Early on, Lars Pos’s parents noticed that they couldn’t keep him busy for long with a puzzle: they couldn’t get a job done or their son gave back the brain teasers, with all the pieces in the right place. ‘In primary school he taught himself mathematics, with YouTube videos,’ says Lars’ father, who adds that the mathematics teacher in the seventh grade confessed that he could not teach Lars anything.
Lars is now 18. He sits behind a large desk with scrambled notes. Today is the eleventh day in a row that he takes a math practice test, for which he isolates himself in his attic for four and a half hours. “If you think you can’t do something, think again,” reads a tile above his desk. He is preparing for the International Mathematical Olympiad (IMO).
Lars is one of six Dutch students who, after a long selection process, will represent the country in Oslo on 11 and 12 July. The IMO is the most prestigious international math competition for high school students, and has been held in a different country every year since 1959. During two days, participants are presented with six mathematical puzzles, which they must solve on their own.
Not a number but a proof
These puzzles do not ask for a number, as the result of a complicated sum, but for proof: an unmistakable argument that a certain statement is correct (or incorrect). An example of a proven mathematical theorem is that only four colors are needed to fill in the countries on a map so that no neighboring countries have the same color. Incidentally, this theorem would not be a question at the Olympiad: it took mathematicians more than a hundred years to find a proof.
Many participants go on to become pioneering researchers later in life: More than a quarter of the recipients of the Fields Medal, aka the “Nobel Prize in Mathematics,” were “mathletes” at the IMO. The same goes for the brothers Erik and Herman Verlinde: in 1980 the now leading physicists were in the Dutch six.
Although participants receive medals as individuals, the country with the highest total score in the corridors is the ‘winner’ of the Olympiad. Usually that is China, the United States or Russia. The Netherlands is 35th in the ranking, but has been on the rise in recent years.
This is partly due to innovations that organizers Quintijn Puite and Birgit van Dalen have implemented since 2006. Then the Dutch scores skyrocketed: in 2014 ‘we’ even became thirteenth out of 79 countries, with three golds, two silvers and a bronze medal. Those slices are awarded from a certain number of points, multiple participants can win them.
The secret behind the increasing success: an extensive selection process, which starts a year and a half before an Olympiad. Lars has been participating in the Dutch Mathematics Olympiad for four years and had to pass seven test moments this year to make the selection. Mathematics talent sometimes comes into the picture as early as primary school, through a national math and math competition.
Remarkably few girls
Striking: the Dutch selections have few girls, in the past ten years only three. And that while the ratio of boys to girls during the first selection rounds is about fifty-fifty.
This may be due to a lack of self-confidence in girls as soon as they start doing sums, says Martina Meelissen, education expert at the University of Twente. Out international research shows that girls believe in themselves less than boys, even if they score equally well.
‘While making an Olympiad question, everyone is actually constantly stuck’, says Johan Konter, one of the supervisors of the Dutch team. ‘I think girls see that more quickly as a signal that they can’t do it. Especially if they have been taken by the hand all their lives by their teachers, implicitly telling them that math is too difficult for them.’
The European Girls’ Mathematical Olympiad (EGMO) has been offering a solution since 2012: it is an international mathematics competition that only girls can participate in. Some find that stigmatizing, but Birgit van Dalen, former board member of the EGMO, says it gives girls a goal to aspire to, making them less likely to leave the selection process. Countries that participate in this girls’ competition have also had more girls in the selections for the Olympiad since 2012, Van Dalen points out.
The IMO’s questions are notoriously complex and incomparable to sums students face at school. These school assignments are intended to practice with a given method: derivatives are for tangents, integrals for areas and the abc formula can be used to find the solutions of quadratic equations. ‘Questions at the Olympiad are puzzles, in which the trick is to find the underlying solution method’, says Konter, himself a participant in 2004 and 2005.
To find the method for such a question, Lars first tries to get a feel for the problem. He plays with the equations, draws a picture or tries some numbers, to discover patterns that can give hints about “how the problem behaves,” as Lars puts it.
Lars and his teammates are taught these kinds of strategies during intense training days. After a brief lecture on a specific topic, the participants dive into exercises and then discuss the solutions with the trainers. Everyone receives feedback focused on their own talents and areas for development. For example, Lars made a mess of his scrap paper, so the advice was to bring it into order.
Too many questions to solve on purpose
For some participants, the ‘math battle’ is a highlight. It’s a somewhat playful game, with the team split in two and both teams given a morning to complete eight old IMO assignments. The trio then reunite to challenge each other to present their solutions. Teams win points for a correct solution or if they can point out an inaccuracy in the other team’s elaborations. Ten questions are deliberately too many to solve in one morning, which inevitably challenges teams to present an elaboration they hadn’t gotten around to. ‘Then they are confidently bluffing in front of the board,’ says Puite.
During the training sessions, the coaches also pay attention to the psychological aspects of the game. For example, Puite advised a previous team to regularly put ideas ‘in the fridge’ to come back to them later. It worked: afterwards he saw that one of his team members had drawn a refrigerator on his scrap paper, full of sketches and equations.
Lars does not suffer much from tension. “I’m really looking forward to it,” he says. Mathematics is simply his hobby. In his spare time, he makes TikTok videos about math. His most popular video: about his final exam in mathematics B, with more than a million views.
His teammates can also benefit from it. Like Lars, Jelle Bloemendaal (18, bronze medalist at the previous edition) has already taken courses at the university. Lars and Jelle want to become professors in the future. Another teammate, 15-year-old fifth-grader Mads Kok, already took his final exams in Mathematics B in the fourth grade. He then got a 9.8. Lars also had a score like that, but he immediately went for a resit: ‘I want a 10.’
What is the state of mathematics education in the Netherlands?
If there were such a thing as a championship for the mathematics level of students, the Netherlands would just miss a podium place. ‘We’ are in place four, according to the latest Program for International Student Assessment (Pisa) report, which looks at the numeracy of 15-year-olds. Gold, silver and bronze go to Japan, Korea and Estonia respectively. In another global ranking, the Netherlands is in the ninth Place.
‘I think we are doing well,’ says Ebrina Smallegange, chair of the Dutch Association of Mathematics Teachers. This is partly because Pisa looks at how well students can apply the material they have learned, something that Dutch mathematics education focuses on. ‘When Dutch students practice with the Pythagorean theorem, they do so on the basis of questions with a practical context.’ Questions like: ‘The stump of a broken tree is one meter high, and the top of the tree touches the ground 10 meters from the stump. How tall was the tree when it was still standing?’
It is remarkable that Dutch mathematics education scores high, while Dutch students have on average fewer teaching hours in mathematics than neighboring countries. After the introduction of the second phase, it was decided that mathematics should be given the same number of hours as other subjects: students spend three to four teaching hours a week doing sums. The high place in the mathematics ranking is therefore partly due to effective working from home, assisted by strong ‘shadow education’, such as tutoring and exam training.
Nevertheless, the Education Inspectorate has identified worrying developments. According to The State of Education 2022 mastery of basic arithmetic and mathematics has declined in recent years, among both first and third graders.
In addition, the number of unsatisfactory marks for mathematics on the final exams has increased: on average, about 23 percent of the students scored unsatisfactorily over all four levels, from 43 percent on the management vocational track to 14 percent on the VWO. Sun one and a half million The Dutch have low grades, which means that this group has difficulty functioning in society due to a lack of basic mathematical skills.
An obvious explanation is a growing shortage of qualified mathematics teachers, fueled by a high workload, few promotion opportunities and a low salary. Schools often fill the gap by putting students in teacher training in front of their class, even before they have graduated: ‘the green pick’, in the words of Smallegange. Their lack of experience detracts from the quality of education, but also hinders the pleasure that student-teachers experience from teaching, which makes them more likely to turn their backs on the subject.
Finally, experts cite the poor transfer options for VMBO and HAVO students as a possible cause. The latest Pisa report has shown that the mathematics grades of the best-performing VMBO students are at the level of the lowest-scoring VWO students. However, it is not easy for students to climb from one level to the next.