This chapter explores how societies perceived importance of mathematics influences students' engagement and performance in the subject. Perceptions of the importance of mathematics are explored through data about students’ and parents’ views of the subject’s role in young people’s futures. The chapter also looks at factors that might influence how mathematics is perceived, notably the association between mathematics and labour-market outcomes and the role of tertiary education requirements in encouraging mathematics take-up in upper secondary education.
Mathematics for Life and Work
A Comparative Perspective on Mathematics to Inform Upper Secondary Reform in England
Abstract
Higher numeracy skills have greater wage premia than high literacy skills
The wage advantage for high numeracy, compared to high literacy, skills, is 1.0 USD per hour worked across the OECD on average. However, in England, the relative rewards on the labour market for high numeracy skills (compared to high literacy skills) are more modest than in some OECD countries.
Tertiary education requirements partially shape upper secondary take-up of mathematics
In many countries where studying mathematics is not mandatory, tertiary education requirements work as a practical lever to ensure students study mathematics.
England is the only country among the focus systems where some form of mathematics is not a standard requirement for tertiary entry.
Students and parents in the United Kingdom place high value on mathematics
15-year-old students in England see mathematics as important for their future, yet there are limited options to pursue mathematics post-16.
Many systems, such as British Columbia (Canada), Denmark, Ireland, New Zealand and Singapore provide upper secondary mathematics at different levels and with different options to cater to different students’ ability and future ambitions.
One of the factors that might influence countries’ outcomes in mathematics – i.e., the share of students taking mathematics and their performance – is how important the subject is likely to be for individuals’ access to further education opportunities and rewarding and fulfilling jobs after upper secondary education. Related to this are students’ and their families’ perceptions of the importance of mathematics for their future careers and education opportunities.
The role of the labour market1
Most labour markets reward high numeracy skills slightly more than high literacy skills
Higher cognitive skills (measured by the numeracy, literacy, and problem-solving domains of PIAAC) are systematically related to higher wages (Hanushek et al., 2015[1]). On average, across the OECD, the difference in average hourly earnings between highly skilled employees (Level 4 or 5 in PIAAC) and the lowest skilled employees (Level 1 or below in PIAAC) in numeracy and literacy is respectively of 7.8 and USD 6.8. Premia vary across countries, with premia to numeracy being the highest in Ireland and the United States, where an increase of one standard deviation in numeracy proficiency is associated with a wage increase of 28% and 24%, respectively (OECD, 2012, 2015, 2018[2]). On average across OECD countries, high numeracy skills are associated with USD 1 more per hour compared with high literacy skills (Figure 8.1).
High numeracy skills are associated with much higher wages in Japan and Singapore
While numeracy proficiency seems to be an important predictor of wage differentials, it is important to understand if the wage premium is associated with higher skills in general, or higher numeracy skills specifically. The difference between the numeracy and literacy premium is particularly high in Singapore and Japan. In these countries, individuals with high numeracy skills earn USD 3.2 per hour more, compared to the wage premia of high literacy skills (Figure 8.1). The strong rewards for high mathematics skills might influence the high levels of anxiety, that students in these countries seem to feel to perform well in mathematics (see Chapter 7).
The premium for high mathematics skills on the labour market is much lower in England
In contrast, in England and Northern Ireland (United Kingdom), the wage premium associated with high numeracy skills compared with high literacy skills is comparatively small (USD 0.4 and USD 0.6 per hour, respectively) and below the OECD average Figure 8.1. Young people’s decision not to study mathematics to higher levels in England might be a partially rational decision, as they are unlikely to experience large rewards on the labour market, in contrast to countries like Japan, Korea, Singapore or even other English-speaking countries such as Ireland or the United States.
Wage premia to skills are shaped by a country’s labour-market and social institutions. Factors such as union density, employment protection, regulations and size of the public sector, among others, can influence the structure of sectors, the economy, and consequently the wage premia to certain skills (Hanushek et al., 2015[1]). In England, the relatively modest wage premia to high numeracy skills might be influenced by the structure of the labour market where high numeracy skills are not integrated across a wide range of sectors and posts.
Difference in medium hourly earning between highly skilled employees (Level 4 or 5) and the lowest skilled employees (Level 1 or below) in numeracy and literacy
Note: The hourly income premium for high skills is calculated as the difference medium hourly earning between highly skilled employees (Level 4 or 5) and the lowest skilled employees (Level 1 or below).
Source: OECD (2012, 2015, 2018[2]), Survey of Adult Skills (PIAAC), https://www.oecd.org/skills/piaac/data/ (accessed on 14 November 2023).
The digital and green transitions may increase demand (and wage premia) for high numeracy skills
The twin-transition towards a digital and green economy is changing the skills needed in a modern economy, demanding a large amount of highly skilled labour, with a wide range of skills – including information-processing skills, socio-emotional skills and metacognitive skills (OECD, 2023[3]). While the Artificial Intelligence (AI) workforce is currently concentrated in a few high-skilled occupations (Green and Lamby, 2023[4]), the green transition will require skills that support innovation and adaptability. The expansion of sectors such as renewable energy, clean technology, and software services is likely to increase demand for individuals with mathematics and numeracy-related skills. For countries to have resilient economies that can make the most of new opportunities created by changing and evolving sectors, they will need a steady supply of good science, technology, engineering and mathematics (STEM) skills. The increasing demand for such skills, combined with the high-paying profile of some related jobs, might contribute to changing labour market rewards associated with mathematics, and relatedly, public perceptions around the usefulness of learning mathematics and acquisition of numeracy skills.
The role of tertiary education
Most tertiary institutions require mathematics as part of general upper secondary completion certificates for entry
In most countries across the OECD, selection into tertiary education requires or is informed by upper secondary certification. In all OECD countries, access to first-degree tertiary programmes (in public or private institutions) requires a minimum qualification level, which is usually an upper secondary completion certificate (OECD, 2019[5]). Since upper secondary in most OECD countries requires students to undertake mathematics, at least in general education as part of their upper secondary certification, by extension tertiary education in all these systems requires students to have done some form of mathematics during upper secondary education. Among the focus countries for example, mathematics is indirectly required by tertiary institutions as part of upper secondary certification in Austria, British Columbia, Denmark, and New Zealand (Table 8.1).
England is the only system where mathematics requirements are the exception rather than the rule for tertiary entrance
In England, while students are required to take mathematics during General Certificate of Secondary Education (GCSEs, 14-16), GCSE certifications are not typically required by tertiary institutions for entry. There is no set body of courses required at A level (16-18), with institutions and courses requiring different subjects and grades depending on their own policies and demand for places. Achievement in mathematics is only required for tertiary programmes with a high mathematical content such as mathematics, physics, or engineering. This contrasts with the situation across the focus countries, where there are some requirements related to students’ mathematics achievement for all students for tertiary entrance (Table 8.1. Mathematics-related requirements for tertiary).
OECD countries and Singapore
X Existing Requirements
O Non-existing requirement
Note: 1 In England, mathematics is required until 16, when students take the GCSEs. At the following stage, 16-18 students can choose to continue studying mathematics or not. 2 There is a requirement for Leaving Certificate Applied.
Source: Federal Ministry of Education, Science and Research of Austria (2024[6]), https://www.bmbwf.gv.at/Themen/schule/schulsystem/sa/ahs.html (accessed on 22 January 2024); Federal Ministry of Education, Science and Research of Austria (2024[7]), https://www.bmbwf.gv.at/Themen/schule/schulsystem/sa/bmhs.html (accessed on 22 January 2024); (British Columbia Government, 2023[8]) Denmark Ministry of Children and Education (2024[9]) https://eng.uvm.dk/upper-secondary-education/national-upper-secondary-education-programmes (accessed on 22 January 2024); Denmark Ministry of Children and Education (2024[10]) https://eng.uvm.dk/upper-secondary-education/vocational-education-and-training-in-denmark (accessed on 22 January 2024); NZQA (2024[11]), https://www2.nzqa.govt.nz/ncea/subjects/select-subject/mathematics-and-statistics/ (accessed on 22 January 2024).
Students’ and parents’ views on the importance of mathematics
Across the OECD, students recognise the importance of mathematics for their future
Instrumental motivation to learn mathematics is related to students’ drive to learn the subject based on their perception that it is useful for them and their future studies and careers (Eccles, 2002[12]; Miller and Brickman, 2004[13]). Data from PISA 2012 show that students’ instrumental motivation to learn mathematics is high, with 78% of students across the OECD agreeing or strongly agreeing that learning mathematics will improve their career prospects (OECD, 2013[14]).2 On average across the OECD, 70% of students believe that learning many things in mathematics will help them get a job (OECD, 2013[15]).
Instrumental motivation is particularly high in English-speaking countries
Across the OECD countries, English-speaking countries are clustered together with high levels of instrumental motivation to learn mathematics (Figure 8.2) (OECD, 2013[15]). The United Kingdom stands out with the third highest level of student instrumental motivation across OECD countries. In Australia, Canada, Ireland, New Zealand and the United States, students’ instrumental motivation is above the OECD average. Despite some perceptions that mathematics is not considered to be essential in English-speaking countries (Sam and Ernest, 2000[16]; Charles et al., 2014[17]) (see Chapter 7), learners in these countries clearly attribute value to mathematics and are aware of its importance for their future academic and labour-market outcomes. In contrast, some high-performing systems such as Japan and Korea have the lowest levels of instrumental motivation across the OECD, again contradicting the stereotype that these societies attribute greater value to mathematics. Similarly, in some systems like Austria and the Netherlands, economies where technical skills are important and where everyone must do mathematics in upper secondary, instrumental motivation is comparatively low.3
OECD countries and Singapore
Note: This index is scaled so that OECD countries have an average near 0 and a standard deviation near 1. Higher values on the index indicates greater student motivation. Countries are ordered according to the Index of Instrumental Motivation, from lower to higher,
Source: OECD (2013[14]), PISA 2012 Online Education Database, https://www.oecd.org/en/data/datasets/pisa-2012-database.html (accessed on 27 July 2023).
Male students and those from higher socio-economic backgrounds report higher instrumental motivation
Across the OECD, (apart from Türkiye and Iceland) 15-year-old boys report higher instrumental motivation to learn mathematics than girls (OECD, 2013[14]). The gap is particularly wide in European countries with well-developed vocational upper secondary systems such as Austria, Germany, the Netherlands and Switzerland reflecting other data around the large gender differences in mathematics performance and attitudes towards the subject in these countries (see Chapters 3 and 7).
On average across OECD countries, students from advantaged backgrounds report higher levels of instrumental motivation to learn mathematics than their peers from disadvantaged backgrounds (OECD, 2013[14]). This might reflect the greater information and networks that students from more advantaged backgrounds typically access around careers and future educational opportunities (Perico E Santos, 2023[18]). Although this is not the case in eight OECD countries, including Austria, Germany and Switzerland, three countries with well-developed vocational systems, and in Singapore, where mathematics is deep-rooted, and all students tend to take some form of mathematics (Chapter 4).
Across the OECD, a very high share of 15-year-olds’ parents recognise the importance of studying mathematics
On average across OECD countries, parents are almost unanimous that studying mathematics is important, with 91% of students having parents who agree or strongly agree that studying mathematics is important (OECD, 2013[14])4. In only three countries (Latvia, Japan and the Slovak Republic), less than 85% of students have parents who “strongly agree” or “agree” that studying mathematics is important. In contrast, many English-speaking countries (such as the Australia Canada, New Zealand, United Kingdom and the United States) are among those with the highest shares of students with parents who believe that studying mathematics is important (94%-95%).
These data seem to contrast with some of the literature and popular culture that suggests that parents in western nations, in particular English-speaking ones, attach less importance to mathematics achievement (Sam and Ernest, 2000[16]; Charles et al., 2014[17]) (see Chapter 7). The figures for Japan and Korea (68% and 85%, respectively) also suggest that parents in these countries - despite the reported perception that parents in some high-performing east Asian countries care more about mathematics that their western counterparts - do not emphasise the importance of mathematics more than parents in other systems. In Japan, parents’ socio-economic background is significantly associated with their perceptions of the importance of mathematics, with 28 percentage points difference in the views between parents of advantaged and disadvantaged students. The association between socio-economic background and parents’ perceived importance of mathematics in Japan suggests that perceptions of mathematics in this country are influenced by material conditions and background.
Students’ and parents’ attitudes towards mathematics are similar
Across OECD countries, there is a positive relationship between the attitudes of 15-year-olds towards mathematics, and those of their parents Figure 8.3. In Denmark and Singapore for example, both students and their parents have positive attitudes towards the subject. Similarly, countries where attitudes are less positive – Austria, Belgium, Czechia, Hungary, Korea, the Netherlands, Slovak Republic, and Slovenia – parents and students are clustered around more negative views about the importance (parents) and enjoyment (students) of mathematics. While the views of parents and their children are shaped by a wide range of factors, the views of both groups are likely a strong influence on each other.
Students reported enjoyment of mathematics and parents’ views on the importance of mathematics (OECD countries and Singapore)
Source: OECD (2013[14]), PISA 2012 Online Education Database, https://www.oecd.org/en/data/datasets/pisa-2012-database.html (accessed on 27 July 2023).
Very high wage premia for strong mathematics skills might influence student perceptions and wider cultural views towards the subject
In countries where students stand to benefit from high numeracy skills with very strong premia in terms of wages on the labour market – notably in Japan, the United States and Singapore (Figure 8.1) - it seems a rational choice to study mathematics, even when not compulsory, and to perform well. As well as potentially influencing student decision making about which subjects to study and future careers, wage premia might also indirectly shape societal views around the importance of mathematics. If students and their families perceive that young graduates with strong mathematics skills are well rewarded on the labour market, this is likely to contribute to wider perceptions of the subject’s importance. From a comparative perspective, the relatively modest rewards for high mathematics skills (relative to literacy skills) in England (USD 0.4 per hour compared to the OECD average of USD 1.0) might contribute to perceptions of the subject being a nice addition, rather than an essential skill. Labour-market rewards might also interact with cultural views, i.e., mathematics skills might be associated with very high wages in Singapore because, as a society, these skills are highly valued.
Requirements for mathematics by tertiary institutions can encourage high mathematics take-up when it is not compulsory
In countries where mathematics is not compulsory in upper secondary - such as Ireland and Singapore - the entrance requirements set by tertiary institutions can play a major role in shaping student participation. While students are not formally required to take mathematics during upper secondary education in Ireland and Singapore, almost all tertiary programmes include some form of mathematics in their entry requirements (Table 8.1). This contributes to nearly universal take-up of the subject in both countries, and even widespread perception in Ireland that it is compulsory (Chapter 4).
The competitive nature of tertiary entry in England and the narrow structure of the upper secondary certification creates a disincentive for students to take mathematics
There is significant demand for tertiary education in England, with more young people in the United Kingdom achieving tertiary degrees (51% of 25-34-year-olds in 2022) compared to the OECD average (40%) (OECD, 2023[19]). Entry to tertiary education is also competitive, based on upper secondary certifications, most frequently A level grades. Since students typically take just three or four A levels, each subject mark carries greater weight than individual subjects in other systems where students typically take 6-9 subjects in upper secondary education (Stronati, 2023[20]). In England, achieving a lower grade in just one subject could result in a student missing a place on their desired course in tertiary education. Given this context, students tend to rationally choose the subjects where they are likely to achieve the highest marks. While A level students who achieve the highest grades in GCSE maths (Grades 9-7) frequently also achieve high grades in A level maths, for those with less than Grade 7/A, comparatively low A level results are more frequent. In 2017, holders of Grade 6/B in GCSE mathematics most frequently achieved Grade D (28.8%) in A level mathematics, closely followed by Grade E (28.5%) (Rodeiro and Williamson, 2022[21]). Rationally, A level maths becomes a difficult choice for all but the highest performing students in mathematics who also wish to pursue mathematics-related subjects in tertiary education.
Instrumental motivation matters for mathematics performance
On average across OECD countries, a change of one unit in the index of instrumental motivation to learn mathematics translates into an 18 score-point difference in mathematics performance (OECD, 2013[15]). Among the OECD countries with lower instrumental motivation, communication to students as well as information about the role of mathematics for future careers could help to increase performance.
In England, high instrumental motivation at 15 contrasts with low take-up of mathematics post-16
The very high instrumental motivation to study mathematics in England among 15-year-old students – the fourth highest across all OECD countries - combined with their high enjoyment and high self-efficacy in the subject (Chapter 7), contrasts with the very low levels of students continuing mathematics just one year later at 16. Just 14.6% of 16-18-year-olds in England study mathematics at A level, compared to around at least half of students at the end of upper secondary education in the focus systems and almost universal participation in some (see Table 8.2) (Department for Education, 2023[22]) Data around perceptions of mathematics suggest that there is demand among students and their families in England to study mathematics. It would also not suggest that in England, at least among students at 15, that mathematics is perceived in a distinctly different way, such as being less important or valued, than in other countries.
A level mathematics appears to cater to a small core of high performing mathematicians
One of the dominant factors for the sharp contrast in students’ perceptions of mathematics in England at 15 and take-up post-16 might be the offer. Providing different levels and options of mathematics to reflect a range of student interests, future ambitions and abilities is a common feature of mathematics upper secondary provision across the focus countries in this report and OECD countries more widely (Chapter 5) (Stronati, 2023[20]). This is not the case in England, where the main way to continue studying mathematics is mathematics A level. Compared with other A level subjects, entrants to maths predominantly achieve the highest grades in GCSE mathematics – Grades 7/A-9/A*. In 2017, only 7.5% of students who achieved a Grade 6/B (which is considered a “strong pass”) or below continued to study A level maths post-16. Data presented in Chapter 5 showed that other A level subjects have a flatter entrance profile, with a more equitable share of students choosing the subject based on GCSE grades (see Figure 5.2).
Achievement data also suggest that students who achieve Grade 6/B and below in GCSE maths frequently achieve comparatively modest grades in the subject at A level if they continue with it. In 2017, for students who had achieved a Grade 6/B in GCSE mathematics, just 35.41% achieved a Grade A*-C. The same figure for A level chemistry was almost 10 percentage points higher (43.03%) (Rodeiro and Williamson, 2022[21]). The results would seem to validate previous research which found that students who achieved a Grade B/4 in GCSE mathematics chose not to continue the subject at A level because they saw it as “notoriously difficult”, among other reasons (QCA, 2006[23]). Perhaps related to the entrance profile of students to A level maths, results tend to strong. In 2022/23, over two-fifths of students achieved Grades A/A*, which is higher than in many other A level subjects (data are discussed in Chapter 5, see Figure 5.3). In addition, the subject has particularly extensive depth and breadth when compared internationally. Overall, this creates the perception that A level maths caters effectively to the needs and interests of the country’s highest performing maths students but less effectively for proficient students i.e. those who achieve Grades 6/B or 5/C.
Core Maths was introduced in 2015 to cater to students wishing to continue mathematics post-16 but not take the A level i.e. typically students achieving Grades 6/B and 5/C in GCSE maths. However, so far, this potentially large group of students have not chosen to study Core Maths. In 2023, just 1.9% of 19-year-olds achieved Core Maths. Some of the main factors for low take-up include the qualification’s difficult position in a 16-18 education landscape and tertiary selection that is axed around A levels, as well as low awareness (Homer et al., 2020[24]). See Chapter 5 for a fuller discussion of Core Maths.
Table 8.2 provides a summary of the data reviewed in this chapter around the perceived importance of mathematics. The text below provides an overview of the key policy insights identified in this chapter with a particular focus on England based on these data and other sources.
Above OECD average
Below OECD average
Note: Green indicates the country performs better than the OECD average; Pink indicates the country performs worse than the OECD average. 1 The share of young people studying Level 3 programmes in England’s Qualification Framework. Level 3 includes programmes which correspond to the end of upper secondary education. This number does not include young people re-taking GCSE (GSCEs are a Level 2 programme); 2 There is missing data on the participation in mathematics on the Vocational education and training (EUD) programme, since it depends on the students’ specific specialization; 3 Students assessed in 14 or more credits in mathematics at Level 3 NCEA in 2021; 4 In Ireland and Singapore the requirement does not exist formally, but in practical terms, almost all students must take mathematics due to other levers
Source: OECD (2013[14]), PISA 2012 Online Education Database, https://www.oecd.org/en/data/datasets/pisa-2012-database.html (accessed on 20 September, 2023); OECD (2012, 2015, 2018[2]), https://www.oecd.org/skills/piaac/ (accessed on 20 September, 2023); OECD (2023[19]), Education at a Glance 2023: OECD Indicators.
1. High numeracy skills are associated with greater wage premia than high literacy skills
When students are making choices about which subjects to study and where to invest their time in upper secondary education, communicating key information about the labour-market outcomes of different skills – such as high numeracy skills being associated with greater wage premia than high literacy skills – is important to shape their choices. It is also important for policy makers to understand that while high numeracy skills are well rewarded in all economies, the rewards vary across countries. In Singapore for example, the very strong wage premia for high numeracy skills may create a strong incentive to study and perform well in mathematics and contribute to societal perceptions of the subject. In contrast, in countries where the reward is more modest such as England, relative to literacy skills, this creates fewer incentives around mathematics and might also influence (and reflect) societal perceptions of it being less important.
Policy pointers for England
Communicate the potential labour-market rewards that are associated with numeracy skills to students, schools, and families.
2. Tertiary entrance exerts strong incentives for take-up of maths, and can potentially influence national policy goals
In cases where mathematics is not compulsory until the end of upper secondary education, when all tertiary institutions typically require mathematics achievement for entry, this acts as a very strong driver on student take-up and performance in mathematics (as is the case in Ireland). Across the focus countries in this report, England is the only country where mathematics – either directly or indirectly through upper secondary certification – is not typically required for tertiary entrance. In England, mathematics is only required for tertiary courses with a high mathematical content – such as mathematics or physics. As well as influencing the drivers for upper secondary mathematics, the narrow targeting of mathematics for tertiary entry to small group of subjects might contribute to, and perpetuate, the perception that mathematics is the preserve of a minority of talented mathematicians, rather than an important skill for everyone in society.
Policy pointers for England
Collaborate with tertiary institutions to consider how selection requirements can be used as a lever to promote greater take-up of mathematics at the upper secondary level.
3. Consider expanding the range of post-16 mathematics options in England to cater for the diversity of student strengths, interests and future ambitions
Self-reported data from 15-year-old students and parents suggest that these individuals in the United Kingdom hold some of the strongest beliefs around the importance of mathematics across OECD countries. This is line with other data which suggest that comparatively high shares of young people in England enjoy mathematics and feel well-equipped to solve mathematics problems and questions (Chapter 7). Yet post-16 provision of mathematics in England tends to cater to a “clever core” of high-performing students who are either naturally gifted in mathematics, or are capable students prepared to “slog” hard to achieve a good grade.
If England wishes to promote greater participation in mathematics post-16, it will be important to consider how the available options can be more responsive to the diversity of students’ strengths, interests and future aspirations. Paradoxically, the current narrow provision of mathematics post-16, alongside the narrow range of tertiary subjects for which it is required, likely contributes to (and might even actively create) the societal perception that mathematics is hard and unnecessary for most people. The sharp contrast in how students view mathematics at 15 compared with views around mathematics A level would seem to support this conclusion.
Policy pointers for England
Build on students’ and families’ positive views of mathematics and its importance by communicating the value of continuing mathematics post-16.
Provide a wider range of options and levels of mathematics across upper secondary education (14‑18) that reflects different student interests, abilities and future aspirations.
References
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← 1. Data about labour market rewards is from the first cycle PIAAC, the Survey of Adult Skills. This data was collected in three rounds, the first of which took place between 2011 and 2012. It is important to point out that since then it is possible that the labour market reality may have changed in some countries.
← 2. The instrumental motivation index was not included in PISA 2022.
← 3. It is important to reiterate the extent to which self-reported data may be impacted by response-style bias.
← 4. The question about parents’ views of the importance of studying maths was not included in PISA 2022.