroo said:

I have such mixed feelings about this.

Peter did work through AOPS Counting and Probability this past year. And I think it was good conceptual material that isn't often covered at this level.

OTOH, he hated it. He LOVES math; he thinks and breathes and adores math, and yet he dreaded that AOPS book. And now he says that math is "bland" and "confusing". When I asked him what additional subject he wanted to add to his schedule this week (we are ramping up to the full fall lineup), he chose history over math. Huh? He hates history and has almost always delighted in the whole plethora of math resources we have used.

The last time he was down in the dumps about math was when he finished AOPS pre-algebra and started AOPS algebra. It got so severe then that I switched him to a different algebra. This time, though, we soldiered on because there wasn't another good C&P resource. But I'm not sure I made the right choice. He is just so turned off and disheartened by math right now, and I lay most of the blame on the AOPS style of textbook.

I do think they are a good repository of problems, but I can just use Alcumus for that. That is what we did for Geometry. I chose a couple strong, interesting, conceptual, but straight-forward, explicitly taught geometry resources. Throughout the year I also had him work through the Alcumus geometry sections to ensure that he was tackling more challenging, rigorous problems that forced him to integrate concepts and think outside the box.

I can definitely relate. Sometimes it's so hard to know if something is going to ultimately have been the right path. 

Would you mind sharing what algebra and geometry resources you ended up using? 

[pgr]

1 minute ago, kokotg said:

Yes--it was a bad fit for my super perfectionist oldest because he was used to math being easy; being SUPPOSED to struggle to answer all the questions did not work for him. My youngest is my other mathy kid, and I'm hoping he'll fare better with AOPS because he'll get there through Beast Academy, so he'll be used to it. 

Yes! He's a perfectionist, and that's exactly the issue he's having. 

 

[Not_a_Number]

1 minute ago, kokotg said:

Yes--it was a bad fit for my super perfectionist oldest because he was used to math being easy; being SUPPOSED to struggle to answer all the questions did not work for him. My youngest is my other mathy kid, and I'm hoping he'll fare better with AOPS because he'll get there through Beast Academy, so he'll be used to it. 

To be fair, being used to math generally being tricky is a good thing 😉 . But I can see how being used to it being easy would get in the way of that. 

I tend to start my kid on "math is frustrating" pretty early, lol. I'm mean and start that way back in kindergarten 😛 . 

[Not_a_Number]

9 minutes ago, wendyroo said:

He LOVES math; he thinks and breathes and adores math, and yet he dreaded that AOPS book. And now he says that math is "bland" and "confusing".

Man... I'm thinking more about this, and this is SO disappointing 😕 . I've taught DD9 combinatorics when she was 6; I'm currently tutoring another mathy 6-year-old in combinatorics, and she's also getting it and having a blast. We're currently coloring bears and ice creams, lol. (I did the same thing back when DD9 was little.) 

There's really no reason for combinatorics to be bland and confusing 😕 . It's a fun, hands-on subject with ample visuals and plenty of chances to check your intuition. I love it for kids of a wide variety of ages. 

Edited August 3, 2021 by Not_a_Number

[wendyroo]

4 minutes ago, pgr said:

Thank you so much for all the suggestions! I'm going to go look at Foerster again; I think I checked it out for DD, but AOPS has been a good fit for her so I didn't pursue it further. I'd forgotten about it... 

I've also order Crocodiles and Coconuts, so there's that, right? 🙂

I just remembered one other resource that I have looked at but never used.

James Tanton (whose other materials I have used and loved) offers a middle school math series on Edfinity. They are not "full" courses, but rather deep, conceptual introductions to a variety of topics along with challenging problem sets (auto-graded with performance analysis).  His courses are:  8 Tips to Conquer Any Problem; Counting and Probability; Numbers and the Number System; Structure, Patterns and Logic; and Relations and Equations. They are online, though, which I know you said had not worked in the past.

[kokotg]

2 minutes ago, Not_a_Number said:

To be fair, being used to math generally being tricky is a good thing 😉 . But I can see how being used to it being easy would get in the way of that. 

I tend to start my kid on "math is frustrating" pretty early, lol. I'm mean and start that way back in kindergarten 😛 . 

yes--I agree, in theory--but there was a lot of pick your battles going on with homeschooling that one 😉 . This was my kid who would have meltdowns when he was 6 because you can't erase crayon. Fortunately, it doesn't seem to have broken him forever; he's still a perfectionist, but he's a lot more patient about it now. But, yeah, wariness of it happening again is one reason we're doing Beast Academy with my youngest (it either wasn't out yet or was very new and not on my radar yet with his brother). 

[Not_a_Number]

1 minute ago, kokotg said:

yes--I agree, in theory--but there was a lot of pick your battles going on with homeschooling that one 😉 . This was my kid who would have meltdowns when he was 6 because you can't erase crayon. Fortunately, it doesn't seem to have broken him forever; he's still a perfectionist, but he's a lot more patient about it now. But, yeah, wariness of it happening again is one reason we're doing Beast Academy with my youngest (it either wasn't out yet or was very new and not on my radar yet with his brother). 

Oh, I do know how that goes. We're currently very much in the midst of the "pick your battles" issue 😛 . 

[UHP]

24 minutes ago, Not_a_Number said:

I've taught DD9 combinatorics when she was 6; I'm currently tutoring another mathy 6-year-old in combinatorics, and she's also getting it and having a blast. We're currently coloring bears and ice creams, lol. (I did the same thing back when DD9 was little.) 

I'd love to hear more about combinatorics for 6-year-olds.

34 minutes ago, wendyroo said:

He is just so turned off and disheartened by math right now, and I lay most of the blame on the AOPS style of textbook.

I only know Art-of-problem-solving from their beast academy books. Do the books for older kids have something in common (an "AOPS style"?) with BA?

I admire Beast Academy, with growing reservations.

editing to add that I could have asked @pgr the same question:

Quote

I feel he's definitely capable of the actual math (and does understand and perform the computations) but the format seems to freak him out and he just feels overwhelmed.

Can you tell something about the format?

Edited August 3, 2021 by UHP

[Not_a_Number]

1 minute ago, UHP said:

I only know Art-of-problem-solving from their beast academy books. Do the books for older kids have something in common (an "AOPS style"?) with BA?

I admire Beast Academy, with growing reservations.

It's all discovery method, but what I tend to think of as an untested discovery method, without much grappling about what kids actually find hard. Otherwise, I don't know that they are terribly similar. I think they have different authors, in fact. 

[wendyroo]

6 minutes ago, Not_a_Number said:

Man... I'm thinking more about this, and this is SO disappointing 😕 . I've taught DD9 combinatorics when she was 6; I'm currently tutoring another mathy 6-year-old in combinatorics, and she's also getting it and having a blast. We're currently coloring bears and ice creams, lol. (I did the same thing back when DD9 was little.) 

There's really no reason for combinatorics to be bland and confusing 😕 . It's a fun, hands-on subject with ample visuals and plenty of chances to check your intuition. I love it for kids of a wide variety of ages. 

Peter had already had a lot of fun introductions to those topics starting very young. He went into AOPS C&P with a solid basic understanding...and a wealth of enthusiasm. He devoured James Tanton's math Great Courses. He happily watches Numberphile Youtube videos for hours and then plays around with the concepts and tries to expand on them. He is currently trying to prove 3n+1...completely in his head as he falls asleep.

Geometry isn't his favorite (I don't blame him), so he was all in when I said we could spend a couple days a week doing C&P to get a break from all the trig and proofs. He likes the subject, he just does not click with AOPS textbooks.

What I sense is that AOPS is teaching him to beat his head against the wall, give a sigh of relief when he finally accidentally hits the magic brick that unlocks the right answer, and then give a sigh of frustration because he still has no clue why that is the right answer and therefore knows that the next problem and the next and all the rest of them are going to be just as incomprehensible. There never is an "aha" moment, but rather just a "thank God that one is over" moment before despairing starting up the next one.

Realistically, the AOPS book taught him very, very little. So, the problems that he already knew how to do, or that were just a baby step of challenge above what he could already do, were great. But lacking any meaningful instruction (at least in any form that he could connect with), the more difficult problems were just torture that he "got through" with little understanding or growth.

[Not_a_Number]

1 minute ago, UHP said:

I'd love to hear more about combinatorics for 6-year-olds.

We do a LOT of questions like "How many ice creams do you get if we have 4 choices for the first scoop and 5 choices for the second scoop?" Except that we of course name the scoops and actually color things in and discuss how it all works 😄 . We arrange things into arrays, until it's clear to the kids inside and out that you multiply, then we move onto 3 scoops... 

I don't have a curriculum, though. Just some pictures of bears and ice creams 😉 . I can send you some of the worksheets my 6-year-old tutee is doing, if you like. They aren't THAT sophisticated, but I think they get down to the core of the issues. 

[Not_a_Number]

2 minutes ago, wendyroo said:

What I sense is that AOPS is teaching him to beat his head against the wall, give a sigh of relief when he finally accidentally hits the magic brick that unlocks the right answer, and then give a sigh of frustration because he still has no clue why that is the right answer and therefore knows that the next problem and the next and all the rest of them are going to be just as incomprehensible. There never is an "aha" moment, but rather just a "thank God that one is over" moment before despairing starting up the next one.

That sounds really annoying for him! Can you give me an example of a question that makes him feel like that? 

[UHP]

2 minutes ago, Not_a_Number said:

I don't have a curriculum, though. Just some pictures of bears and ice creams 😉 . I can send you some of the worksheets my 6-year-old tutee is doing, if you like. They aren't THAT sophisticated, but I think they get down to the core of the issues. 

I'd be very excited to see them.

[Not_a_Number]

6 minutes ago, UHP said:

I'd be very excited to see them.

I'll post in the other group in a bit 🙂 . 

[wendyroo]

32 minutes ago, pgr said:

I can definitely relate. Sometimes it's so hard to know if something is going to ultimately have been the right path. 

Would you mind sharing what algebra and geometry resources you ended up using? 

For Algebra, he made it through several chapters of AOPS algebra, and then we bailed and worked through Chuckles the Rocket Dog and the remaining sections on Alcumus (supplemented with Khan Academy and ProfRobBob videos on YouTube if he struggled with a concept).

Then we took a detour for 6 months. He did James Tanton's Great Courses series, The Power of Mathematical Visualization, which he LOVED. There are problem sets in the Guidebook, so it kept him busy for a while. He loved James Tanton so much, that we then went straight into his Geometry course - which was a big hit, despite DS not really liking geometry. Then I got my hands on a library copy of Geometry: A Guided Inquiry which we kept for as long as we could to work through the explorations that interested us the most. Meanwhile, DS worked his way through the geometry topics on Alcumus and again supplemented with Khan and ProfRobBob to make sure he had a firm foundation in all the topics he needed.

In the future, I think I will use Foerster algebra 1, Geometry: A Guided Inquiry (through Math Without Borders), Foerster for algebra 2 (this is what DS is using this year), and then either Foerster for PreCalc and Calc or Derek Owens courses.

[Not_a_Number]

19 minutes ago, wendyroo said:

In the future, I think I will use Foerster algebra 1, Geometry: A Guided Inquiry (through Math Without Borders), Foerster for algebra 2 (this is what DS is using this year), and then either Foerster for PreCalc and Calc or Derek Owens courses.

To be fair, some kids do thrive with the AoPS approach. I probably would have: I absolutely loved problem-solving and I enjoyed the frustration that came with it. AoPS would have gotten me to spend more time thinking about the math, and that would have been a win. 

[bensonduck]

40 minutes ago, wendyroo said:

For Algebra, he made it through several chapters of AOPS algebra, and then we bailed and worked through Chuckles the Rocket Dog and the remaining sections on Alcumus (supplemented with Khan Academy and ProfRobBob videos on YouTube if he struggled with a concept).

Then we took a detour for 6 months. He did James Tanton's Great Courses series, The Power of Mathematical Visualization, which he LOVED. There are problem sets in the Guidebook, so it kept him busy for a while. He loved James Tanton so much, that we then went straight into his Geometry course - which was a big hit, despite DS not really liking geometry. Then I got my hands on a library copy of Geometry: A Guided Inquiry which we kept for as long as we could to work through the explorations that interested us the most. Meanwhile, DS worked his way through the geometry topics on Alcumus and again supplemented with Khan and ProfRobBob to make sure he had a firm foundation in all the topics he needed.

In the future, I think I will use Foerster algebra 1, Geometry: A Guided Inquiry (through Math Without Borders), Foerster for algebra 2 (this is what DS is using this year), and then either Foerster for PreCalc and Calc or Derek Owens courses.

Foerster’s Algebra 2 and Precalc (the Key Press edition) both have very nice sections on combinatorics/discrete math with a variety of problems at different difficulty levels. DD has really enjoyed them. 

[Not_a_Number]

8 minutes ago, bensonduck said:

Foerster’s Algebra 2 and Precalc (the Key Press edition) both have very nice sections on combinatorics/discrete math with a variety of problems at different difficulty levels. DD has really enjoyed them. 

How far up combinatorics do they go, if you don't mind me asking? 

[bensonduck]

39 minutes ago, Not_a_Number said:

How far up combinatorics do they go, if you don't mind me asking? 

Not nearly as advanced as, say, AOPS intermediate C&P, which I just looked at the TOC online for. 
 

i don’t have the algebra 2 here, but these are the section titles for 2 of the precalc discrete math chapters. (Last one is like limits, derivatives, integrals). 
 

14-1 introduction to probability 

14-2 words associated with probability

14-3 two counting principles 

14-4 probabilities of various permutations

14-5 probabilities of various combinations 

14-6 properties of probability

14-7 functions of a random variable

14-8 mathematical expectation 

15-1 introduction to sequences and series

15-2 arithmetic, geometric and other sequences 

15-3 series and partial sums

FWIW, DD is also currently taking a contest prep combinatorics class given by a local math circle. The Foerster stuff is nowhere near as hard as the hw for that class. She can do 2-3 sections of this a day and get most of them right. but spend 2 hours puzzling over a couple of the contest prep problems (and get several wrong). 
 

But, the way Foerster lays it out is so clear that sometimes it gives her an insight. Today she realized while working on one of the Foerster sets that she did actually know how to solve one of the contest hw problems, and dashed upstairs to her hw papers immediately to write it out before she forgot. So we are keeping Foerster. 🙂

[mathnerd]

5 hours ago, pgr said:

 

It intimidates him. He's very self-directed in general (really, he resists any parent directed teaching of math), but with AOPS I think he feels like the explanations are less of an "aha!!" moment (as they were for his older sister) and more of a "duh, you didn't figure out the super clever way to do it, ya ding-dong" moment. He's been leery of AOPS since his sister started the pre-algebra book. Even Beast Academy, which he liked, made him "feel like an idiot" at times. I don't think it's a matter of the language or the text - he's worked through other text heavy materials without any issue. I think it's a preconceived mindset that he's not going to grasp concepts immediately and therefore it's not even worth trying as he's "already failed". 

As for Dolciani, he just really didn't like the text at all. The little he completed was through clenched teeth and it didn't feel like he was internalizing any of it. 

To be fair, he's my most sensitive kid. He's very bright and his personality is fairly mature, but if a curriculum doesn't fit him, there will be a LOT of resistance to working through it and, I've learned, there will be very little learning. 

Some people use MEP and like it a lot. I have used it infrequently as one of my sources to pull out review problems in the past. Since it is free, you could download it to see if your son shows any interest in it.

[Clemsondana]

@wendyroowe had a similar experience with AoPS.  I attributed it to kid being young and having low frustration tolerance, but...yes, the feeling that you had to guess the magic way to solve the problem was very frustrating.  We actually still use it, but it was a circuitous path with lots of breaks.  In pre-A, we took off a lot of time, did the Arbor Press materials, did some Life of Fred, moved more slowly, etc - whatever it took to get kid past the 'I hate math' situation..  We ended up doing pre-A, A, and Adv. A taking 1.5 years each, while simultaneously doing Life of Fred.  My kid actually liked NT and C&P and was OK with geometry but probably wasn't going to particularly like that subject no matter what program we used.  

At this point kid is fine with the program, although I don't know if they actually like it or just prefer the familiar, but absolutely requires that I have something else that they can do on busy days because they've learned that having any sort of time pressure makes AoPS too frustrating.  And they became willing to take help or hints to figure out some problems.  They are able to intuit a lot of the things they are supposed to be learning - as you said, some of it seems obvious - while other parts are things that they would never figure out without seeing a worked problem so that they can figure out the principle that they are supposed to apply.  The program has succeeded at the goals of them learning math and possibly at trying to look to see if there is a manipulation to make a problem easier to solve rather than brute forcing through everything.  But, I wouldn't say that there had been many 'a-ha' moments.  

[wendyroo]

13 hours ago, Not_a_Number said:

That sounds really annoying for him! Can you give me an example of a question that makes him feel like that? 

A random example from chapter 6, whose notebook work shows all the signs of intense frustration and head banging:

For any positive integer n, let O(n) be the sum of the odd digits of n and E(n) be the sum of the even digits of n. Let
          x = O(1) + O(2) + O(3) + ... + O(100)
and    y = E(1) + E(2) + E(3) + ... + E(100)

Find x and y.

He tried working on that problem for so long. None of the problems with solutions really applied or helped.  In fact, one key fact highlighted in a blue box in that section is "There's not always a slick formula or solution. Sometimes you just need to be organized and grind out an answer", which is not at all applicable or helpful in this problem.

The answer guide says:
"Note that in x, the digit 1 occurs ten times in the units place (in 1, 11, 21, ..., 91) and ten times in the tens place (in 10, 11, 12, ... 19) also." Peter had gotten this far on his own. "Therefore, x = 20(1 + 3 + 5 + 7 + 9) + O(100) = 500 + 1 = 501." That "therefore" is doing some heavy lifting. Obviously he could see it once they showed it to him, but being taught that trick did nothing to help him tackle the very next problem:

Mack the Millipede starts at (0,0,0) at noon and each minute moves one unit in either the positive x-direction, the positive y-direction, or the positive x-direction. Thus, after 1 minute he could be at (1,0,0), (0,1,0), or (0,0,1); after two minutes he could be at [long list of points he could be at). How many different paths could h take to (3,5,2) which don't pass through (1,3,1)?

Right from the start the answer key throws out: "To get to (3,5,2), each path corresponds to a 10-letter string where each letter is X, Y, or Z (where X indicates a step in the x-direction, Y indicates a step in the y-direction, and Z indicates a step in the z-direction)." Peter had never thought of it that way...the book had never before suggested or taught him to think of a similar problem in that way.

Next it says, "The number of such strings is 10!/3!5!2!" Peter had gotten that. But then, the answer key says, "The number of paths that stop at (1,3,1) is the number of ways to get from (0,0,0) to (1,3,1) multiplied by the number of ways to get from (1,3,1) to (3,5,2)." This was the "aha" moment that the book had not adequately lead him to discover. As soon as I read that from the answers, then he took off and finished the problem correctly, but I have no clue how the book expected him to make that leap other than through intuitive luck or being told the answer.

That seems to be the theme of the AOPS books (or at least how Peter perceives it):
      Here are a bunch of hard problems which you will either intuitively understand and be able to solve, or not. It not, we will show off our slick way of solving them, not so much to gradually building up your skills and intuition, but more to prove that we are smarter than you.

[Not_a_Number]

5 minutes ago, wendyroo said:

A random example from chapter 6, whose notebook work shows all the signs of intense frustration and head banging:

For any positive integer n, let O(n) be the sum of the odd digits of n and E(n) be the sum of the even digits of n. Let
          x = O(1) + O(2) + O(3) + ... + O(100)
and    y = E(1) + E(2) + E(3) + ... + E(100)

Find x and y.

He tried working on that problem for so long. None of the problems with solutions really applied or helped.  In fact, one key fact highlighted in a blue box in that section is "There's not always a slick formula or solution. Sometimes you just need to be organized and grind out an answer", which is not at all applicable or helpful in this problem.

The answer guide says:
"Note that in x, the digit 1 occurs ten times in the units place (in 1, 11, 21, ..., 91) and ten times in the tens place (in 10, 11, 12, ... 19) also." Peter had gotten this far on his own. "Therefore, x = 20(1 + 3 + 5 + 7 + 9) + O(100) = 500 + 1 = 501." That "therefore" is doing some heavy lifting. Obviously he could see it once they showed it to him, but being taught that trick did nothing to help him tackle the very next problem:

Mack the Millipede starts at (0,0,0) at noon and each minute moves one unit in either the positive x-direction, the positive y-direction, or the positive x-direction. Thus, after 1 minute he could be at (1,0,0), (0,1,0), or (0,0,1); after two minutes he could be at [long list of points he could be at). How many different paths could h take to (3,5,2) which don't pass through (1,3,1)?

Right from the start the answer key throws out: "To get to (3,5,2), each path corresponds to a 10-letter string where each letter is X, Y, or Z (where X indicates a step in the x-direction, Y indicates a step in the y-direction, and Z indicates a step in the z-direction)." Peter had never thought of it that way...the book had never before suggested or taught him to think of a similar problem in that way.

Next it says, "The number of such strings is 10!/3!5!2!" Peter had gotten that. But then, the answer key says, "The number of paths that stop at (1,3,1) is the number of ways to get from (0,0,0) to (1,3,1) multiplied by the number of ways to get from (1,3,1) to (3,5,2)." This was the "aha" moment that the book had not adequately lead him to discover. As soon as I read that from the answers, then he took off and finished the problem correctly, but I have no clue how the book expected him to make that leap other than through intuitive luck or being told the answer.

That seems to be the theme of the AOPS books (or at least how Peter perceives it):
      Here are a bunch of hard problems which you will either intuitively understand and be able to solve, or not. It not, we will show off our slick way of solving them, not so much to gradually building up your skills and intuition, but more to prove that we are smarter than you.

Interesting. I think of the first problem as definitely a “either you see it or you don’t” kind of question, but I do think of the second problem as a straightforward application of the multiplication principle.

That being said, I’ve felt very strongly that Intro to C&P does not adequately develop the multiplication principle, and then expects kids to be able to use it in novel contexts without preparation, which is unfair and frustrating. So your example confirms that.

It’s really too bad. The C&P topics themselves are marvelous. It’s sad that they are obviously not presented in a way that sparks joy for most kids!!!

[Not_a_Number]

12 hours ago, bensonduck said:

Not nearly as advanced as, say, AOPS intermediate C&P, which I just looked at the TOC online for. 
 

i don’t have the algebra 2 here, but these are the section titles for 2 of the precalc discrete math chapters. (Last one is like limits, derivatives, integrals). 
 

14-1 introduction to probability 

14-2 words associated with probability

14-3 two counting principles 

14-4 probabilities of various permutations

14-5 probabilities of various combinations 

14-6 properties of probability

14-7 functions of a random variable

14-8 mathematical expectation 

15-1 introduction to sequences and series

15-2 arithmetic, geometric and other sequences 

15-3 series and partial sums

It kind of looks like it jumps through some very hard stuff quite quickly! I personally like spending quite a lot of time on basic combinatorics before tackling probability. 

 

12 hours ago, bensonduck said:

FWIW, DD is also currently taking a contest prep combinatorics class given by a local math circle. The Foerster stuff is nowhere near as hard as the hw for that class. She can do 2-3 sections of this a day and get most of them right. but spend 2 hours puzzling over a couple of the contest prep problems (and get several wrong). 

But, the way Foerster lays it out is so clear that sometimes it gives her an insight. Today she realized while working on one of the Foerster sets that she did actually know how to solve one of the contest hw problems, and dashed upstairs to her hw papers immediately to write it out before she forgot. So we are keeping Foerster. 🙂

I've heard nothing but good stuff about Foerster 🙂 . 

What contest prep class is she taking, if you don't mind me asking? 🙂 

[Janeway]

My child has requested Dimensions for his math. But my favorites before this are Jacobs, Foersters, and Dolciani.

[Janeway]

Oh yeah, I didn’t mean my above post to mean I don’t like Dimensions. I just meant it is what we plan for next. It looks good and good for the child who took well to Singapore math already.

Edited August 5, 2021 by Janeway

[pgr]

OK I'm looking at (for) Foerster and now realized that, while I was able to get my hands on Dolciani and Lial through interlibrary loan last year, Foerster was one that I could only find for purchase and that's where the search stopped. I haven't actually held it in hand. 

This time I'm going to buy it used and actually give it a shot. DS has completed SM, Jousting Armadillos, three chapters of AOPS Pre-Algebra, and four chapters of Jacobs Algebra. 

Should I go for trying Foerster's Algebra 1 from here? There isn't a "pre-algebra", correct? Does it matter which edition? I found the Classics Edition (2006) used.

[Shoeless]

On 8/7/2021 at 12:49 PM, pgr said:

OK I'm looking at (for) Foerster and now realized that, while I was able to get my hands on Dolciani and Lial through interlibrary loan last year, Foerster was one that I could only find for purchase and that's where the search stopped. I haven't actually held it in hand. 

This time I'm going to buy it used and actually give it a shot. DS has completed SM, Jousting Armadillos, three chapters of AOPS Pre-Algebra, and four chapters of Jacobs Algebra. 

Should I go for trying Foerster's Algebra 1 from here? There isn't a "pre-algebra", correct? Does it matter which edition? I found the Classics Edition (2006) used.

We're jumping into Foerster's Algebra 1 after Jousting Armadillos.  I think we made it through 4 chapters of AOPS Pre-A before throwing in the towel. I don't know if there's a Pre-A for Foerster's, but I think you've covered enough Pre-A concepts from JA and some AOPS pre-A that you can jump into Algebra 1. The first chapter or two will be mostly review of concepts you've seen in JA and the AOPS pre-A. 

[pgr]

8 hours ago, MissLemon said:

We're jumping into Foerster's Algebra 1 after Jousting Armadillos.  I think we made it through 4 chapters of AOPS Pre-A before throwing in the towel. I don't know if there's a Pre-A for Foerster's, but I think you've covered enough Pre-A concepts from JA and some AOPS pre-A that you can jump into Algebra 1. The first chapter or two will be mostly review of concepts you've seen in JA and the AOPS pre-A. 

Thank you, that's reassuring! What edition do you have? I don't know how much the edition matters. 

[Not_a_Number]

8 hours ago, MissLemon said:

We're jumping into Foerster's Algebra 1 after Jousting Armadillos.  I think we made it through 4 chapters of AOPS Pre-A before throwing in the towel. I don't know if there's a Pre-A for Foerster's, but I think you've covered enough Pre-A concepts from JA and some AOPS pre-A that you can jump into Algebra 1. The first chapter or two will be mostly review of concepts you've seen in JA and the AOPS pre-A. 

What made you finally give up on AoPS?

[Noreen Claire]

On 8/3/2021 at 8:07 PM, wendyroo said:

Then we took a detour for 6 months. He did James Tanton's Great Courses series, The Power of Mathematical Visualization, which he LOVED. There are problem sets in the Guidebook, so it kept him busy for a while. He loved James Tanton so much, that we then went straight into his Geometry course... *snip*

Thanks for these recommendations!

Edited August 9, 2021 by Noreen Claire

[Shoeless]

5 hours ago, pgr said:

Thank you, that's reassuring! What edition do you have? I don't know how much the edition matters. 

I have the Classic edition. 

 

5 hours ago, Not_a_Number said:

What made you finally give up on AoPS?

It was very dense to work through, and felt like it was difficult for the sake of being difficult. There were a lot of times we thought "why are we doing this?!" Also what wendyroo said about it being a bunch of hard problems with slick answers that you either get or you don't. Sometimes I would read the solution and still not understand how they arrived at the answer. 

We may come back to it one day to explore. Kiddo had completed an entire "normal" 3rd grade program before we started BA and that worked like a charm. Maybe we will do something like that. 

[Not_a_Number]

18 minutes ago, MissLemon said:

It was very dense to work through, and felt like it was difficult for the sake of being difficult. There were a lot of times we thought "why are we doing this?!" Also what wendyroo said about it being a bunch of hard problems with slick answers that you either get or you don't. Sometimes I would read the solution and still not understand how they arrived at the answer. 

We may come back to it one day to explore. Kiddo had completed an entire "normal" 3rd grade program before we started BA and that worked like a charm. Maybe we will do something like that. 

Honestly, I think the problems are the best things about those books, not the pedagogy. That means it's best to do them after you already have a decent level of mastery of the content... 

I'm currently still pulling a LOT of problems out of the Intro to Algebra book (and occasionally from Pre-Algebra.) They are fun problems! I just wouldn't teach them the way they were taught in there... 

Edited August 9, 2021 by Not_a_Number

[Shoeless]

1 hour ago, Not_a_Number said:

Honestly, I think the problems are the best things about those books, not the pedagogy. That means it's best to do them after you already have a decent level of mastery of the content... 

I'm currently still pulling a LOT of problems out of the Intro to Algebra book (and occasionally from Pre-Algebra.) They are fun problems! I just wouldn't teach them the way they were taught in there... 

That is what I had in mind: work some problems after he's acquired enough mastery. He is definitely motivated to work the material! 

[Clemsondana]

3 hours ago, Not_a_Number said:

Honestly, I think the problems are the best things about those books, not the pedagogy. That means it's best to do them after you already have a decent level of mastery of the content... 

I'm currently still pulling a LOT of problems out of the Intro to Algebra book (and occasionally from Pre-Algebra.) They are fun problems! I just wouldn't teach them the way they were taught in there... 

I think that's why my kid did fine once we started doing Life of Fred concurrently.  I don't think it's the magic of LOF, although the fact that it's short is what makes it possible to do both programs in a reasonable amount of time.  But, having had some introduction to a concept, kid didn't feel like they just had to stare blankly at problems until they figured it out.  

But, I'm not a huge fan of discovery for complicated concepts.  Maybe it's from my teaching of biology, but...they gave Watson and Crick a Nobel for figuring out the structure of DNA, so it seems unlikely that vast swaths of high school students will discover it on their own.  I don't know that bioogy is unique in that...  🙂