When Estonia gained independence from the Soviet Union in 1991, it took the chance to reshape the country’s school education system. Mailis Reps, the incumbent education minister, recalls the concluding argument in any debate often ran: “Let’s try something that works in Sweden or Finland.”

Many others have done similarly. Every three years, the OECD (Organisation for Economic Cooperation & Development) publishes results of the Programme for International Student Assessment (PISA) with the latest out on December 3. PISA tests the reading, maths and science skills of 15-16-year-olds in the OECD’s member countries, as well as volunteers not in this club of mostly rich countries. The results provide a means to directly compare different education systems. It is now nearly two decades since the first batch results were released. Back then, there was a surprise. Finland, not previously renowned for its education, topped the table when it came to reading, and excelled in other categories, as well.

This Nordic country seemed to have discovered a way to get brilliant results without the discipline and intense workload of East Asian champions like Japan and South Korea, which were the other top scorers at the time. Educationists descended on Helsinki. They reported back that not only was education free and comprehensive, but teachers were highly respected, well-trained and left to get on with their jobs, which frequently involved enabling children to discover things for themselves. Schools in countries from Scotland to South Korea sought to mirror Finnish education.

Yet Finland’s image as an educational Utopia now seems somewhat out of date. The latest PISA results show a fall in its average score, as they have every round since 2006. Gaps between rich and poor pupils are widening, distressing for a country that prides itself on equality. Estonia, once a mere imitator, is now the highest achiever among OECD countries.

The parable of Finland helps to explain why there has been little overall progress since PISA began. The hope at the turn of the millennium was that the wealth of new information provided by the tests would help identify why some school systems do so well. Others would follow their lead, causing results to rise across the board. But although spending per pupil in the OECD has risen by 15 percent in the past decade, performance in reading, maths and science remains essentially the same as when the tests started.

Part of the reason for the lack of overall progress is that schools have less influence over results than is commonly assumed. Culture and other social factors, such as adult literacy, matter more, meaning that even well-informed policymakers can only make so much difference.

Other factors are also beyond the control of education ministers. Immigration plays an important role, with recent arrivals scoring below locals in most countries. Finland has seen a small uptick in the number of migrant pupils taking PISA over the past decade. More than four-fifths do not speak Finnish at home, helping to explain the big gap in performance between them and local students.

Finland’s decline may make the wonks who rushed to copy its schools seem silly. But looking deeper, there are still lessons to learn from Finland’s example. Despite the country having a reputation for cuddly teaching, it used to take a slightly more hardline approach. In 1996, four years before the first batch of PISA results, a group of British researchers visited the country. They found “whole classes following line by line what is written in the textbook, at a pace determined by the teacher…We have moved from school to school and seen almost identical lessons — you could have swapped the teachers over and children would not have noticed the difference.”

By the time the results came out, many Finnish schools had started to move in a very different direction, confounding touring policymakers. A forthcoming study by Aino Saarinen and colleagues at the universities of Helsinki and Oulu analysing PISA data from 2012 and 2015, concludes that children in schools which gave pupils more freedom to direct their own learning had lower scores in maths and science. Those from poor and migrant families suffered the most.

Any country hoping to import the Estonian model in its entirety is likely to be disappointed. The country has seen fast economic growth over the past three decades, which is associated with better results. And migration out of the country, combined with a lower birth rate, means the school population has fallen by 29 percent since 2000, leaving an unusual education system.