Need help finding a book? Have questions about particular items?
Below is the "map" of all of our textbooks. Click on any book title to learn more about it.
The top row of the map consists of our core curriculum , which parallels the standard prealgebra-to-calculus school curriculum, but in much greater depth both in mathematical content and in problem-solving skills. We recommend that students proceed through our core curriculum in left-to-right order, supplementing with non-core books as desired.
Still unsure? Please contact us for a specific recommendation.
If you still don't know which book to choose after reading the recommendations below, then click here to receive a personalized recommendation from AoPS staff.
Our Beast Academy elementary school curriculum is currently available for students in grades 1 through 5.
Beast Academy 1A is the first part in a four-part series for students ages 6–8. Level 1A includes chapters on counting, shapes, and comparing.
Beast Academy 1B is the second part in a four-part series for students ages 6–8. Level 1B includes chapters on addition, subtraction, and categories.
Beast Academy 1C is the third part in a four-part series for students ages 6–8. Level 1C includes chapters on addition & subtraction, comparison, and patterns.
Beast Academy 1D is the fourth part in a four-part series for students ages 6–8. Level 1D includes chapters on big numbers, measurement, and problem solving.
Beast Academy Guide 2A and its companion Practice 2A are the first part in a four-part series for students ages 7–9. Level 2A includes chapters on place value, comparing numbers, and addition.
Beast Academy Guide 2B and its companion Practice 2B are the second part in a four-part series for students ages 7–9. Level 2B includes chapters on subtraction, expressions, and problem solving.
Beast Academy Guide 2C and its companion Practice 2C are the third part in a four-part series for students ages 7–9. Level 2C includes chapters on measurement, addition and subtraction strategies, and odds & evens.
Beast Academy Guide 2D and its companion Practice 2D are the fourth part in a four-part series for students ages 7–9. Level 2D includes chapters on big numbers, algorithms, and problem solving.
Beast Academy Guide 3A and its companion Practice 3A are the first part in a four-part series for students ages 9–10. Level 3A includes chapters on shape classification, skip-counting, and perimeter and area.
Beast Academy Guide 3B and its companion Practice 3B are the second part in a four-part series for students ages 9–10. Level 3B includes chapters on multiplication, perfect squares, and the distributive property.
Beast Academy Guide 3C and its companion Practice 3C are the third part in a four-part series for students ages 9–10. Level 3C includes chapters on variables, division, and units and measure.
Beast Academy Guide 3D and its companion Practice 3D are the fourth part in a four-part series for students ages 9–10. Level 3D includes chapters on fractions, estimation, and area.
Beast Academy Guide 4A and its companion Practice 4A are the first part in a four-part series for students ages 10–12. Level 4A includes chapters on shapes, multiplication, and exponents.
Beast Academy Guide 4B and its companion Practice 4B are the second part in a four-part series for students ages 10–12. Level 4B includes chapters on counting, division, and logic.
Beast Academy Guide 4C and its companion Practice 4C are the third part in a four-part series for students ages 10–12. Level 4C includes chapters on factors, fractions, and integers.
Beast Academy Guide 5A and its companion Practice 5A are the first part in a four-part series for students ages 11–13. Level 5A includes chapters on 3D solids, integers, and expressions & equations.
Beast Academy Guide 5B and its companion Practice 5B are the second part in a four-part series for students ages 11–13. Level 5B includes chapters on statistics, factors & multiples, and fractions.
Beast Academy Guide 5C and its companion Practice 5C are the third part in a four-part series for students ages 11–13. Level 5C includes chapters on sequences, ratios & rates, and decimals.
Beast Academy Guide 5D and its companion Practice 5D are the fourth part in a four-part series for students ages 11–13. Level 5D includes chapters on percents, square roots, and exponents.
Prealgebra and Algebra
Students who have completed an elementary school curriculum but have not taken a Prealgebra (or equivalent) course should start with Prealgebra . Students who have worked with square roots, basic variable expressions such as 2x + 3, and basic linear equations such as the equation 2x + 7 = 23, but who have not taken an Algebra 1 course or an equivalent, may be ready to move on to Introduction to Algebra .
Beyond Basic Algebra
Students who have completed a basic algebra course (such as a typical school Algebra 1 course) are ready for most of our Introduction series. Consider a break from algebra with Introduction to Counting & Probability and/or Introduction to Number Theory . Our Introduction to Algebra text goes well beyond the typical algebra curriculum, so you might consult the text's diagnostic post-test to see if your student might need to spend some time with Introduction to Algebra before continuing to Introduction to Geometry . Introduction to Geometry is the most challenging of the Introduction-level books.
Advanced High School Math
Students without discrete math experience might start with our Introduction to Counting & Probability text before moving on to our Intermediate series of books. Intermediate Algebra should be completed before Precalculus , which should precede Calculus . The Intermediate Counting & Probability book is appropriate at any point in the sequence after Intermediate Algebra .
A comprehensive textbook covering Algebra 2 and topics in Precalculus. This book is the follow-up to the acclaimed Introduction to Algebra textbook. In addition to offering standard Algebra 2 and Precalculus curriculum, the text includes advanced topics such as those problem solving strategies required for success on the AMC and AIME competitions.
A comprehensive textbook covering precalculus topics. Specific topics covered include trigonometry, complex numbers, vectors, and matrices. Includes many problems from the AIME and USAMO competitions.
A comprehensive textbook covering single-variable calculus. Specific topics covered include limits, continuity, derivatives, integrals, power series, plane curves, and differential equations.
Contest Preparation Recommendations
Elementary school contests.
Math Olympiads in the Elementary and Middle Schools spans grades 4-8, and offers a nice supplement to any elementary school curriculum. Creative Problem Solving in School Mathematics offers lessons and problems, while the other two books listed below offer problems and solutions from past contests.
Middle School Contests
The Art of Problem Solving Introduction series offers both a full math curriculum and problem solving training for middle school and beginning high school math contests. Over 1000 problems from major contests are included among the AoPS series of books. Our Art of Problem Solving Volume 1 and Competition Math for Middle School are designed specifically for contest preparation, and we also offer books published by MATHCOUNTS .
High School Contests
In addition to offering a full curriculum for middle school and early high school students, the Art of Problem Solving Introduction series provides training for early high school contests such as the AMC 10. Meanwhile, our Intermediate series delivers a full curriculum for high school students alongside training for more advanced contests, such as the AIME and the Harvard-MIT Tournament.
Our classic Art of Problem Solving Volume 1 and Volume 2 have helped prepare students for major high school contests for over 20 years. We also offer books published by the Mathematical Association of America , which administers the AMC, and the Mandelbrot Competition .
High School Olympiads
National high school olympiads target the most experienced high school students in their respective countries. For example, the USA(J)MO in the United States is an invitational exam given to roughly 500 high scorers on preliminary contests. Our Intermediate series is useful for students just getting started with olympiads, and we offer several books from Titu Andreescu and the United Kingdom Mathematics Trust that target Olympiad students.
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Training Today's Brightest Minds to Solve Tomorrow's Problems
Art of problem solving brings its problem-solving teaching methods to local academic centers, with one virtual campus and 12 locations in the us, and more being added every year., we challenge students.
More than test preparation, our rigorous math, science, and language arts classes inspire students to reach their full potential.
FROM COAST TO COAST
We deliver the AoPS curriculum to eager learners in communities across the United States.
Where Exploration Meets Challenge
Art of Problem Solving has been a leader in math education for high-performing students since 1993. We launched AoPS Academy in 2016 to bring our rigorous curriculum and expert instructors into classrooms around the United States. With campuses in 8 states (and growing!), our approach nurtures a love for complex problem solving, which is fully incorporated into all our math, science, and language arts courses. Most importantly, our students become part of a community of motivated learners that helps elevate them to new heights.
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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
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.
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 Math Evangelist Who Preaches Problem-Solving
September 13, 2022
Richard Rusczyk, 50, at the Art of Problem Solving campus in San Diego.
Philip Cheung for Quanta Magazine
When Richard Rusczyk became interested in math competitions as a middle schooler in the early 1980s, the contest problems looked nothing like the ones in his math classes. He couldn’t find any book to guide him — there were only the problems themselves.
In some of the more advanced competitions he participated in as he moved on to high school, he couldn’t solve a single problem. Gradually, though, he figured out how to “kind of connect the dots, and back out what was actually going on,” he said. He learned a lot of math, but also something he considers even more important: the art of problem-solving.
Later, as an undergraduate at Princeton University, he saw classmates struggling in math classes despite having gotten perfect scores in high school. Their earlier classroom experiences had taught them to memorize a grab bag of tricks, he said. “When you get to college, that doesn’t work anymore.”
So Rusczyk and a competition-loving classmate, Sandor Lehoczky, set out to write the book their 13-year-old selves would have devoured. The resulting two-volume series, The Art of Problem Solving , opens by addressing readers: “Unless you have been much more fortunate than we were, this book is unlike anything you have used before.” From the start, the books sold 2,000 copies per year — “enough to cover rent,” Rusczyk said. Word of mouth grew, and over the 30 years since, well over 100,000 math enthusiasts have bought copies.
Today, Rusczyk’s company, Art of Problem Solving (AoPS), offers not just a large array of textbooks but also online and in-person math classes for “ambitious problem solvers” that serve nearly 25,000 students each year. These courses include both contest prep classes and subject-matter courses, but they have a common goal of fostering a problem-solving mentality. The company is currently expanding its elementary school materials, called Beast Academy, into a full curriculum, with the goal of bringing the problem-solving mindset to more than just self-selected math lovers.
This mindset “should be baked into the curriculum,” Rusczyk said. “It shouldn’t be the thing you do on every third Friday.”
Quanta spoke with Rusczyk about how to turn math learners into problem solvers. (In the interest of full disclosure, our interviewer’s child has taken AoPS classes, and her sister taught AoPS summer camps online in the first year of the pandemic.) The interview has been condensed and edited for clarity.
Your Beast Academy textbooks are comics, and you introduce concepts through story. The characters are talking about their math homework on the school bus, or they’re in woodworking class, or they’re on a field trip. What made you choose that approach?
You can’t lecture a third grader. You need to have a back-and-forth. The comic book structure we use has little kid monsters in conversation with each other, parents, teachers, the different characters in the universe.
Beast Academy’s illustrated math guides.
So you can model exploration, you can model overcoming challenges, you can model being OK with being wrong. You can create the environment for the child emotionally and intellectually. Every year we have parents sending in pictures of their kids dressing up as various characters for Halloween. They are putting themselves in these spaces.
We spent months trying to figure out: What is our delivery mechanism? We had 150 pages of worksheets, and we’re like, “No, this doesn’t work.” And then in one five-minute stretch, someone said comic books, and someone else said monsters. And we got a fantastic artist and started building out the books.
The lessons you’re trying to teach seem to go far beyond any specific math content, or even specific problem-solving techniques.
One of the main things we’re trying to get across is just the mindset of openness and willingness to engage with things we don’t understand at first. This is something kids are naturally inclined to do. But then something happens during elementary school, particularly in math classes, and we train that out of them.
We’re trying to encourage kids not to lose this curiosity or get into a mindset where the goal is to do everything perfectly. Because we have machines for that now. When we set kids up to compete with computers, we’re setting them up for failure, because anything a computer can do, it’s going to do better.
Within Beast Academy, the kids have different strengths. There’s one that’s wacky and does outlandish things that are sometimes not right, but sometimes really insightful. There are characters that are very precise and organized. And there’s a character who emerges over time as just plain brilliant. These are all different aspects of approaching different types of problems.
Video : Richard Rusczyk, founder of Art of Problem Solving, discusses how to bring out the joy, creativity and beauty in math.
Photo by Philip Cheung for Quanta Magazine; Video by Emily Buder/Quanta Magazine and Noah Hutton and Jesse Aragon for Quanta Magazine
Your materials for older students don’t incorporate a storytelling framework. But one striking thing about them is how each new chapter or class session begins not by introducing concepts, but with a collection of problems. What made you choose that format?
This was how I learned math. It was a pretty powerful way to learn.
When I started experiencing high school math Olympiads, it was two years of getting zero right on every single test. That was really frustrating. But it was safe, because it was a math contest, and who really cares? It wasn’t the first-year math class in college, staring at four problems and thinking, “I am not going to be able to do this, I am not going to be a scientist, I’m not going to be an engineer.”
That’s the experience our educational system gives to a lot of students. They think they’re not good enough, because the first time they’ve had this experience is when they get to college. They’re good enough, they just haven’t been prepared.
So we show the problems first. If a student discovers math for themselves, it becomes their math, instead of just something that was told to them. They’re not always going to get there, and that’s fine. Or sometimes they’re going to do it very differently than we did. That’s great too.
Your classes tend to attract kids who are already excited about math, and that in turn attracts teachers with strong math backgrounds. It’s one thing to make a system that works well for such enthusiastic and experienced participants, and another to make something that will work in classrooms everywhere. What challenges do you anticipate in scaling up your Beast Academy materials to a full curriculum?
We are approaching it first as a learning experience for us. We have a strong perspective on a certain type of student, and a strong conviction about some of the approaches we think should be taught to students. As to how to best deliver those resources to teachers and students in different environments, that’s something we’re more than humble about.
I’ll step back further and say I believe a lot of the troubles in education right now are technology companies going to schools and saying, “This is how you should do things.” It has to be a partnership between the content providers and the most important delivery mechanism these kids will ever have, which is the teacher in the room and the other kids.
Two or three years ago, we started working with schools using Beast Academy as a supplement, and that’s been pretty successful. But to reach more students and have a deeper impact on them, you really want to be the entire experience.
Rusczyk with his staff at the San Diego office.
When you say that Beast Academy has been successful as a classroom supplement, how do you measure that?
We just had a study completed in a school district in Minnesota. It was a little over 1,000 students in three groups: a “gifted” group, that passed some test; “Rising Scholars” students, who I think are defined as kids from diverse communities that didn’t pass this test but were close; and other students. They looked at the students’ performance on the Minnesota [standardized] test, and how that varied with the number of lessons they did on Beast Academy online. And they found a very strong relationship — the students who did more than, like, 150 or 200 lessons grew by a much larger margin than the kids who did 15 lessons, or no lessons. One really interesting thing is, the effect size was largest in the Rising Scholars group.
Who chose how many lessons kids did — the teachers, or the kids themselves?
It was during the pandemic, so my guess is a little of both. The outliers are almost certainly kids choosing it themselves. Whether this is revealing that the material teaches the kids or the material unlocks the kids, I’m not sure it matters, right? You have to give them material that’s going to make them want to do it. Getting the student to a place where they are interested in struggling with whatever you’re showing them, that for a lot of kids is the whole game.
There’s a lot of debate in educational circles about whether kids at both the high and the low end of performance are best served by being put on separate tracks or the same track. It sounds like you feel pretty strongly about giving extra challenge to kids who are ready for it.
We want to give students the materials that are most suited to help them realize their potential. If you give students material that is not speaking to them, you’re not giving them the opportunity to realize that potential.
When you remove advanced programs, you remove them for all students. So there’s going to be some kid who’s brilliant, but she will never know. And that’s a missed opportunity for her and for us, because these are the highest-leverage people in terms of making medical and technological advances.
Rusczyk at Torrey Pines State Natural Reserve in San Diego.
Creating those experiences also helps the students find their people. Part of what we do with Art of Problem Solving is our online community. For some students, it’s the only place where they feel safe expressing a love of math and science, because it is not part of the culture of their schools.
When I went to math competitions for the first time, the thing that resonated with me was, not only were there other kids who liked the same geeky stuff I did, there were adults who were excited about me being good at math, and they weren’t my parents, they weren’t my teachers. They weren’t required by profession or relation to be happy that I could do math. I had never seen that before.
Math competitions can be great for kids who are naturally competitive, but that’s not all kids. What can we offer the other kids?
It’s one of the great failings of the math community that the primary way you can explore deep interest in math is through competitions. When I was a student, contests were the only game in town.
This has gotten less true in the last 10 to 15 years, which is great. Now there are summer camps that are not contest-focused, and math circles that came out of the Eastern European tradition where professors work with the top students in their city.
I started one of these math circles at UCSD here in San Diego before I started Art of Problem Solving. And we had Efim Zelmanov, a Fields medalist, come give a talk. This was joyous, beautiful math — he was just so magnetic and happy to be there. So I thanked him for coming, and his answer was, “Well, I’m here to do this because this is what people did for me growing up.” And I’m sitting here thinking, I have exactly the opposite answer. We’re building these things because we didn’t have this sort of stuff.
It seems like Beast Academy, the imaginary school in the comic books, is the kind of place you would have dreamed of attending as a kid. You’ve said that some kids dress up as their favorite Beast Academy monster for Halloween, but what about you? Is there a monster you especially identify with?
Bits and pieces of various characters. But I might have identified most with Fiona [the math team coach]. In her day, she was pretty strong. But her interest is in sharing beautiful, interesting things with students, and helping them become stronger than she was.
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STEM Partnership Program with Problem-Solving Mindset Expands to More Schools
- By Dian Schaffhauser
An organization that runs math competitions, develops math textbooks and curriculum, and runs math and language arts classes for students across the country in grades 2-12 is expanding a program that helps students develop problem-solving minds. Art of Problem Solving (AoPS) produces AoPS Online (math courses), AoPS Academy (math curriculum for physical classes) and AoPS Beast Academy (online and face-to-face courses for elementary students). Recently, AoPS announced that it plans to grow Lumen , a grant-funded program focused on identifying the best, scalable model for delivering math enrichment to young learners from communities underrepresented in STEM.
The first Lumen classes took place in September 2020 in a partner school in Atlanta, GA. Over that school year, trainers worked with five schools and about 130 students. During summer 2021, AoPS has been running a free preparatory summer camp that introduces low-income students to the problem-solving mindset and learning. Those efforts included the use of Beast Academy.
Now, the organization said it plans to reach at least 500 students in 10 or more partner schools in California, Georgia, Illinois, North Carolina, New York, Puerto Rico, Tennessee and Washington, D.C. All but one of the first-year schools will be returning and enrolling more students in more grades.
AoPS instructors will use the coming year to experiment and refine programmatic elements, including a direct-to-families model, curriculum scope/pace and gradual release instruction.
"One of our big goals is to create strong mathematical thinkers who value a robust math culture," said Chris Smith, director of outreach at AoPS and head of the Lumen program, in an e-mail. "We are building out a mathematics enrichment ecosystem around the program centerpiece — virtual, instructor-led classes — in order to deepen the math culture at school and at home by creating an inter-school Lumen community."
Smith said plans also included sharing resources to support parents, school teachers and site leaders using Beast Academy.
In the first year, noted Smith, Lumen saw "above expected increases" in three areas:
- The percentage of students showing positive problem-solving mindset ("Struggle is important to learn math");
- The percentage of students showing positive math interest and identity ("I like to be in environments where people like doing math"); and
- The percentage of students doing problems beyond assigned work or being involved in community events.
The coming year will also add an inter-school math competition pilot, Smith said, "to create a more diverse pipeline of students for middle school math competitions."
A big objective is to matriculate students to "great middle/high school mathematics enrichment programs," he said. That will involve creating "pipelines" of Lumen students who enter Bridge to Enter Advanced Mathematics (BEAM) , a sister organization of AoPS in New York and Los Angeles.
About the Author
Dian Schaffhauser is a former senior contributing editor for 1105 Media's education publications THE Journal, Campus Technology and Spaces4Learning.
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