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I am an Art of Problem Solving Drop-out.

• art of problem solving

By Jenn in Mo , September 21, 2010 in High School and Self-Education Board

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We're a mathy family here, so I'm feeling kind of like a failure here, but I closed the book today and said, "Enough." My math-loving son was diligently struggling through hours of math a day and getting nowhere. It took nearly two months to get through two chapters and I know he couldn't pass any review tests. He understands algebra, but this is....different. My husband and I are struggling to understand half of the problems ourselves...and this is our *thing*, ya know?

I haven't heard a negative word about AoPS yet, so it's kind of embarrassing to admit, but I just do not "get" some of these questions. Anyone that gets it feel like helping to clear the mud on this one?

2.38 What number must be in the blank in the expression 3(x+7)-_(2x+9) if the expression is the same for all values of x?

The solution manual says that "if the expression is the same for all values of x, then the x's in 3(x+7) must cancel out with those in _(2x+9).

My question is...WHY must they cancel out? It's a random, unfinished number sentence. What is in the original problem that tells me they must cancel? What am I missing here? Knowing they must cancel, we can work the problem, but I'm not grasping why I should know they cancel each other out. :svengo:

My other question is, what do I do with this book now? Do I take him through NEM and then come back to this or avoid it forever? I've never given up on a program before. I chose it because the other algebra books were too easy. We've ran into hard things in other books before, but stopped and worked through and moved on. Every day I see him patiently ramming his head into the AoPS wall and it's not something I can help him just "work through" this time. Even though I know that, I still hear Frankie Avalon in my head singing AoPS Drop-Out. :blush:

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2.38 What number must be in the blank in the expression 3(x+7)-_(2x+9) if the expression is the same for all values of x?   The solution manual says that "if the expression is the same for all values of x, then the x's in 3(x+7) must cancel out with those in _(2x+9).   My question is...WHY must they cancel out? It's a random, unfinished number sentence. What is in the original problem that tells me they must cancel? What am I missing here? Knowing they must cancel, we can work the problem, but I'm not grasping why I should know they cancel each other out. :svengo:   My other question is, what do I do with this book now? Do I take him through NEM and then come back to this or avoid it forever? I've never given up on a program before. I chose it because the other algebra books were too easy. We've ran into hard things in other books before, but stopped and worked through and moved on. Every day I see him patiently ramming his head into the AoPS wall and it's not something I can help him just "work through" this time. Even though I know that, I still hear Frankie Avalon in my head singing AoPS Drop-Out. :blush:

(Okay LOL on the Frankie Avalon - I love that song!)

But if the value of the expression is the same for all values of x, that means there won't be any x's left when you simplify it. Otherwise the value of the expression would change for each different possible x.

Have you considered the classes? I know it's a lot of money for a maybe (although I think you have three weeks to bail and get a refund) but I find that there are things I should know but can't always blurt out right when DS needs them... and I like the idea of having someone else who is prepared to do it and other kids who can add to the discussion. Even one math jam left me going "wow - this guy rocks"... :) DS is starting two AoPS classes this year, so I'm not really speaking from experience yet, but I know I'd be stuck going "uhhhhhh...." even on things I really should be able to get. It is hard stuff, and not the "I can teach this in my sleep" of other algebra and geometry programs. I've tutored those for years, but AoPS really is quite a bit more.

8filltheheart

Well, I was in a serious minority (a group of 1, me ;) ) on the k8 board when a mom asked about AoPS for a slow, methodical avg student and I said I would not recommend it. Everyone else was saying that they were accessible to all students.

I have a lot of good math students (I had 1 take alg in 5th, 1 in 6th grade, and 3 others in 7th), but I only have 1 child that I would use AoPS with. He is not just good at math; he is passionate about math. He lives and breathes math. He has taken several AoPS classes and they are tough. He spent hours this summer on their alg 3 challenge sets. Thing is........he wants the challenge. That sort assignment literally makes him smile and jump right in.

My other kids do not desire that type of math depth. They used/are using programs like Foerster. I do not think they are being deprived at all. My ds that loves AoPS thinks mathematically and sees the world that way. The others are just good at math. :)

FWIW......I don't think you have anything to be ashamed of. The books are designed for the top 2-3% of all math students (not all students). They just aren't for everyone. (I couldn't teach them if I tried. He either takes their online classes or has a math coach for them. They are wayyyyyyyyyy beyond my abilities and my dh's as well (and he is an engineer! ;) )

ETA: Thought I should share that if I had known about AoPS umpteen yrs ago, I would have wanted my oldest to try them. I do think they stretch mathematical comprehension beyond the norm......basing that on the fact that my 14 yos now talks some strange language that I don't have a clue about what he is saying. All that said, I **know** that the rest of my older kids would say no way. (as a matter of fact my 11th and 6th graders did!! )

Guest Cheryl in SoCal

Well, I was in a serious minority (a group of 1, me ;) ) on the k8 board when a mom asked about AoPS for a slow, methodical avg student and I said I would not recommend it. Everyone else was saying that they were accessible to all students.   I have a lot of good math students (I had 1 take alg in 5th, 1 in 6th grade, and 3 others in 7th), but I only have 1 child that I would use AoPS with. He is not just good at math; he is passionate about math. He lives and breathes math. He has taken several AoPS classes and they are tough. He spent hours this summer on their alg 3 challenge sets. Thing is........he wants the challenge. That sort assignment literally makes him smile and jump right in.   My other kids do not desire that type of math depth. They used/are using programs like Foerster. I do not think they are being deprived at all. My ds that loves AoPS thinks mathematically and sees the world that way. The others are just good at math. :)   FWIW......I don't think you have anything to be ashamed of. The books are designed for the top 2-3% of all math students (not all students). They just aren't for everyone. (I couldn't teach them if I tried. He either takes their online classes or has a math coach for them. They are wayyyyyyyyyy beyond my abilities and my dh's as well (and he is an engineer! ;) )

:iagree:I haven't used it yet but have been looking through the Intro to Counting and Probability and a bit of the Intro to Algebra and from what I have seen I wholeheartedly agree. No math curricula is the answer for every student but IMHO AoPS is going to be a good fit for the minority of students. One of my ds's would DIE if I had him use AoPS and another I think will like it because he thinks that way, though we'll only know after we try it.

I had a look at the algebra and geometry and found the layout visually confusing, which is kind of weird since in some ways it is not as busy or distracting as textbooks in general. But it is packed solid, and hard to read as a text, if that makes any sense. And algebra is my own strength. My dd went for Discovering Algebra instead.

The geometry book struck me similarly as user-unfriendly, but that may be again just my visual reaction to such a dense text.

However, that similar packing did not bother dd with the data and probability books, which she greatly enjoys. So maybe it depends on the kid (and grown-up) as well as on the area of math involved.

(Okay LOL on the Frankie Avalon - I love that song!)   But if the value of the expression is the same for all values of x, that means there won't be any x's left when you simplify it. Otherwise the value of the expression would change for each different possible x.

Ha! Lightbulb! Thank you! Regardless of what x is, the expression will equal the same thing. You're speaking my language. The book is not. :tongue_smilie:

I am relieved to hear these responses. He loves math and enjoys a challenge, but I couldn't at all say that he is passionate about math. I had forgotten that Foerster was on my list of maybes before I heard that AoPS was the crème de la crème of algebra texts. So....NEM or Foerster....thoughts?

I know absolutely nothing about NEM, so I can't offer any insight there. I have used Foerster with all of my older kids, including my ds that now uses AoPS. He used Foerster for both alg 1 and alg 2. His first AoPS courses were Intro to Counting and Prob and their alg 3 courses online and he owns several of their other "off normal track" math books that he works through on his own.

My oldest used Foerster and it more than prepared him for university level cal and an engineering major.

I'm not sure I can explain the differences very easily. Foerster is a solid math program and they absolutely learn the math skills they need to perform high level math problems, etc. No question.

AoPS helps them process math in a completely different fashion. Ds goes around "discovering" concepts and "proving" things like why x equals some bizarre thing or how an indefinite number of fractions add.......I don't know......I just nod my head!!! :lol: He thinks he wants to double major in astrophysics and math. For him it is a match. I have only ever met 2 other people that think that way.......one is now majoring in math and the other has a phD in math. For the rest of mere mortals, I think we are fine w/o it!

In The Great White North

Dc used/are using Foerster. They arde very solid math books. I have the AoPS Problem Solving, Counting & Probability and Number Theory books. Dc don't like them. They are not straight forward. Dc like to have an example, an explanation and get the problems done. Foerster does this for them. AoPS does not.

AoPS is for people who like to PLAY with their math. If your idea of a great time is to go round and round with a math problem til you figure it out, AoPS is for you. Yes, the top 2-3% of math students in the country are more likely to enjoy that, but even they don't always like that.

I've seen but not used Foerster, so I can't compare... but NEM is good challenging work. Most of it is more straightforward than AoPS (examples first, exercises second) but there are Challenge sections and Mathematical Investigations that could be frustrating in the same ways AoPS can be. They do (in those sections) throw you in and expect you to dig yourself out. And to some extent they leave some gaps in the regular explanations too -- nothing huge, but enough that sometimes the student (or the teacher) has to connect the dots.

C_l_e_0..Q_c

I'm in the opposite situation. We're a NEM drop-out. I'm so much happier as a mom with AoPS *and* the online class. Someone else is teaching math to my math kid!

(and I"m good at math too, I did math all the way to a Master's level, although it was not my major - I'm an engineer, we need math )

My son is truly having a blast with the online class. He did Algebra 1 over the summer. The kids at the summer pool who learned he was doing a math class assumed it was remedial, until they saw a problem! LOL. Sweet nerd revenge. :)

The math classes are totally worth the cost. Plus they force the kids to move forward, and not spend 2 months on 2 chapters. In 15 weeks, they did 14 chapters (possibly 13, I'm not sure) so the interest is kept high.

at the beach

I agree that AoPS is for people who enjoy playing around with math. I think I am one of those who said something along the lines that more people can be successful with it than the top few percent. But I think I also said that sometimes the solutions/explanations gloss over things or skip a step, assuming readers will see that step in the problem when they might not. I felt it could be used by more than just the top few percent because I think that kids often underestimate their abilities. I also agree with the pp that even kids in the top few percent who can do it may not want to do it because it does take a lot of time and puzzling.

I was terrified of math from 8th grade on. I never took math in college but took logic to avoid it. When I signed my daughter up for AoPS this summer, I decided to give the book a try. I did the first three chapters. I wanted to help my daughter if she needed it, but she was the one helping me :001_huh: and the class moved so fast that I couldn't keep up.

The problem that you mention, to me, looks like it is asking you to make the 2x the same as the 3x so the only thing that works is 3/2. How do you know it will cancel? I think you know that because it's a subtraction problem. Maybe I am oversimplifying this.

Maura in NY

NEM is an integrated program - Algebra/Geometry/Trig and rolled together. It's challenging, in a good way, but it doesn't fit the typical Algebra/Geometry/Algebra II/Trig-PreCalc/Calc track.

FWIW, my ds used NEM 1 in 7th, thinking he would stick with it for 4 years. Instead, we switched. He didn't use Foerster's Algebra I, but he did use Foerster for Algebra II and PreCalc. Great real world application problems.

We used AoPS for several months and also found some of the problems strangely worded. But, our biggest problem with AoPS was not enough repetition.

We are using Foerester's Algebra now. It has more than enough problems for us, but it's much easier to eliminate problems than try to add more in.

Miss Marple

Not a drop-out yet, but we are doing AoPS very slowly and I've added NEM2 back as the primary math. Ds is still working through the geometry book (45 minutes per day), but we've put the algebra book away because he already did LOF Beginning Algebra and the NEM should cover the bases thoroughly.

I'm finding that hormones cause my son to be less inquisitive and less dedicated right now. He does great with math, so I chose the other program I love - Singapore NEM, and it is going very well.

If we never finish the AoPS books that will be OK because NEM is the primary curriculum (which we will finish). I know that any exposure ds has had with AoPS has helped fine tune his mathematical abilities.

Well, I was in a serious minority (a group of 1, me ) on the k8 board when a mom asked about AoPS for a slow, methodical avg student and I said I would not recommend it

:iagree: I cannot imagine how frustrated a student and a parent would be trying to work through this program and thinking that it is accessible for all students!

The problems in NEM can be plenty challenging at times. My son did NEM 1 before switching to AoPS.

Regarding AoPS Algebra 1, they introduce Algebra 2 concepts, too. That doesn't make it easier! Ds thought the middle of the text was difficult and often trudged through the problems, but then he flew through the last few chapters. He thought they were easier, even many of the challengers. I don't know if they really were, or if he just started to get the hang of the text and problems.

When it comes to math, it's so important to pick what works and then bite off and chew well at a pace that's suitable for the student. I wouldn't hesitate to step back and reconsider if something wasn't working.

  AoPS is for people who like to PLAY with their math. If your idea of a great time is to go round and round with a math problem til you figure it out, AoPS is for you. Yes, the top 2-3% of math students in the country are more likely to enjoy that, but even they don't always like that.

I agree entirely with the bolded.

If anybody is deciding whether to go with the AoPS classes, there's a Math Jam on the subject this afternoon/evening (7:30 Eastern, I believe). It will include sample questions from the class, so you can try them out.

Math Jams are free informational sessions, usually hosted by Richard Rusczyk, who is always responsive to questions. If he can't answer your question within the confines of the session, he'll likely invite you to e-mail him and he'll help you decide whether a class is right for your family.

We're mathy. . . and we're AoPS drop outs as well.

Dd & I tried Number Theory for a couple/few months. It actually went OK so long as *I* worked through *every section* and *every problem* on my own before dd tried it (or simultaneously sitting together).

The exploration and problem solving was interesting. I rather enjoyed it. But, I just *don't have time* to do it right now.

We dropped it after a few chapters -- which were successful but slow b/c I just couldn't make myself find the time to do it often enough to keep up w/ dd's needed pace.

So sad. . .

Now y'all are scaring me. My dd loved the AoPS Number Theory book so much this summer, I bought Alg I for her (but we don't start for another year...) I had been planning on Foerster's, so I've got both ready to go (well, I still need that pesky Foerster's Solutions manual...)

We're mathy. . . and we're AoPS drop outs as well.   Dd & I tried Number Theory for a couple/few months. It actually went OK so long as *I* worked through *every section* and *every problem* on my own before dd tried it (or simultaneously sitting together).

Dd and I worked through all the examples together, but then she did the problem sets pretty much on her own (except I let her skip the challenge problems at the end of the chapters). Was your dd just needing you to sit with her for the "lesson" part, or also the problem sets? I didn't mind working through the lesson with her... I actually learned a lot myself and had fun... :tongue_smilie: For some reason I really like the layout and presentation of these books... OTOH the Lial's layout really drove me crazy when I first saw it (I'm getting used to it now that my other dd's working through BCM).

But now you guys are intimidating me a bit... :001_huh: I do think the Algebra text looks more challenging than the Number Theory, but I'm hoping after she's gotten through Singapore DM1, she'll be preparerd (or I guess we'll do Foerster's after all...)

I found the solutions manual for Foerster this afternoon! I finally called the publisher and it turns out that they renamed the book and it is now called Classic Edition instead of Foerster's. The ISBN # is 0201861003. I can't find it used anywhere, but it is available new at pearsonschool.com.

I'm still torn though. I loved Singapore so well and would like to try going on with NEM. But I don't want to commit to it being his math for all of high school. I hear that Foerster does an excellent job with proofs, which I think are important. I may end of tossing a coin before this is over.

This is exactly what I was trying to express in the other thread! It's just as much about the approach as the difficulty, imo. Yes, you need to be a good math student, but I dont' think you need to be a TOP math student. Not in the sense of the top 2% to 3%, at any rate. I can't imagine my dd would score anywhere near that high, but she loves AoPS.

And you can be a top math student, but if you hate this approach, it will be very hard to persevere and succeed.

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Art of Problem Solving Math Books Review

What is art of problem solving.

Founded in 1993 by former USA Math Olympiad winner Richard Rusczyk, Art of Problem Solving (AoPS) is a company that produces rigorous math instruction courses and products that can help outstanding math students develop a more thorough understanding of math concepts, as well as help prepare them for success in math competitions. 

From textbooks to online classes to physical learning centers, AoPS offers a variety of educational products and services that can help challenge kids, deepening their knowledge and strengthening their mathematical thinking.

AoPS Math textbooks

Art of Problem Solving has created a series of textbooks for middle and high school math textbooks that are designed to give outstanding math students a deeper and more rigorous curriculum in math. 

Originally designed to help talented math students prepare for competitions, over the years AoPS’s textbook line has expanded to offer full curriculums in middle and high school math courses, and their problem-based and rigorous approach to math has made them very popular with parents across the world as a top enrichment option. 

What Grades and Math Subjects does AoPS Math cover?

Art of Problem Solving textbooks cover middle and high school math, as well as competition prep.  

Generally speaking, the AoPS math textbooks can be broken down into two curricula- introductory and advanced – that roughly correspond to most middle and high school math programs (in terms of overall scope, that is). 

Parents of younger math enthusiasts should note that Art of Problem Solving covers elementary school math (Grades 1-6) in their Beast Academy series, which you can read about in our review .

Introductory Curriculum (Middle School)

Advanced curriculum (high school) .

When taken as a whole, Art of Problem Solving’s math textbooks cover the topics included in most US Math curricula, as well as touching on a few topics that aren’t usually covered in most public high school programs. 

That said, the point isn’t really to get kids learning college level math or a curriculum beyond high school math, but instead to get students to develop their problem solving skills and develop more creative and flexible mathematical thinking, to get them to recognize and appreciate different approaches to problem solving, as well as getting a better understanding of the why of math, rather than just focusing on how to compute problems. 

As such, AoPS’s curricula tend to go deeper into your typical middle and high school math topics, letting kids examine concepts more rigorously, more thoroughly and with more challenging problems than they would otherwise be able to do in other math courses. 

Art of Problem Solving Contest Prep

In addition to their more academically-focused textbooks, Art of Problem Solving also offers a variety of books designed to further enrich exceptional students or help with preparing for math contests and Olympiads.

These books generally tend to work on developing stronger problem solving skills, going far deeper into various concepts and exploring far more challenging questions and problems, while introducing various approaches for understanding and solving them quickly and effectively.

Geared more for gifted enrichment and contests preparation, each of these books tend to go over a greater variety of concepts and topics, touching on concepts in Geometry, Algebra, Number theory and more, and aren’t really bound to any linear curriculum. 

In addition, the problem sets, geared as they are to helping students prepare for national tournaments and contests, are far more challenging and in-depth than would be expected of even an advanced middle or high school course.

For these reasons we don’t usually think this series is where parents should necessarily start off when working on math at home, but in our experience we do feel they are great supplements to the main textbooks and can be excellent for enrichment purposes and preparing for contests.

How Art of Problem Solving Teaches Math

Aops pedagogical approach.

Art of Problem solving is a big believer in teaching through solving problems. 

The books consequently include a wide variety of problems, many of which kids will have never encountered before.

In fact, some come directly from various math competitions such as:

• The American Mathematics Competitions (AMC)  
• The Harvard-MIT Math Tournament

The general idea is that by getting kids to work through problems themselves, and more importantly discovering how to solve certain problems, kids will develop a deeper understanding of the material. 

As a result, AoPS Math textbooks are quite problem set heavy.

Explanations of each concept are quite short and to the point and are followed by a good deal of exercises for students to try out on their own.

When introducing these textbooks, parents should expect that kids will have to think things through a bit more and work out the answers themselves without a lot of hand holding or spoon feeding, and that there will be a heavier emphasis on logic and proof than other curricula. 

All this really drives home Art of Problem Solving’s place as a resource for outstanding or talented math students who don’t need a lot of time or explanation to grasp the material. 

Consequently, students who are less adept at math may find the instructions a little too short and too quick and may need extra help in order prevent getting frustrated by skill and knowledge gaps as the exercises come rolling in

Lesson structure

Regardless of the book in question, Age of Learning’s lessons tend to follow a particular format.

The books are made up of several chapters, each of which covers a particular topic within the subject and contains several sections. 

Each section is then typically broken down into various related concepts, an overview of the types of problems kids may come across (both common and uncommon) and often the various factors that can affect outcomes.

In Introduction to Algebra, for example, when discussing multivariable linear equations, the chapter is divided up into an introduction, a discussion of substitution, elimination, some word problems, common and uncommon problem sets, different variables and so on.

As kids go through their lessons, they are given lots of examples to try and lessons tend to work through some of them step-by step in a fairly in-depth and rigorous manner to demonstrate concepts. 

Sections typically end with a variety of exercises for that section and, at the end of each chapter, there are review and challenge problems. 

Review problems go over and test what the student has learned with similar problems, while challenge problems go a step further and test mastery of the material with far more challenging questions. 

If kids get stuck, there are always hints and solutions that are helpfully included in the back of the book ( no cheating !)

Look and feel 

As you might expect from a problem solving and word problem-heavy methodology, these textbooks contain lots of typical math diagrams and pictures floating about to go along with and illustrate the word problems.

AoPS textbooks also tend to have a lot of floating boxes that highlight important information for kids, including: 

• Pointing out various strategies they can take on given concepts or problems
• Offering extra work
• Giving extra information
• Even offering “bogus” solutions that point out the most common mistakes made by students when solving a problem

Despite its rigor, Art of Problem Solving does its best to keep its material from becoming too dry and boring, which we appreciate. 

The books are written in a very casual tone, which makes it feel as if a math-whiz friend were explaining the material rather than a textbook. 

There are also a good deal of amusing and interesting examples and concept demonstrations sprinkled throughout, sometimes even involving sly pop culture references (some of which may go over kids heads, but parents will appreciate).

Does this approach really work?

Due to its philosophy and the way it teaches, we feel the Art of Problem solving takes more or less a constructivist/Problem Based Learning approach to teaching math where, instead of receiving formal lectures about math, students build up their own knowledge and skill by working through and solving various problems.

This learner-centric approach to teaching math and science actually has been linked to positive outcomes when teaching math and science , fostering greater problem-solving skills, improving self-motivation and encouraging creative and critical thinking skills as they relate to mathematics. 

Past customers have also reported that the series challenges their students pretty thoroughly, increasing the depth of their knowledge on relevant subjects and increasing their speed at solving difficult-math problems, sometimes dramatically. 

It is perhaps unsurprising, then, that the Art of Problem Solving curriculum is often used in honors math classes across the US. 

Some Drawbacks to Art of Problem Solving Textbooks and Curriculum

Can be time consuming.

Due to its focus on doing exercises, exploring concepts and working through problems to gain a better understanding of the subject matter, Art of Problem Solving can take a little more time to work with than some other programs.

This can be particularly true as AoPS tends to use far more challenging questions than kids are used to, some of which are in formats they haven’t seen before. 

While great for learning, this approach isn’t exactly a time saver. It’s not uncommon, for example, for parents to report spending up to 45 min (or more) each day on math (in addition to other homework). 

Can be tricky to jump into from another curriculum

With its particular approach and pedagogy, as well as its more rigorous approach to mathematics and problem solving (including the use of proofs), Art of Problem Solving can be somewhat tricky to get used to if you jump into it from another curriculum. 

Because math is a cumulative process, kids who begin Art of Problem solving without having at least reviewed some of the foundational material in previous books can find themselves lost or slowed down by skill and knowledge gaps they didn’t realize they had. 

Helpfully, the AoPS website does have free, printable diagnostic assessments for each book to help parents determine if their kids are at the right skill level. 

Discovery approach can frustrate some learners

Despite the fact that Age of Problem Solving’s approach has been shown to get results and improve the mathematical thinking and skills of talented math students, sometimes it just isn’t the right approach for the student. 

AoPS often requires students to play around with numbers and concepts and discover missing information themselves. 

Some students, even really talented students, can get frustrated by this approach and may prefer a more straightforward, traditional math course where they can get down to computation and see their results more quickly. 

Who is Art of Problem Solving For?

Overall, we think Art of Problem Solving is a great resource for parents and kids looking for a far more thorough, challenging and enriched math program.

It is an ideal course for students who demonstrate an aptitude for math and are looking to deepen and strengthen their math skills with more challenging grade-level material.

We think AoPS textbooks can be particularly good for students interested for more rigorous preparation for math-heavy STEM subjects in university , where their greater focus on problem solving, proofs and logic skills will be a strong asset, such as with physics, engineering and even computer science,

We also think that Art of Problem solving’s textbooks and methodology can be an excellent base material for students interested in or preparing for math contests and olympiads (AMC 10, AMC 12, MATHCOUNTS and the like), particularly their Contest Math Prep Series, as they promote creative approaches to problem solving and strengthen mathematical thinking that kids can use when faced with new problems.

Who is Art of Problem Solving Not Great For?

That said, Art of Problem Solving textbooks are obviously not for every student. 

These books are not the best curriculum for kids who are struggling with math concepts as AoPS math is primarily aimed at enriching math study. 

AoPS math goes far deeper into the material with far more rigor, exploring various high school and middle school math topics at a more advanced level and with more challenging problem sets, while emphasizing multiple approaches to problem solving and flexibility when approaching new math problems. 

Struggling students, while they often can benefit from learning the why’s behind math, can usually spend their time better by reviewing the fundamentals and practicing basic strategies, as well as by working on more targeted skill development with programs like IXL and Khan Academy .

Similarly, we don’t feel that AoPS textbooks are really the best resource for preparing for the SAT and other timed standardized tests where answering speed and efficiency (and test taking strategies) can be far more effective when it comes to success than gaining a deep understanding of concepts and working through problems.

In these instances, kids are better served through specific standardized prep programs that will work with them on developing their proficiency at solving very particular types of questions. 

Finally, AoPS textbooks are also not the best solution for kids looking to explore college level math as, despite its more challenging nature, AoPS math goes deeper into middle school and high school math topics (algebra, geometry, number theory, single variable calculus), rather than beyond it.

Price: How much do AoPS Textbooks Cost? 

The price of AoPS math textbooks really depends on the particular book and subject you’re interested in. 

Generally speaking, though, each book costs between $45 and $70, which is roughly the same as the average middle or high school textbook .

The length of each book varies, however, from just under 300 pages of instructional material in some cases to well over 700 in others.

Unlike many other middle and high school textbooks, however, these are designed to serve as a complete curriculum for each topic as every book contains instructional material as well as hundreds of practice problems, hints, and a step-by-step solution guide that itself is usually a couple hundred pages long as well. 

Bottom Line:

If you have a talented middle or high school math student and you’re looking for ways to nurture their excellence, Art of Problem Solving’s math textbooks might be right for you.

Although certainly not for everyone, with their challenging curriculum and in-depth exploration of math concepts, AoPS can foster better problem solving skills, stronger analytical ability and improved creative and critical math thinking, all of which can help students take their math skills to the next level.

About the Author

David Belenky is a freelance writer, former science and math tutor and a tech enthusiast. When he’s not writing about educational tech, he likes to chill out with his family and dog at home.  

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The Art of Problem Solving Math

The Art of Problem Solving (AoPS) math courses for grades five through twelve were designed for high-performing math students. The publisher says on their website ,

 We present a much broader and deeper exploration of challenging mathematics than a typical math curriculum and show students how to apply their knowledge and problem-solving skills to difficult problems. We help students learn the critical problem-solving skills necessary for success at mathematics competitions (such as MATHCOUNTS and the AMC), top universities, and competitive careers.

Their courses cover much more than typical math courses for middle through high school. They have courses that cover the standard sequence at advanced levels, plus other courses that take students deeper into the math needed for physics, engineering, computer science, and other math-based careers.

 AoPS students often work a few years ahead of other students, which means that capable fifth or sixth graders might start with Prealgebra . Note that AoPS is the publisher of Beast Academy math courses for grades one through five, and those courses prepare students to move right into AoPS Prealgebra.

Courses and Format Options

AoPS lists five courses as part of their “Introductory Curriculum” for students up through tenth grade : Prealgebra, Introduction to Algebra, Introduction to Counting & Probability, Introduction to Geometry , and Introduction to Number Theory . Their “Intermediate Curriculum” for advanced high school students includes Intermediate Algebra, Intermediate Counting & Probability, Precalculus , and Calculus . Even so, students in a traditional program can still use these courses following a more typical timeline and concentrating on the required courses.

The website page for each course has two free diagnostic tests (PDFs) that help determine whether a student has the prerequisites for the course or whether they already have mastered what the course covers. These tests are accessed by clicking on “Are You Ready?” and “Do You Need This?” on each course’s description page.

Students do not need to complete all books in the series, but if they start the series in sixth grade, they should be able to complete most of them. Students who want to participate in math competitions might also be interested in AoPS books written specifically for that purpose: Competition Math for Middle School; the Art of Problem Solving, Volume 1: the Basics ; and the Art of Problem Solving, Volume 2: and Beyond . (The titles of the last two books do not begin with capital T.)

AoPS sells printed or online books or a combination of both. They also offer live, online options for all courses and a self-paced-online option for Prealgebra and Introductory Algebra A. (The online courses might be a great way for eager students to find the community support they need to enter competitions.)

The printed textbooks have separate solutions manuals with worked-out solutions for every problem. The online books include the solutions, and they also integrate the textbooks with interactions with the AoPS community, Alcumus (described below), and the free videos (also described below). The textbooks vary in length; those for the standard courses (except Calculus ) run from 528 to 720 pages, while other courses have from 256 to 400 pages.

Free videos are available online for Prealgebra, Introduction to Algebra , and Introduction to Counting & Probability . You can view these without having to pay or register. The videos do not replace the textbooks or online classes but supplement them. There are one or more videos for each lesson, all taught by Richard Rusczyk, a very engaging presenter as well as a former USA Mathematical Olympiad winner. I highly recommend watching them.

How the Courses Work

The courses divide the content into chapters, with several lessons within each chapter. Each lesson begins either with brief instruction or a set of three or more problems. Students should try to solve the problems on their own. The lesson continues with thorough explanations for how to solve each problem, and this is where most of the instruction is presented. This strategy very much reflects the title of the series, the Art of Problem Solving—students are focused on developing problem-solving skills as well as accuracy.

After studying the solutions, students have another set of problems to solve, a few of which are drawn from advanced math exams (no longer in use), such as the AHSME (American High School Mathematics Examination).

Lessons often use blue boxes to highlight key concepts, important ideas, and warnings about common mistakes.

There are Review Problems at the end of each chapter but no quizzes or tests for any of these courses. (The second diagnostic test for each course, titled “Do You Need This?,” could function as a final exam if needed.) The publisher’s explanation to me regarding this was: “Since our curriculum focuses on teaching students mathematical concepts and problem-solving skills, we believe that students who are using our textbooks have mastered the material if they can successfully solve the Review Problems at the end of each chapter.”

Alcumus, AoPS’s online learning system, is available for free to all students, even if they have not purchased any AoPS course. Alcumus adapts to the student’s performance, giving them problems to solve that are appropriate for their level—problems to solve in addition to those in their course. Alcumus can be used alongside the Introductory Curriculum courses, whether in print or online. (Students using courses from other publishers for pre-algebra through geometry should also find the program useful.) Alcumus provides ambitious students with work that will both reinforce and stretch their skills.

The AoPS website offers many other resources for advanced math students, including information about competitions, online forums, and training for competitions.

AoPS math courses should be fantastic for avid math students who are eager to learn and go deeper, but they also offer excellent and thorough instruction for the average student.

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Instant Key

• Need For Parent or Teacher Instruction: low
• Learning Environment: all situations
• Grade Level: grades 5-12
• Special Audience: gifted
• Educational Methods: traditional activity pages or exercises, multisensory, highly structured, critical thinking
• Technology: video, supplemental digital content, other ebook, online
• Educational Approaches: eclectic
• Religious Perspective: secular

Publisher's Info

• Art of Problem Solving, Inc.
• PO Box 2185
• Alpine, CA 91903
• [email protected]
• https://artofproblemsolving.com/

Note: Publishers, authors, and service providers never pay to be reviewed. They do provide free review copies or online access to programs for review purposes.

Disclosure of Material Connection: Some of the links in the post above are "affiliate links." This means if you click on the link and purchase the item, I will receive an affiliate commission. Regardless, I only recommend products or services that I believe will add value to my readers. I am disclosing this in accordance with the Federal Trade Commission's 16 CFR, Part 255 "Guidelines Concerning the Use of Endorsements and Testimonials in Advertising."

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The Art of Problem Solving: Master Proven Strategies for Effective Decision Making, Critical Thinking, and Creative Solutions Paperback – July 3, 2024

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• Print length 84 pages
• Language English
• Publication date July 3, 2024
• Dimensions 6 x 0.19 x 9 inches
• ISBN-13 979-8332123641
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• ASIN ‏ : ‎ B0D8Q6NX18
• Publisher ‏ : ‎ Independently published (July 3, 2024)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 84 pages
• ISBN-13 ‏ : ‎ 979-8332123641
• Item Weight ‏ : ‎ 4.5 ounces
• Dimensions ‏ : ‎ 6 x 0.19 x 9 inches
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Art of Problem Solving, Algebra

If your student has completed a 6th grade math program and you’re looking for something more rigorous, the Art of Problem Solving Pre-Algebra and Introduction to Algebra could be a good fit. Be warned, though; AoPS unapologetically states: The text is written to challenge students at a much deeper level than a traditional middle school prealgebra course.

Developed by the mathematicians who created the Mandlebrot competition, AoPS takes math beyond the “plug and chug” method of memorizing formulas and then just crunching numbers with a calculator. Instead, students are taught how to solve problems – lots and lots of problems.

AoPS is extremely text-heavy, which could be a problem for kids who need visual supports to help them stay focused. Pages are packed with information, kind of like reading a word-for-word lecture that a teacher may give in class. The good part is that, if you can make it through all the reading, you probably won’t have many questions. It’s that thorough and well-explained.

Parents don’t have to be strong in math to be able to use this text with their kids – as long as you do the lessons together. The handy icon system helps you identify tricky concepts you might want to spend extra time covering. The Solutions Manual gives answers to every problem. It also includes an explanation for how to get the answer for many of the Review and Challenge problems.

Check out the Free Alcumus site , hosted by AoPS . Try some of the thousands of problems that supplement the Pre-algebra and Intro to Algebra text and you’ll get a feel for whether this program will be a good fit for your math loving kid.

Not sure what level you should start with? Visit the AoPS website’s Recommendation page and look for the Are You Ready? and Do You Need This? links to find placement tests for each textbook. If you’re still stuck, you can contact AoPS staff and they’ll help you decide.

Date of Review: 05/26/2015

Alessandra homeschooled her kids from kindergarten into college. In the early 2000s, she founded the Maryland Homeschool Association, a secular and inclusive statewide advocacy group. With a master;s degree in education, Alessa has written curriculum for nonprofis, a local community college, as well as supplemental material for homeschool families.

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