These competitions are a wonderful experience for participants, who represent their country at the highest level. Apart from the irreplaceable intellectual challenge, students I’ve taken to the IOL - Computational Linguistics - on two occasions have made terrific lasting friendships. There’s no other experience like it.
Great overview of the decline in AMC participation and accessibility. Contests are such an important way to get kids excited about challenging math. I wish I had the answers for how we turn this around — there’d be a lot of value to contest opportunities as a “normal” school experience.
Thank you for writing this, particularly about the lack of access to the AMCs in rural areas. Parents often need to fight or drive long distances to find a seat for their students. Meanwhile, the MAA seems to have an ambivalence about the AMC that is mystifying, about such a valuable undertaking in a world with rampant grade inflation.
The MAA may disagree, but the AMC is in fact a college admissions test. Currently CalTech and MIT ask specifically for AMC scores (though they are not required for admission).
I've heard about cheating at the highest levels, but there's no need to cheat, when the MAA takes a hands off approach in the name of avoiding "bureaucratization." Students can report on college applications any reasonable score they want, and there is no way to verify, there is no official score reporting, no way to determine who qualified for AIME and who did not.
I've heard insiders describe the MAA as a "ghost ship." At so many levels they don't seem to care about this most historic and beloved exam.
Sad to hear the “ghost ship” rumor. I know nothing of the MAA’s internal organization; but once an org like that loses its way, it can be very hard to turn around. There is no real accountability. I wonder if someone with a strong interest in math contests and a bunch of money (fair number of tech bros might fit this description) can be prevailed upon to offer the MAA a large donation to fund updated grading, security, record-keeping and marketing systems in return for meaningful changes in the AMC’s governance. Namely, putting more people who are capable and passionate about the mission and credibility of the exam in charge.
I'm curious about your footnote regarding the idea that the AMC is a bad first-round filter due to its emphasis on speed and arithmetic accuracy rather than proofs; do you have an alternative proposal for what the first round could look like in a way that would feasibly scale to an entire nation?
I read the blog post you linked, which made some good points, if a little hyperbolic (a hypothetical IMO gold medalist who couldn't advance from the AMC to the AIME? really?). They also wrote a subsequent post which suggested a potential future alternative of writing proofs for all questions in the AMC to be checked by AI – quite the suggestion given that the post was written in 2009! In any case, something like that does seem like it may be feasible if a bit noisy, but I worry that it might even be _more_ exclusionary, since the vast majority of students in the US have never seen proofs outside of two-column geometry ones.
I think it is entirely possible to write questions that allow long-form answers without being more exclusionary. In a lot of cases an existing AMC/AIME question can be used verbatim or with minimal changes, and this would just amount to students having to show their work. (This has a design advantage that a tiny arithmetic error will not cost the student the entire problem.) The questions you would want to avoid are those for which the answer is easy to guess but hard or technical to prove; however we already basically exclude such questions anyway from answer-only exams.
In fact my impression is most countries already do something like this (where long-form answers appear much earlier). To give examples in English language where the open-to-everyone contest is like this:
- Canada Open Math Challenge mixes some full proofs as well as a hybrid questions (where a correct answer earns full marks but you earn partial marks for your work even when the final number is off).
- British Math Olympiad round 1 is just fully proof-based.
India's first round is numerical, but their second round (the Regional Math Olympiad) is proof-based. More broadly speaking, in many large countries, there are often regional proof-based olympiads that feed into a larger national olympiad to deal with the scaling problem of grading. I agree the use of AI is an another possible approach to scaling the grading that wouldn't have been previously possible, but might be in the future.
Regarding the idea of developing the competition as a standardized talent identification test to attract enrollment, I think that is unnecessary. There already exist widely taken standardized exams that could act a first filter for potential math talent. The trick is to connect students’ performance on these exams to recruitment to take the AMC (and to exposure to more advanced math resources in general).
For example, the PSAT/NMSQT is widely taken by high school students in the fall of their junior year because of the potential to obtain National Merit Scholarships. Any student scoring in the top 2-3% on the PSAT math section should get direct outreach which strongly encourages them to take the AMC12 along with guidance on the online resources to prepare. Notification and encouragement to their school might be helpful as well. Identifying students earlier than Grade 11 is probably desirable, and tests like the PSAT10, PSAT8/9 and the various state standardized middle school exams might all be ways to find the students who should be exposed to math contests. None of these tests are true talent identifiers, since they cannot distinguish between the merely bright and the very gifted, but they make up for that in being already established, with wide and even universal coverage. The missing AMC competitors are surely found amongst their top performers. Is this type of outreach already happening?
Also, I am curious if the MAA has ever commissioned market research with math teachers and school administrators to understand the barriers to more broadly offering the test. Is it just awareness or something more?
In my high school years (2010s), our high school’s AMC offering was organized by one (young) math teacher who was also the Math Club’s advisor. It was viewed as school business insofar that anyone *could* opt to take it during the school day, but only the nerds do and everyone else would prefer to have their usual class. That’s why I’m struck by the Dr. Kent Merryfield quote. I wonder if there’s something to be learned from how that commonplace status came to be back then. What kind of marketing/negotiating with schools was done to allow the AHSME to take up a school day, and why has that stopped?
I think the biggest factor (as you mentioned in the article) is the disconnect between competition math and school math. In an ideal system, any good student without additional training should be able to participate in an entry level competition and enjoy it. If interested, they can move up the ladder. This is far from today's reality. Schools have excluded anything beyond the mere basics from its mission, almost to the extent of being openly hostile to it. By forcing math competition out of school, they made the competition both more elitist and more commercial, which further contribute its unpopularity.
Any kinds of thing has art vs science, and in terms of olympiad, art is something that makes the problems beautiful or interesting (or a problem sets, like subjects distribution), while science is making the problem technical and that trained students have advantages (so I think TST's has more of this flavor, but i dont know). Some people emphasize the difficulty of the problem and thus science, and vice versa; but as you wrote, we need both. To balance the ``experience'' as a personal life and ``fairness'' as a society.
This is the quote by Franz Kafka:
“[Art] must be the axe for the frozen sea within us”.
These competitions are a wonderful experience for participants, who represent their country at the highest level. Apart from the irreplaceable intellectual challenge, students I’ve taken to the IOL - Computational Linguistics - on two occasions have made terrific lasting friendships. There’s no other experience like it.
Great overview of the decline in AMC participation and accessibility. Contests are such an important way to get kids excited about challenging math. I wish I had the answers for how we turn this around — there’d be a lot of value to contest opportunities as a “normal” school experience.
Thank you for writing this, particularly about the lack of access to the AMCs in rural areas. Parents often need to fight or drive long distances to find a seat for their students. Meanwhile, the MAA seems to have an ambivalence about the AMC that is mystifying, about such a valuable undertaking in a world with rampant grade inflation.
The MAA may disagree, but the AMC is in fact a college admissions test. Currently CalTech and MIT ask specifically for AMC scores (though they are not required for admission).
I've heard about cheating at the highest levels, but there's no need to cheat, when the MAA takes a hands off approach in the name of avoiding "bureaucratization." Students can report on college applications any reasonable score they want, and there is no way to verify, there is no official score reporting, no way to determine who qualified for AIME and who did not.
I've heard insiders describe the MAA as a "ghost ship." At so many levels they don't seem to care about this most historic and beloved exam.
Sad to hear the “ghost ship” rumor. I know nothing of the MAA’s internal organization; but once an org like that loses its way, it can be very hard to turn around. There is no real accountability. I wonder if someone with a strong interest in math contests and a bunch of money (fair number of tech bros might fit this description) can be prevailed upon to offer the MAA a large donation to fund updated grading, security, record-keeping and marketing systems in return for meaningful changes in the AMC’s governance. Namely, putting more people who are capable and passionate about the mission and credibility of the exam in charge.
I'm curious about your footnote regarding the idea that the AMC is a bad first-round filter due to its emphasis on speed and arithmetic accuracy rather than proofs; do you have an alternative proposal for what the first round could look like in a way that would feasibly scale to an entire nation?
I read the blog post you linked, which made some good points, if a little hyperbolic (a hypothetical IMO gold medalist who couldn't advance from the AMC to the AIME? really?). They also wrote a subsequent post which suggested a potential future alternative of writing proofs for all questions in the AMC to be checked by AI – quite the suggestion given that the post was written in 2009! In any case, something like that does seem like it may be feasible if a bit noisy, but I worry that it might even be _more_ exclusionary, since the vast majority of students in the US have never seen proofs outside of two-column geometry ones.
I think it is entirely possible to write questions that allow long-form answers without being more exclusionary. In a lot of cases an existing AMC/AIME question can be used verbatim or with minimal changes, and this would just amount to students having to show their work. (This has a design advantage that a tiny arithmetic error will not cost the student the entire problem.) The questions you would want to avoid are those for which the answer is easy to guess but hard or technical to prove; however we already basically exclude such questions anyway from answer-only exams.
In fact my impression is most countries already do something like this (where long-form answers appear much earlier). To give examples in English language where the open-to-everyone contest is like this:
- Canada Open Math Challenge mixes some full proofs as well as a hybrid questions (where a correct answer earns full marks but you earn partial marks for your work even when the final number is off).
- British Math Olympiad round 1 is just fully proof-based.
India's first round is numerical, but their second round (the Regional Math Olympiad) is proof-based. More broadly speaking, in many large countries, there are often regional proof-based olympiads that feed into a larger national olympiad to deal with the scaling problem of grading. I agree the use of AI is an another possible approach to scaling the grading that wouldn't have been previously possible, but might be in the future.
Regarding the idea of developing the competition as a standardized talent identification test to attract enrollment, I think that is unnecessary. There already exist widely taken standardized exams that could act a first filter for potential math talent. The trick is to connect students’ performance on these exams to recruitment to take the AMC (and to exposure to more advanced math resources in general).
For example, the PSAT/NMSQT is widely taken by high school students in the fall of their junior year because of the potential to obtain National Merit Scholarships. Any student scoring in the top 2-3% on the PSAT math section should get direct outreach which strongly encourages them to take the AMC12 along with guidance on the online resources to prepare. Notification and encouragement to their school might be helpful as well. Identifying students earlier than Grade 11 is probably desirable, and tests like the PSAT10, PSAT8/9 and the various state standardized middle school exams might all be ways to find the students who should be exposed to math contests. None of these tests are true talent identifiers, since they cannot distinguish between the merely bright and the very gifted, but they make up for that in being already established, with wide and even universal coverage. The missing AMC competitors are surely found amongst their top performers. Is this type of outreach already happening?
Also, I am curious if the MAA has ever commissioned market research with math teachers and school administrators to understand the barriers to more broadly offering the test. Is it just awareness or something more?
In my high school years (2010s), our high school’s AMC offering was organized by one (young) math teacher who was also the Math Club’s advisor. It was viewed as school business insofar that anyone *could* opt to take it during the school day, but only the nerds do and everyone else would prefer to have their usual class. That’s why I’m struck by the Dr. Kent Merryfield quote. I wonder if there’s something to be learned from how that commonplace status came to be back then. What kind of marketing/negotiating with schools was done to allow the AHSME to take up a school day, and why has that stopped?
I think the biggest factor (as you mentioned in the article) is the disconnect between competition math and school math. In an ideal system, any good student without additional training should be able to participate in an entry level competition and enjoy it. If interested, they can move up the ladder. This is far from today's reality. Schools have excluded anything beyond the mere basics from its mission, almost to the extent of being openly hostile to it. By forcing math competition out of school, they made the competition both more elitist and more commercial, which further contribute its unpopularity.
Sorry if my English is strange.
Any kinds of thing has art vs science, and in terms of olympiad, art is something that makes the problems beautiful or interesting (or a problem sets, like subjects distribution), while science is making the problem technical and that trained students have advantages (so I think TST's has more of this flavor, but i dont know). Some people emphasize the difficulty of the problem and thus science, and vice versa; but as you wrote, we need both. To balance the ``experience'' as a personal life and ``fairness'' as a society.
This is the quote by Franz Kafka:
“[Art] must be the axe for the frozen sea within us”.