After AOPS intro books

[Anonymous]

Anonymous wrote:

Anonymous wrote:Did they really finish the books?

Is Alcumus all Blue on Hard level? Mathcounts Trainer a breeze, all 4 levels?

If so, your kid is ready to win USAMTS (at home Olympiad), get a high score on the AMC 10 in October, and qualify for USAJMO.

Anyway, if you want to move up the curriculum, obviously you can move on to the next book in the series, Intermediate Algebra.

I wouldn't describe it as any harder than Mathcounts trainer at the state level. Mostly just takes time and effort.

What is "it"?

[Anonymous]

This is a great time to get into Formal Logic, something that AoPS is strangely deeply allergic to, despite caring a lot about "proofs".

QED: https://teorth.github.io/QED/

Natural Number Game: https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_game/

Intro book by one of the greatest logicians of the past century: https://www.amazon.com/Beginners-Guide-Mathematical-Logic-Mathematics/dp/0486492370

Also other Smullyan books like "What is the name of this book?"

The Moscow Puzzles and then USSR Olympiad Problem Book.

Journey into Mathematics

[Anonymous]

Also, review the books. One problem with working through a book is that the problems are mostly solved using the technique introduced in the past few pages

Or summative mastery, you need to go back and do random problems from the whole book and then series to make sure you are remembering after the current week.

[Anonymous]

http://euclidea.xyz (all the related apps) for constructive geometry.

[Anonymous]

Anonymous wrote:We have been doing AOPs books at home; intro to algebra, intro to number theory, intro to counting and probability, and intro to geometry.
In a few months, we will be done. (We are doing cover to cover, but skip some very difficult Qs).

DC is grade 6. I am wondering if the intermediate AOPS books may be too difficult for DC. Intermediate books are for high schoolers, right? Or, can you handle it if you finish the intro books?

Do you have any suggested book that can be in-between the intro and intermediate AOPs books. It may be good to do easier books for a while, but normal books like Scholastics seem too easy. Any suggestion?

"We are doing cover to cover, but skip some very difficult Qs" I think the values of those books are the difficult questions, those questions force the kid to think deep and struggle. If you skip some of them (not sure how many), I do not think you have really finished those books. We are doing those books at home as well and we do not skip any questions, it really takes time to finish one book. I let the kid to do all questions, and we do not give hints unless it is absolutely necessary.

[Anonymous]

OP. This post is full of insightful comments!

I totally agree that if DC goes back to the past chapter/book, DC probably cannot answer immediately. . .
It's been literally years since we started the intro books.

"Do not skip any question" -- We are trying, but in our case, some challenge Qs (one or two per chapter) are impossible to solve even if we look at answers.

We will focus on reinforcing foundation/having fun with the next book, and then think about the next step. We still have 2+ years before finishing middle school, and studying ahead too much is unnecessary.

[Anonymous]

Anonymous wrote:OP. This post is full of insightful comments!

I totally agree that if DC goes back to the past chapter/book, DC probably cannot answer immediately. . .
It's been literally years since we started the intro books.

"Do not skip any question" -- We are trying, but in our case, some challenge Qs (one or two per chapter) are impossible to solve even if we look at answers.

We will focus on reinforcing foundation/having fun with the next book, and then think about the next step. We still have 2+ years before finishing middle school, and studying ahead too much is unnecessary.

This is ok, it's by design. There are a few challenge questions (usually the starred ones at the end) that are very difficult. I would say it's worth at least giving them an attempt, especially if the kid is interested. But as they're generally significantly harder than most of the material in the book as well as the initial challenge questions, it's totally ok to give hints as needed, or skip if realizing they cannot make progress on them. That said, I wouldn't skip all the challenge questions; you should certainly have your child try the first half of the challenge set and hopefully he can do some of them, especially if given the provided hints.

[Anonymous]

Anonymous wrote:

Anonymous wrote:We have been doing AOPs books at home; intro to algebra, intro to number theory, intro to counting and probability, and intro to geometry.
In a few months, we will be done. (We are doing cover to cover, but skip some very difficult Qs).

DC is grade 6. I am wondering if the intermediate AOPS books may be too difficult for DC. Intermediate books are for high schoolers, right? Or, can you handle it if you finish the intro books?

Do you have any suggested book that can be in-between the intro and intermediate AOPs books. It may be good to do easier books for a while, but normal books like Scholastics seem too easy. Any suggestion?

"We are doing cover to cover, but skip some very difficult Qs" I think the values of those books are the difficult questions, those questions force the kid to think deep and struggle. If you skip some of them (not sure how many), I do not think you have really finished those books. We are doing those books at home as well and we do not skip any questions, it really takes time to finish one book. I let the kid to do all questions, and we do not give hints unless it is absolutely necessary.

AoPS book doesn't have non-difficult questions. Starred questions are VERY hard. Especially for young students, it's great to skip them all the first time through and then try them a year or more later.

[Anonymous]

No one is policing your AoPS book usage. You can grab a copy of Intermediate Algebra and let your kid check it out. If it's too difficult, have your kid review sections from the earlier books or work on some alcumus in any areas that they haven't mastered.

[Anonymous]

I recommend going back and reviewing all 4 topics already studied, pushing deeper into the challenge material. Doing AoPS Intermediate Algebra is plenty of deep material for 7th and beyond.

6th grade is a transition year. In K-5 kids have lots of free mental time and can zip through a lot of math quickly. Starting in 6th, they have several other classes with real homework (or fluffy classes but your kid should supplement at home with Khan or YouTube or something to go deeper into Science/Humanities/World Language, and do extra reading and writing.

[Anonymous]

I love AoPS. Their books are great, but once you get to the intermediate level the pacing seems off. They could stand to spend more time on some concepts that they gloss over. Now maybe it's fine if your kid happens to be that statistically rare kid that will do AIME at 13 or spends 6-8 hours a week reading math textbook each week. I don't feel it's sufficient even for very bright students at a higher level.

[Anonymous]

Anonymous wrote:I love AoPS. Their books are great, but once you get to the intermediate level the pacing seems off. They could stand to spend more time on some concepts that they gloss over. Now maybe it's fine if your kid happens to be that statistically rare kid that will do AIME at 13 or spends 6-8 hours a week reading math textbook each week. I don't feel it's sufficient even for very bright students at a higher level.

"statistically rare kid that will do AIME at 13 or spends 6-8 hours a week reading math textbook each week." has always been the target audience, and the program is advertised as such. That said, the age level isn't the key thing, since there is no age gating on the content.

"Doing AIME" means learning intro Algebra, Geometry, Counting, and Number Theory, with a "math IQ" multiplier to be able to solve tricky/hard problems that rely on clever combinations and applications of these basic facts. This is "gifted/talented middle shooler" territory. An 8th grade "math head", who treats math seriously the way another kid treats soccer seriously, can qualify for AIME... or at least could have 10 years ago, when the ever rising difficulty level was substantially lower.

"Passing AIME" is very different matter.


How is the pacing off? You are allowed to progress at your own pace and spend more time practicing any topic.

How is it both insufficient for higher level and also not slow enough for low level?

What do you mean by "higher level"? Do you mean older students (like 16+ and learned calculus?), or higher ability students within a subject like Algebra and Geometry?

[Anonymous]

Anonymous wrote:

Anonymous wrote:I love AoPS. Their books are great, but once you get to the intermediate level the pacing seems off. They could stand to spend more time on some concepts that they gloss over. Now maybe it's fine if your kid happens to be that statistically rare kid that will do AIME at 13 or spends 6-8 hours a week reading math textbook each week. I don't feel it's sufficient even for very bright students at a higher level.

"statistically rare kid that will do AIME at 13 or spends 6-8 hours a week reading math textbook each week." has always been the target audience, and the program is advertised as such. That said, the age level isn't the key thing, since there is no age gating on the content.

"Doing AIME" means learning intro Algebra, Geometry, Counting, and Number Theory, with a "math IQ" multiplier to be able to solve tricky/hard problems that rely on clever combinations and applications of these basic facts. This is "gifted/talented middle shooler" territory. An 8th grade "math head", who treats math seriously the way another kid treats soccer seriously, can qualify for AIME... or at least could have 10 years ago, when the ever rising difficulty level was substantially lower.

"Passing AIME" is very different matter.


How is the pacing off? You are allowed to progress at your own pace and spend more time practicing any topic.

How is it both insufficient for higher level and also not slow enough for low level?

What do you mean by "higher level"? Do you mean older students (like 16+ and learned calculus?), or higher ability students within a subject like Algebra and Geometry?

I mean exactly what I wrote. It's geared to those 13 year olds who will do well on AIME or students who want to study a math text for 6-8 hours per week. They rush through many fundamental concepts in the first 10 chapters.

[Anonymous]

Anonymous wrote:

Anonymous wrote:I love AoPS. Their books are great, but once you get to the intermediate level the pacing seems off. They could stand to spend more time on some concepts that they gloss over. Now maybe it's fine if your kid happens to be that statistically rare kid that will do AIME at 13 or spends 6-8 hours a week reading math textbook each week. I don't feel it's sufficient even for very bright students at a higher level.

"statistically rare kid that will do AIME at 13 or spends 6-8 hours a week reading math textbook each week." has always been the target audience, and the program is advertised as such. That said, the age level isn't the key thing, since there is no age gating on the content.

"Doing AIME" means learning intro Algebra, Geometry, Counting, and Number Theory, with a "math IQ" multiplier to be able to solve tricky/hard problems that rely on clever combinations and applications of these basic facts. This is "gifted/talented middle shooler" territory. An 8th grade "math head", who treats math seriously the way another kid treats soccer seriously, can qualify for AIME... or at least could have 10 years ago, when the ever rising difficulty level was substantially lower.

"Passing AIME" is very different matter.


How is the pacing off? You are allowed to progress at your own pace and spend more time practicing any topic.

How is it both insufficient for higher level and also not slow enough for low level?

What do you mean by "higher level"? Do you mean older students (like 16+ and learned calculus?), or higher ability students within a subject like Algebra and Geometry?

This past year, there were fewer than 200 kids in grades 7 and below that took the AIME. I'm pretty sure that makes them statistically rare.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:I love AoPS. Their books are great, but once you get to the intermediate level the pacing seems off. They could stand to spend more time on some concepts that they gloss over. Now maybe it's fine if your kid happens to be that statistically rare kid that will do AIME at 13 or spends 6-8 hours a week reading math textbook each week. I don't feel it's sufficient even for very bright students at a higher level.

"statistically rare kid that will do AIME at 13 or spends 6-8 hours a week reading math textbook each week." has always been the target audience, and the program is advertised as such. That said, the age level isn't the key thing, since there is no age gating on the content.

"Doing AIME" means learning intro Algebra, Geometry, Counting, and Number Theory, with a "math IQ" multiplier to be able to solve tricky/hard problems that rely on clever combinations and applications of these basic facts. This is "gifted/talented middle shooler" territory. An 8th grade "math head", who treats math seriously the way another kid treats soccer seriously, can qualify for AIME... or at least could have 10 years ago, when the ever rising difficulty level was substantially lower.

"Passing AIME" is very different matter.


How is the pacing off? You are allowed to progress at your own pace and spend more time practicing any topic.

How is it both insufficient for higher level and also not slow enough for low level?

What do you mean by "higher level"? Do you mean older students (like 16+ and learned calculus?), or higher ability students within a subject like Algebra and Geometry?

I mean exactly what I wrote. It's geared to those 13 year olds who will do well on AIME or students who want to study a math text for 6-8 hours per week. They rush through many fundamental concepts in the first 10 chapters.

I don't get it. If you are studying a text "6-8 hours" and that's a long time, then, if anything, it would be a longer book that you are putting more time into getting through, not a shorter rushed book.

But really, how is the length of study related to how many concepts per chapter?