by Chiara Monticone
Analyst, Directorate for Education and Skills
Mario Piacentini
Analyst, Directorate for Education and Skills
Films about mathematicians have become incredibly popular: many of us now know about John Nash’s beautiful mind. Fewer people have heard the extraordinary story of Srinivasa Ramanujan, a genius of comparable stature to Nash. Ramanujan was nothing more than a promising 16-year-old student from a poor family in South India when he came across A Synopsis of Elementary Results in Pure and Applied Mathematics, a compilation of thousands of mathematical results used by English students. Starting from the textbook, Ramanujan taught himself mathematics. After failing to get into university in India, he sent a letter to one of the great scholars of that time, Godfrey Harold Hardy, who noticed his talent and invited him to Cambridge. Hardy quickly understood that, in spite of his amazing feats in mathematics, Ramanujan lacked the basic tools of the trade of a mathematician. If he was to fulfil his potential, he had to acquire a solid foundation in mathematics. The Cambridge mathematician worked tirelessly with the Indian genius to harness his creativity to the then-current understanding of the field without destroying his confidence. One good textbook and one outstanding teacher changed the fate of a man and the evolution of number theory and analysis.
There are poor students like Ramanujan who show that achieving great results in their education and professional life is possible. But “possible” is not sufficient: education and social policy should make poor students’ success “probable”. This month’s PISA in Focus and a new OECD report, Equations and Inequalities: Making Mathematics Accessible to All show that millions of students around the world – especially those from socio-economically disadvantaged backgrounds – often have few opportunities to develop their mathematics skills.
Many students who participated in PISA 2012 reported that they have hardly been exposed to fundamental concepts in mathematics, like arithmetic means or linear equations, which form the basis of the numeracy skills that they will need to thrive as adults. Disadvantaged students are even less exposed to these concepts. For example, the share of advantaged students who reported that they know well or have often heard the concept of quadratic function is 20 percentage points larger, on average across OECD countries, than the share of disadvantaged students who reported so; and the difference between these two groups of students is larger than 30 percentage points in Australia, Austria, Belgium, France, New Zealand, Portugal, the Slovak Republic, the United Kingdom and Uruguay. The relationship between the content covered during mathematics class and the socio-economic profile of students and schools is stronger in countries that track students early into different study programmes, that have larger percentages of students in selective schools, and that transfer less-able students to other schools.
Exposure to formal mathematics tasks and concepts (involving equations or functions, for example) has an impact on performance, particularly on the most challenging PISA tasks; and differences in familiarity with mathematics are strongly related to the performance gap between advantaged and disadvantaged students. On average across OECD countries, differences in familiarity with mathematics account for about 19% of the performance difference between these two groups of students. In Austria, Belgium, Brazil, Germany, Hungary, Korea, Portugal, Switzerland, Thailand and the United States, more than 25% of the performance difference between advantaged and disadvantaged students is related to familiarity with mathematics. The report shows that exposure to applied mathematics tasks (like working out from a train timetable how long it would take to get from one place to another) has a weaker association with performance in PISA, but can stimulate engagement with mathematics and boost self-confidence, particularly among low-achieving students.
Widening students’ opportunities to learn mathematics is not an impossible task, but it may require certain readjustments, from reforming the structure of the education system to improving curriculum focus and coherence, and sharing teaching practices that use time more effectively. For example, Finland, Germany, Poland and Sweden have reformed their school tracking systems to reduce the impact of socio-economic status on students’ access to mathematics and achievement. At the school level, some charter schools in the United States have shown that longer instruction time, individualised support to students, strict behaviour norms, a strong work ethic among students and high expectations for all students can improve the achievement of students in low-performing, disadvantaged schools. Teachers need to be supported in using pedagogies, such as flexible grouping of students or co-operative learning, that increase learning opportunities for all students in mixed-ability classes.
In the end, disadvantaged students’ success in mathematics should become a common tale, not a hyped, romantic screenplay for a Hollywood blockbuster.
Links:
Equations and Inequalities: Making Mathematics Accessible to All
PISA in Focus No. 63: Are disadvantaged students given equal opportunities to learn mathematics? Chiara Monticone and Mario Piacentini
PISA à la Loupe No. 63: Les élèves défavorisés bénéficient-ils des mêmes possibilités d’apprentissage en mathématiques? (French version)
Getting beneath the Veil of Effective Schools: Evidence from New York City
Equity and Quality in Education: Supporting Disadvantaged Students and Schools
Analyst, Directorate for Education and Skills
Mario Piacentini
Analyst, Directorate for Education and Skills
Films about mathematicians have become incredibly popular: many of us now know about John Nash’s beautiful mind. Fewer people have heard the extraordinary story of Srinivasa Ramanujan, a genius of comparable stature to Nash. Ramanujan was nothing more than a promising 16-year-old student from a poor family in South India when he came across A Synopsis of Elementary Results in Pure and Applied Mathematics, a compilation of thousands of mathematical results used by English students. Starting from the textbook, Ramanujan taught himself mathematics. After failing to get into university in India, he sent a letter to one of the great scholars of that time, Godfrey Harold Hardy, who noticed his talent and invited him to Cambridge. Hardy quickly understood that, in spite of his amazing feats in mathematics, Ramanujan lacked the basic tools of the trade of a mathematician. If he was to fulfil his potential, he had to acquire a solid foundation in mathematics. The Cambridge mathematician worked tirelessly with the Indian genius to harness his creativity to the then-current understanding of the field without destroying his confidence. One good textbook and one outstanding teacher changed the fate of a man and the evolution of number theory and analysis.
There are poor students like Ramanujan who show that achieving great results in their education and professional life is possible. But “possible” is not sufficient: education and social policy should make poor students’ success “probable”. This month’s PISA in Focus and a new OECD report, Equations and Inequalities: Making Mathematics Accessible to All show that millions of students around the world – especially those from socio-economically disadvantaged backgrounds – often have few opportunities to develop their mathematics skills.
Many students who participated in PISA 2012 reported that they have hardly been exposed to fundamental concepts in mathematics, like arithmetic means or linear equations, which form the basis of the numeracy skills that they will need to thrive as adults. Disadvantaged students are even less exposed to these concepts. For example, the share of advantaged students who reported that they know well or have often heard the concept of quadratic function is 20 percentage points larger, on average across OECD countries, than the share of disadvantaged students who reported so; and the difference between these two groups of students is larger than 30 percentage points in Australia, Austria, Belgium, France, New Zealand, Portugal, the Slovak Republic, the United Kingdom and Uruguay. The relationship between the content covered during mathematics class and the socio-economic profile of students and schools is stronger in countries that track students early into different study programmes, that have larger percentages of students in selective schools, and that transfer less-able students to other schools.
Exposure to formal mathematics tasks and concepts (involving equations or functions, for example) has an impact on performance, particularly on the most challenging PISA tasks; and differences in familiarity with mathematics are strongly related to the performance gap between advantaged and disadvantaged students. On average across OECD countries, differences in familiarity with mathematics account for about 19% of the performance difference between these two groups of students. In Austria, Belgium, Brazil, Germany, Hungary, Korea, Portugal, Switzerland, Thailand and the United States, more than 25% of the performance difference between advantaged and disadvantaged students is related to familiarity with mathematics. The report shows that exposure to applied mathematics tasks (like working out from a train timetable how long it would take to get from one place to another) has a weaker association with performance in PISA, but can stimulate engagement with mathematics and boost self-confidence, particularly among low-achieving students.
Widening students’ opportunities to learn mathematics is not an impossible task, but it may require certain readjustments, from reforming the structure of the education system to improving curriculum focus and coherence, and sharing teaching practices that use time more effectively. For example, Finland, Germany, Poland and Sweden have reformed their school tracking systems to reduce the impact of socio-economic status on students’ access to mathematics and achievement. At the school level, some charter schools in the United States have shown that longer instruction time, individualised support to students, strict behaviour norms, a strong work ethic among students and high expectations for all students can improve the achievement of students in low-performing, disadvantaged schools. Teachers need to be supported in using pedagogies, such as flexible grouping of students or co-operative learning, that increase learning opportunities for all students in mixed-ability classes.
In the end, disadvantaged students’ success in mathematics should become a common tale, not a hyped, romantic screenplay for a Hollywood blockbuster.
Links:
Equations and Inequalities: Making Mathematics Accessible to All
PISA in Focus No. 63: Are disadvantaged students given equal opportunities to learn mathematics? Chiara Monticone and Mario Piacentini
PISA à la Loupe No. 63: Les élèves défavorisés bénéficient-ils des mêmes possibilités d’apprentissage en mathématiques? (French version)
Getting beneath the Veil of Effective Schools: Evidence from New York City
Equity and Quality in Education: Supporting Disadvantaged Students and Schools