Anonymous wrote:It's true thay AOPS Intermediate Algebra has a lot of more abstract math (like factoring and solving polynomials, conic sections, and functional equations), that isn't relevant to the STE part of STEM.

If you aren't focused on math for math's sake, you can skip a lot of the AOPS material and problems, and stick with Khan and Brilliant type stuff which focuses more on the math for engineering and technology.

Polynomials are not relevant in science and engineering?? I beg to differ.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:FCPS has been releasing less information about the level of math of incoming students over time, not sure how FCAG got the numbers for classes of 2020 and 2021, maybe FOIA?

But yeah, there were less-and-less kids admitted with only Algebra 1 in 8th with that downward trend as far back as 2005 at least (when class of 2009 was applying) along with a significant increase in the proportion of kids who are post-Geometry in 8th. I'm not sure how much of this is due to changes in FCPS policies/instruction that enabled kids to reach higher math sooner vs. a shift in culture of parents enabling their kids moving forward in math faster through outside enrichment or summer studies (not taking a position on whether the latter is a good or bad thing, but seems FCPS is attempting to discourage so much emphasis on such practices by not tying that advancement so closely to TJ admission chances).

TJ Admitted students who took Algebra 1 in 8th
----
Class of 2008: 61%
Class of 2009: 56%
Class of 2010: 43%
Class of 2011: 41%
Class of 2012: 26%
Class of 2013: 17%
Class of 2014: 21%
Class of 2015: 14%
Class of 2016: --%
Class of 2017: --%
Class of 2018: --%
Class of 2019: --%
Class of 2020: 07%
Class of 2021: 04%
Class of 2022: --%
Class of 2023: --%
Class of 2024: --%
Class of 2025: --%
Class of 2026: --%
Class of 2027: --%

TJ Admitted students who took math beyond Geometry in 8th
----
Class of 2008: 06%
Class of 2009: 07%
Class of 2010: 08%
Class of 2011: 06%
Class of 2012: 07%
Class of 2013: 09%
Class of 2014: 10%
Class of 2015: 14%
Class of 2016: --%
Class of 2017: --%
Class of 2018: --%
Class of 2019: --%
Class of 2020: 29%
Class of 2021: 35%
Class of 2022: --%
Class of 2023: --%
Class of 2024: --%
Class of 2025: --%
Class of 2026: --%
Class of 2027: --%

I think that dramatic shift toward very far acceleration in ways mainly achievable outside of school or only in a handful of MSs speaks to why the test was scrapped and new process created. I think it’s good that kids can follow the options available throughout FCPS and still qualify.

Agreed. You shouldn’t have to have outside enrichment to succeed at TJ. I do think a good number of kids at TJ have some type of outside enrichment. My kid is interested in STEM so he participates in STEM extra curriculars, camps, and math enrichment. He also does rec sports and other activities. He has friends in the math enrichment who are there because their parents don’t think that they are learning enough at school, his friends don’t like it but they don’t have a choice.

Do we have an idea about how many kids with Algebra 1 attended TJ the past two years?

But that's exactly the point, one shouldn't have to enrich if everything worked well and actual math was taught in school. There's no easy fix to that other without major changes to the system, and as a result there is no easy fix for parents with money who perceive that their child does not learn and therefore can't compete with others. This is the exact thing with many other things in this area. Consider travel sports, or music. Music in particular is really bad; very few kids can effectively learn an instrument without private lessons. Why is that? Because the schools are barely able to teach them in band or strings class at school. They could do it, but not without more resources, money, and additional music classes each week.

Anonymous wrote:

Anonymous wrote:OP with an update:

DS took the AMC 8 as a 6th grader. He scored 17-19 on three practice tests. He scored an 18 on this years test, so he made the honor roll.

He enjoyed the practice tests and is already eyeing the AMC 10 for next year.

Why? He has so much room to grow in AMC 8 and he's eligible for another 2 years.

A couple of reasons: Doing very well on the AMC 10 (or the AMC 12) leads to a path to the Olympiad (via the AIME, USA(J)MO, MOSP, etc). The AMC 8 does not have anything after it. Alternatively, (and more importantly) practicing AMC 10 problems would allow him to extend his range on the AMC 8 (i.e have a better shot at solving the most difficult AMC 8 problems, #20-25), as well as improve on other contests such as Mathcounts, etc.

Anonymous wrote:OP. We have been doing AOPS's Contest Math for Middle School (small paperback) after the intro series. It was a good book to practice, but DC is sick of it (we repeated the missed questions up to 4 times). Then, I randomly purchased from Amazon Learn or Review Trigonometry Essential Skills, but it is too easy.

DC is not math genius, and we are not that interested in pushing for the contest math direction. DC recently took AMC8 at school though.

I looked at the AOPS's Intermediate Algebra book, and it seems too difficult/unnecessary. Alcumus is recommended, and we will do, but I am looking for a next book to work on.

Is AOPS's precalculus book a bad idea (wondering this book may be easier than Intermediate Algebra?), or do you recommend just repeat Intro to Algebra book for a second round?

While starting to learn the beginning of AoPS Precalc would not be a bad idea, I would personally not recommend it until they have a very good grasp of algebra. Despite its smaller size, the precalc book has more difficult material than Intermediate algebra (for the most part). The book is very different from a typical K12 precalculus book. It essentially teaches three topics in great depth, connecting them all together: 1) Trigonometry in the first third of the book, 2) Complex Numbers in the second part of the book, and 3) Fundamentals of Linear algebra (vectors, matrices in both 2D and 3D) as well as a final chapter on solving tough geometry problems using vectors and other tools learned in the book. Some of the problems (not all) can be very difficult, and a few have appeared in past high school Olympiads such as the USAMO, etc.

I think the most important principle is that your DC should enjoy math (CMMS is a lovely little book, but I don't think it was a great idea to have made them repeat problems they missed 4 times, as that is not a recipe for enjoyment...) One way to do that is to solve lots of interesting problems at an untimed and relaxed pace. A few ways that could be done is by perusing the AoPS site and cherry picking problems that look interesting to them (i.e from the past AMC 8 or even AMC 10 questions) or perhaps via playing Alcumus (which itself contains a very large collection of problems, many from past contests).

Earlier in this thread I have recommended for you Anna Burago's Mathematical Circle Diaries. If your DC finished the Intro series, Year 2 (the second book in the two book series) would be more appropriate. It contains many interesting problems organized by various topics, that are excellently curated, similar to AoPS. It introduces students to some difficult ideas that most don't see until a discrete math course in college (i.e Pigeonhole Principle, Invariants, Parity, Combinatorics, Graph Theory, etc) via approachable problems aimed at advanced middle schoolers. Some of these topics are really very lovely, but sadly AoPS did not include them in their books (other than perhaps in their Intermediate Counting and Probability book, which is an amazing but challenging book, on par with their Precalculus or Calculus book).

Lots of misinformation in this thread:

- There is only one precalculus class from the college board, it's called 'AP precalculus', (not 'AP Precalculus AB' or 'AP Precalculus BC').
- It is not necessary to learn any calculus topics such as limits, prior to taking a calculus class (calc AB or BC).
- I haven't seen evidence to the claim that Calculus BC covers 50% more topics than Calculus AB.

The traditional advice is still valid:

1) Students should have a strong understanding of algebra, functions, and trigonometry (as equivalent to what is taught in an honors precalculus course) to be prepared for Calculus BC. It is not necessary to learn any calculus topics, as Calculus BC covers calculus from the beginning.

2) Students who do not feel comfortable with the faster pace of Calculus BC, or who do not feel they have a strong understanding of the fundamentals (algebra, functions, and trigonometry), would be better off taking Calculus AB.

Regarding the recent trend of taking two years of calculus, i.e Calc AB followed by Calc BC, it is unnecessary for most students, mainly because much of Calculus BC is a repeat of AB. If this trend is popular now, it is likely because more students are unprepared for a calculus class but are accelerated enough in their math course sequence that they have the time to take both in two years while not having any other suitable math choices in the second (senior) year.

Another contributing factor is that Calculus AB is no longer perceived as competitive for STEM majors, which puts pressure on students to take BC, if they can. I don't think this is absolutely necessary for most colleges, but I can see the logic of it in today's more competitive environment with regards to top colleges.

It's unfortunately the norm these days, OP.

The below eye opening read describes the sad reality of how mathematics is typically taught (or rather not taught) in K12, and it does so very eloquently. It should be required reading for anyone interested in their child's education. There's a also a short section about geometry that is spot on:

https://maa.org/sites/default/files/pdf/devlin/LockhartsLament.pdf

For those interested, the full book is on Amazon.

https://www.amazon.com/Mathematicians-Lament-School-Fascinating-Imaginative/dp/1934137170

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Do they take Calc BC in 11th grade in order for it to show up on the college application? I don't think getting an A in senior year mattered?

Many take it the 2nd year. Or, maybe TJ students did this before the admissions standards were lowered.

I thought AP Calculus AB/BC needs Algebra 1/2/Geometry and Precalculus, that's 4 years of math starting at 7th. How could anyone get AP Calc at 10th grade?

One way is to test out of a class, or take a version of it during the summer. This seems to be common with geometry.

Anonymous wrote:

pettifogger wrote:

Anonymous wrote:What about for those who are not necessarily into math competition? My DC is in first grade has been doing BA online and with books and enjoys it a lot. I thought maybe could do a summer camp but concerned it might turn DC off if it's too competition focused and not as fun as the online version (he loves the comics of course). I just want to nurture curiosity and love of math and not necessarily competitiveness. RSM might be too boring?

Many BA questions tend to be very similar to questions from typical elementary math contests such as MOEMS, etc. So if he enjoyed Beast a lot, then by extension he enjoyed many math contest like problems. The common theme is that both are a source of thought provoking and interesting questions.

Working through math competition problems doesn't necessarily have to mean competing live in timed contests with others. He can work on past math contest problems at his own pace at home without competing against anyone. All the AMC 8 past contests are freely available on the AoPS site. Just treat math competition questions like any other math problems, but with the additional benefit that they are typically more creative and challenging which will end up stimulating his curiosity and teaching him many interesting things.

Thanks. I know the founder was also a math competition afficionado. But we have no experience with that. It might be that DC will want to participate in it and that's fine but we like BA because of what he learns, not to prep for competitions. Was just wondering if that makes us weird among BA parents.

Not at all weird. The BA curriculum is extremely well done for the purpose of teaching authentic mathematics in an inspiring way to develop critical problem solving and thinking skills. While it's true that those who learn it thoroughly would get a leg up in math contests, that's just icing on the cake and purely optional. The main event is the wonderful mathematical content developed to engage and challenge kids.

Back in the late 90s, before BA was conceived, and before the main AoPS curriculum books were created, RR wrote the first two original Aops books (Volume 1 and Volume 2) which do indeed focus on math contest material (they are relatively small and sparse, introducing mainly content aimed at students who had some initial experience with contests). While these books are still great, they are a far cry in terms of teachable content from the subsequent AoPS core curriculum books, and the BA books that came after them (which supposedly were developed to supposedly ease the difficult transition that students had to make when diving into their first AoPS book, such as Prealgebra, etc).

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Welcome to the real world. You have to be able to work with other people, and in some cases drag up stragglers, and you’re evaluated on the basis of whether or not your team gets the job done.

If that’s uncomfortable for you or your child, gainful employment may not be their (or your) best option.

a school environment of peers of entirely different than a work environment. And if it's standard then yes she'll have to suck up doing most of the work when she gets dud partners and get used to it I guess. But it felt like way more of these (or maybe just more bad luck on partners) this year vs last which is why i asked.
- OP

PP. Sure, it's different, but it's a decent analog for what they'll experience later in life. When you get right down to it, most of life (including work, parenting, being part of a family) is graded group work. Life isn't fair, and one of the best things you can do for your kid is to help them understand this and help them move beyond the anxiety that unfairness creates if it's out of their control. This is coming from decades of TJ experience, btw.

I’m not aiming to reinforce anxiety and sure you have to work together as adults but the school dynamics are really different from how team projects operate at work. There is much more accountability and recourse in the latter if someone isn’t doing the part they were assigned.

It’s been 3 major projects now in just the last few months where DC has ended up doing an outsized amount of the work.

Useful reality check that this amount of group projects is normal. It still strikes me as a really high amount but if it is what’s been going on for years and just is the norm then yes they’ll just need to suck it up.

But I’m biased because I hated group projects too as a kid.

- OP

Isn't the simple solution here for her to chat with her teacher about it? A good teacher would normally ask each individual in the group to write out which portions of the projects they were responsible for/worked on. As long as she shows that she did the bulk of the work, the teacher should then find a solution for her for the next project (either via extra credit, or assigning her partners who do pull their weight).

Anonymous wrote:What about for those who are not necessarily into math competition? My DC is in first grade has been doing BA online and with books and enjoys it a lot. I thought maybe could do a summer camp but concerned it might turn DC off if it's too competition focused and not as fun as the online version (he loves the comics of course). I just want to nurture curiosity and love of math and not necessarily competitiveness. RSM might be too boring?

Many BA questions tend to be very similar to questions from typical elementary math contests such as MOEMS, etc. So if he enjoyed Beast a lot, then by extension he enjoyed many math contest like problems. The common theme is that both are a source of thought provoking and interesting questions.

Working through math competition problems doesn't necessarily have to mean competing live in timed contests with others. He can work on past math contest problems at his own pace at home without competing against anyone. All the AMC 8 past contests are freely available on the AoPS site. Just treat math competition questions like any other math problems, but with the additional benefit that they are typically more creative and challenging which will end up stimulating his curiosity and teaching him many interesting things.

Anonymous wrote:

pettifogger wrote:

Anonymous wrote:

pettifogger wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:https://www.baconsrebellion.com/wp/tj-math-students-note-lowering-of-standards/

The teachers said that the average score for their final exam for TJ Math 4 — equivalent to trigonometry — was “in the low 70s with a substantial minority scoring below 50%,” calling the results “the lowest scores we’ve ever seen,” even amid a “lowering of standards” at the school for the course.

"The students in the spring semester course of Math 4, which the email is about, include Class of 2024 students, the last class admitted through the merit-based admissions tests that the school board eliminated in December 2020, and students from the Class of 2025, admitted through the new race-based admissions process."

Asra pushing BS, as usual.

Sure focus on the messenger, to distract from the message. Asra Nomani, author's intro says she is an asian american TJ parent. Racists like you target anyone asian american.

The TJ Math teacher is stating that standards have been lowered:

"The math teachers noted that the final exam was “substantially easier” than final exams given to previous classes. The teachers said the students had “unprecedented supports provided to you this semester, including extra practice quizzes, bonus quizzes, practice worksheets, and a practice final exam, all things that were not given to previous students.”

The teachers continued:

We expected to see scores rise, not drop, with our lowering of standards."

The math test got eliminated from admissions. They don't know the middle-school readiness of the kids being admitted, and TJ Math teachers are left to deal with the problem.

And it sounds like the TJ Math Teachers are not the best. The posts here and in other places make it sound like the math Teachers assume the kids are strong at math and require the students to teach themselves. That is the impression I have been left with. The kids are not given much in the way of in class explanation, they are given resources that they can look at one their own, and are left to ask questions if they can’t figure it out.

If that is the case, then it would work well for kids whose parents have been sending their kids to RSM or AoPS and who have been participating in math competitions and are quick to pick up material or are in supplemental classes that explain the material for them. That would be the same group of parents who could afford prep classes for the old Quant test as well as parents like me who have been sending their kid for outside math because in school math is slow. It would not work for kids who come from families who didn’t/don’t know about those resources and can’t afford those resources.

It could be that the math department needs to start teaching math with an understanding that 25% of their population is coming in totally unprepped (no RSM, AoPS, Math Counts at MS) and that they need to help firm up abilities.

So if you think that teachers are not teaching, what do you imagine teachers and students are instead doing during class?

DP. The math teaching at TJ has, more than once, been most charitably described as a flipped classroom - and less charitably described as destroying any love or like of math in students.

It gives me pause. My DC is an 8th grader and interested in science more than math, but the two go hand-in-hand.

Flipped classroom is an interesting model. It can work well provided kids do a bit of legwork ahead of time. Usually this means doing the reading (which for math would equate to trying some problems on their own at home), then coming to class to discuss various approaches/ideas. I believe this is not uncommon at some high schools. Phillips Exeter has a few videos posted on their YouTube channel showing this in action, i.e students show problems on the board while the teacher sits back and mostly let's them discuss their approaches with occasional guidance thrown in. One thing to note is that PE classes are tiny (less than 10-15 students) so this specific implementation would not scale well. With large classes it would have to be done differently, i.e students discuss in 6-8 person groups at a table and the teacher rotates through groups. For problems that the groups are struggling with, the teacher can then lecture to the entire class on the board. Alternatively, a mix of lecture and flipped classroom model would work well too with larger classes (i.e one period teacher does a traditional lecture with examples, and another period students are working on application problems in groups).

As for your comment about destroying any love for math, I'm failing to see how that could be a widespread thing at TJ. Harshly timed tests? Problems that are more difficult on average than the homeworks?

How can teacher practically teach or reteach pre-calculus concepts when the kids admitted don't have the prerequisite algebra background that they should have learnt in middle school? The math test, which is primary mechanism to screen kids' proficiency of middle school math has been gutted in the name of equity.

Logically, incoming freshmen with gaps in algebra wouldn't be starting with precalculus. They would take a placement test and start with something like geometry and hopefully would also be given periodic assignments that expose algebra and other math gaps and compel them to work hard to fill them.

Due to the wide gap in middle school math programs, not all incoming students may be equally prepared. But that doesn't mean that motivated students cannot work hard to catch up their first year.

Anonymous wrote:

pettifogger wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:https://www.baconsrebellion.com/wp/tj-math-students-note-lowering-of-standards/

The teachers said that the average score for their final exam for TJ Math 4 — equivalent to trigonometry — was “in the low 70s with a substantial minority scoring below 50%,” calling the results “the lowest scores we’ve ever seen,” even amid a “lowering of standards” at the school for the course.

"The students in the spring semester course of Math 4, which the email is about, include Class of 2024 students, the last class admitted through the merit-based admissions tests that the school board eliminated in December 2020, and students from the Class of 2025, admitted through the new race-based admissions process."

Asra pushing BS, as usual.

Sure focus on the messenger, to distract from the message. Asra Nomani, author's intro says she is an asian american TJ parent. Racists like you target anyone asian american.

The TJ Math teacher is stating that standards have been lowered:

"The math teachers noted that the final exam was “substantially easier” than final exams given to previous classes. The teachers said the students had “unprecedented supports provided to you this semester, including extra practice quizzes, bonus quizzes, practice worksheets, and a practice final exam, all things that were not given to previous students.”

The teachers continued:

We expected to see scores rise, not drop, with our lowering of standards."

The math test got eliminated from admissions. They don't know the middle-school readiness of the kids being admitted, and TJ Math teachers are left to deal with the problem.

And it sounds like the TJ Math Teachers are not the best. The posts here and in other places make it sound like the math Teachers assume the kids are strong at math and require the students to teach themselves. That is the impression I have been left with. The kids are not given much in the way of in class explanation, they are given resources that they can look at one their own, and are left to ask questions if they can’t figure it out.

If that is the case, then it would work well for kids whose parents have been sending their kids to RSM or AoPS and who have been participating in math competitions and are quick to pick up material or are in supplemental classes that explain the material for them. That would be the same group of parents who could afford prep classes for the old Quant test as well as parents like me who have been sending their kid for outside math because in school math is slow. It would not work for kids who come from families who didn’t/don’t know about those resources and can’t afford those resources.

It could be that the math department needs to start teaching math with an understanding that 25% of their population is coming in totally unprepped (no RSM, AoPS, Math Counts at MS) and that they need to help firm up abilities.

So if you think that teachers are not teaching, what do you imagine teachers and students are instead doing during class?

DP. The math teaching at TJ has, more than once, been most charitably described as a flipped classroom - and less charitably described as destroying any love or like of math in students.

It gives me pause. My DC is an 8th grader and interested in science more than math, but the two go hand-in-hand.

Flipped classroom is an interesting model. It can work well provided kids do a bit of legwork ahead of time. Usually this means doing the reading (which for math would equate to trying some problems on their own at home), then coming to class to discuss various approaches/ideas. I believe this is not uncommon at some high schools. Phillips Exeter has a few videos posted on their YouTube channel showing this in action, i.e students show problems on the board while the teacher sits back and mostly let's them discuss their approaches with occasional guidance thrown in. One thing to note is that PE classes are tiny (less than 10-15 students) so this specific implementation would not scale well. With large classes it would have to be done differently, i.e students discuss in 6-8 person groups at a table and the teacher rotates through groups. For problems that the groups are struggling with, the teacher can then lecture to the entire class on the board. Alternatively, a mix of lecture and flipped classroom model would work well too with larger classes (i.e one period teacher does a traditional lecture with examples, and another period students are working on application problems in groups).

As for your comment about destroying any love for math, I'm failing to see how that could be a widespread thing at TJ. Harshly timed tests? Problems that are more difficult on average than the homeworks?

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:https://www.baconsrebellion.com/wp/tj-math-students-note-lowering-of-standards/

The teachers said that the average score for their final exam for TJ Math 4 — equivalent to trigonometry — was “in the low 70s with a substantial minority scoring below 50%,” calling the results “the lowest scores we’ve ever seen,” even amid a “lowering of standards” at the school for the course.

"The students in the spring semester course of Math 4, which the email is about, include Class of 2024 students, the last class admitted through the merit-based admissions tests that the school board eliminated in December 2020, and students from the Class of 2025, admitted through the new race-based admissions process."

Asra pushing BS, as usual.

Sure focus on the messenger, to distract from the message. Asra Nomani, author's intro says she is an asian american TJ parent. Racists like you target anyone asian american.

The TJ Math teacher is stating that standards have been lowered:

"The math teachers noted that the final exam was “substantially easier” than final exams given to previous classes. The teachers said the students had “unprecedented supports provided to you this semester, including extra practice quizzes, bonus quizzes, practice worksheets, and a practice final exam, all things that were not given to previous students.”

The teachers continued:

We expected to see scores rise, not drop, with our lowering of standards."

The math test got eliminated from admissions. They don't know the middle-school readiness of the kids being admitted, and TJ Math teachers are left to deal with the problem.

And it sounds like the TJ Math Teachers are not the best. The posts here and in other places make it sound like the math Teachers assume the kids are strong at math and require the students to teach themselves. That is the impression I have been left with. The kids are not given much in the way of in class explanation, they are given resources that they can look at one their own, and are left to ask questions if they can’t figure it out.

If that is the case, then it would work well for kids whose parents have been sending their kids to RSM or AoPS and who have been participating in math competitions and are quick to pick up material or are in supplemental classes that explain the material for them. That would be the same group of parents who could afford prep classes for the old Quant test as well as parents like me who have been sending their kid for outside math because in school math is slow. It would not work for kids who come from families who didn’t/don’t know about those resources and can’t afford those resources.

It could be that the math department needs to start teaching math with an understanding that 25% of their population is coming in totally unprepped (no RSM, AoPS, Math Counts at MS) and that they need to help firm up abilities.

So if you think that teachers are not teaching, what do you imagine teachers and students are instead doing during class?

Anonymous wrote:Also, one more q, will BA give new problems if you redo a lesson or is it the same probs? Not that it makes a huge difference as I doubt my son would remember the old answers but would be nice to do more practice in lieu of receiving the books. (I guess that's how they get you to buy the books.)

Not fully sure, but you can experiment by clicking redo and see if it changes the problems, or the order, or both. If you're also thinking of buying books, note that the guidebooks are exactly the same as the digital version so you would only need to get the workbooks (practice books). Also I strongly recommend you join the two facebook groups I posted earlier in this thread, any kind of specific question down to specific problems are asked and you will get a lot of feedback on everything BA/AoPS related. Also note that the challenging/enrichment topics are in the "upstairs" section in the online version, I believe those correspond to some of the problem sections in the workbooks.

Anonymous wrote:

Anonymous wrote:

pettifogger wrote:

Anonymous wrote:Is BA a complete curriculum or supplement? Could it be used in conjunction with Khan Academy or Kumon worksheets as a complete curriculum? DC is home schooled for the time being and just wondering how thorough BA is.

It's a full curriculum and it's pretty thorough, particularly with regard to problem solving, making lots of conceptual connections, and many challenging problems. While it does of course contain basic exercises at the beginning of each chapter/topic, some parents find that their kids needed a bit more practice on the drill type questions. For that, anything such as Kumon/random worksheets can be used.

It's important to guide/support the child, especially initially when they are not used to the feeling of being stuck and want to quickly give up if they can't think of anything in a minute. Ideally work some of the problems together with them, and read the provided hints/solutions as they're very helpful. Some parents do the problems themselves ahead of time so that they can explain/help their kids effectively when they do get stuck Initially it's a big step for kids (and some adults) to switch away from thinking in a very procedural fashion, but once they get used to it, it's very much worth it for the critical thinking skills.

Thanks! I have noticed this already as we work through BA2 and am working on balancing providing support and encouraging persistence. Are the practice books useful for the extra practice over and above the online material or are you talking about a different kind of practice like memorizing basic facts and procedures? Does BA teach all the basic procedures or concepts the child would encounter on Kumon worksheets and elsewhere?

It sounds like your child would be better in a program like RSM where they teach the math concepts and dive more deeply into those concepts. AoPS and BA are solid options for kids who already understand the fundamentals or grasp the fundamental skills quickly and easily.If your kid is not one of those kids then you need a parent who can explain the fundamentals and provide extra drill questions/support. The AoPS in-person/online classes use the BA books in the classroom environment but there is a Teacher to walk the kids through the books. We noticed that the Teacher needed to have some kids stay online after class to review material with them pretty much every week. It isn’t an easy program. I think people on this forum think that BA is challenging but doable for everyone because they have kids that grasp math concepts quickly but those kids are the rarity. They also have/are parents who can guide their kids through the BA books but, again, those people are the rarity.

RSM works well for a kid who needs some level of support, that is what the first level of class is for, as well as kids who can grasp the material quickly and want to dive deeper. There are more RSM store fronts then AoPS for a reason, more kids can succeed at RSM then in AoPS because of how the courses are designed. RSM has the math competition classes that they offer for the kids who want to delve into more creative math problems.

Both programs are great, we have used both and ended up with RSM simply because it was a lot closer and saves us an hour of drive time. But they are not inter changeable. AoPS is more niche. If I was was looking for a program for a homeschool kid, I would probably look at RSM because it offers a more traditional approach that moves quickly and cna go deep.

My quibble with RSM was that they have not published any books or material that I can just buy and evaluate. AoPS has all the books published and I can buy them from their website and evaluate their scope and depth by working through samples of it. Anecdotally, I saw a few RSM worksheet like samples from a friend in a different state and they did not look challenging. So outside of their math contest preparation class, I'm unsure as to what and how they are learning since there is no way to access anything without enrolling in a class.