This chapter provides an overview of the importance of mathematics for individuals and their societies. It presents data to show how a foundation of robust mathematical skills is associated with better outcomes in terms of employment, financial decision making, as well as wider health and well-being outcomes. Given the report’s focus on upper secondary education, it discusses the specific role that this stage of education plays in the development of maths skills. Finally, it introduces the overall report by setting out the context of mathematics in upper secondary in England (United Kingdom). It also introduces six focus systems that are featured in this report for comparative analysis – Austria, British Columbia (Canada), Denmark, Ireland, New Zealand and Singapore.
Mathematics for Life and Work
Abstract
This report was produced by the OECD Above and Beyond: Transitions in Upper Secondary Education project (see Box 2.1 for further information about the project) at the request of England (United Kingdom) to look at how systems internationally deliver mathematics education in upper secondary. The report brings together international data, analysis and insights from discussions with systems to:
Explore the outcomes of different systems in mathematics in upper secondary education through the analysis of international data (Chapter 3).
Identify the requirements that different systems set for the study of mathematics in upper secondary education, exploring how far this is associated with different patterns of participation and performance (Chapter 4).
Advance understanding of how systems cater to the needs of different students and their future ambitions by looking at the different levels and options that students can take in mathematics (Chapter 5).
Provide an overview of the depth and breadth of mathematics across different systems by analysing the curricula and selected examination questions associated with mathematics programmes across different systems (Chapter 6).
Discuss the concept of culture in the context of mathematics and look at students’ views towards the subject across different countries (Chapter 7).
Explore how the views of students, their parents and demand for mathematics in labour markets and post-secondary education might shape participation in mathematics and views towards the subject (Chapter 8).
The Transitions in Upper Secondary Education project develops analysis on how upper secondary education can be designed to meet diverse learner needs and promote equitable outcomes by developing comparative analysis on pathways and assessment and certification. Countries engage with the project through a range of flexible options that contribute to an expanding international evidence base on upper secondary education.
Source: OECD (n.d.[1]), Above and Beyond: Transitions in Upper Secondary Education
Mathematics is critical for individuals and societies
Mathematical skills – the capacity of individuals to reason mathematically and use mathematical concepts, procedures, facts and tools to describe, explain and predict phenomena (OECD, 2018[2]) – are essential for daily life, work and personal decision-making. Box 2.2 discusses the terms mathematics and numeracy and their interdependence. There are high stakes associated with weak mathematical skills for individuals and their societies, linked to financial, economic, health and well-being outcomes.
Mathematics underpins financial literacy
Financial literacy, which is the combination of awareness, knowledge, skill, attitude and behaviour necessary to make sound financial decisions and ultimately achieve individual financial well-being (OECD INFE, 2011[3]), is linked to mathematical skills (Skagerlund et al., 2018[4]). Financial literacy influences an individual’s well-being because it shapes how they make decisions about issues that carry major consequences for their, and their families’ lives, such as calculating mortgage repayments, tax returns and pension investments. Individuals with weak mathematical skills risk making decisions that negatively affect them. Research in the United States has found that adults who are unable to calculate the gain from an interest rate of 2% are less likely to have an effective retirement plan (Lusardi and Mitchell, 2011[5]; Alessie, Van Rooij and Lusardi, 2011[6]). A report from the United Kingdom has estimated that decisions linked to poor numeracy skills cost the average individual GBP 460 annually (Rose Martin et al., 2014[7]).
Weak mathematics skills likely interact with disadvantage – individuals from more disadvantaged backgrounds are less likely to have strong mathematical skills (OECD, 2013[8]; OECD, 2023[9]). Disadvantage might be compounded and entrenched by weak mathematical skills that leads to poor financial literacy and hinders individuals’ ability to make sound decisions for their financial well-being.
Mathematical skills influence employment and earnings
Analysis of the OECD’s Survey of Adult Skills (PIAAC) (see Chapter 3 for a description of PIAAC) has found that having low numeracy skills (at or below Level 1 in the PIAAC framework) is associated with an increase in the risk of adults being unemployed or inactive by around 7% compared with individuals with high numeracy skills (Levels 4 or 5 of the PIAAC framework). The influence of numeracy skills on employment is greater than that of literacy (Jonas, 2018[10]). Individuals with high numeracy skills also tend to earn more. Analysis of the PIAAC data found that adults with high numeracy skills have an average hourly income 13% higher than adults with low numeracy skills (when controlling for other factors). Again, the influence of numeracy skills is greater than that of literacy (Jonas, 2018[10]). Chapter 8 discusses the labour market rewards associated with mathematics in greater detail.
Countries and international institutions use different terms to refer to mathematical skills and how they are held and used across societies. These terms include mathematics, mathematical literacy, numeracy, quantitative skills and quantitative literacy. Most literature and discussion on mathematical skills distinguishes between mathematics – which is generally understood as the academic study of numbers, geometry, algebra, measurement, and data – and numeracy which is the ability to understand, use and apply mathematical and statistical skills and knowledge across a range of contexts (Tout, 2020[11]) These two concepts are not the same but are interdependent. Mathematics provides individuals with the theoretical foundations while numeracy requires the use and application of mathematical knowledge and skills across working and personal lives (Tout, 2020[11]). This implies that education systems and societies cannot choose one or the other but rather need to promote both numeracy and mathematics:
… numeracy is not the same as mathematics, nor is it an alternative to mathematics. Today’s students need both mathematics and numeracy. Whereas mathematics asks students to rise above context, quantitative literacy is anchored in real data that reflect engagement with life’s diverse contexts and situations (Steen, 2001, p. 58[12]).
Mathematics in this report
This report uses mathematics as it is outlined in the OECD Programme for International Student Assessment (PISA) 2022 Mathematics Framework. Mathematics in PISA reflects the capacity to reason mathematically and to formulate, employ and interpret mathematics to solve procedures in a variety of real-world contexts. For example, when confronted with a situation:
Mathematically literate students use their mathematics content knowledge to recognise the mathematical nature of a situation or problem and formulate it in mathematical terms by using mathematical reasoning.
Students solve the resulting mathematical problem using the mathematics concepts, algorithms and procedures that they have learnt at school. In solving a problem, students may also need to make strategic decisions about selecting which mathematical tools to use and the order to use them, which also requires mathematical reasoning.
Finally, students evaluate the mathematical solution by interpreting the results within the original real-world situation (OECD, 2018[2]).
Mathematical skills transcend age boundaries, reflected in the conceptual continuity between mathematics as viewed by PISA and PIAAC's numeracy specifications. However, relevant differences between the two arise. In PIAAC, task realism goes beyond that of PISA, as the context from which the problems are drawn no longer relates to the school learning environment. PISA also makes frequent use of formal mathematic symbolisation, which most adults out of school are less familiar with (OECD, 2009[13]).
Source: OECD (2009[13]), “PIAAC Numeracy: A Conceptual Framework”, OECD Education Working Paper No. 35; OECD (2018[2]), PISA 2022 Mathematics Framework Draft; Steen, L. (2001[12]), “Mathematics and Numeracy: Two Literacies, One Language”, The Mathematics Educator, Jrnl Singapore Assoc. Math Educators; Tout, D. (2020[11]), “Critical Connections Between Numeracy and Mathematics”, Issues in the Teaching of Mathematics.
Mathematical skills influence how individuals take decisions
Mathematics is also linked to non-economic outcomes for individuals, and the overall quality of decision-making. Mathematical skills have been found to predict errors of judgement in decisions linked to analysing probability, with more numerate individuals being less swayed by how information is presented or misleading reasoning (Liberali et al., 2012[14]). People with strong numeracy skills are more likely to take strategic, rationally defined risks (Pachur and Galesic, 2013[15]; Jasper et al., 2013[16]) and to process available information correctly, distinguishing what is relevant or not. PIAAC data has also found that more numerate people are more likely to seek adequate information before making decisions (Jonas, 2018[10]).
Individuals with stronger mathematical skills report better health outcomes
The association between the quality of decision-making and mathematical skills might help to explain the correlation between health outcomes and numeracy through links to perceptions and understanding of risk, and the ability to collect and interpret information to make sound decisions. According to PIAAC, on average the probability of reporting good to excellent health is 22 percentage points higher for adults with high numeracy compared to those with low numeracy (Jonas, 2018[10]). Numeracy is also a stronger predictor of adult subjective health i.e., perceived state of health, than literacy. Adults with high numeracy are 65% less likely to report poor health than those with numeracy proficiency at Level 1 or below (compared to 30% for literacy skills) (Jonas, 2018[10]).
The cumulative impact of low mathematical skills for societies is substantial
Given the wide range of ways in which mathematics shapes individuals’ outcomes, the cumulative impact of low skills across an economy is likely to be significant. A study from the United Kingdom estimated that in 2012, low levels of adult numeracy cost the country the equivalent of around GBP 20.2 billion or 1.3% of the country’s Gross Domestic Product (GDP) every year1. This estimate reflects assumptions based on lower incomes for individuals, reduced employer profit through lower worker productivity and reduced government income through lower tax income and higher unemployment benefits (Rose Martin et al., 2014[7]). On average across OECD countries, statistical estimates suggest that skills have a powerful effect on growth. Based on historical trends, improvements in mathematics and science performance of 15‑year‑olds in the Programme for International Student Assessment (PISA) are estimated to be associated with an increase in annual GDP per capita growth rates (OECD, 2010[17]). Of course, the impact of low mathematical skills for both individuals and society goes beyond economic measures, extending to social contexts and well-being which cannot always be quantified.
Upper secondary education is essential for promoting mathematical skills across society
Upper secondary education is the final period when the full student cohort is in a structured school setting and governments have a significant role in shaping the content and organisation of young people’s learning. At this moment, education systems have a responsibility to help all young people develop the mathematical knowledge and skills that are foundational to the discipline. This is especially important because, depending on how different education systems function and the structure of national labour markets, for some individuals this is their last occasion to engage in structured learning of mathematics concepts. Young people in this phase of education are also transitioning to the adult world, where making well-informed decisions founded on mathematical skills will become increasingly more important and carry increasingly greater stakes. Helping young people develop the ability to use and apply mathematical concepts across complex, real-world situations is essential.
Developing positive feelings towards numbers in upper secondary can help protect against a lifetime of mathematics anxiety and avoidance
Mathematical skills interact with mathematics anxiety (Skagerlund et al., 2018[4]). Mathematics anxiety is a negative attitude towards numbers which impairs working memory when individuals are undertaking computations (Hembree, 1990[18]). It often continues into adulthood because it results in individuals avoiding mathematics and financial decision-making, impeding opportunities to grow these skills and make timely, well-informed financial actions or decisions (Krinzinger, Kaufmann and Willmes, 2009[19]). Upper secondary education can play a critical role in preventing the negative cycle of mathematics anxiety, avoidance and low financial literacy by contributing to positive experiences and perceptions of mathematics.
Ensuring equitable access to mathematics skills in upper secondary can support more equitable societies
Mathematical skills are distributed inequitably across societies, and more so than literacy skills (Jonas, 2018[10]). This is particularly harmful to equity and societal outcomes overall given the greater significance that mathematics plays in many financial and economic outcomes compared with literacy. From one perspective it might seem intuitive that literacy skills tend to be more equitably distributed across society – most individuals cannot escape using literacy skills on a daily basis by writing emails, reading factual information and taking decisions, and reading the news and forming views about society. Yet, as the discussion above set out, mathematical skills are required across individuals’ daily lives meaning that those with lower mathematics skills are at a significant disadvantage which carries concrete financial, economic and even health-related implications for them. As the last phase of structured schooling, upper secondary education is central to promoting equitable access to, and acquisition of, mathematical skills.
Defining upper secondary education
Upper secondary education refers to ISCED 3, in the International Standard Classification of Education (ISCED). Some of the defining features of upper secondary are an increasing range of options and differentiation, and the preparation it provides for individuals to either enter work or tertiary education (Box 2.3) (UNESCO Institute for Statistics, 2012[20]).
The International Standard Classification of Education (ISCED) was developed to provide an international system for classifying countries’ education systems. This international classification aims to support understanding and interpretation of the inputs, processes and outcomes of education systems from a global perspective and to ensure comparable data.
According to ISCED 2011, the principal characteristics of upper secondary education are:
Programmes at ISCED Level 3, or upper secondary education, are typically designed to complete secondary education in preparation for tertiary education or provide skills relevant to employment, or both.
Programmes at this level offer students more varied, specialised and in-depth instruction than programmes at ISCED Level 2. They are more differentiated, with a greater range of options and streams. Teachers are often highly qualified in the subjects or fields of specialisation they teach, particularly in the higher grades.
Programmes classified at ISCED Level 3 may be referred to in many ways, for example: secondary school (stage two/upper grades), senior secondary school, or (senior) high school.
Source: UNESCO Institute for Statistics (2012[20]), International Standard Classification of Education, ISCED 2011, https://uis.unesco.org/en/topic/international-standard-classification-education-isced (accessed on 12 December 2023).
Supporting theoretical, technical and occupation-related skills
One of the ways that education systems can meet the diverse needs and aspirations of students in upper secondary education, promote universal completion of this level of education and meet national economic needs is through the provision of vocational education. The vast majority of systems across the OECD (37) provide separate vocational or general programmes in upper secondary education (Stronati, 2023[21]):
General education programmes are designed to develop learners’ general knowledge, skills and competencies, as well as literacy and numeracy skills, often to prepare participants for more advanced education programmes at the same or a higher ISCED level and to lay the foundations for lifelong learning.
Vocational education programmes are designed to enable learners acquire the knowledge, skills and competencies specific to a particular occupation, trade, or class of occupations or trades (OECD/Eurostat/UNESCO Institute for Statistics, 2015[22]).
A minority of OECD countries do not provide separate vocational programmes, although they frequently provide occupationally-related studies and options for students. Chapter 5 discusses how some systems provide applied and workplace mathematics in the absence of formal vocational programmes.
Upper secondary education across OECD countries
Despite the common definitional characteristics of upper secondary education, the structures and design of this level of education differ significantly across OECD countries. Figure 2.2 provides an overview of the duration, starting and ending age of upper secondary education and the ending age of compulsory education across OECD countries. Key similarities and differences across countries include:
Duration of upper secondary education: Upper secondary education typically lasts three years, but among OECD countries the duration ranges from two years (as in Ireland2 and Lithuania) to five years (as in Italy).
Starting age: The typical starting age is 15, but in some countries, students start earlier, at age 14 (Italy and England) while in other students start far later, at 17 (Lithuania).
Age of completion: The typical age for young people upon completion of upper secondary is 17, but it ranges between 17 (Switzerland) and 20 (Iceland).
Compulsory education and upper secondary education: Across the OECD, a full cycle of upper secondary education is compulsory in only eight education systems. However, participation in upper secondary education is partially compulsory (i.e. compulsory for the first years) in 19 OECD countries (Perico E Santos, 2023[23]).
Selection into upper secondary programmes: Depending on the education system, students are selected into different programmes at different ages. On average across OECD countries, the age of first selection is 15 and selection most frequently occurs at the beginning of upper secondary education. In some countries, the age of first selection is far earlier, corresponding to the beginning of lower secondary education (e.g. age 10 in Austria and Germany and age 12 in the Netherlands). In contrast, in a few countries with comprehensive systems (e.g. Canada, New Zealand and the United States), there is no selection of students into different education programmes until after the end of formal schooling, when students transition into tertiary education, further education or employment.
Note: It is assumed that age references refer to age on 1 January of the reference year. Ending age of compulsory education might refer to the age that each individual student reaches depending on the birth date, meaning that students can leave school during the school year whenever they have attained that age, or it can refer to the age of students during the school year, meaning that students must complete the school year during which they reached the compulsory ending age. Compulsory ending age refers to education and not training. For example. In France the ending age of compulsory education is 16 but training is compulsory up to age 18. Selection in New Zealand occurs after upper secondary education, as only one programme is provided at this level. However, from age 16, students are allowed to leave the initial schooling system and enrol in an ISCED 3 or ISCED 4 vocational programme in a post-school institution. In the United States, the ending age of compulsory education varies between 16 and 18 depending on the state. Greece provided the correct ending age of compulsory education (15 instead of 14). Lithuania provided the correct age of selection (15 instead of 14) and of ending age of compulsory education (18 instead of 16). New Zealand provided the correct age of selection (18 instead of 15). The Slovak Republic provided the correct age of selection (15 instead of 11). Slovenia provided the correct starting age of upper secondary education (15 instead of 14). Countries are ranked in alphabetical order. UK refers to the United Kingdom. NI refers to Northern Ireland.
Source: OECD (2022[24]), Education at a Glance 2022; OECD (2019[25]), PISA 2018 Online Education Database, https://www.oecd.org/en/data/datasets/pisa-2018-database.html (accessed on 10 November 2023).
Country focus in the report
While this report draws on data and information from across all OECD countries, it focuses on the mathematics curricula, programmes and outcomes in six systems (Table 2.1), as well as England (United Kingdom).
An overview of the six focus systems
The six focus systems were chosen because they all achieve comparatively high performance in mathematics yet are diverse. The focus systems reflect a range of different types of upper secondary education, including systems with a well-developed and historical vocational sector (such as Austria), others with comprehensive systems (such as British Columbia (Canada)), and others with flexible, modular upper secondary systems (such as New Zealand). The focus systems also provide the opportunity to look at mathematics education across a wide range of contexts to try to understand the importance of cultural perceptions of mathematics for participation and performance. A detailed overview of requirements for mathematics across the six focus systems and England, as well as the upper secondary programmes, levels and options in mathematics is provided in Annex A.
Throughout the report, data, information, and practices across the six focus systems are provided alongside comparative data and information for England. Depending on data availability, sometimes data for the United Kingdom or Great Britain are used instead of England-specific data.
Selected indicators for focus systems
Note: The number of general upper secondary programmes of England and Singapore counts programmes that are sequential. In England, students are enrolled in the general programme (GCSEs / Key Stage 4) at 14-16; and A levels at 16-18. In Singapore it accounts for 3 general programmes of “Secondary Education” that students take from the age of 13 (Express, Normal (Academic)), Normal (Technical) and from 16/17, A-Levels. The share of 15–19-year-olds enrolled in vocational upper secondary education for England is the figure of the United Kingdom, and for British Columbia data for Canada is used. In Denmark, the EUX programme is a vocational education and training programme for people who wish to combine a vocational education with an upper secondary exam. For that reason, it is included it in this table as a vocational programme, even if it is codified as a general programme in the ISCED mapping, under the EGYM framework. The average PIAAC score in numeracy (2012) for British Columbia is the one of Canada. The three rounds of PIAAC took place in the years 2012, 2014 and 2017.
m Missing value
Source: OECD (2022[26]), Education at a Glance 2022 - Annex 3; Stronati (2023[21]), The design of upper secondary education across OECD countries: Managing choice, coherence and specialisation; OECD (2013[8]), OECD Skills Outlook 2013: First Results from the Survey of Adult Skills; OECD (2019[25]), OECD (2023[27]), PISA 2022 Online Education Database, https://www.oecd.org/en/data/datasets/pisa-2022-database.html (accessed on 10 February 2024)
Upper secondary education in England
From a comparative perspective, there are several features that make upper secondary education in England distinct in contrast with other OECD countries. At four years, upper secondary in England is comparatively long, and students begin upper secondary education comparatively earlier than in other countries (Figure 2.2). Unlike many systems, the first mainstream point of selection does not begin at the start of upper secondary education, but rather part-way through, at 163. The selection point at 16 is a high‑stakes transition that is associated with national examinations – the General Certificate of Secondary Education (GCSEs). Few other OECD countries have a high stakes certification part-way through upper secondary education. This structure reflects the historical evolution of upper secondary in England. At 16, the GCSEs (previously Ordinary Levels or O-Levels) have historically functioned as an exit examination for many students, and influenced selection into post-16 study, notably the Advanced Levels (A levels) and vocational qualifications. it was not until the late 1980s and early 1990s that the majority of students remained in full-time education after 16 (in 1994, just over half 16-18-year-olds (57%) were in full-time education (Department for Education, 2022[28])).
Since 2015, it has been compulsory for students to remain in education or training up to 18 (UK Parliament, 2008[29]). In this context, GCSEs now fulfil primarily a selection function. Most upper secondary institutions require students to achieve five GCSEs at Grades 4-9 to enroll in a 16-18 general education course (i.e. A levels) or equivalently levelled vocational education course such as T Levels (Department for Education, 2023[30]). Students who do not achieve the five GCSEs at Grades 4-9 can access more practically-oriented vocational education. Students who do not achieve at least a Grade 4/C in mathematics or English literature or language continue to work towards achieving this in post-16 education.
References
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[1] OECD (n.d.), Above and Beyond: Transitions in Upper Secondary Education.
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← 1. This number is based on a range of assumptions and is the central figure. More restrained assumptions might result in estimates as low as GBP 6.7 billion or 0.4 per cent of GDP while more generous assumptions result in estimated costs as high as GBP 32.6 billion, or 2.2 per cent of GDP. The estimate does account for costs to the health service or criminal justice system (Rose Martin et al., 2014[7]).
← 2. In Ireland, there is the potential to have three years of upper secondary education with a Transition Year followed by two years of the Leaving Certificate Established, Vocational or Applied.
← 3. At the start of upper secondary education (14), students take some GCSE subjects, such as mathematics and English language, at different tiers of difficulty.