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An article by Krassimir Manev, Department of Informatics, New Bulgarian University and President of IOI 2014-2017, and Neli Maneva,  Bulgarian Academie of Science, Institute of Mathematics and Informatics for the "Olympiads in Informatics" vol. 11 book (2017).

As defined in The Glossary of Education Reform (Glossary, 2017): “The term curriculum refers to the lessons and academic content taught in a school or in a specific course or program“. Very frequently the word is used to denote just the list of courses offered by a school, but such understanding of the term is more appropriate for some external use – to demonstrate briefly to the community or some institutions the essence of the proposed education. Here we will consider the notion in its depth. As the above mentioned Glossary underlines: “… curriculum typically refers to the knowledge and skills students are expected to learn …” which includes:

• The learning standards or learning objectives the students are expected to meet.
• The units and lessons that teachers teach.
• The assignments and projects given to students.
• The learning resources – books, materials, videos, presentations and readings, used in a course.
• The assessment resources – tests, tasks, projects and other materials used to evaluate student’s learning.
  
  

(...)

After presenting the national reports of the participants in a Workshop a natural question raised: Is it possible to have universal and unique ISCC? The opinion of the most of the participants was that it seems impossible. Some arguments for this are listed below:

•  The general educational structure of different countries presented in the Workshop is very different! We expect that if a larger number of countries decide to apply such ISCC then the differences will be even more drastic.
• The Countries have various history of introducing education in Computing and so – different level of experience in teaching these disciplines, different traditions, different quantity and quality of teachers, different computing resources, etc.
• The specific structure of the economy of the countries supposes different models of school education in Computing. For example, some countries with developed software industries will need a model which is different from the model of countries in which there is no such industry and there no intentions to develop it. That is why it seems more realistic that not a single Curriculum but many different Curricula have to be created even in one specific country. The question is: are we able to predict what exactly will be necessary for education in Computing in each country, depending of its specific needs and to predefine some fixed number of Curricula, developing them in depth. The answer again is – rather not! That is 96 Kr. Manev, N. Maneva why it seems more appropriate for our goals a set of curriculum elements to be developed as well as guidance for using these elements in order to create many specific curricula. Good example for such kind of activity are the mentioned above efforts of the professional organizations ACM and IEEE-CS to elaborate and maintain during the years a system of curriculum elements and guidance for creating specific curricula in Computing for the university stage of education. That is why these efforts are resumed in the next chapter as well as a proposal how the methodology of ACM-IEEE curricula guidance group could be tuned for our goals.

ACM-IEEE Computing Curricula Guidance

ACM-IEEE Computing Curricula Guidance is not a single methodical act. It has about 20 years history. It is a persistent work of the ACM-IEEE Computing Curricula Guidance work group, which started with a single recommendations updated on a regular base through the year that recently led to specific recommendation for the different fields of the Computing domain. That is why this important work could be a model for creating and future maintenance of corresponding guidance for development of the ISCC.

The ACM-IEEE curriculum guidance work groups are based on some principles, that seem to be applicable to our goals:

• Curriculum guidance should not only identify the fundamental knowledge and skills of the domain but should provide a methodology for creating specific courses, defining their content and the appropriate order of teaching them.
• The required body of knowledge must be as small as possible.
• Curriculum guidance must strive to be international in scope, broadly based and must include professional practice as an integral component.
• The rapid evolution of Computing requires an ongoing review of the corresponding curricula recommendations through the years.
• Curriculum guidance must be sensitive to progress in technology, pedagogy and lifelong learning.
  
  3.2. Structure 
  
  
• Computing is a broad, scientific and practical human activity domain including a corpus of teaching elements – both theoretical (knowledge) and practical (skills), having computers as main objects – their creation as well as their programming and usage. On a Metodology for Creating School Curricula in Computing 97
• Body of knowledge of the domain describes it‘s fundamental concepts, theories and notions. Core of knowledge specifies the body of knowledge elements, for which there exists a broad consensus that they are essential for the education in the domain. Body of knowledge is hierarchically structured in fields, areas, units and topics.
• Learning objectives are composed of two parts – a set of requirements that all students should be able to meet and set of requirements to promote individual assessment of each student achievements.
• Curriculum models present different approaches for organizing the educational process among which the creator of a specific Curriculum could choose. ACMIEEE guidance considers three level of models – introductory, intermediate, and advanced.
• The part Course descriptions contains detailed description of the courses – both compulsory and elective. Course is the main structural object of each curriculum. One discipline could be covered by one or more courses and one course could be dedicated to one or more disciplines. Some other parts of the guidance structure could be also considered on the next stages of development of guidance for ISCC.

(...) We propose to use the body of knowledge from the version of ACM-IEEE guidance from 2001 and, after a broad discussion/questioning in IOI community and outside, to extract the areas and the units that are appropriate for the school. It will be necessary for sure to append some units or/and topics that are considered nowadays not appropriate or not necessary for the universities, but are important for school students. As the presentation of the countries that participated in the Workshop shows, there is some corpus of knowledge in the area IT (let us call it computing literacy) that is traditionally studied in schools, but not as university program, and have to find place in ISCC. The units of core of knowledge have to be identified as a result of the discussion/questioning mentioned above. Further we can choose an appropriate quantity of class hours for each unit. A similar process of deleting/appending has to be done for the individual topics of each included in the body unit (core or elective). In parallel, the corresponding educational objectives have to be edited with the respect of the age of the student. It is quite possible that in our recommendations we will have to define few alternative versions of the learning objectives connected with each individual topic, unit and even area, depending on the chosen educational model.

Identifying the necessary educational model in our case will be the most important and difficult task. As mentioned above the model is the element of each curriculum that has to introduce a flexibility in the process of creating curricula. This will be our instrument to cover as many as possible concepts of organization of education on different age levels of the school, as well as of the different kind of schools. Let us start with the levels of education which exist in the educational system of each country (and could be different). In most countries there are three levels in secondary school – primary, intermediate and high. In Bulgarian system, for example, two models exist for the level of education:

• 1–4 grades as primary, 5–8 grades as intermediate, 9–12 grades as high.
•  1–4 grades as primary, 5–7, grades as intermediate, 8–12 grades as high.

The trend is the first of them to be eliminated soon or later. There is also trend to separate the high level to two sublevels 8–10 grades and 11–12 grades in order to give a possibility for some specialization in the sublevel 11–12 of the students. Similar subdivision is predicted in (Computer Science, 2012). In addition we have to consider also existence of some special schools – mathematical, language, art, sport, professional, etc. That is why it is necessary to define very carefully the core units of the body of knowledge which to be common for the national educational system in order to give to each student, graduated in secondary school the possibility to continue her/his education in an university program of Computing does not matter in what kind of school is graduated. As well as to classify the elective units of the body in such a way that the curricula for the specialized schools to include the most appropriate for the peculiarities of the school elective units. In Bulgarian system, for example, the courses are classified in 3 categories – compulsory, compulsory-elective (which means that the students have to take m among the proposed set of n such courses) and free-elective (which means that students are not obliged at all but could take as many such courses as they would like). In last category the corresponding school could include any course which is appropriate to the profile of the school (professional school of machine engineering, for example, could include learning of one CAD/CAM system, which is inappropriate for other schools). Is it possible to define different kind of models also on the base of preferred main fields – CS-oriented (most appropriate for mathematical and engineering schools), IToriented (more appropriated for language, art and sport schools), CS&IT-oriented (more appropriated for regular schools), etc.

The most important difference between university models (we mean the classic universities but not the so called liberal art, where the educational model is more close to the models of secondary schools) and the school models is that in the university pro and the school models is that in the university programs in the domain of Computing in each moment students take few courses from the domain. In secondary school model we will have in each moment only one or maximum two courses in the domain with 1-4 class hours per week – asking for more class hours for Computing nowadays seems not realistic.

So the model has to include some „class hours per week“ scheme, which defines the grade, number of courses, class hours per week and distribution of the class hours between the two courses (or between IT and CS if the model includes only one course).

Read more about the implementation of the model and the full article here.

The very first European Junior Olympiad in Informatics - eJOI was launched today with an official ceremony in the Aula of the Sofia University “St. Kliment Ohridski”.

Attending the ceremony and greeting the teams and guests were the President of the Republic of Bulgaria Rumen Radev, the European Commissioner for the Digital Economy and Society Maria Gabriel and the Minister for Education and Science for the Republic of Bulgaria Krasimir Valchev. The European Commissioner for Education, Culture, Youth and Sport Tibor Navracsics sent his greetings to all participants from Brussels, wishing them success in this fundamental undertaking. Amongst the official guests were the ambassadors from the participating countries as well as representatives from the institutions and businesses who supported the event.

“It is exciting to be here with you, because I believe in the success of the European Junior Olympiad. I am confident, that it will build on your previous achievements. Today, this Olympiad goes from an idea to becoming a reality. Like every beginning, it starts with expectations and brings your hopes for victory. I believe that with each passing year, it will connect more and more teams from Europe, and perhaps, from other continents.” said Rumen Radev, President of the Republic of Bulgaria.

In her speech, Mrs. Gabriel showed her enthusiasm for the Olympiad as well: “Whatever the technology and society would see, what we must not lose out of focus is our humanity. This is what I see in you - minds, talents and people - all questing new challenges. You're all winners, keep the memories shared together and those connections close. From today onwards, all participants in this Olympiad have a new mission – you are the ambassadors of the future!”

The contribution to education, information and the future digital society was not missed by Mr. Valchev’s greetings as well. Another very special and interesting guest was Mario Bakalov - pilot of the world’s largest passenger aircraft, the Airbus A380, who wished many happy and safe landings to all: “The fascination to fly has been there all my life. All of you - you have a goal. You came here to be the best and meet new challenges, and i know the next days will be hard. I encourage you to fight, to follow your goals and to never give up. Many people have told me I would not succeed. Prove that you're the best team, act as an individual but also as a strong team. I admire you.“

The Initiative Committe of eJOi 2017 is: Biserka Yovcheva, CEO of A&B School of Informatics, Alexey Hristov, Chairman of the Management Board of The Natural Sciences Olympic Teams Association in Bulgaria, Elena Marinova, Chairman of the Development Board of the Natural Sciences Olympic Teams Association and President of Musala Soft, and Krassimir Manev, President of the International Olympiad of Informatics (IOI) 2014 – 2017. eJOI’s four initiators didn’t hide their great excitement about the realization of the Olympiad, and together with the Patrons, announced the official start of this year’s competition.

Teams from 22 Council of Europe member states arrived in Sofia to take part in eJOI. Being a host, Bulgaria is the only country to participate with two teams whilst all others compete for medals with one four-person team.

eJOI has two competition days – the 9th and 11th of September – taking place at the Sofia Tech Park. Results can be followed live on the eJOI website. The climax of the competition will be the final at 13:00 on September the 11th (Monday) in the John Atanasoff Forum, Sofia Tech Park. Participants’ emotions will peak as they learn their rankings seconds after the competition ends, sharing victory and disappointment with their team leaders.

All Bulgarian contestants won medals at the very first paneuropean competition in Informatics for students under 15,5 years. Closing ceremony was held on 12th September 

Sofia, Bulgaria, 12th September 2017. In the Aula of Sofia University “St. Kliment Ohridski” was held the official closing and awarding ceremony of the first European Junior Olympiad in Informatics eJOI. A total of 8 gold, 14 silver and 22 bronze medals were handed to the most talented young programmers of all 22 participating countries, members of the Council of Europe. First in the ranking by number of points and a gold medalist of eJOI is Nikoloz Birkadze (Georgia).

As a host, Bulgaria was represented by two teams:

Bulgaria Team 1 -  Leaders: Plamenka Hristova and Elena Dimitrova 

• Martin Kopchev - 8th grade, 8 клас, High School of Natural Sciences and Mathematics - Gabrovo (HSNSM), golden medal 
• Georgi Petkov - 8th grade, HSM - Varna, bronze medal 
• Zahary Marinov - 9th grade, HSM - Pleven, silver medal
• Konstantin Kamenov - 8th grade, HSM-Sofia, sillver medal

Bulgaria Team 2: Leaders: Kinka Kirilova and Bistra Teneva 

• Victor Kojouharov - 9th grade, HSNSM- Ruse, bronze medal
• Dobrin Bashev - 9th grade, HSNSM-Gabrovo, silver medal
• Andon Todorov - 8th grade, HSNSM- Blagoevgrad, silver medal
• Marin Yordanov - 8th grade, PHSNSM- Shumen, silver medal

The official closing ceremony of eJOI was attended by Prof. Dr. Anastas Gerdzhikov, Dean of Sofia University “St. Kliment Ohridski”, host of the event, as well as by the Deputy Prime Minister of the Republic of Bulgaria Tomislav Donchev.

“I would like to thank everyone here that the first European Junior Olympiad in Informatics is taking place in Bulgaria“, said in his speech Prof. Dr. Anastas Gerdzhikov, Dean of Sofia University “St. Kliment Ohridski”. He expressed gratitude to everyone who contributed to the success of eJOI and admitted that he is happy to see Bulgaria being a pioneer in the field again. Excited by the successful closing of the Olympiad and the honor to be the first elected President of eJOI, Prof. Krassimir Manev said: “The best young programmers of Europe are gathered here today.” He acknowledged his colleagues and the guides of eJOI. “I`m exceptionally content with how eJOI was held”, concluded Prof. Manev.

During the ceremony it was announced that the next host country of eJOI will be Russia. Russia is the country with the best team performance in the first edition of the Olympiad.  

A week has passed full of unforgettable emotions and new experiences for all participants in the first European Junior Olympiad in Informatics. Besides having the chance to benchmark their knowledge and skills in competitive programming with their mates aged up to 15.5 years from many other countries members of the Council of Europe, the talented young people got acquainted with the cultural and historical heritage of Bulgaria by visiting some of the most prominent places of interest in Sofia and Plovdiv. (Read more about their daily programs and visits in the other, previous issues of the eJOI Newsletter—find them here)

In each of the two contest days – September 9th and 11th – held in Forum “John Atanasoff” at Sofia Tech Park, the contestants had to solve three problems in informatics with the total number of points that they could possibly collect being 600 for both days. The results were followed in real time on eJOI website. The most emotional moment of eJOI was the very end of the contest at 1:00PM on September 11th when the system automatically terminated and the contestants met their team leaders for the first time impatiently sharing impressions, success and disappointment. To greet them in person minutes after the finale arrived the President of the Republic of Bulgaria for 2012-2017 Rosen Plevneliev. He talked to the contestants and team leaders and was the first to congratulate the number one in the ranking.

This post details my overall experiences as an observer for Bulgaria at the 57th international math olympiad, which took place in Hong Kong, between July 6th and July 16th 2016; there will be a subsequent post listing day-to-day impressions, plus some photos.

That was my first time behind the scenes of the IMO, so pretty much everything was new to me. Hopefully this post can be of use to anybody curious about the inner workings of the olympiad!

The happy news

The happy news is that this time our team did remarkably well compared to the last few years; we ranked 18th among about 110 countries1, and we haven’t done that well since 2008. Moreover, we were impeccable on the easy problems 1 and 4 (with 84/84 points), which helped everybody get a medal (which hasn’t happened since 2010). We ended up with 3 silver and 3 bronze medals, a solid batch. Overall, I think that’s pretty impressive for a 7-million country2.

The problems

The problems were for the most part beautiful; my favorites are 3,5,6 (3 and 5 are both from Russia!), and I dislike 4, which to me is just a sequence of calculations with no significant ideas involved (though one can argue that 1 can also be solved like that). Problems 1 and 2 were fairly standard.

The consensus among the individual members of the jury whose opinions on the difficulty I got to hear (conditional on the problem’s position) seemed to me to be the following:

• Problem 1: hard
• Problem 2: easy
• Problem 3: somewhat hard
• Problem 4: somewhat easy
• Problem 5: somewhat hard
• Problem 6: easy

This matched my views. Such deviations are normal, since you can’t make a perfect exam with such a small shortlist (8 problems from each area) and so little time. However, I do think the jury’s opinion was swayed by the unfortunate position of problem 1 as G1 (easiest geometry) and problem 6 as C7 (next-to-hardest combinatorics) in the shortlist. But more on that later.

The consensus among the contestants (given the results) seemed to be that we underestimated 2 and 6, though the unforeseen difficulty of 6 was likely psychological (because it’s 6). So while some people (especially on AoPS) were quick to predict high cutoffs, things ended up at 29 for gold.

The ‘flat distribution’3 trap

There was a point during the problem selection when there was a real danger of the vote swinging towards an easy exam that wouldn’t distinguish well between contestants. The thing is that there are now many “new” countries at the IMO which have a (understandable) tendency to vote for problems more accessible to the less technically prepared contestants. I believe that most, if not all, of the problems at the olympiad should be as accessible as we can make them, and rest on simple but creative arguments, as opposed to heavy theory and standard machinery. A notorious example of the latter is problem 6 from IMO 2007. As for positive examples, I think problems 5 and 6 in this IMO were perfect. However, my feeling is that on average there is a non-negligible negative correlation between difficulty and accessibility among the shortlist problems; I’m guessing the reason is that it’s just darn hard to come up with perfect olympiad problems.

Anyway, something – maybe it is this correlation trap, or maybe they just want easy points for their teams – seemed to drive the newer countries to prefer easier problems, which would have in turn led to an exam that doesn’t distinguish contestants much. That’s something we don’t want4, because it makes us feel like the whole IMO was a waste of time. Happily, several conscientious team leaders spoke up against the “flat” motion, and miraculously the jury changed their minds (yes that’s something people don’t usually do).

Considerations during problem selection

Beauty will save the world?

I was surprised by how much non-mathematical considerations can shape the exam. For example, well before any problems are chosen, all team leaders vote in the so-called beauty contest where problems are rated on 3-degree scales according to their difficulty and beauty. What surprised me wasn’t that problem 6 was rated as the most beautiful in the shortlist (it simply is very, very neat); it was that it became problem 6 instead of problem 3 or 5, which would have made more sense given its difficulty. This decision seemed to be a combination of three things:

• the position of the problem as C7 in the combinatorics section of the shortlist, which probably made it seem harder than it is;
• the choice of problems 1,2,4 and 5: a total of four easy and medium problems, one from each area, are chosen before the hard problems, but are not assigned exact positions on the exam beyond that5. So by the time you’re choosing how to order the hard problems 3 and 6, you face additional constraints; and
• the jury’s overwhelming consensus that #6 must be an exceptionally beautiful problem.

I find the last reason convincing, but not convincing enough in the context of this exam; given the results, I believe many students were misled by this ordering of the problems and didn’t try problem 6 just because it was problem 66.

Half geometry, half something

Another interesting, though not as prominent, feature of problem selection was that some team leaders argued that certain problems just can’t be put into one of the four neatly labelled boxes ‘algebra’, ‘combinatorics’, ‘geometry’ and ‘number theory’. In this year’s exam, these were problems 3 (formally number theory) and 6 (formally combinatorics). Problem 3 is a glorious mix of number theory and geometry (and some might argue combinatorics), while for problem 6 the geometric nature of the configuration matters – it doesn’t work with pseudosegments (a set of arcs every two of which intersect in at most one point).

This way, the supporters of this point of view argued, we get one more geometry problem out of those two, so people shouldn’t be sad that only one problem from the geometry part of the shortlist ended up in the exam. As another example, during the selection a problem from the algebra section of the shortlist competed for a spot among the easy/medium problems as if it was combinatorics.

I’m a big fan of this way of thinking, and I think it works especially well with the mechanism that picks one problem from each area for the easy/medium problems first. For one thing, the ideal number of problems from each area at the IMO is 1.5, and once you’ve chosen each 1, you feel a little awkward; but that’s backward thinking, already assuming you’re sticking to the mechanism for easy/medium problems. I believe a better reason is that often the most beautiful and hard problems are both beautiful and hard precisely because they combine insights from different areas. In this sense, we had a good IMO.

Geometry should be solved by geometric, and not algebraic, intuition

This makes total sense, and I’m a big fan. There was a geometry problem easier than G1 in the shortlist which was quickly shot down because it was easily amenable to various computational techniques.

On the other hand, one person on our team did a completely computational solution of problem 1, too (and got full marks).

Ordering within the shortlist

Finally, this is somewhat trivial, but it does matter more than you might think: I already mentioned above that in the case of problem 6, its position as C7 in the shortlist mattered. In fact this happens with many problems. At the IMO there isn’t much time for team leaders to get acquainted with the solutions to all the problems in the shortlist, not to mention to try and solve them by themselves. So what happens is that the way the problems are ordered by the problem selection committee in the shortlist is given more credibility than it probably deserves. So team leaders could really use some helpers during problem selection. This brings us to…

Your part as an observer

The main thing to know is that pretty much the only thing observers can’t do is vote – only the team leader of each country can – but even so, they can consult with the leader to influence their vote. There was ample opportunity, both during breaks and during discussions, to chat with leaders about the current situation.

Apart from that, observers can offer help at each stage of the olympiad. The deep, complicated principle at work here is that two heads are better than one:

• upon arrival, they can get to know the shortlist, and give according advice to the leader. For example, what we did with my leader was split the problems by area, according to our favorites: he took algebra and number theory, and I took geometry and combinatorics.
• when marking schemes are out, observers can similarly get to know their ins and outs.
• during the competition, when contestants’ questions arrive, the fittest observers can outrun other team leaders walking between the table where questions arrive and the queue for sending back the answers, thus delivering the answers to their team members several minutes earlier7
• after the competition, they can help grade the contestants papers, so that the leader can have a better idea of any potential weak spots well before coordination8.
• observes can participate in coordination, though keep in mind that during a given problem’s coordination, only two people among the team leader, deputy leader and observers can represent a country.

For a concrete example of how observers can even help changing the final score, during one of our problems’ coordination, there was a student from our team with some partial results that we believed were worth 1 mark. The solution could be completed using Gaussian integers, as in one of the official solutions; however, the student’s paper had no mention of that idea. The precise mix of arguments he had given turned out to be a one-of-its-kind at the olympiad, so it was up to the head coordinator for that problem to make the final decision. He ended up insisting on 0 marks, unless we could show them a continuation of the student’s ideas without Gaussian integers. We had about one hour to figure it out, and luckily, with the last 4% of my phone’s battery I found a solution on AoPS which we could use, and we got our 1 mark.

Beyond helping, observers are free to attend all jury meetings.

All this is very good if you’re a country with enough sponsors that can send observers along; however, it seems that poorer countries are at a disadvantage because they’re missing all these benefits.

There is the related question of whether team leaders can send scans of contestants’ papers to people back home; while until this year the rules allowed for that, the jury accepted a change according to which leaders can consult people not at the olympiad, but cannot communicate the precise details of the papers (such as scans) with them. This policy makes sense by itself I think, but it deepens the above problem…

The atmosphere and people at the 57th IMO

It was amazing to witness mathematicians from 110+ countries come together for a cause that serves the brightest high-school math students in the world. While one can argue that different countries have different interests (for example, countries with well-trained students might prefer different problems to countries with inexperienced students), jury meetings were conducted in a spirit of goodwill, and, what’s more notable, rational arguments were able to change the vote several times.

My only disappointment was during the final jury meeting, when medal cutoffs are decided. This year there seemed to be about 25 countries missing during this meeting. For other jury meetings that’s not a tragedy, but in the final meeting you need 2/3 ofall jury members to vote ‘yes’ if you are to allow more than exactly half the contestants to get medals. So what happened this year was that we needed 72 votes to give a dozen more medals instead of a dozen fewer, and there were about 80 jury members present… so it didn’t work.

Other than that, the atmosphere was relaxed, and it was not unusual for people to joke during the jury discussions (kudos to Geoff Smith, the president of the IMO, for being an especially jolly guy).

I got to talk to some of the team leaders, and it seems most are involved in academic mathematics through teaching or research. Unfortunately, language still seems to be somewhat of a barrier. In the first several jury meetings, the policy was for more complicated questions to be translated into the other official languages of the IMO – Russian, French and Spanish – but at some point we dropped it, and people seemed to be OK with that. But I still felt that some leaders weren’t at ease when addressing the jury in English, and that gave native English speakers a bit of an advantage in terms of persuasiveness.

Events and logistics

This year’s IMO was extremely well-organized, thanks to our diligent Hong Kong hosts (and, likely, to the generous sponsorship). There wasn’t much free time for leaders and observers, but the organizers managed to cram in some cool events. Hong Kong was as beautiful as it was warm and humid (a lot), and the Hong Kong University of Science and Technology’s campus offered some stunning views.

Perhaps most memorable among the events was the “Forum on mathematics in society”, or rather one of the talks in it, in which Professor Man Keung Siu raised the question “Does society need IMO medalists?”. Thanks to Professor Siu, the full text is available here, and I warmly recommend it. The main thesis was that while society doesn’t need the IMO medalists per se, it does need people who are aware of the role of mathematics in the world and in human civilization, and are not afraid to reason about its basic principles. So the value of the IMO is that it drives a large mass of people worldwide to improve their mathematical skills. Here’s a particular excerpt that serves as a bit of an answer to the question in the title (it’s actually taken from the book “Alice in Numberland: A Students’ Guide to the Enjoyment of Higher Mathematics”):

My good friend, Tony Gardiner, an experienced four-time UK IMO team leader, once commented that I should not blame the negative aspects of mathematics competitions on the competition itself. He went on to enlighten me on one point, namely, a mathematics competition should be seen as just the tip of a very large, more interesting, iceberg, for it should provide an incentive for each country to establish a pyramid of activities for masses of interested students. It would be to the benefit of all to think about what other activities besides mathematics competitions can be organized to go along with it. These may include the setting up of a mathematics club or publishing a magazine to let interested youngsters share their enthusiasm and their ideas, organizing a problem session, holding contests in doing projects at various levels and to various depth, writing book reports and essays, producing cartoons, videos, softwares, toys, games, puzzles, … .

So there you go, the IMO is not completely useless!

Acknowledgements

I’d like to thank the people involved in the training of the Bulgarian team, who invited me to be an observer at this IMO.

I’d also like to thank the American Foundation for Bulgaria for their generous support, which made it possible for me to attend the entire event free of charge. More importantly, the AFB has been consistently sponsoring the Bulgarian national math team for more than 10 years now. Finally I’d like to thank the “Georgi Chilikov” Foundation for their support for the team, and their broader contributions to education in Bulgaria.

1. However, people reporting on the IMO often fail to mention that there are usually several countries that send fewer than six people, so it’s not fair comparing team results across all countries. This year, there were about 15 such countries, so the correct number is more around 95.
2. Though we have done more impressive things in the past: for example, see our resultsfrom the 90s. Also, it seems to be an interesting mathematical problem to normalize IMO performance with respect to country population.
3. Here, ‘flat distribution’ means that when you plot the scores of all the contestants in order, the resulting graph is mostly composed of several flat plateaus
4. Some related stackexchange discussion here
5. This is a recent mechanism (since 2012), and it seemed, until this year, to have the side effect of forcing problems 3 and 4 to be geometry.
6. On the bright side, our team got lucky, and several people tried it. In the end, two people solved it, which gave us a considerable advantage.
7. OK, this was probably just a by-product of the logistics of this IMO’s question answering process.
8. Coordination is the process through which team leaders and observers negotiate the marks on their team’s papers with the official graders of the IMO, the coordinators. Since many of the papers are in a language unknown to the coordinators, they often need some additional clarifications. But coordination also offers the opportunity to argue for more credit when a contestant’s solution deviates from the marking schemes.

A. Makelov