This chapter looks at how different systems across the OECD set requirements for upper secondary students to study mathematics. It brings together information on the six focus systems as well as OECD countries more broadly to identify trends in the requirements countries set for learners to engage with mathematics. The chapter also looks at participation and performance data. It aims to identify if requirement policies, such as the share of the student cohort that is required to study mathematics and for how long, are associated with different levels of participation in mathematics.
Mathematics for Life and Work
A Comparative Perspective on Mathematics to Inform Upper Secondary Reform in England
Abstract
Few systems require all students to study mathematics for the duration of upper secondary
All systems generally require all students to study some form of mathematics at least for some part of upper secondary education.
However, across the focus systems, only Austria requires students to study mathematics for the duration of upper secondary education.
In Ireland and Singapore, mathematics is not technically required for the duration of upper secondary, but in practice, almost all students study it.
British Columbia (Canada) and Denmark require students to take mathematics in upper secondary but they have the option to stop mathematics before the end.
High participation in mathematics can be achieved in absence of compulsory requirements
Some systems achieve very high levels of participation despite mathematics not being compulsory for the duration of upper secondary, notably Ireland and Singapore.1
Factors like tertiary selection, student advice and guidance and school-level policies for subject choice can also significantly shape participation in mathematics.
High levels of participation are a common feature of systems with high mathematics achievement but high participation alone is not sufficient
In some systems – notably Austria and Denmark – graduates from vocational upper secondary programmes achieve strong numeracy proficiency. This achievement is notable given that graduates from vocational upper secondary programmes on average across the OECD demonstrate lower proficiency levels than graduates from general programmes.
In contrast, in some systems where participation in upper secondary mathematics is high – such as British Columbia and Ireland, young adults demonstrate numeracy skills below the OECD average.
An overview of requirements for mathematics programmes and options is provided in Annex A.
1. Mathematics is compulsory for the duration of upper secondary for Leaving Certificate Applied students although in 2022 these students only represented 5.8% of the upper secondary cohort in Ireland (Ireland State Examination Statistics, 2023[24]).
Overview of mathematics requirements
All OECD countries require students to study some form of mathematics in upper secondary education
All the focus systems, as well as England (United Kingdom), set formal requirements for young people to undertake some mathematics in upper secondary education (Table 4.1 and Table 4.2). Countries do not set requirements for mathematics alone: countries also set requirements for a student’s mother tongue language or national language (Stronati, 2023[1]). This reflects the understanding and evidence which has underscored the necessity of mathematics and reading and writing for young people’s success in tertiary education, training, work and more generally in social life. Students who do not acquire these competencies by the end of upper secondary are considered at risk, as they are more likely to struggle in the adult world (OECD, 2019[2]).
Few systems require all students to study mathematics for the entirety of the upper secondary cycle
While it is very common to require students to study mathematics in upper secondary education, across the focus systems this requirement only applies to all students for the entirety of the upper secondary cycle in Austria (Table 4.1).
Source: Federal Ministry of Education, Science and Research of Austria (2024[3]), https://www.bmbwf.gv.at/Themen/schule/schulsystem/sa/ahs.html (accessed on 21 January 2024); Federal Ministry of Education, Science and Research of Austria (2024[4]), https://www.bmbwf.gv.at/Themen/schule/schulsystem/sa/bmhs.html (accessed on 21 January 2024); British Columbia Government (2023[5]), https://curriculum.gov.bc.ca/provincial/grade-10-numeracy-assessment (accessed on 21 January 2024); Denmark Ministry of Children and Education (2024[6]), https://eng.uvm.dk/upper-secondary-education/national-upper-secondary-education-programmes (accessed on 21 January 2024); Denmark Ministry of Children and Education (2024[7]), https://eng.uvm.dk/upper-secondary-education/vocational-education-and-training-in-denmark (accessed on 21 January 2024); Department for Education (2024[8]), https://educationhub.blog.gov.uk/2023/08/24/gcse-results-day-what-to-do-if-you-didnt-get-the-grades-you-were-expecting (accessed on 26 September 2024); National Council for Curriculum and Assessment (2024[9]), https://curriculumonline.ie/senior-cycle (accessed on 21 January 2024); NZQA (2023[10]), https://www.nzqa.govt.nz/ncea/subjects/literacy-and-numeracy/level-1-requirements (accessed on 21 January 2024); Singapore Ministry of Education (2024[11]), https://www.moe.gov.sg/secondary/schools-offering-full-sbb (accessed on 21 January 2024); Singapore Ministry of Education (2024[12]), https://www.moe.gov.sg/post-secondary/a-level-curriculum-and-subject-syllabuses (accessed on 21 January 2024).
Policies for setting requirements
Systems tend to adopt two broad approaches for setting requirements for mathematics
Across the focus systems, and OECD countries more broadly, education systems tend to take two broad approaches for mathematics requirements:
Setting minimum standards with flexibility on when (and sometimes how) this is demonstrated.
A group of systems (some Australian states, some Canadian provinces, New Zealand, and England, Northern Ireland and Wales (United Kingdom)) set minimum standards for either mathematics or numeracy and literacy or reading and writing (Box 4.1). Students are to complete these standards before the end of upper secondary education. The recent changes to New Zealand’s numeracy requirements mean that students will be able to complete their numeracy requirement even earlier, in Years 9 or 10, in lower secondary education.
Assigning different standards depending on the type of programme
In countries where students can be placed into multiple different options linked to the specialisation of their upper secondary programme, the content and level of mathematics is often shaped by their specialisation. Among the focus countries, this is the case in Austria, Denmark and Singapore. In the vocational programmes in these countries, inclusion and coverage of mathematics depends on the vocational specialisation that students take. Where students opt to study more technical or occupational areas, they are likely to cover more mathematics content while other specialisations have less mathematics. All programmes, regardless of focus, will include some mathematics.
This approach is also common in many continental European systems (Stronati, 2023[1]). In France, Germany, Italy and the Netherlands for example, students can specialise in mathematics and so their specialisation requires them to study advanced mathematics (Hodgen, Pepper and Sturman, 2010[13]).
British Columbia (Canada) combines both approaches of setting a minimum standard and requiring students to take mathematics as a subject: in British Columbia students take a proficiency assessment in numeracy in Grade 10 (15) and are required to take mathematics courses until at least Grade 11.
The Grade 10 Numeracy Assessment in British Columbia
In Grade 10 (age 15), students in British Columbia take a provincial numeracy assessment. The assessment aims to measure the application of numeracy to realistic situations, requiring them to employ the knowledge and skills considered to be essential for future success. Students develop the skills needed for the assessment across the course of their education. Student performance is reported as a proficiency level. While students are required to take the assessment for graduation, achieving a particular proficiency level is not required. Students can take the numeracy assessment up to three times with only their best proficiency level appearing on their graduation transcript (upper secondary leaving certificate). British Columbia also has two literacy assessments in Grades 10 and 12 which are organised similarly.
Te Reo Matatini me te Pāngarau, Literacy and Numeracy co-requisite
Upper secondary students in New Zealand take the National Certificate for Educational Achievement (NCEA). The NCEA exists at distinct levels which students work towards progressively during upper secondary education. New Zealand is currently changing its requirements for mathematics in upper secondary education, linked to concerns about standards. Prior to the changes, any level of the NCEA certification required students to achieve 10 numeracy credits at Level 1 or higher. Achieving the 10 credits requires taking and passing three unit or achievement standards that cover 17 different options at Level 1 (or higher). The units were either internally or externally assessed. Once students had completed the numeracy credits at Level 1, they were no longer required to study mathematics.
The current reform of the NCEA introduces new assessments in literacy and numeracy – called Te Reo Matatini me te Pāngarau or Literacy and Numeracy co-requisites. The new co-requisites are digital assessments taken by students when they are ready – typically in Year 10 (age 14) – but students will be offered the assessments from Year 9 (age 13) onwards and they can choose to take them at any time. The assessments aim to ensure that students have functional literacy and numeracy skills in preparation for transitions into tertiary education or the labour market. The new assessments have already been trialled in some schools and with the first sitting taking place in May 2024. While the new te reo matatini, pāngarau, literacy, and numeracy are not formally part of the NCEA qualification, they are mandatory and students have to receive the 20-credits from the co-requisites to be awarded the NCEA qualification. Once students have completed the co-requisite, there is no requirement for them to take mathematics.
Source: NCEA Education (2023[14]), Seven planned changes to strengthen NCEA; British Columbia Government (2023[5]), Grade 10 Numeracy Assessment; British Columbia Government (2021[15]), Grade 10 Literacy Assessment, British Columbia Government (2022[16]), Grade 12 Literacy Assessment.
The relationship between requirements and participation in mathematics
Mathematics is not required for all students in general upper secondary education in Ireland and Singapore but in practice almost all students take it
In Ireland, only Leaving Certificate Applied students – which represented just 5.8% of the upper secondary cohort in 2021 – are required to study mathematics in upper secondary education (Ireland Department of Education, 2021[17]). In contrast, the country’s upper secondary students who are enrolled in either the Established or the Vocational Leaving Certificate (94.1% of the cohort in 2021) are technically not required to study mathematics. Students taking their Leaving Certificate typically take around 6-8 subjects, of which none are technically compulsory (National Council for Curriculum and Assessment, 2023[18]). In practice, the vast majority – just over 98% in 2019, 2020 and 2021 – of Leaving Certificate students take mathematics as a subject. Approximately the same share of students take English and slightly less, around 92% in 2019, 2020 and 2021 took Irish (Table 4.2).
While neither English nor mathematics are compulsory in Ireland, tertiary education creates a major incentive because most institutions require mathematics as part of the Leaving Certificate for entry (The Institute Of Guidance Counsellors, 2017[19]) (see Chapter 8). Most schools require students to take mathematics as a Leaving Certificate subject and school timetabling means that students are generally required to take mathematics from a practical perspective.
In Singapore, students enrolled in the country’s A-Levels are also not technically required to study mathematics, although the vast majority do. Tertiary education is an important influence on take-up with mathematics at H1 or H2 levels required for a broad range of courses from business and accountancy to computer science and engineering, sciences and of course mathematics (National University of Singapore, n.d.[20]). Another influence on students’ participation in mathematics is the design of upper secondary education. The A-Levels in Singapore were delinked from the A levels in the United Kingdom in 2002 and reformed to promote greater breadth and diversity in students’ subject choices (Singapore Examinations and Assessment Board, n.d.[21]). Students typically take three H2 subjects and one H1 subject, and one of these must be from a contrasting discipline. For students taking humanities and arts subjects, mathematics is a common choice for the contrasting discipline, which they might take at the H1 or H2 level.
Note: 1 England data are for 2018/19; 2 In England, since 2014/15, most pupils are required to continue to study mathematics at post-16 as part of their study programme if they have not achieved a Grade 4 or above in GCSE mathematics (or an equivalent qualification). 3 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). 4 In British Columba, the share of the cohort studying mathematics at the end of upper secondary education is not available. However, there is data on the number of enrolments on different mathematics options in Year 12 (see Chapter 5). 5 Data for New Zealand shows the share of students assessed in 14 or more credits in mathematics at Level 3 NCEA in 2021.
Source: Statistics Austria: (2024[22]), https://www.statistik.at/en/statistics/population-and-society/education (accessed on 07 February 2024); Denmark Statistics (2024[23]), https://www.dst.dk/da/Statistik/emner/uddannelse-og-forskning/fuldtidsuddannelser/ungdomsuddannelser (accessed on 07 February 2024); Ireland State Examination Statistics (2023[24]), https://www.examinations.ie/statistics/?l=en&mc=st&sc=r19 (accessed on 07 February 2024); NZQA (2023[25]); Department for Education (2023[26])
More than half of students in New Zealand continue to take mathematics until the end of upper secondary education
While students are not required to study mathematics for the duration of upper secondary education in New Zealand, in practice more than half the cohort – 57.9% in 2021 – continue to study mathematics to the achievement level that corresponds with the final year of upper secondary education (NCEA Level 3) (Table 4.2). While the formal requirement is to study mathematics at NCEA Level 1 until 14 credits have been achieved at this level, in practice many schools encourage students to study mathematics at Level 2 and even at Level 3. This likely reflects a national understanding that Level 2 of the NCEA reflects an appropriate level of competence that will ensure young people have the knowledge and skills that they need on the labour market or in tertiary education. Successful completion of NCEA Level 2 is required to certify completion of upper secondary education (NZQA, 2023[27]). When the new numeracy co-requisite is introduced, there are expectations that many schools may still require students to complete mathematics at Level 2 (Box 4.1).
Setting minimum achievement standards shapes future mathematics participation in different ways
While there are similarities in the approach across some English-speaking systems in setting minimum standards for mathematics achievement, there are also significant differences in how they operate. One notable distinction is the role that the mathematics standard plays in influencing future participation. In England and New Zealand, the mathematics requirement sets a minimum standard that young people must achieve and once they have done so, there is no formal requirement for them to continue studying mathematics. In practice, since students in England study for GCSE mathematics over 14-15 and students in New Zealand are typically expected to work towards their Level 1 NCEA at 15, this means that in both systems, students can stop mathematics around the same age.
In New Zealand, over half of the cohort (57.9% in 2021) take mathematics for NCEA Level 3, which is the most advanced level of NCEA that students typically study in the final year of upper secondary education. There may be higher shares of students taking mathematics overall since some students may still be working towards a Level 1 or 2 NCEA qualification in their final year of upper secondary education. In contrast, just 14.6% of post-16 students in England were taking an advanced mathematics qualification in 2020/21 – AS or A levels – and shares would be even lower if just focusing on A level students taking mathematics in their final year of upper secondary education (Table 4.2). The comparatively high shares of students in New Zealand who take mathematics beyond the Level 1 requirement is one reason why participation might not fall when the new co-requisite is introduced and which most students will take in Year 10, around age 14 (Box 4.1). In some schools, policies around subject taking and timetabling might also encourage students to take mathematics, even when they have completed national requirements.
In British Columbia (Canada) while the Grade 10 Numeracy Assessment must be taken as part of the province’s graduation requirement, it does not set a minimum standard that enables students to stop studying mathematics. Students must continue to study mathematics in Grade 10 and take further courses in Grade 11 and/or 12 for graduation requirements (Table 4.1) (British Columbia Ministry of Education and Child Care, 2022[28]).
Vocational students in Austria and Denmark spend more time studying science, technology, engineering and mathematics than in the other focus countries
As well as considering the share of students who study mathematics in upper secondary education and for how long, it is also important to consider how much of their course is devoted to mathematics and related subjects. The OECD collects international data on the main focus of vocational upper secondary students’ programme of study.
In England, the share of vocational upper secondary qualifications devoted to science, technology, engineering and mathematics (STEM) is lower than in most continental European countries with historically strong vocational systems. In the United Kingdom, STEM subjects are the main area of study for less than a third (28.5%) of vocational upper secondary students, compared with Austria (41.2%) and Denmark (43.7%), where STEM is main field of study for over two in five vocational students (Figure 4.1). This suggests that it is not just enrolment in vocational education that matters for mathematics outcomes but also promoting the study of mathematics-related subjects within vocational programmes.
The main subject of a programme or qualification is determined by the detailed field in which the majority (i.e. more than 50%) or a clearly predominant part of the learning credits or students’ intended learning time is spent
Note: The share of students enrolled in the STEM field is a selection of sub-fields of the fields of education as defined in UNESCO’s International Standard Classification of Education(ISCED) Fields of Education and Training 2013, in which fields of education and training are defined as the subject matter taught in an education programme; Missing data for the OECD average, Canada, Japan, Mexico, and the United States. All countries’ data does not include all students in upper secondary education for STEM as it only refers to Vocational education and training (VET) students who take the STEM subjects.
Source: OECD (2022[29]), Education at a Glance 2022 - Annex 3.
Is there are relationship between requirements and performance in mathematics?
Data on the numeracy proficiency of 16-24-year-olds with general and vocational upper secondary certification provides the closest internationally comparative information on the numeracy skills of young adults after completing different kinds of upper secondary programmes (Figure 4.2).
In most countries, graduates from vocational programmes have lower numeracy proficiency then graduates from general programmes
The difference between general and vocational graduates in PIAAC is around 30 points in Austria (27.5), Denmark (24.8) and Singapore (37) as well as other systems with relatively strong vocational systems such as the Netherlands (36.6), Finland (32.5) and Germany (32.7). In the other focus countries – such as Canada (3.0), England (19.3) and Ireland (17.2) – the performance difference is less pronounced. The smaller performance difference does not necessarily imply better numeracy outcomes, because the numeracy scores of individuals with both general and vocational qualifications are comparatively low.
Graduates of both vocational and general programmes in Austria, Denmark and Singapore demonstrate high numeracy skills
In Austria, Denmark and Singapore,16-24year-olds from both vocational and general programmes achieve high numeracy proficiency (Figure 4.2). This suggests that these systems are particularly effective in supporting numeracy skills across both educational pathways. Austria is the only country which requires all students enrolled in general upper secondary education to study mathematics and these individuals have the highest numeracy proficiency across all countries (except the Netherlands). Students completing general upper secondary programmes in Denmark, where the vast majority of the cohort study mathematics for at least two out of three years, and Singapore, where in practice almost all students who take A-Levels study mathematics – also have very high numeracy skills.
Vocational students in these countries also achieve comparably strong numeracy skills. It is notable that holders of vocational upper secondary qualifications in Austria and Denmark demonstrate higher numeracy proficiency than graduates from general upper secondary education in England and Ireland. Students in the vocational upper secondary programmes in Denmark and in Austria’s Colleges of Higher Vocational Education and Training (BHS) are required to study mathematics for the duration of upper secondary education.
Upper secondary graduates from general programmes in Canada, England and Ireland have comparatively low numeracy skills
According to the PIAAC data, young people (16-24) finishing upper secondary general education in the other three focus countries – Canada, Ireland and New Zealand – as well as England, have comparatively low numeracy scores, and their performance is relatively similar. Given the wide variations in requirements to study mathematics and patterns of participation across these four countries, this suggests that ensuring high levels of mathematics take-up does not immediately lead to higher numeracy skills.
One reason for the higher numeracy skills of students in Austria and Denmark may be the content of mathematics programmes (Chapter 6) and the role of mathematics in society (Chapter 8). It is also likely that because the data presented focuses on individuals who attained upper secondary education as their highest level of education and does not include tertiary education holders, the data underestimates the impact of upper secondary education for skills development. While this affects all countries, since these data represent learners aged 16-24, it might disproportionally depress numeracy proficiency for countries like England, where individuals tend to complete tertiary education earlier (average age of first time graduates in the United Kingdom is 23) compared to countries like Austria (24) and Denmark (26), where graduation ages are typically older (OECD, 2020[30]). Tertiary attainment is also greater in the United Kingdom, 58% of 25-34-years-old attain tertiary education, compared to 43.1% in Austria and 49% in Denmark (OECD, 2023[31]).
OECD countries and Singapore
Note: Chile, Greece, Israel, Lithuania, and Singapore have 2016 data (Round 2). Mexico, and the United States have 2019 data (Round 3); Missing OECD average. Data on individuals who have completed upper secondary education focuses on individuals for whom this is the highest level of education they have attained, meaning it does not include students with tertiary qualifications. New Zealand was not included as the data includes post-secondary diplomas, i.e. qualification that are post-secondary but are offered at ISCED level 3.
Source: OECD (2012, 2015, 2018[32]), Survey of Adult Skills (PIAAC) (2012, 2015, 2018), https://www.oecd.org/skills/piaac/data/ (accessed on 14 November 2023).
This chapter has identified several common trends in how systems set requirements for mathematics in upper secondary education. In line with these trends, several policy pointers can be identified for countries, and for England in particular, when setting requirements for mathematics in upper secondary education.
1. Few systems require all students to study mathematics for the duration of upper secondary
All the focus systems, and OECD countries more generally, require all students to study some form of mathematics in upper secondary education. This reflects the unequivocal importance of mathematics for individuals and their economies. Yet, among the focus systems, only Austria requires the full student cohort i.e. both general and vocational students, to study mathematics for the full duration of upper secondary education. In most other cases, students may be able to stop mathematics before the end of upper secondary education or the requirement to study mathematics throughout upper secondary education only applies to specific cohorts.
Policy pointers for England:
While participation levels in mathematics at the end of upper secondary education in England are low by comparative standards, policies around taking mathematics in upper secondary education are not especially distinct from an international perspective. Ireland and Singapore have fewer requirements than England and in British Columbia, Denmark and New Zealand, students can stop mathematics before the end of upper secondary education.
Other factors, related to the mathematics offer (see Chapters 5 and 6) and wider perceptions of the subject at the upper secondary level and tertiary demand (see Chapters 7 and 8) are likely to be important for raising participation in England.
2. High participation in mathematics can be achieved in the absence of compulsory requirements
In both Ireland and Singapore, mathematics is not a required subject for students, yet both systems achieve very high rates of participation and there are also high rates in New Zealand. These systems’ experiences underscore the importance of the wider ecosystem that influences young people’s decisions when considering policies to promote participation in mathematics. Notably in Ireland and New Zealand, school-level practices and guidance encourage students to take mathematics until the end of upper secondary. Demand for mathematics from tertiary education providers and the labour market are also reported to drive take-up of mathematics in Ireland and Singapore (see Chapter 8).
Policy pointers for England:
Invest in levers that influence young people’s perceptions of mathematics’ importance and the drivers for taking it at 16-18, such as:
Working with tertiary education to explore how they set expectations for mathematics for tertiary selection is critical to shape students’ desire to engage with the subject at 16-18.
The advice and guidance that students receive around continuing mathematics post-16 and helping to communicate its role for life outcomes, such as financial and health decisions.
School-level practices for taking mathematics post-16 and the scheduling of classes can also influence how students engage with the subject. In the same way that most schools at 14-16 in England provide students with a set of directed choices for their GCSEs such as requirements to study a humanities subject, a foreign language, an arts subject, etc., despite those subjects not being mandatory. Similar school-level practices for mathematics between ages 16-18 could be considered.
3. High levels of participation are a common feature of systems with high mathematics achievement, but high participation alone is not sufficient
Promoting high participation in mathematics is not sufficient to achieve high outcomes. In some systems where studying mathematics is almost universal until the end or near the end of upper secondary, as in Ireland and British Columbia, young adults (16-24) who have completed upper secondary education still have numeracy skills below the OECD average. In contrast, countries with strong vocational upper secondary systems achieve strong outcomes in mathematics, across both general and vocational graduates. This is the case in Austria and Denmark among the focus countries, but also applies to other systems such as Czechia, Germany and the Netherlands. The outcomes in these systems among vocational students are particularly notable given the lower scores of vocational students on average across the OECD. Some of these systems – such as Austria and Denmark – also achieve the greatest growth in mathematics skills between PISA at 15 and PIAAC at 24 (see Chapter 3). In Austria and Denmark, a significant share of upper secondary vocational students’ programmes – around 40% - is devoted to STEM-content.
In countries with vocational upper secondary programmes, consideration should be given to the amount of time and learning that is devoted to mathematics-related content.
Policy pointers for England:
Note that high participation in mathematics does not automatically translate to high levels of achievement. Teaching and learning policies, as well as resourcing are also critical to explore.
Strong vocational systems seem to support strong mathematics achievement for all students, and for students in vocational education in particular. Students in vocational upper secondary education tend to enter with lower achievement in comparison to their peers in general upper secondary education so the high achievement of these students, and the significant growth in their mathematics skills between 15 and 24, is notable. England might work with these countries to explore how mathematics in these systems is taught, with the more applied, technical learning perhaps helping to protect students from the risks of low achievement. In these systems, vocational students also tend to spend more time devoted to STEM-related subjects in contrast to England and other systems internationally.
Table 4.3 sets out the key insights around how countries set requirements for mathematics in upper secondary education and identifies potential policy pointers for England, based on these insights and comparative country practices.
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← 1. Mathematics is compulsory for the duration of upper secondary for Leaving Certificate Applied students although in 2022 these students only represented 5.8% of the upper secondary cohort in Ireland (Ireland State Examination Statistics, 2023[24]).