At the same time I understand the attractiveness of an Olympiad with an easy first round – it allows not-so-well-trained children to try and enjoy. This is the reasoning behind competitions like “Kangaroo”, and it makes sense. Not to mention that they simply do not teach mathematical proof at the US schools, and that I cannot imagine a first-round American test other than multi-choice. I believe that the US schema worked well enough for some time, while the set of children quickly solving easy problems was close to that who could do mathematical proofs. I am not sure this is still the case, partly because there now is a huge group of children trained to do an AMC problem in 3 minutes. They still do not do well on complex problems, but it is extremely difficult to compete with them in the first and second rounds. ]]>

https://ru-math.livejournal.com/114368.html (Russian text) ]]>

1) Поздравляю Вас с 8 Марта!

2) Мне кажется невозможным ввести в олимпиадную практику задачи на доказательство, если таких задач практически нет при обучении в школе. Это как пропасть в два прыжка преодолевать.

3) По моему убеждению, в России есть три олимпиады с превосходными задачами, и я затрудняюсь сказать, какая из этих олимпиад лучше. Во-первых, это Турнир Городов (https://turgor.mccme.ru/). Во-вторых, Санкт-Петербургская городская олммпиада (https://www.pdmi.ras.ru/~olymp/). И в-третьих, Московская. (https://olympiads.mccme.ru/mmo/). Кстати, московская олимпиада вот уже три года не является этапом Всероссийской. Так получилось. У нас тут свои олимпиадные тараканы…

Also, the American Regions Math League (which mathletes from dozens of states participate in) features a “Power Question”, which is a multi-hour problem involving several proofs and questions on a single topic. It is very exciting.

]]>I have the most experience with Equations, and you come across diverse topics such as prime factorization, modular arithmetic, and change of base. You set up a few restrictions for a round, arrange the number/operations cubes to form an expression, then you and your opponents go back and forth putting cubes in play until someone can come up with a solution using the cubes. You can also claim that no solution is possible. When it comes time to write a solution, you must be able to prove it to your opponents, or disprove an opponent’s solution. You’re not required to write a full “rigorous” proof, just enough to show you’re correct, but in the training for these games students are encouraged to learn theorems and prove them to come up with strategies they can use. These games definitely helped me think about math differently and I personally think they have the best chance of getting many kids interested in math, instead of just the kids in advanced math classes. The only downside is that these games are not that widespread. National competitions typically have teams from Florida, Louisiana, and Michigan and don’t have very many teams from other states.

]]>There’s one more competition MAA (and AMC, in particular) is trying to spread around the US – Math Wrangle, an adaptation of the Russian Math Battle. It requires not only solving problems that require proof but also presenting solutions and criticizing solutions presented by others. This competition can be equally well adopted for high school and middle school level and for more or less advanced kids, too. Math Wrangles were demonstrated at a number of national meetings – JMMs 2010, 2011, and 2012, and MathFest 2011, and a number of regional meetings, and they will be staged again at the MathFest in Madison this year and at JMM 2013 in San Diego, plus at the annual conference of the National Association of Math Circles – Circle on the Road – in Washington, DC, April 13-15, 2012. Math Wrangle rules and problem sets can be found at https://sigmaa.maa.org/mcst/

]]>We’re moving in this direction in the US, too. There’s been the Colorado olympiad for more than a decade, and now the Bay Area Math Olympiad (https://bamo.org) is about to have its 14th exam. For the last several years, BAMO has also had a separate exam for kids up to grade 8, so they can get an early start on these kinds of problems. I’m sure there are other regional exams like these but I don’t know about them.

ARML has long had the power round and a power contest once or twice a year that kids can do at their schools. The Mandelbrot contest also has an excellent team round involving proof-writing.

There are also tests like the USAMTS that help kids prepare for this kind of thinking and writing.

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