Image copyright Reuters Image caption Disadvantaged students in Shanghai are better at exams than rich students in the US

Education Secretary Nicky Morgan says she wants England to get into the top five of the international Pisa tests for English and maths by 2020.

The man in charge of the Pisa tests, Andreas Schleicher, says the evidence from around the world reveals some big myths about what makes for a successful education system.

1. Disadvantaged pupils are doomed to do badly in school

Teachers all around the world struggle with how to make up for social disadvantage in their classrooms. Some believe that deprivation is destiny.

And yet, results from Pisa tests show that the 10% most disadvantaged 15-year-olds in Shanghai have better maths skills than the 10% most privileged students in the United States and several European countries.

Children from similar social backgrounds can show very different performance levels, depending on the school they go to or the country they live in.

Education systems where disadvantaged students succeed are able to moderate social inequalities.

They tend to attract the most talented teachers to the most challenging classrooms and the most capable school leaders to the most disadvantaged schools, thus challenging all students with high standards and excellent teaching.

Some American critics of international educational comparisons argue that the value of these comparisons is limited because the United States has some unique socio-economic divisions.

Image copyright Reuters Image caption The US education system has high costs but very mixed results

But the United States is wealthier than most countries and spends more money on education than most of them, its parents have a higher level of education than in most countries, and the share of socio-economically disadvantaged students is just around the OECD average.

What the comparisons do show is that socio-economic disadvantage has a particularly strong impact on student performance in the United States.

In other words, in the United States two students from different socio-economic backgrounds vary much more in their learning outcomes than is typically the case in OECD countries.

2. Immigrants lower results

Integrating students with an immigrant background can be challenging.

And yet, results from Pisa tests show no relationship between the share of students with an immigrant background in a country and the overall performance of students in that country.

Even students with the same migration history and background show very different performance levels across countries, suggesting that where students go to schools makes much more of a difference than where they come from.

3. It's all about money

South Korea, the highest-performing OECD country in mathematics, spends well below the average per student.

Image copyright AP Image caption Family backing: Parents in South Korea light candles for their children taking exams

The world is no longer divided between rich and well-educated countries and poor and badly-educated ones. Success in education systems is no longer about how much money is spent, but about how money is spent.

Countries need to invest in improving education and skills if they are going to compete in an increasingly knowledge-based global economy.

And yet, educational expenditure per student explains less than 20% of the variation in student performance across OECD countries.

For example, students in the Slovak Republic, which spends around $53,000 (£35,000) per student between the age of 6 and 15, perform on average at the same level at age 15 as the United States which spends over $115,000 (£76,000) per student.

4. Smaller class sizes raise standards

Everywhere, teachers, parents and policy-makers favour small classes as the key to better and more personalised education.

Reductions in class size have also been the main reason behind the significant increases in expenditure per student in most countries over the last decade.

And yet, Pisa results show no relationship between class size and learning outcomes, neither within nor across countries.

Image caption Andreas Schleicher runs the OECD's influential Pisa global league tables

More interestingly, the highest performing education systems in Pisa tend to systematically prioritise the quality of teachers over the size of classes. Wherever they have to make a choice between a smaller class and a better teacher, they go for the latter.

Rather than putting money into small classes, they invest in competitive teacher salaries, ongoing professional development and a balance in working time.

5. Comprehensive systems for fairness, academic selection for higher results

There is a conventional wisdom that sees a non-selective, comprehensive system as designed to promote fairness and equity, while a school system with academic selection is aimed at quality and excellence.

Image copyright Getty Images Image caption Red Army school in Sichuan, China: There is nothing incompatible about high results and fair access

And yet, international comparisons show there is no incompatibility between the quality of learning and equity, the highest performing education systems combine both.

More from the BBC's Knowledge economy series looking at education from a global perspective

None of the countries with a high degree of stratification, whether in the form of tracking, streaming, or grade repetition is among the top performing education systems or among the systems with the highest share of top performers.

6. The digital world needs new subjects and a wider curriculum

Globalisation and technological change are having a major impact on what students need to know.

Image copyright Thinkstock Image caption Curriculums that are "mile-wide, inch-deep" do not work as well as in-depth study

When we can access so much content on Google, where routine skills are being digitised or outsourced, and where jobs are changing rapidly, the focus is on enabling people to become lifelong learners, to manage complex ways of thinking and working.

In short, the modern world no longer rewards us just for what we know, but for what we can do with what we know.

Many countries are reflecting this by expanding school curriculums with new school subjects. The most recent trend, reinforced in the financial crisis, was to teach students financial skills.

But results from Pisa show no relationship between the extent of financial education and financial literacy. In fact, some of those education systems where students performed best in the Pisa assessment of financial literacy teach no financial literacy but invest their efforts squarely on developing deep mathematics skills.

More generally, in top performing education systems the curriculum is not mile-wide and inch-deep, but tends to be rigorous, with a few things taught well and in great depth.

7. Success is about being born talented

The writings of many educational psychologists have fostered the belief that student achievement is mainly a product of inherited intelligence, not hard work.

The findings from Pisa also show this mistaken belief, with a significant share of students in the western world reporting that they needed good luck rather than hard work to do well in mathematics or science. It's a characteristic that is consistently negatively related to performance.

Teachers may feel guilty pushing students who are perceived as less capable to achieve at higher levels, because they think it is unfair to the student.

Image copyright AFP Image caption Talent or hard work?: An opera singer stands before ice domes made by students

Their goal is more likely to be enabling each student to achieve up to the average of students in their classrooms, rather than, as in Finland, Singapore or Shanghai-China, to achieve high universal standards.

A comparison between school marks and performance of students in Pisa also suggests that teachers often expect less of students from lower socio-economic backgrounds. And those students and their parents may expect less too.

This is a heavy burden for education systems to bear, and it is unlikely that school systems will achieve performance parity with the best-performing countries until they accept that all children can achieve at very high levels.

In Finland, Japan, Singapore, Shanghai and Hong Kong, students, parents, teachers and the public at large tend to share the belief that all students are capable of achieving high standards.

Image copyright Getty Images Image caption Examiners look at students' work submitted for places at an academy of fine art in Shaanxi province, China

Students in those systems consistently reported that if they tried hard, they would trust in their teachers to help them excel.

One of the most interesting patterns observed among some of the highest-performing countries was the gradual move away from a system in which students were streamed into different types of secondary schools.

Those countries did not accomplish this transition by taking the average and setting the new standards to that level. Instead, they "levelled up", requiring all students to meet the standards that they formerly expected only their elite students to meet.

In these education systems, universal high expectations are not a mantra but a reality.