**Introduction**

According to the Australian Curriculum, Assessment and Reporting Authority (ACARA), in the past decade around 71-73% of Year 12 students were enrolled in mathematics subjects every year.[i] On the face of it, Year 12 enrolments in mathematics in Australia have remained quite stable as a proportion of all students who complete high school exams in the last decade or so. However, what these numbers do not show, is whether these students study just one, or more maths subjects, and at what level.

The Australian Mathematical Sciences Institute (AMSI) has collected data on participation in mathematics subjects in Year 12 for many years. Collecting enrolment data in individual maths subjects is not just important to get a sense of how many students finish high school with some mathematics under their belt. It is also crucial to know at what level they study mathematics in Year 12 to know how prepared they are to embark on tertiary study. What the AMSI data collection continues to show is that the proportion of students taking more advanced, calculus-based levels of mathematics as their “highest” maths subject has been in long-standing decline.

All this must be seen against the backdrop of a growing Australian school population, with increasing numbers of students staying in school until completing Year 12 and going to university afterwards. The number of students completing Year 12 with a secondary school certificate (such as the HSC in New South Wales, the VCE in Victoria and so on) has been steadily growing. In 2008, around 181,000 year 12 students completed school with a qualification. In 2019, that number was over 200,000, with a peak of 219,000 in 2017.

Moreover, between 2008 and 2019 the number of domestic students starting university has grown substantially, from roughly 180,000 new bachelor students in 2008 (106,000 in the 16-19 age group) to more than 252,000 in 2019 (with over 174,000 between the ages 16-19).[ii] The number of domestic students embarking on an undergraduate STEM degree grew by more than 65%, from 35,498 in 2008 to 59,562 in 2019.[iii] Many degrees in other areas such as Management and Commerce and Health also have significant quantitative components. Annual new enrolments in undergraduate Health degrees alone increased by over 80% in the same period.[iv] However, the increasing academic aspirations have not been accompanied by a similarly growing take up in Year 12 of mathematical subjects at intermediate and higher levels which are intended to prepare students for university study in these types of degrees.

**How to interpret the data**

Since 2018 we classify the various senior secondary school mathematical studies offered in Australia as *higher**, intermediate* and *elementary* levels of mathematics.[v] The *higher* level is representative of the Australian Curriculum Level Specialist Mathematics, *intermediate* represents Mathematical Methods and *elementary* combines both Essential and General Mathematics.[vi]

Most states and territories now broadly follow the Australian Curriculum, except for New South Wales and the Australian Capital Territory. Note that we classify students from New South Wales who study at least Extension 1 as “*higher*” mathematics students, even though technically only students who study both Extension 1 and 2 are deemed fully equivalent to students of Specialist Maths in other states.[vii]

In this paper we have included data for all Year 12 mathematics students enrolled through the secondary boards of studies and the Australian International Baccalaureate (IB) in all states and territories, for the years 2008 to 2019. Keeping in mind that students often enrol in mathematics subjects at more than one level—for example in both an *intermediate* and *higher* maths subject – where possible we display the most advanced level of mathematics students have chosen, with overlapping enrolments in lower level maths subjects taken out. The figure below therefore gives the best indication of the level of preparedness of students to enter university degrees—especially degrees with a mathematical component such as science, engineering and commerce.

In previous AMSI publications of Year 12 participation data the proportion of students was calculated as a percentage of the Year 12 population eligible to complete examination. After review of our data collection, we are now calculating it as a percentage of Year 12 students that have completed the secondary school examination in their state or territory. While this means that the historical collection of enrolment numbers has remained the same, the calculated percentages can no longer be compared with earlier publications on this subject.

**Higher and intermediate participation rates**

In most states a student enrolled in a *higher*-level study must also enrol in an *intermediate* level study. The data below represents the most advanced level that students were enrolled in. For example, an *intermediate* student is one who was enrolled in an *intermediate* level subject but not in a *higher* level subject.

**The NUMBER and PROPORTION of Australian higher mathematics students**

Year: | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

% | 11.6% | 11.2% | 10.9% | 10.3% | 10.2% | 10.3% | 10.6% | 10.1% | 10.0% | 10.0% | 10.1% | 10.1% |

# students | 20903 | 21090 | 21306 | 20422 | 20617 | 21189 | 21507 | 21665 | 21450 | 21855 | 22066 | 20265 |

Cohort size | 180949 | 187791 | 195526 | 198997 | 202970 | 206636 | 202867 | 213593 | 214709 | 219410 | 217643 | 200917 |

**The NUMBER and PROPORTION of Australian intermediate mathematics students **

Year: | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

% | 23.3% | 22.5% | 21.5% | 21.3% | 21.0% | 20.4% | 20.6% | 20.2% | 20.5% | 20.6% | 21.1% | 20.5% |

# students | 42174 | 42249 | 42070 | 42307 | 42605 | 42232 | 41756 | 43106 | 43957 | 45205 | 45924 | 41214 |

Cohort size | 180949 | 187791 | 195526 | 198997 | 202970 | 206636 | 202867 | 213593 | 43957 | 219410 | 217643 | 200917 |

The total number of students in

*intermediate*and

*higher*maths peaked in 2018 before dropping significantly in 2019. For the most part, the drop can be explained by the substantial change in the Queensland secondary school qualification system and the introduction of the QCE, which caused an overall decrease in Year 12 students sitting or completing the high school examination.

However, despite the rise (and fall) in the total population of students completing Year 12 certificates, the proportion of students undertaking mathematics at the *higher* level has remained stubbornly low and has in fact decreased compared to ten years ago. The same applies to the percentage of students studying at the *intermediate* level which decreased again after a slight increase in 2018 and overall is lower now than a decade ago.

Altogether, only 30.6% of students with a Year 12 qualification studied mathematics to at least *intermediate* level in 2019, compared to 34.9% in 2008.

Download PDF graph of students studying higher and intermediate mathematics in Australia

*Higher*** mathematics gender split**

*Higher*

In 2019 only 38.6% of the students undertaking *higher* mathematics were female, which stands in stark comparison to the fact that there was a larger proportion of females (52%) completing Year 12.

**The NUMBER of female and male Australian higher mathematics students **

Year: | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

female | 7819 | 7940 | 7894 | 7562 | 7422 | 7683 | 7663 | 7966 | 8174 | 8262 | 8550 | 7816 |

male | 13084 | 13150 | 13412 | 12860 | 13195 | 13506 | 13844 | 13699 | 13276 | 13593 | 13514 | 12449 |

The female participation rate for *higher* mathematics studies was 7.5% in 2019 compared to 7.6% in 2018. Both those years saw a slight increase in female participation compared to prior years when participation generally did not exceed 7.2 or 7.3%. The male participation rate increased slightly from 12.8% in 2018 to 12.9% in 2019. Over the last decade, male participation has decreased more than female participation leading to a very slight narrowing of the gender gap in the last few years.

Download PDF graph of students studying higher mathematics

*Intermediate*** mathematics gender split**

*Intermediate*

The overall participation rate for students studying *intermediate* mathematics decreased slightly to 20.5% in 2019 against 21.1% in 2018. The female participation rate in 2018 was relatively high at 20.2% before dropping again to 19.4% in 2019. Of all *intermediate* students, more than 49% was female, and the gender balance has been nearly even over the last decade.

Download PDF graph of students studying intermediate mathematics

**The NUMBER of female and male Australian intermediate mathematics students**

Year: | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

female | 20811 | 20973 | 20570 | 20489 | 20580 | 20231 | 20412 | 20856 | 21438 | 22122 | 22645 | 20257 |

male | 21363 | 21276 | 21500 | 21818 | 22025 | 22001 | 21344 | 22250 | 22519 | 23081 | 23272 | 20954 |

*Elementary*** Participation Rates **

*Elementary*

The *elementary* category includes studies equivalent to both Essential and General Mathematics in the Australian curriculum. As with *higher* and *intermediate* maths, students may be enrolled in more than one subject. However, given the variety of elementary subjects in different states, it is not possible to reliably estimate how many students combine an *elementary* with an *intermediate* subject or are enrolled in two *elementary* subjects. In addition, some studies count towards the students’ ATAR scores and some do not. In this section we therefore only include unadjusted enrolments in General Mathematics, as these are generally counted towards the ATAR.

In 2019 there were 97,752 enrolments at the level of General Mathematics. The enrolment numbers have declined considerably in 2018 and 2019 after a period of growth. There have been changes to courses and assessment practices in the period 2016-2019 (such as the introduction of the QCE). These along with other factors which cannot be determined from the data are likely to be responsible for the decline in numbers, in particular in 2018 and 2019. In some states, the enrolment in Essential level mathematics (generally not counted towards the ATAR) seems to have increased to the detriment of General Mathematics, which warrants further investigation.

Year: | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

% | 52.0% | 51.0% | 52.6% | 53.2% | 52.9% | 52.3% | 50.9% | 51.1% | 50.0% | 49.8% | 45.6% | 48.7% |

# students | 94101 | 95759 | 102883 | 105870 | 107332 | 108154 | 103244 | 109225 | 107282 | 109330 | 99292 | 97752 |

Cohort size | 180949 | 187791 | 195526 | 198997 | 202970 | 206636 | 202867 | 213593 | 214709 | 219410 | 217643 | 200917 |

**Note: **AMSI would like to thank Frank Barrington, Michael Evans and Susan James for their invaluable efforts in driving and maintaining this annual data collection.

**References**

[i] https://www.acara.edu.au/reporting/national-report-on-schooling-in-australia/national-report-on-schooling-in-australia-data-portal/year-12-subject-enrolments#view2.

[ii] https://docs.education.gov.au/node/34161 – 2008 Commencing students, Table 2; https://docs.education.gov.au/node/55052 – 2019 Commencing students, Table 1.2.

[iii] Total domestic commencements in an undergraduate degree in natural and physical sciences, engineering, and information technology in 2008 and 2019 – source: UCube (http://highereducationstatistics.education.gov.au/). Note these numbers include all age groups, not just recent school leavers.

[iv] Total domestic commencements in an undergraduate degree in health in 2008 and 2019 – – source: UCube (http://highereducationstatistics.education.gov.au/). Note this includes all age groups, not just recent school leavers.

[v] Previously AMSI referred to *advanced**, **intermediate* and *elementary*. We adjusted the terminology to avoid confusion with the New South Wales subject Advanced Mathematics, which we classify as *intermediate.*

[vi] https://australiancurriculum.edu.au/senior-secondary-curriculum/mathematics/.

[vii] https://www.uac.edu.au/future-applicants/admission-criteria/year-12-qualifications.