Recent AMC changes

…and how some ambitious students can reap huge benefits

There have been some major shifts in the college admissions landscape over the last few years. These shifts have changed the value of the AMC for certain students, and they have also changed how a student should prepare.


Brief recap: what’s the AMC?

It’s an annual exam run by the MAA for high-school math fans and “mathletes” featuring much more difficult questions than the SAT/ACT. Therefore it does a farbetter job of identifying early talent. It is also the “feeder” exam for the US Math Olympiad team.

Why do I care?

Because the way students get into top colleges has changed so much that our intuitions about what “ought to be enough” no longer apply.

How has the AMC itself changed?

  • It’s now given in November instead of January
  • It’s now given online as well as at schools
  • It’s become consistently more difficult over the past five to ten years
  • Participation by students outside the US has skyrocketed

These changes don’t make a huge difference yet, but what they imply about the future of the AMC does.

How has its importance changed?

I should probably write a longer essay about this, but in a nutshell: The ACT/SAT can easily distinguish between a mediocre student and a good one. But they can’t distinguish between good and great. Instead, these tests inadvertently distinguish between hard-working and very-hard-working, with little focus on talent beyond a certain moderately high level.

Talent—i.e. potential future success—is what’s most important to colleges, but the ACT/SAT isn’t giving colleges the insight they need into this dimension. (This underlies some of the recent shifts in the testing industry.) That task is increasingly falling to other sources, and the AMC is quickly becoming one of the main ones.

How has preparing for it changed?

The same way that preparing for the ACT/SAT changed about 20 or 30 years ago: it’s becoming professionalized. What used to be an exam that you could just decide to take cold on test day has become something you prepare for for an extended period.

Also, the way you prepare has changed, because there are really two routes to success on the AMC:

  1. Pretend it’s the LSAT, and just work dozens and dozens of past exams until you have pretty much seen it all
  2. Pretend it’s a “thinking competition,” and learn new problem-solving skills that work in a wide range of situations

Option #1 is more popular, especially outside the US, because it’s easier to plan out how to do it, and for many international students, simply spending hundreds of hours coming to master the test is a viable option.

Option #2 is a better choice for many US students because they have less time to devote, have more resources to devote to developing true expertise, and need more of the general problem solving skills this training develops. 

I’ll say that last part again in a different way: the US has been lagging most developed countries in critical thinking and general problem-solving for quite a while now. The AMC helps our best and brightest learn the critical skills that are necessary for high-level competitiveness in future markets, and which most of the student population increasingly lacks.

What should I be asking in response?

If you haven’t considered the AMC, you should ask these questions:

  • Do I enjoy math (or at least, do I enjoy it when it’s interesting)?
  • Is it important to me to attend a top school and/or to have a challenging and rewarding career in technology, science, and/or research?
  • Could I see an academic study becoming for me what varsity sports are for student athletes?

If you’re already planning to prepare for the AMC, or have started preparation, you should ask these questions:

  • Do I have a concrete, realistic plan for success?
  • Historically, have I gained at least ten points per month of preparation on my practice tests?
  • Am I continuing to improve?
  • Is what I’m learning still both helpful and interesting?

What should I be doing?

A few thoughts about the ACT/SAT

If you’re heading to college, you’re almost certainly going to take the ACT or SAT at least once. I’d like to set the record straight on a few things so that we can all minimize unproductive time and effort, especially in light of the fact that most students take these tests during school years that are already very busy.

On preparation

ACT/SAT preparation is a big industry encompassing a wide range of options. I don’t think that “low quality” providers are terribly common, but I do think that it’s important to match a provider to your needs, because there is a wide range, and fit matters. There are three issues in particular that come up around ACT/SAT prep that I think are worth calling out:

  1. On variable depth: Lots of ACT/SAT prep is done by those who did well on the tests themselves but whose teaching experience (and, sometimes, incentive to ensure student success) can vary widely. If you are unaware, this can cause problems. If you are savvy about it, though, this can be an opportunity to get what you need for less money overall. 
  2. On score bands: What you need to improve your score is not only affected by what kind of person you are. It’s also affected by where you are on the score curve. For example, tell me where you are scoring, and I’ll tell you whether vocabulary, grammar rules, reading style, or attention management are probably costing you the most points on the verbal sections of these tests. Some teachers are aware of this and some aren’t; some specialize in a narrow score band and some don’t. But whenever I talk with a parent for the first time, I note whether they have considered this important part of the decision process. 
  3. On the grapevine: It’s great to be well-connected! Just be aware that Suzy’s great tutor may or may not have actually been a great tutor. Maybe she was just great for Suzie. (This is also why I encourage tutors to be selective about whom they take on. “Taking all comers” is good in the beginning, but it isn’t a good long-term plan for most.)

Basic pro facts

Here is some “inside baseball” about these tests. Most of the pro tutors I know are delighted when clients have already considered these ideas:

  • No school cares which test you pick. Really. (If you have a reputable college counselor telling you otherwise, then please trust that you’re in a very specific and unusual situation.) So just pick the one you do best on (see below), or pick the one whose test date happens when you need it to, and move on. 
  • There is no “penalty for guessing.” Neither test currently assigns negative fractional points for incorrect answers. Which is unfortunate, because you’d be better off if they did. This video helps to explain why that’s true (even though it may seem “obviously” false). The punch line is: without “penalty” points, you’re forced to spend the last minute of your testing time bubbling in random answers to whichever questions you haven’t yet answered. 
  • Most students will get comparable scores on the two tests. Of those who do better on one or the other, it’s a 50/50 chance which one you’d do better on (see also “subjective preference” below). The best way to determine whether you are a student who does better on one or the other is to take one of each in comparable circumstances and compare the two scores using a concordance table from either organization. 

That said, if you believe that taking both tests is not in your best interests (e.g. because you have very limited time), then here are some rules of thumb:

  • If you read especially slowly (e.g. have a tested learning difference, esp. low processing speed) then the ACT is going to penalize you extra hard for it. Prefer the SAT.
  • If you are considered a linear thinker and/or your primary school strategy is to “grind it out,” then the ACT is going to be more in your wheelhouse. The ACT lends itself better to simply learning all the material and techniques, then delivering on test day. Prefer the ACT. 
  • Conversely, if you are considered a good test-taker and/or your primary school strategy is to wing it, this suggests a preference for the SAT, which remains slightly more gameable in this way. Prefer the SAT.
  • Crucially, most students express a subjective preference for the ACT. This is not to be confused with “most students do better on the ACT,” which is simply not true; scores are normed to reflect percentile rankings. 

This last point might be worth expanding a bit. 

In other words, schools aren’t looking at your raw scores per se; they’re looking to see whether you did better than most others. The all-too-popular canard that “the ACT is better for most students” is not only wrong, it betrays a deep misunderstanding of the whole situation. The score is normed across all test-takers. That preference, therefore, gets normed out of the score. In other words, the ACT “feels better” to everyone else too, and so thanks to the norming that happens across this particular zero-sum game, it’ll all come out in the wash. 

And let me emphasize: the best way to select is to take one of each test in comparable circumstances, and then to compare the two scores using a concordance table from either organization. 

As I say to students who are ready to hear it: the hard truth here is that you’re not here to have a good time; you’re here to get a job done, and that means a good score. So don’t let your preferences guide your decision unless they are likely to affect your outcome. Your score is the thing to focus on. Structure your preparation (and your test selection) in the way that will lead to the outcome you want. 

This framing helps put a more human face on the underlying mathematical truth about the way these tests are scored, and on the need in life to be able to jump through the occasional tricky hoop.

Some thoughts for top students

If you’re in the top tenth or so of students (i.e. if you test at the 90th percentile or higher), then the game is a bit different for you, since it’s no longer about being able to solve problems that few others can. Instead, for you, it’s about not making avoidable errors.

In other words, as you move to the top of the curves, these tests go from being winners’ games to being losers’ games

Let me unpack that a bit. The people who score in the middle of the pack — say, an SAT 1200 or an ACT 21 — are playing winners’ games, where doing better relies on getting more problems right. By contrast, the people who score at the top of the pack — say 1400+ on the SAT or 28+ on the ACT — are playing losers’ games, where doing better relies on just performing consistently while others make mistakes.

This means that beyond a certain point, the winning strategy shifts from trying to get more right, to trying to make fewer unforced errors.

This is where preparation passes outside the realm of what most of us think of as fact- and tactics-based “test prep” and into softer skills adjacent to psychology, habit formation, and self-awareness.

I created a short (ten minutes maybe?) free mini-course on this called What Am I Missing? that you are welcome to give to anyone you’d like, and to take yourself. It gets into more detail than comfortably fits here.

Consider the long game

Parents, please take an uncomfortable moment to consider the unlikely scenario where the student wins admission to a school that’s hard enough that they wind up dropping out. Now consider the less dramatic but much more common version: the school is hard enough that they wind up needing continued help throughout their undergraduate years and even beyond. (These do happen; I’ve seen both first-hand.)

My point is that we’re all working together here to execute a successful launch. This means both success and actual launch.

One of the ways this can positively affect SAT/ACT prep for active parents and their kids is the explicit recognition that a bad run at these tests can in many cases be a very positive milestone in the long run. There’s nothing like an unexpectedly difficult run at an important test to challenge expectations and catalyze a bit more self-awareness. After all, if the SAT/ACT is hard enough to shake you up, what does that say about every test you are going to face over the next four years?

Now is the time to either downshift or step up. It is absolutely possible to gain new knowledge, to gain new skills, to try on new perspectives, to embody new strategies, to experiment in the service of self-improvement. 

You’re about to do that for four years. Why not start right now? 

But again, you have to see this as a long game in order to get these long-term benefits from these immediate disappointments.

A historical side-note

Originally, the SAT was an aptitude test and the ACT was an achievement test. 

  • The SAT has its origins in trying to assess which enlisted soldiers were officer material (and which didn’t belong in the army in the first place). I.e. assessing undemonstrated potential
  • The ACT, by contrast, has always aimed to assess what material a student actually knows, as a fraction of the material that the student is supposed to know. 

In other words, the SAT tried to determine how capable you were in general, and the ACT tried to determine whether you’d already learned what you were supposed to have learned by then. The tests have evolved over time (mostly with the SAT drifting towards the ACT), but there are still some shadows of their origins in their modern incarnations. 

Radiolab did a great series on this and a few related issues. But please note: it sometimes gets almost as dark as it is consistently fascinating.

Other quick links

  • I do SAT and ACT prep professionally, especially for high scorers. My buddy Ted Dorsey (of Wes & Ted’s Excellent Conversation) does even more, and across a wider range of student types. My former company bodsat.com has some very good programs that I helped design. You can call any of us, and if we aren’t the right fit for you, we’ll steer you in the right direction.
  • I know a lot of specialists who can help in various ways, and I see connecting people as an important (and enjoyable!) duty. If you need specific help, let me know what you’re looking for and I’ll do my best. And if you’re a fellow professional, please get in touch to let me know what you do best, so that I can help connect you with families who need it.
  • I mentioned my quick, free mini-course “What Am I Missing? earlier. I’m linking it here as well: wescarroll.com/waim. Feel free to explore it, and to share it.

Quote of the week, from an adult student:

”I missed this one because I (stupidly) assumed that…”

Don’t be so hard on yourself, sister. Assumptions are just shortcuts that didn’t ace their job. I would say that you jumped to a conclusion, didn’t notice that you’d jumped, and so you didn’t think to question it. Happens to the best of us. Let me help you up, dust yourself off, and let’s try again, hey? Right on.

Improvement means being wrong a lot. That’s not stupidity. It’s just the “cost of doing business” when you’re trying to get better.

The key bit is that you examine why that unhelpful assumption was poised for you to grab onto in the first place. It was probably there for (what used to be) a good reason. Re-assessing the reasoning, and possibly re-visiting your conclusion, is a very helpful way to keep no-longer-helpful habits and assumptions from continuing to re-assert themselves.

Last words

Hey, thanks for showing up here. I hope you found it helpful, or at least interesting.

I’m [email protected].com, I read all feedback personally, and I really do care whether this was helpful, and how I can make it better next time around.

Let’s talk about the AMC.

They say that the best time to plant a tree is 20 years ago, but today would be second-best. That’s how I feel about writing about the American Math Competition (AMC): I wish I had spent more time writing about it in the past, but I’ll do the next best thing and write right now.


Who cares?

You do, if you have (or are, or know) a student in high school who is interested in STEM and generally good at school. 

That student (plus their support structure) is usually focused on these three goals:

  1. Get good at core skills needed through adult life
  2. Build out a resume that opens doors later
  3. Get through this craziness without excessive friction or stress

For these students, the AMC remains a little-known but very powerful tool for helping to accomplish these goals.

Can this wait?

Not if you want to participate this school year. The AMC 10 and AMC 12 exams, usually given in February, are being given in November this year. This means much less time to prepare, but crucially, it also means that participating seniors will get to use their good scores in the college admissions process. 

Another benefit: those who participate this year will have much more time to prepare for the second level of the competition (the American Invitational Math Exam, or AIME) in March, if they qualify in November. In past years, students would discover they qualified for AIME with a week or less to spare before competing. This year, competitors will have months to prepare.

This matters for a couple reasons, but the one most focus on is that top schools want to know when an applicant made the cut for AIME. It’s one of those distinguishers that can really matter, esp. for schools with STEM-focused reputations and/or “elite standing.”

Recent testing trends

  • Over the last 20 years, high school has generally become a more systematized “accomplishment treadmill,” with the advantages and disadvantages that this implies
  • Over the last several years, the ACT and SAT have taken significant credibility hits. These include equity issues, doubts about correlation to college success, rejection by major universities, and most recently logistical difficulties simply being able to sign up for and take the test 
  • Side note: one problem with these tests that has always been lurking under the surface is that whatever it is that they test, they test it best for the people in the middle of its bell curve, but their results are most scrutinized for the people at the top of its bell curve. I.e. a harder test would be better-suited for the people who need it most
  • Nonetheless, competition for college admissions has remained very high 

College admissions offices, understanding all these trends, are continuing to use the AMC as a distinguishing characteristic among otherwise hard-to-distinguish strong students. 

I expect that the AMC will continue to increase in prominence in the coming years.

What I observe

Students who prepare for the ACT or SAT tend prepare by filling knowledge gaps, which is all to the good. For most students, this remains the main focus throughout their preparation.

Students at the high end of the curve who prepare seriously, though, only start their preparation the same way. Before too long, they run out of facts to learn and techniques to leverage, because the test simply doesn’t cover that much material that they haven’t already learned. (This is a big part of what I meant when I said that the test is geared towards students in the middle of its curve, but the students who care about it most are the ones at the top of its curve.)

This is the point at which things start going sideways:

  • Preparation becomes an exercise in meticulousness, sometime to the exclusion of engaged critical thinking. For these students, these tests are about simply not letting their attention drift as they answer easy question after easy question. (In my view, this selects for the wrong skills and habits among “top” students, and sets them up for trouble later. If you see it differently, I recommend the movie Brazil. It’s really good, and I hope you like it as much as I do, even though it makes me cringe to watch it.)
  • Also, preparation often becomes an exercise in anxiety management. I feel better about this consequence, since anxiety management is a real-life skill for sure. But I think we can all agree that that’s not the thing we all want to be selecting for in this context either. 

I’ve also observed that students preparing for tests that really challenge them develop skills that in my view hold much higher value overall: critical thinking, self-awareness and self-management, self-evaluation and metacognition, and creative problem-solving.

What I sometimes advise

If the ACT or SAT isn’t hard enough to allow you to show off your real skills, and you like STEM, then the AMC is probably worth looking at:

  • You get to work on problems that are harder than anything your teacher would subject your whole class to
  • You get to explore interconnections in the math you already know without having to learn a ton of new material
  • You get to practice the critical skill of making progress even on incomplete information 
  • Top universities actively solicit your AMC 12 score. This tells you everything you need to know about its importance to them

Recent trends in the AMC

At the top levels, the AMC can be seen as a feeder program for the International Math Olympiad. The US, Russia, and China have been vying for top honors at the IMO for the last few years now. I genuinely don’t know how much of this should be attributed to good coaching; I’m impressed by head coach Po-Shen Loh — he’s clearly focused on teaching well instead of merely on being smart, and you’d be shocked at how many miss that — but that’s all I know, because I’m not anywhere near the inner circle at that level.

But what I do know is that Richard Rusczyk’s project Art of Problem Solving has become the dominant force in this area. What started as a pair of (excellent) books and a thriving community has become the 900-pound gorilla in the space; practically every serious student competitor has some relationship with AoPS. There’s a ton of good stuff to say about AoPS, but I’ll also mention that two false impressions often come out of students’ initial foray there:

  1. “There’s a ton of math I need to learn in order to be successful here.”
  2. “Reading through other people’s solutions is the best way to learn.”

Regarding #1, it would be more correct to say that AoPS will help you learn a ton of math, and a relatively small slice of it is needed for AMC success. Figuring out what’s important remains more art than science, data analysis notwithstanding, because — at least at the AMC level — doing a good job of using what you know is generally more valuable than knowing more.

And regarding #2, AoPS rightly discourages this perspective, and actively, but you can only do so much when such a large proportion of your site is dedicated to the thing you’re telling everyone to use only judiciously. I mean, it’s been said plenty before: math is not a spectator sport. Doing math — and analyzing your steps and missteps after the fact — is the way to get good at it. Deliberate practice isn’t easy, often isn’t fun, and it certainly isn’t your default behavior when you’re reading a web site. But it’s the best way. Unfortunately, almost no students get this, at least not at the early levels.

A few related videos

I’m happy to help directly

  • There’s no charge for a scheduled video chat with me. (If you have a personal connection to me, please mention it, but it’s not necessary.)
  • My online AMC prep course is open for business. If you need to learn the fundamentals of AMC math, this is the place for you.
  • I know a lot of specialists who can help in various ways, and I see connecting people as an important (and enjoyable!) duty. If you need specific help, let me know what you’re looking for and I’ll do my best. And if you’re a fellow professional, please get in touch to let me know what you do best, so that I can help connect you with families who need it.

Other quick links

  • My buddy Amie Dorsey and I just recorded the 13th episode of our (now-monthly) podcast WATEC: The Excellent Conversation. You can just search for it on your podcast app, or watch it on YouTube. They’re about an hour each, and you’ll find links to snippets of the conversation in the comments so that you can browse for what’s most interesting to you. 
  • Wes Carroll’s Puzzler introduces parents and students alike to AMC problems and related brain-teasers. (No scratch paper required!) It’s fun for families to challenge each other around the kitchen table, and it’s also good for listening on your walk or run.

As I’m sure you know, subscribing to either or both of them lets us notify you when new episodes are ready, and also helps others to find them.

Last words

Hey, thanks for showing up here. I hope you found it helpful, or at least interesting. Subscribe to my newsletter (i.e. this) at wescarroll.substack.com.

I’m [email protected], I read all feedback personally, and I really do care whether this was helpful, and how I can make it better next time around. 

Here’s to another great school year for us all!

Three things I’m grateful for today

  • Pretty much everyone I talk to these days has a higher-than-usual level of difficulty and frustration, but we’re all working hard to keep that stuff from leaking into our conversations unwittingly. I really appreciate that emotional effort.  I’m also grateful that being on the receiving end of that effort helps me do my part on the sending end.
  • My AMC students are hitting that wall where they realize that what they’ve always done before isn’t going to keep working, and they have to pick up entirely new skills. Scary …and exciting! Seeing that realization dawn really makes this work feel worthwhile for me.
  • I’m grateful to have a job that I like enough to keeping working hard at, even when things are rough.

Get more of this and my book. For free.