But I never really tried out math competitions. I sat the AMC once — the only year my high school offered it. Beyond that, my parents and I didn’t know much about math contest options.

I think I would have enjoyed math competitions, but that’s definitely not true of every mathematically talented kid. We encourage all National Math Stars to try out one contest and see how it feels. If they hate the pressure, they never have to sit a contest again! If they love it, there’s a great array of contests out there for every age group.

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Why do contests?

For those who enjoy competition, we see lots of benefits:

• Contests are motivating! Students who want to win put in extra effort to prepare by learning/practicing new problem-solving strategies

• Contests build resilience. Students who are used to being the best at math discover that there are people out there even better at math than they are… and that’s a valuable lesson to learn early

• Contest math exposes students to areas of mathematics they might not otherwise see. The classic subjects of contest math — algebra, geometry, combinatorics, and number theory — are topics most students don’t see until high school (in the case of algebra and geometry) or college (in the case of combinatorics and number theory). Contests pose interesting problems in these areas much earlier

• Contests are a great way to meet peers and mentors. This is especially true of contests with an in-person component

Taking a positive approach

Of course, contests can also feel like a source of pressure and lead kids into negative spirals. We’ve seen some Stars be pretty crushed when they didn’t achieve the awards or ranking they were hoping for. We’ve adopted a few informal principles to keep competition experiences positive:

• Pick the competition format thoughtfully, and be willing to try out a few different contests/formats. There are team contests, individual contests, and contests with a mix of team and individual events. There are virtual, in-person, and hybrid contests. There are (at older ages) timed and untimed contests

• Make it clear that winning is not the goal. In your child’s first exploration of contests, the goals are: (1) see which types of contests they find fun, and (2) increase exposure and fluency through practice. Your child may then decide they want to win — but it’s best if that decision comes from them, and if it comes after they’ve determined this is a corner of the math world they enjoy

• Align the competition topic to the student’s goals and interests. Math contests aren’t right for everyone, and they aren’t the only STEM contests out there. If your budding math genius is more of a builder, maybe a robotics competition is a better fit than pure math

Elementary school contest options

There are lots of math competitions out there! What follows are a few options our Stars in grades 2-5 have participated in and enjoyed.

Math Kangaroo Individual Contest

• Website: https://mathkangaroo.org/mks/

• Grades: K-12

• Format: 75-minute timed test (24 problems through grade 4; 30 in grades 5+)

• Timing: Once per year, in March

• What we like: Accessible contest with in-person and virtual options. Questions are well-written and pose interesting logical, spatial, and quantitative challenges that reward creative problem-solving over accelerated exposure to advanced topics. Awards are well-calibrated: they are competitive but not overly sparse (all top-3 scores by state and top-20 scores nationally are recognized, resulting in 7K+ awards in 2026), so kids must work hard but can get a taste of contest success

• Math Kangaroo also recently launched an in-person team competition. We’re eager to try it out in 2027!

Girls’ Adventures in Math (GAIM)

• Website: https://www.girlsadventuresinmath.com/

• Grades: 3-8

• Format: Two-hour team competition (in teams of 4)

• Timing: Once per year, in April

• What we like: Many students love working in teams rather than solo to explore difficult problems! This contest is themed around the lives of extraordinary women, so there are fun history and girls’ empowerment threads throughout. Teams can collaborate in person or over video conference, so kids can do math with their besties regardless of physical location

• GAIM is designed for girls, but does not exclude teams or team members based on gender

Noetic Learning Math Contest (NLMC)

• Website: https://www.noetic-learning.com/mathcontest/

• Grades: 2-8

• Format: 45-minute timed test (20 problems)

• Timing: Twice per year, in November and April

• What we like: Short, low-pressure contest. Two dates per year mean kids have many shots at success — they can treat one as a warm-up and gun for a medal on the other. The highly (perhaps overly) inclusive awards system gives all top-10% scorers medals and all top-50% scorers ribbons, so it’s easy to take home hardware

• Only students who participate at school and testing center sites are eligible for awards, but anyone can take NLMC at home and get their score (and digital certificates)

MathCON

• Website: https://www.mathcon.org/

• Grades: 4-12

• Format: 50-minute timed test (32 problems), followed by in-person finals

• Timing: first round in January-March, finals in May

• What we like: One of the few nationwide elementary school contests with an in-person component. Stars who qualify for the finals love traveling to compete! The in-person event includes not only math (100-minute timed test), but also a cubing contest, talent show, photo contest, and much more

  

Of course, there are many more options. MOEMS, Math League, Math Madness, RSM’s International Math Contest, Continental Math League (CML), and Southeast Asian Mathematical Olympiad (SEAMO) are all popular in elementary school. MATHCOUNTS, one of the leading middle school competitions, is also in the process of developing a program for grades 3-5.

Whichever contests you try out, remember that this is just for fun. While plenty of successful mathematicians (and founders, inventors, quantitative traders, etc.) were contest whiz kids, plenty of others never had a taste or aptitude for competition. Your contest results don’t determine your mathematical future.

I am on vacation for the next two weeks! I’ll be back on September 11th with part 2: a guide to middle and high school competitions, plus tips on contest preparation.

(This was back in fall 2023. The National Math Stars team was just me, working with a dozen brave families who had agreed to form our pilot cohort.)

My mind raced. What could be wrong? Had this Star (who we’ll call X) gotten hurt? Did they get in trouble at school? Were the moving out of the country?

I called back X’s mom and, after a brief game of phone tag, we connected.

“X is having a math emergency,” she told me.

“A math emergency?”

She explained. There was a challenge problem on his Art of Problem Solving homework that he didn’t know how to tackle. The due date was approaching and office hours had passed, so he had nowhere else to turn. If he didn’t figure it out, he’d have to submit his homework with the problem unsolved!

Of course, being a math nerd myself, I couldn’t resist suggesting a direction for X to explore as he continued to attempt the problem.

But my other response was the point: not knowing how to solve a math problem is not an emergency. (And risking a score of less than 100% on a homework assignment isn’t an emergency, either.)

I understand why it can feel like an emergency. If you’re a very talented young mathematician who has mostly been doing school math, those problems have likely never seemed hard. You’ve never had to think for many minutes (or hours) to find a way in, never had to try multiple failed approaches before making progress, never had to give up on a problem for now and come back with fresh eyes.

Those are all normal experiences when you finally encounter math at your level. But they can trigger panic: What if the fact that this is hard means I’m not actually good at it? (Just as often, it’s a parent who panics: What do I do now that the math my kid is working on has surpassed my own math knowledge? How can I help them succeed? What if my inability to do so means they don’t get the scores they need to get into college…?)

We use three tools to get kids and parents through this discomfort:

1. Create low-stakes environments for math. Math classes outside of school don’t show up on your transcript. Summer camps, mentoring sessions, and math circles aren’t graded at all! These exploratory spaces are opportunities to wrestle with problems for a long time, with no consequences for slow (or no) progress

2. Fight perfectionism directly. We tell families repeatedly that challenge is good, and that getting 100% means you almost certainly aren’t being challenged. We run optional mini-courses for our Stars on socio-emotional skills (with the wonderful Dr. Shirley), including building confidence and overcoming perfectionism

3. Share what real mathematics looks like. Many problems in math remain unsolved after years of effort by the world’s brightest minds. When breakthroughs do come, it’s often thanks to collaboration and perseverance. Knowing these stories can help reassure young mathematicians: at a certain level, being unable to solve a problem is the usual state of things!

Of course, these tools aren’t magic. Kids and parents still worry when things feel hard. But over time, we can help them see challenge as less of an emergency.

To X and X’s mom, if you end up reading this post: this is one of my favorite stories from the National Math Stars pilot. Please don’t feel like you did anything wrong by calling me in this situation. We were all figuring out together what National Math Stars should be!

Our favorite providers have a few things in common: fast (and/or flexible) pacing, a specific focus on advanced learners, and a level of problem-solving rigor that students rarely encounter elsewhere. What follows is a partial, biased set of recommendations that check those boxes and are beloved by families.1

Best for rigorous curriculum

If you want your child to get the core “school math” curriculum outside of school (perhaps because you’re unhappy with the depth or speed of your school’s mathematics classes, or because you are homeschooling), there are two clear choices.

• Beast Academy / Art of Problem Solving (AoPS) is the most popular provider for National Math Stars families. The rigorous curriculum teaches students both school math and extension topics (such as number theory), with great depth and a particular emphasis on creative problem-solving techniques. They introduce new topics through puzzles to help students discover concepts and techniques for themselves. AoPS’ many format options mean most families can find a modality that suits them. Students work at their own pace through Beast Academy Online or AoPS Online Self-Paced, participate in synchronous text-based classes through AoPS Online, take video conferenced classes through AoPS Virtual Campus, or attend classes in-person at a nearby AoPS Academy.

• Russian School of Math (RSM) has an especially large footprint in California and Massachusetts. While more focused on accelerating school math achievement than AoPS, they excel at explicitly teaching logical reasoning and problem-solving frameworks. Students who enjoy a structured, traditional classroom environment but yearn for advanced content tend to enjoy RSM. They offer both in-person and online video classes.

A word of warning: AoPS and RSM are unusual in that they cover the K-12 curriculum and are a good fit for advanced learners. Most outside-of-school, curriculum-aligned math companies (e.g., Kumon, Mathnasium) primarily provide remediation and so focus on routine rather than creative problem-solving. We don’t recommend these for mathematically extraordinary students. That time and money can be better spent on courses that confront students with richer problems.

Best for enrichment and exploration

If you don’t care about covering the school curriculum, many great classes focus on interesting, advanced math your kids won’t see in school. Two come up over and over in conversations with parents:

• Adventures with Mr. Math is an online program that teaches “math detective” skills to over 1,000 gifted kids. Their classes are interactive and discovery-oriented, and the National Math Stars who participate consistently love them. As a bonus, participants find that Adventures with Mr. Math tends to improve their math competition performance. (It’s not designed or marketed as a competition prep class, but the skills it teaches are useful in contests!)

• IMACS is an online program that teaches enriching mathematics and computer science to gifted students. Parents love their small classes, focus on critical thinking skills, and ability- rather than age-based placements.

Best for competition prep

If your kid is motivated by competitions, they don’t just want to sit contests — they want to win. You can focus their outside-of-school math learning on the content and techniques that will help them excel.

• Art of Problem Solving is on this list twice, but it’s impossible to suggest competition prep resources without naming them. Pretty much every member of the U.S. IMO2 team (i.e., the top competitive mathematicians in the country) trained with AoPS. They have a contest prep math series focused on AMC/AIME,3 as well as the MathWOOT program, which helps AIME takers make the jump to Olympiad qualification (and success).

• LIVE by Po-Shen Loh delivers classes in a uniquely engaging format. In-video live chat and acting-trained math coaches make for a lively time. The courses cover contest math topics that are not part of the typical school curriculum. On top of regular classes, LIVE coaches conduct free, public demo solves of contest math problems. Our Stars who take LIVE classes get really into them, and get very excited about chances to meet their celebrity instructor Po-Shen Loh in person (which are more frequent than you might think — he maintains a packed public speaking schedule all around the world).

• GeodeMath is a small program run by John Berman, who leads the U.S. IMO team. His courses teach competition topics (algebra, combinatorics, geometry, number theory) and develop students’ proof-writing skills. These are explicitly not “competition prep” courses, but the topics and skills covered are a good fit for those who want to excel in the AMC/AIME/USAMO series.

Best for after calculus

Oops, you finished calculus at 12 (or 10 or 16). Now what? One great option is local university classes, if you’re near a school with a strong math department. For Stars without that option, or who want college-level courses tailored for advanced younger students, we recommend:

• Euler Circle runs in-person (SF Bay Area), online, and hybrid classes that are oriented towards research rather than competitions. These classes are far more rigorous than any of the college math classes I took (in high school or in college). For students who might be interested in conducting math research, Euler Circle builds the fundamental skills (and provides a potential path to research mentorship for the highly motivated).

• Stanford offers online courses for advanced high school students through both their Pre-Collegiate University-Level Online Math & Physics program and Stanford Online High School. We haven’t had National Math Stars take these courses yet, but we’ve heard good reviews from other parents in our network. The Pre-Collegiate program is less expensive and carries Stanford University Continuing Studies Credits, but the Online High School has a more extensive catalog of courses (and can replace regular high school for full-time students).

What did I miss? If your mathematically extraordinary student loves the classes they take outside of school, please share!

First, a cop-out: the process varies by state, by district, and even by individual school. I can’t give you a step-by-step guide. But I can give you some cross-regional pointers.

Involve your child

You shouldn’t be doing this for your ego (“well, my kid skipped a grade…”), you should be doing it for your child’s learning.

So before you advocate for anything, talk to your child about their experiences. Are they bored in all subjects, or just some? Is an awesome teacher already providing great within-classroom differentiation? Do they love their current classmates? Do they prefer the company of age peers or older students?

Their answers might give you a hypothesis about the best course of action, but make sure they agree. Help them understand their acceleration options and let them tell you what they want. If possible, bring them into the advocacy process.

Do your research

Figure out whether a process for acceleration already exists in your school or district.

• Perhaps they do single-subject or full-grade acceleration by examination

• Perhaps they convene a committee of teachers and school counselors to discuss academic and emotional preparedness and make a determination

• Perhaps they run an acceleration “trial period” with the option to keep the acceleration or revert to the original grade based on student, parent, and teacher experience during the trial

This may be covered in your school’s or district’s parent handbook. If not, don’t be shy about asking school administrators for their acceleration process and policies.

If your school hasn’t accelerated students before and doesn’t have an official process, research whether district or state policy (A) requires them to provide acceleration options, and (B) dictates a certain process. For instance, the Texas Education Agency has clear guidance on acceleration via Credit by Examination. Even a Texas family whose school is new to acceleration can know exactly what to request.

Of course, there’s the formal process as written on paper… and there’s what it actually takes to navigate it. If other parents in your district have accelerated their students, talk to them and get the tea.

Gather data

Your school might tell you exactly what data they need as part of an acceleration case. (Many schools use the digital Integrated Acceleration System, the paper-based Iowa Acceleration Scale, or their own variant on these.)

If they don’t, you should still gather data to ground your discussions with the school. This could include evidence of:

• Ability: scores on group tests of ability (e.g., CogAT, NNAT) and/or individually administered IQ tests (e.g., Stanford-Binet or WISC)

• Achievement: proof that your child is academically prepared for more difficult work and won’t suffer from learning gaps. State test scores, iReady or MAP data, and/or performance in advanced courses outside of school (plus an explanation of how the content in those courses maps to the standard curriculum)

• Social and emotional readiness: teacher and/or counselor confirmation that your child has good interpersonal skills with both peers and teachers, is a positive presence in the classroom, and is excited about acceleration

When we work with National Math Stars parents on acceleration, we pull together a portfolio with all existing relevant data. This provides a starting point for productive conversations, and allows our discussions to focus on any remaining points of doubt and how to address them.

Assume best intent

No one goes into school administration for riches and glory. The people you’re working with want what’s best for kids, including yours.

That doesn’t mean you shouldn’t advocate persistently for your child’s needs, but it does mean you should be collaborative rather than combative. Take requests for additional data or trial periods as constructive concern for your child, not needless bureaucratic barriers. If one route to acceleration isn’t possible (e.g., the logistics don’t work for your child to go to a different campus for math), explore alternatives together. Thank every school employee involved in the process for their time and input. (They are probably overworked day-to-day, and your request means additional meetings and paperwork.)

Have we seen situations where the only way for families to get their child’s needs met was to go nuclear? Of course. But destroying your relationship with your child’s school (e.g., by threatening a lawsuit) doesn’t usually lead to great long-term outcomes. If your school is truly unwilling or unable to meet your child’s needs, forcing the situation will only be a temporary fix.1

Myth #1: Kids can run out of math

Your kid might run out of math offered by their school. That’s a solvable problem. They can access college- or graduate-level math through colleges and other providers (like Euler Circle and Stanford Online High School).

They absolutely will not run out of math. Math is a huge field that doesn’t stop at calculus. Our advanced Stars take lots of math classes beyond calculus: Linear Algebra, Differential Equations, Number Theory, Graph Theory, Combinatorics, Discrete Mathematics, and more. I know many math PhDs, and not a single one of them has run out of math!

It would indeed be a bad thing if your math-hungry and talented kid stopped doing math because their school ran out of classes. They shouldn’t take AP Calculus their freshman year and then simply stop doing math for three years. But, per above, there is no reason they have to do that.

Myth #2: Grade skipping hurts kids’ social and emotional development

Every kid is different. For some kids, it’s probably true that being surrounded by older peers would be socially and emotionally negative.

But the data shows that grade skipping is not usually a tradeoff between academic and social fit — it’s good for (most) kids on both dimensions. The most thorough meta-analysis I’ve seen of research on acceleration shows positive impact on academic achievement and slightly positive impact on social-emotional development.

Anecdotally, while we’ve seen Stars struggle to fit in with peers (and suffer from bullying), it has almost never been as a result of acceleration.

While data on radical acceleration (skipping 3+ grades) is less extensive, the limited studies we have also show a positive effect. In a longitudinal study of young Australians with IQs of 160+, outcomes (including life satisfaction and socialization) were most positive among those who skipped at least 2 grades.

Myth #3: Kids who are ahead should get enrichment, not acceleration

This is a false choice. Both enrichment and acceleration have proven value for students. And kids who are ahead — and learn new material quickly — have the luxury of time; they can do both!

The goal should not be a race to algebra (or some other arbitrary milestone). But we find that Stars can comfortably and consistently be ready for an advanced algebra course no later than 6th grade and explore enriching mathematics (and other STEM areas of interest) along the way.

Myth #4: We should avoid acceleration to give my kid a competitive edge

If your kid is at the top of their class and you don’t accelerate them, they may well continue outperform their classmates (unless they get bored and stop trying).

But at what cost? Kids who never encounter challenge don’t develop resilience. When they’re finally faced with a hard problem, they may crumble. (Stars often struggle emotionally and give up quickly when we first expose them to problems at their level. That’s okay for a 10-year-old; we have the time and techniques to equip them with patience and grit. The stakes are higher when your first encounter with challenge is in college or beyond.)

Students who are mathematically extraordinary learn quickly. As long as you’re not pushing them past their limits, they will continue to excel after acceleration. I got As in all my college-level math classes as a young teenager, and so do most of our Stars.

If you’re worried about college admissions, acceleration can tell a compelling story. Admissions officers will be more impressed by a 16-year-old getting the third-best score in their college number theory class than by an 18-year-old getting a top score in their high school calculus class.

Myth #5: If my kid skips grades, they won’t be able to compete in athletics

If your grade-skipped kid wants to be on a school team and it is rostered by grade, they probably will be worse at sports than their peers.

There are alternatives. Your school may be open to letting them join the sports team that matches their age rather than their grade. Your child could also participate in recreational or club sports, which usually determine eligibility based on age.

You should consider whether being good at sports matters to your child and their future. If they deeply love their sport and are driven to excel in it, of course you want to find opportunities for that. If they are just participating for fun and exercise, it might be okay if they aren’t the team MVP. I spent a lot of time on the bench as a 12-year-old on my high school’s soccer team, and that was just fine.

Relatively few people will go on to play sports professionally, or even at the D1 college level. For most kids, you should make schooling decisions based on academics and fit athletics around that.

Myth #6: Acceleration is inequitable

Limits on access to acceleration are inequitable. When the only students who are accelerated are those whose parents know how to ask, many equally talented but less well-resourced peers will be left behind.

But that’s an access problem — one best solved by expanding access (e.g., through automatic enrollment in advanced math for high-performing students), not by narrowing it. In fact, narrowing access to acceleration hurts the least advantaged students the most. Parents with educational and/or financial capital can provide acceleration outside of school, through advanced courses and tutoring. Those with fewer resources rely more on their schools’ offerings, making acceleration a vital option for talented but underserved students.

So please don’t feel like advocating for acceleration is unfair. If you want to help all talented students, encourage your school to develop clear, objective, and proactive acceleration approaches. Your child could be the example that sparks positive change.

When we work with schools to accelerate Stars, we often encounter pushback:

• What if course schedules don’t align for the student to take math with the grade above them?

• What if the math the student needs is on a different physical campus (e.g., an elementary schooler is ready for middle or high school math)?

• What if the student accelerates too much and runs out of math their school/district can offer?

We’ve developed a practical menu of options, and we find at least one of these can usually meet a Star’s needs and work for their school or district.2

1) Skip one (or more) full grade(s)

This is the most traditional form of acceleration, and it’s often the simplest. Many schools have well-defined processes for grade skips (e.g., our Texas Stars have to pass CBEs — credit by examination tests — to advance a grade). There are hoops to jump through, but few logistical obstacles. Schools already have to run a full suite of schedule-compatible classes for each grade level; it doesn’t affect their processes (or cost them anything) to have a younger student in those classes.

If you can’t tell, I’m a big fan of grade skipping. But it’s not a panacea. Not all students are socially ready to spend the school day with older peers (though most advanced students are).3 And for mathematically extraordinary students, grade skips might not fully address their needs — they may still need additional acceleration in mathematics. (That was the case for the three National Math Stars I discussed above. It was also my situation. Even after skipping three full grades, I needed more challenge in some subjects, including mathematics.)

2) Attend math with older grades, in person

Attending a more advanced math class in person is the most engaging option, if schools can make it work.

The two obstacles are usually scheduling and transportation. Scheduling is hard to change, particularly across campuses (e.g., if an elementary schooler needs to go to the middle school). When schedules do align, students still need to get to class. Some of our Stars walk to nearby campuses. Some schools are able to provide bussing. And we’ve even seen some parents pick up their Stars mid-day to drive them between campuses for math classes.

3) Attend math with older grades, on video

Sometimes schedules align but transportation is impossible. (After all, most parents can’t provide mid-day transportation for their children.) Maybe it’s not needed? In 2020, many schools got significant tech upgrades. Some now have strong video conferencing set-ups that allow students to attend classes from afar.

We’ve seen mixed success with this. If you’re the only student Zoom-ing into a class while everyone else is in the room, it’s hard to fully participate. True hybrid models — where many students are video-calling in, and the teacher has experience moderating across the physical and virtual classrooms — are typically more successful.

4) Do math online or independently during school

Often, schools cannot provide a good option. Schedules simply don’t align, or the district doesn’t even offer a suitable math class. Fortunately, there are many excellent advanced math courses available online.4 Students can take these during math time, instead of sitting bored in their grade-level class. There are a few logistics to work out:

• Supervision: most elementary schools require adult supervision of all students, so a child doing independent work can’t just grab an empty office. Our Stars usually work in their school’s library or computer lab, or with noise-cancelling headphones at the back of their math classroom

• Laptop: even schools that have scrapped their 1:1 device policies typically have some loaner laptops available (and/or a computer lab) for online work. They may also allow parents to provide a laptop. Alternatively, students can work independently using a textbook — no device required

• Cost: advanced math classes aren’t cheap. For highly motivated students, self-paced options are considerably more affordable than live instruction (e.g., Beast Academy Online is $100/yr; Beast Academy textbooks and workbooks are even cheaper). Many providers offer partial or full scholarships to families with need. Schools that receive gifted & talented allocations from the state may also be able to use those funds to purchase advanced courses

• Timing: if students prefer a live online class to a self-paced model, the timing of the live class may not align with their school’s math block. We have many Stars in this situation; they typically take the live class outside of school hours and do their homework during school math time

This is the start of a series of posts about in-school acceleration. We’ll explore different options for acceleration, dispel common myths, and dive into tactics you can use to advocate for your child’s acceleration.

I’ll first share my own story. Over the course of my K-12 education, my schools deployed a variety of acceleration methods (full grade skipping, subject-specific skipping, independent studies, early college, etc.). We encountered many typical obstacles and objections (much older peers, “running out of math,” schedule misalignments, graduation requirements, etc.) and found ways to overcome all of them. Behind the scenes, my parents were tireless researchers and advocates — and as I got older, they encouraged me to be my own decision-maker and advocate.

Preschool and elementary years

My school years started in a preschool/daycare center near my mom’s work. That didn’t last long. My parents noticed that the toys on offer were pretty simple — things like giant 10-piece puzzles. They asked if they could bring harder puzzles for me to work on but were told it “would make the other students feel bad.”

They looked around for better options, and they came up short. No one seemed willing to give a 4-year-old materials designed for students much older. So they hit upon a brilliant solution: if I couldn’t learn anything new, at least I could learn it in a different language! I spent the next few years at the International School of Portland, in the Japanese immersion wing.1

After that, I attended a unique private school (CLASS Academy) that did not segregate classes by age. There was no “third grade” or “fourth grade”; there were “sharks” and “dragons.” Which you were depended on the coursework you were ready for, with further differentiation (and opportunities for self-paced independent work) in math and reading.2 My math classes had kids as young as 7 (me) and as old as 13.

I loved it. But it only covered K-8 curriculum. By the time I was 9, CLASS Academy was running out of materials and teachers for me. Also, my parents had adopted two more kids, and private school tuition for three of us was impractical. It was time to make the switch to public school.

Public middle school

2003. My parents strolled into our local public school’s office and said, “We have a 9-year-old who has finished the equivalent of 8th grade. What can you do for her?” To their credit, the principal didn’t run the other way screaming; they agreed to figure out a placement for me.

After trial weeks in the 5th and 6th grades, the school decided to place me in 6th. They put me on a schedule that allowed me to take math with the 8th graders, and they asked the English teacher to give me additional extension assignments.

The next year (7th grade for me), they had to adjust a bit. There was no more math for me in the building, and getting me to the high school mid-day wasn’t feasible. So I sat in the school library and took an online Geometry course (through Johns Hopkins CTY) during math time. I took Spanish with the 8th graders,3 and the physics teacher gave me custom problem sets instead of the regular homework.

Staying for 8th grade would have required even more accommodations. My parents offered me a choice: did I want to skip 8th grade and go straight to high school?4 I wrestled a bit with the decision, but I finally said yes.

Interlude: beyond academics

What about all the other aspects of tween/teen life?

• Friends: I had great friends throughout my schooling. My group of middle school friends was part of why I didn’t immediately jump at the chance to skip 8th grade.

• Dating: The age gap could have made this awkward, but we sidestepped any issues. While I experienced crushes during middle and high school (and attended homecoming and prom with dates), I didn’t seriously date anyone until college.

• Bullying: I was never bullied. Middle school classmates were sometimes catty and mean, but it was general meanness rather than targeted at me for being young/smart. Skipping 8th grade was a great decision in this respect — high schoolers were much nicer!

• Sports: Being 2-3 years younger than everyone else on the team does make you noticeably worse at sports (not that I had particular talent in that area anyway). I tried out a bunch of sports in middle school and sucked at all of them. I played on my high school soccer team but spent a lot of time on the bench.

• Other extracurriculars: Being younger wasn’t a disadvantage in other areas, as far as I could tell. Over the course of middle and high school, I competed in mock trial, performed in theatre productions, built robots, captained the science bowl team, refereed soccer games and babysat neighbors’ kids for spending money, and did all sorts of other typical activities outside of school.

Public high school (plus college classes)

High school schedules tend to assume varying levels (e.g., honors/AP track vs. regular track) and electives, so they are pretty flexible. For my first two years in high school, this worked great: I took math, Spanish, and physics with the juniors and seniors.

But by my junior year, my small high school was out of math and Spanish for me! Fortunately, my parents found a solution. My high school was only a twenty-minute walk away from Lewis and Clark College, and Lewis and Clark had a program allowing advanced high school students to take courses there (for free!). I applied to the program and petitioned for special permission to take multiple classes per semester (it nominally allowed for only one).

For two years, I walked to Lewis and Clark three days a week. I took linear algebra, differential equations, symbolic logic, Spanish literature, and more. I solved the math department’s problems of the week, attended film nights on campus, led peer study sessions, and made the Dean’s List. Hard though this may be to believe, no one in my classes knew I was 13 (or 14 or 15). I’m sure they thought I looked young, but when I revealed my age to a college classmate I’d become close friends with, she was shocked.

Reconciling this with my high school schedule and graduation requirements called for some accommodations:

• My high school gave me permission to leave early or arrive late to some classes, if they were right before/after my college classes

• One semester, I did English as an independent study because no English class was compatible with the rest of my schedule

• Because my high school didn’t count my college classes towards graduation, I was short math credits to graduate. They granted me math credits for TAing calculus and for a math education independent study so that I could get my diploma

Extreme acceleration, not maximum acceleration

This may sound like a race through school. It wasn’t. My parents and I made choices that were right for me, academically and socially.

In theory, I could have accelerated even more. I briefly considered applying to colleges when I was 12. I had maxed out my high school’s offerings in many subjects and had already earned 99th-percentile SAT scores. But I enjoyed high school, and I was still learning (especially with the option to take college courses). Besides, I wasn’t ready to go away to college — and I was pretty sure I wanted an on-campus college experience. By the time I moved across the country for college at 15, it felt right, not rushed.

What I did may be too extreme for many highly advanced students, and it may be insufficient for others! The point of sharing my story isn’t to provide a roadmap you should follow; it’s to reinforce that (A) there are many different ways to make acceleration happen, and (B) acceleration can be a positive experience both academically and socially.

Over the next few weeks, I’ll share other students’ stories, academic research on the impact of acceleration, and practical tips for making it happen.

• Can’t anyone learn math?

• Where’s the line between “good at math” and “math genius”?

• Isn’t this whole idea kind of elitist?

• Is my kid a math genius? How can I be sure?

So let’s dive in.

Does math genius even exist?

If we define “math genius” as an inherent aptitude for mathematics, yes.

Cue the alarm bells: am I saying who can do well in math is predetermined? That there is a ceiling on the potential of kids who aren’t math geniuses? That those with an aptitude for math are better than those without it?

No, no, and no.

An aptitude for math is similar to any other talent that is unevenly distributed across the population. The same way a child might be an unusually precocious artist, display perfect pitch, or be extraordinarily coordinated on the soccer field, so too can they possess talents that lend themselves to mathematics (e.g., understanding of numbers, rigorous logical reasoning, or visual-spatial abilities).1 In all of these fields, genius is neither necessary nor sufficient for success. (You can become really good at something by working very hard at it, even without an inherent advantage! Talent makes it easier to achieve at a high level, but doesn’t guarantee it.)

Longitudinal studies tell us that strong math performance early in life significantly increases the probability that a student will go on to achieve impressive STEM-related outcomes (like PhDs, published research papers, tenured professorships, and patents). Again, early ability doesn’t guarantee any of these outcomes — and plenty of students who weren’t identified as math geniuses go on to do these things, too. But your odds of doing them are higher if you excelled at math early.23

Giftedness = the far-right tail

If we accept that there is a distribution of natural aptitude, what do we mean by terms like “genius” or “gifted”?

The bad news: you’ll find lots of different definitions out there.

The good news: most of them use the same framework.

That framework is the bell curve. We’ll look at the bell curve of IQ: normalized to an average of 100 with a standard deviation (SD) of 15. That means higher scores get rare fast. An IQ of 115 (one SD above the norm) is 84th percentile (i.e., higher than 84% of the population, or top 16%). 130 (two SDs above the norm) is 98th percentile, or top 2%. 145 (3 SDs above the norm) is 99.9th percentile, or top 0.1%.

When people talk about “giftedness” or “genius,” they are talking about the skinny right tail of that curve. Depending on context, they might mean the right tail of IQ overall (e.g., Mensa looks for a top-2% composite score), or they might mean the right tail for a particular skill. They might mean it formally (i.e., you literally took a test and scored in that range) or informally (i.e., you clearly have skills that place you at the top of the distribution, even if those haven’t been — or can’t be — measured by a research-validated instrument).

Within the world of gifted education, many organizations draw a distinction between “gifted,” “highly gifted,” “exceptionally gifted,” and “profoundly gifted,” but they rarely agree on exactly where those lines are. (Some sources set the “profoundly gifted” cutoff at an IQ of 145+, others as high as 180+.) For programs like National Math Stars, these distinctions matter. We have to clearly define our target audience and set admissions criteria.4

For parents, labels are less consequential. The adverb that comes before the word “gifted” matters less than whether your child’s academic and social needs are being met. Generally, the farther on the tails of this distribution your kid is, the harder those needs are to meet (but whether they scored exactly 144 or 146 shouldn’t make much difference, even if organizations and researchers draw a category line at 145).

Math is multi-dimensional

But wait — it’s a little more complicated! Math isn’t an ability. A variety of underlying cognitive skills can contribute to an aptitude for mathematics.

Tests of cognitive abilities recognize this and typically don’t have a “math” section. (The SAT and ACT do, but those are designed to be tests of college readiness and mastery of high-school-level material, not raw aptitude.) When National Math Stars candidates sit the Cognitive Abilities Test (CogAT), they take both the quantitative battery (focused on number puzzles and patterns) and the nonverbal battery (focused on visual and spatial skills). While scores on these sections are correlated at the population level, there are plenty of students who score extraordinarily high on one and average or moderately high on the other.

The Wechsler Intelligence Scale (the mostly widely used IQ instrument in the world) scores five different areas: verbal, visual-spatial, fluid reasoning, working memory, and processing speed. Depending on the math a kid is doing, any combination of those abilities could contribute to success! Again, there is correlation between scores on the different indices, but “spiky” profiles are very possible.

Measuring aptitude is hard

Have you noticed the elephant in the room throughout this post? We’ve been talking about the fact that math aptitude exists, and we’ve been pretending (in all these mentions of tests) that means we can measure it directly.

We can try, but it’s imperfect.

The first challenge is to disentangle aptitude from achievement. Achievement is what a child has learned; aptitude is their ability to quickly learn new things. Aptitude tests shouldn’t require specific content knowledge. IQ tests (and IQ-style tests like the CogAT) are designed to assess underlying cognitive skills rather than ability to solve curriculum-aligned problems. They give a better read on inherent ability than, say, the state end-of-year math test or the SAT. (Sort of.5) But it’s hard to completely eliminate achievement. Reading comprehension, fluency in basic numerical operations, and other school-taught skills can be implicit even in aptitude tests.

IQ tests are also subject to practice effects. Familiarity with question formats boosts scores. (And since the question types used by standard tests go through lengthy validation and normalization processes, they can’t be frequently changed.) This isn’t a problem if you’re genuinely trying to get a read on a kid’s ability — just don’t prep them for the test! But when these tests are used to qualify for programs (like a school gifted program, or National Math Stars), parents will inevitably prepare their children. And the quality of that preparation will skew results.

There are many other fair criticisms of these tests. English language ability can play a hidden role. So can test anxiety. Differences in average performance based on race and socioeconomic status may point to biased design (or, in the case of individually administered IQ tests, biased examiners). Important skills like creativity go unmeasured.

That doesn’t mean there’s no valuable information in these test scores. But they’re not the full picture of a kid’s ability.

Is my kid a math genius?

So where does that leave us? Will an IQ test tell you whether your kid counts as a math genius or not? Would that it were so simple.

If there were one definitive way to answer that question, I wouldn’t have just written 1800+ words on the topic.

If any of these things is true, you can be pretty confident your kid is a math genius:

• They have taken an IQ or IQ-style test and scored several SDs above average in quantitative, visual-spatial, and/or other mathematically relevant skills

• Without significant prompting or guidance, they are engaging with and mastering mathematics well above their typical grade level

• A mathematician (ideally one who has worked with young math geniuses before) did math with them and told you they are extraordinarily talented

Of course, it’s possible none of those things is true and your kid is still a math genius. Maybe they test poorly. Maybe they haven’t had exposure to advanced content or to professional mathematicians.

Most of what I recommend in this Substack will be accessible regardless of whether your kid has been formally recognized. (Some talent searches and scholarship programs require proof of ability; many wonderful advanced math opportunities do not.) If your child is passionate about math, if they won’t shut up about about the patterns they see in the world, if they keep asking you for more and harder puzzles, then cultivating their abilities will pay off, regardless of the number on their IQ test.

And how should you cultivate those abilities? That, dear readers, is what we’ll spend the coming months (years?) exploring.

Welcome to Cultivating Math Genius. If you’re the parent of an extraordinary young mathematician1 and you’re looking for guidance on developing their talents, you’re in the right place!

My story

Why should you read my thoughts on this topic? I’ve experienced it from two sides: as a very advanced math student growing up, and as the leader of a nonprofit that supports such students and their families.

I skipped three grades.2 By 11, I was in high school, and by 13, I had run out of math classes at that high school. (I went to an excellent but small public high school, which didn’t offer math beyond calculus.) My junior and senior year, I walked to nearby Lewis and Clark College for classes like differential equations, linear algebra, symbolic logic, and Spanish literature.3

Acceleration was a lifeline for me. I craved learning and challenge, and there was no way a classroom of my age peers could offer that. I was lucky my parents were able to navigate the school system in my favor, securing accommodations like grade skipping and additional subject-specific acceleration.

They also found me wonderful STEM enrichment opportunities. My mother started several FIRST LEGO League teams, and then helped me start two FIRST Robotics Competition teams. My parents encouraged my participation in Science Bowl and my successful application to National Youth Science Camp. My uncle, a mathematician, gave me outrageously difficult books (I think this was an eighth or ninth birthday present) and posed combinatorics puzzles to stretch my brain.

There’s also a lot my parents didn’t find. When I went away to Olin College of Engineering,4 my classmates told me about all the cool STEM things they’d been up to — a world of math competitions, summer camps, and advanced classes I’d never heard of. Don’t get me wrong: my parents did great, and I began my engineering studies well-prepared, albeit with a little FOMO.

After Olin, I won fellowships to study literature and theater in Europe. I spent a couple glorious years abroad, and then decided I wanted an actual salary. So I headed to Silicon Valley and joined Marissa Mayer’s shiny new Associate Product Manager program at Yahoo! Alongside that job, I joined several nonprofit boards and started to feel the lure of devoting my career to impact work. I got an MBA to gain some actual management skills, spent a few years consulting at Bain (mostly in the social impact space), and then started National Math Stars in 2023.

Through National Math Stars, I now help hundreds of families navigate the advanced STEM ecosystem. Our Math Awards Program celebrates top math achievers in 2nd and 3rd grade. Awardees are invited to apply to our Stars Programs. Stars get long-term, wrap-around support. We help with course selection, school advocacy, extracurricular and summer opportunities, community building, and need-based financial aid.

This work gives me a close look at the biggest questions and challenges parents of mathematically extraordinary students face. The topics and anecdotes I share in this Substack will draw on Stars’ experiences. (I’ll share my own stories too, but the educational landscape has changed a lot since the 1990s and 2000s when I was in school. When it comes to recommending opportunities, I’ll rely on my more recent data from working with Stars.)

Why write this?

The short answer: I’m learning a lot from National Math Stars. I want to share that knowledge with more parents who could use it.

The longer answer: National Math Stars currently serves a few hundred Stars. I hope that number will soon be thousands — and eventually tens of thousands. But it will likely never include every family that could benefit from our expertise.

Maybe you aren’t in a state National Math Stars serves. Maybe you didn’t hear about the program while your child was of eligible age. Maybe you applied but your child didn’t secure one of our very limited spots.

There are over 50 million K-12 students in the United States. By definition, more than half a million are in the 99th percentile! There are lots of headlines about how many children are struggling to gain basic literacy and numeracy skills. There aren’t many headlines about (or resources for) the children who are bored because they mastered their year’s curriculum long ago.

Knowing what to do for those students isn’t easy. But I have some ideas from working with so many of them. I’ll share those here.

What to expect

What should you expect from this Substack? 2-4 posts per month to guide you on your journey. I’ll tackle questions like:

• Should you accelerate your child? How and how much?

• How can you work with your school to accommodate your child’s needs?

• What math should your child explore outside of school? How?

• How should your kid spend their summers?

• Where can you find other ‘math kids’ and their parents?

• Are math contests a good fit for your kid? Which ones?

• How do you help a kid who aces every test through their first experience of being challenged?

• How do you raise a well-rounded math genius, not a calculating machine?

I also want to know what you want to read about! Please feel free to share the questions on your mind.

Thank you for joining me on this adventure.

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