The latest findings of the triennial Programme for International Student Assessment are released today. Andreas Schleicher, who directs the OECD programme, looks at some of the recipes for success in countries that have performed well.

International comparisons are never easy and they aren’t perfect. But PISA, whose 2012 findings are released today, shows what is possible in education. The survey, conducted every three years by the Organization for Economic Cooperation and Development (OECD), helps countries see themselves in the mirror of the results and opportunities delivered by the world’s education leaders.

Even those who claim that the standing of countries in PISA mainly reflects social and cultural factors must now concede that it is possible to improve education. In mathematics, Brazil, Mexico, Tunisia and Turkey rose from the bottom; Italy, Portugal and the Russian Federation have advanced to the OECD average or close to it; Germany and Poland rose from average to good, and Shanghai (China) and Singapore have moved from good to great.

In 40 of the 65 participating countries, results improved in at least one subject area. This is a major tribute to educational efforts all around the world. These countries did not change their culture, or the composition of their populations, nor did they fire their teachers. They changed their education policies and practices – including the way they support teachers, the focus of the forthcoming 2013/4 Education for All Global Monitoring Report.

We focused this year’s PISA assessment on mathematics. Each year, OECD countries alone invest over $230 billion in math education in schools, but poor math skills still severely limit people’s access to better paying and more rewarding jobs. At the aggregate level, inequality in the distribution of math skills closely relates to how wealth is shared within nations.

This PISA 2012 assessment came as countries were still grappling with the aftermath of the economic crisis. The crisis has brought home the urgency of equipping more people with better skills to drive our economies forward, foster employment and reduce social inequality.

A large part of the education challenge is reducing underperformance. Across countries, almost a quarter of 15-year-olds did not even reach Level 2, the baseline in mathematics, where students have to do little more than employ basic algorithms or procedures involving whole numbers. Students in Canada, the Republic of Korea, Shanghai and Singapore did much better: the proportion reaching only Level 2 was one in 10 or less.

According to one estimate, if all 15-year-olds in the OECD area attained at least PISA Level 2 in math, they would contribute $200 trillion in additional economic output over their working lives. Such estimates suggest that the benefits of improvement dwarf any conceivable cost of improvement.

Part of the problem is that underperforming students often suffer from social disadvantage, and many school systems further amplify that disadvantage. According to PISA, advantaged and disadvantaged schools show particularly wide differences in levels of teacher shortages. Attracting the most talented teachers and school leaders to the most challenging classrooms will therefore be key to making headway. Indeed, PISA finds that higher-performing countries are allocating education resources more equitably among advantaged and disadvantaged schools.

Successful school systems also reflect a belief that all students can achieve at a high level and a willingness to engage all stakeholders in education – including students, through such channels as seeking student feedback on teaching practices. New results from PISA also show that students whose parents have high expectations for them tend to have more perseverance, greater intrinsic motivation to learn math, and more confidence in their own ability to solve math problems.

The challenges that school systems face are not just about poor children in poor neighbourhoods, however, but about many children in many neighbourhoods. Only 2% of students in the United States reach the highest level of math performance, demonstrating that they can conceptualise, generalise and use math based on their investigations and apply their knowledge in novel contexts. In Shanghai, by contrast, the share is 31%.

Several countries have shown how the share of top performers in school can be raised significantly, including high performers such as Hong Kong and the Republic of Korea and low performers such as Italy, Portugal and the Russian Federation. The world economy will pay an ever-rising premium on excellence, but raising excellence and improving equity are not conflicting policy objectives. Of the 13 countries that have significantly improved their math performance since 2003, three also show improvements in equity in education, and another nine improved their performance while maintaining an already high level of equity.

Raising outcomes is easier said than done. The status quo has many protectors, and countries need to think and act boldly to effect real changes. We can’t copy and paste school systems wholesale. But PISA has revealed that the world’s most successful school systems share an encouraging number of features.

Everybody agrees education is important. But the test comes when education is weighed against other priorities. How much do countries pay their teachers, compared with other highly skilled workers? Would you want your child to be a teacher rather than a lawyer? How do the media talk about teachers? What we’ve learned from PISA is that the leaders in high-performing systems have convinced their citizens to make choices that value education – their future – more than consumption today.

But placing a high value on education is just part of the equation. Another part is the belief in the possibilities for all children to achieve. The fact that students in some countries consistently believe that achievement is mainly a product of hard work, rather than inherited intelligence, suggests that education and its social context can make a difference in instilling the values that foster success in education.

In the past, different students were taught in similar ways. Today, top school systems embrace diversity by acknowledging that ordinary students have extraordinary talents and personalizing educational experiences.

High-performing school systems also share clear and ambitious standards across the board. Everyone knows what is required to get a given qualification.

And nowhere does the quality of a school system exceed the quality of its teachers. Top school systems pay attention to how they select and train their staff. They watch how they improve the performance of teachers who are struggling and how to structure teachers’ pay. They provide an environment in which teachers work together to frame good practice. And when deciding where to invest, they prioritize the quality of teachers over the size of classes. Not least, they provide intelligent pathways for teachers to advance in their careers.

High performers have also moved on from administrative control and accountability to professional forms of accountability and work organization. They support their teachers to make innovations in pedagogy, to improve their own performance and that of their colleagues, and to pursue professional development that leads to stronger educational practice.

In the past the goal was standardization and compliance; today top performers enable teachers to be inventive. In the past, the policy focus was on providing education; now it’s on outcomes and creating networks of innovation.

The most impressive outcome of world-class school systems is perhaps that they deliver high quality across the entire school system so that every student benefits from excellent learning. Overall, Finland did not come out quite as impressively as in previous assessments, but what makes Finland still special is that only 6% of the performance variation among students lies between schools. Every school succeeds.

Last but not least, high-performing systems tend to align policies and practices across all aspects of the system, make them coherent over sustained periods of time and implement them consistently.

No single combination of policies and practices will work for everyone, everywhere. Every country has room for improvement, even the top performers. That’s why we produce this triennial report on learning outcomes in education: to share evidence of the best policies and practices and to offer our timely and targeted support to help countries provide the best education possible for all of their students. With high levels of youth unemployment, rising inequality, a significant gender gap, and an urgent need to boost growth in many countries, we have no time to lose.