This chapter discusses the importance of mathematics knowledge for acquiring numeracy skills and developing problem-solving abilities. It presents the concept of “opportunity to learn” and argues that measuring opportunity to learn is of critical importance for international comparisons of curricula and student performance. An overview of the data on opportunity to learn in PISA 2012 shows that education systems differ greatly in the degree to which students are exposed to mathematics concepts and also in the way mathematics problems are formulated and presented to students.

What the data tell us

• Numeracy skills are used daily in many jobs and are important for a wide range of outcomes in adult life, from successful employment to good health and civic participation.

• In 2012, the average 15-year-old student in an OECD country spent 3 hours and 32 minutes per week in regular mathematics lessons at school; 13 minutes more per week than the average student did in 2003.

• On average across OECD countries, less than 30% of students reported to know well the concept of arithmetic mean; less than 50% of students reported to know well the concepts of polygon and divisor.

• There are large international differences in students’ average familiarity with algebraic and geometric concepts. Students in Macao-China reported the most familiarity with algebraic concepts, while students in Shanghai-China had the most familiarity with geometric concepts.

• There is only a weak correlation between students’ exposure to applied mathematics and to pure mathematics at the system level, suggesting that the two methods of instruction rarely complement each other.

What these results mean for policy

• All students need mathematics for their adult life. Reducing socio-economic inequalities in access to mathematics content is thus an important policy lever for increasing social mobility.

• In many countries, the small share of students who reported that they know well and understand basic concepts signals the need to increase the effectiveness of mathematics teaching by focusing on key mathematics ideas and making more connections across topics.

• The large differences between the intended, the implemented and the achieved curriculum suggest the importance of regularly collecting data on students’ exposure to mathematics content.

• International comparisons of curriculum standards, frameworks and teaching material can help countries to design reforms that increase the coherence of the mathematics curriculum.

THE IMPORTANCE OF MATHEMATICS SKILLS IN EVERYDAY LIFE

Mathematics teachers are accustomed to answering questions about the usefulness of what they teach. Not only students, but also parents and policy makers often worry about a mismatch between what is taught at school and the quantitative skills needed in everyday life. While it might be difficult to explain why students spend so much time learning algebra and geometry, mathematics is a core part of the curriculum for virtually every secondary student in the world. Is this justified? Should all students learn a significant amount of mathematics beyond what is needed to make simple calculations?

One of the rationales used to explain the central role of mathematics in global education curricula is the idea, dating back to Plato, that mathematics education enhances higher-order thinking skills. Those who are good at mathematics tend to be good thinkers, and those who are trained in mathematics learn to be good thinkers. According to this view, mathematics should be taught for its own sake, rather than to serve more concrete and practical aims.

Beyond the effects of mathematics training on some abstract mental faculties, there is a more intuitive and practical benefit from mastering mathematics at a reasonably good level: mathematics is a gatekeeper. The mathematics studied at school is the main entry point to quantitative literacy, and without solid quantitative skills a person cannot do many jobs. Exam scores in mathematics are, in fact, important factors in determining acceptance into higher education programmes leading to scientific and professional careers.

The demand for STEM (science, technology, engineering and mathematics) professionals has been continuously rising over recent years. For example, employment of STEM professionals across the European Union was approximately 12% higher in 2013 than it was in 2000, notwithstanding the effects of the economic crisis (European Parliament, 2015). Moreover, organisations compete for talent, and many of them now use rigorous quantitative assessments that test both verbal and mathematical ability when selecting employees (Schmitt, 2013).

The value of having quantitative skills has risen over recent years. Our societies are “drenched with data” (Steen, 2001), and the level of number skills needed to carry on daily life activities has increased. Understanding concepts such as “exponential growth” or “line of best fit”, assessing the rate at which a variable is changing or knowing what to expect from the flip of a coin have become important for making informed judgements and choices. Computers have reduced the need for mechanical calculations, but the importance of understanding numbers has...