New analysis shows that both students’ choice of senior school mathematics subjects and their subsequent performance are related to achievement in university science and maths classes.

The Australian Council of Deans of Science commissioned ACER to explore how senior secondary school mathematics subject choice and results are related to biology, chemistry, mathematics and physics pass rates in the first year of university.

The study is the first attempt to examine this issue across a range of Australian universities and science disciplines.

The study analysed 16 436 school completers in their first year of a bachelor degree in science, who undertook first-year biology, chemistry, mathematics or physics subjects. Twelve Australian universities from a mix of university groups, states and metropolitan/non-metropolitan areas provided detailed data for the analysis, which focused on the first semester of 2015, 2016 or 2017.

### Choice of Year 12 maths subject

Four levels of senior secondary mathematics are available in Australian schools: Essential Mathematics (the lowest level of mathematics); General Mathematics; Mathematical Methods; and Specialist Mathematics (the highest level).

Across the four disciplines examined, first-year students at Group of Eight (Go8) universities were more likely than students at other universities to have studied higher-level mathematics (Mathematical Methods or Specialist Mathematics) when in senior secondary school (Figure 1).

### Pass rates by university subject

Regardless of the level of mathematics studied in senior secondary school, the majority of university students passed their first-year subject. In Go8 universities, pass rates ranged from 96 per cent in biology to 83 per cent in mathematics. In non-Go8 universities, pass rates ranged from 88 per cent in biology to 73 per cent in mathematics (Figure 2).

### Pass rates by highest level of Year 12 maths studied

The relationship between the highest level of mathematics undertaken in senior secondary school and first-year pass rates differs between Go8 institutions and non-Go8 institutions. Generally, students whose highest level of school mathematics was General Mathematics had lower first-year subject pass rates than students whose highest level of school mathematics was Mathematical Methods or Specialist Mathematics (Figure 3).

The one exception was first-year mathematics students at Go8 institutions, where those whose highest level of school mathematics was Mathematical Methods had the lowest pass rate (79 per cent). This apparent anomaly is most likely explained by the fact that Specialist Mathematics can only be taken in conjunction with Mathematical Methods: when examining *all* Go8 students who studied Mathematical Methods, the first-year mathematics pass rate increased to 83 per cent.

### Pass rates by Year 12 maths achievement

The *level *of mathematics undertaken in senior secondary school counts, but so does Year 12 mathematics *performance*. Those who were strong performers in Year 12 mathematics (irrespective of the level of mathematics undertaken) have very high first-year pass rates.

Across the four university disciplines examined, students who were in the highest achievement band for General Mathematics in senior secondary school had very high first-year pass rates (between 82 per cent and 96 per cent), as did those in the highest achievement band for Mathematical Methods or Specialist Mathematics (between 93 per cent and 100 per cent).

Of the university disciplines examined in this study, mathematics and physics are the most mathematically intensive. At least half of the small proportion of first-year mathematics students who were in the middle or lower achievement bands in General Mathematics, as well as Go8 mathematics students with low/very low achievement in Mathematical Methods, did not pass a first-year mathematics subject. Physics students with these characteristics also experienced relatively low pass rates.

Interestingly, students who were in the top two achievement bands for General Mathematics achieved similar or higher first-year pass rates than students with low/very low performance in Mathematical Methods or Specialist Mathematics.

Additional analysis explored whether mathematics background is related to first-year subject outcomes after taking into account ATAR, senior secondary background in a corresponding science discipline and other student characteristics. After controlling for these factors, students’ mathematical background remained related to first-year subject outcomes in each of the four disciplines examined in Go8 universities, and for first-year biology, chemistry and mathematics (but not physics) outcomes at non-Go8 universities.

### Pass rates by Year 12 science participation

Having studied a science subject in a corresponding discipline in senior secondary school is also related to success in first-year biology and chemistry, but not first-year physics (Figure 4).

### Students with low mathematics background

A small proportion (2-6 per cent) of first-year students enrolled in science degrees at Go8 universities, and 17 to 28 per cent of first-year science students at non-Go8 universities, had not undertaken General Mathematics, Mathematical Methods or Specialist Mathematics in senior secondary schools. This group includes students who had undertaken Essential Mathematics (the lowest mathematics level in the Australian Curriculum) or had not undertaken any mathematics in senior secondary school.

This ‘low mathematics’ group includes a significant proportion of high achievers as measured by ATAR, some of whom may have opted for a lower level of mathematics in order to maximise their score. More than 40 per cent of the ‘low mathematics’ group had an ATAR of 80 or above, and almost 12 per cent of non-Go8 students and 23 per cent of Go8 students had an ATAR of 90 or above. The ‘low mathematics’ group also included students who did not use ATAR as the basis of admission to university (56 per cent of this group in Go8 universities and 13 per cent in non-Go8 universities).

The first-year pass rates of the ‘low mathematics’ group in Go8 universities ranged from 94 per cent in biology subjects to 74 per cent in physics, which was similar or slightly lower than the pass rates for those whose highest level of senior secondary mathematics was General Mathematics (Figure 5).

In non-Go8 universities, the pass rates of this group ranged from 93 per cent in biology to 81 per cent in mathematics. The non-Go8 ‘low mathematics’ group therefore had higher pass rates than non-Go8 students who had undertaken General Mathematics, Mathematical Methods or Specialist Mathematics in senior secondary school.

Further analysis showed that the pass rates for ‘low mathematics’ students were *higher* than the pass rates of students in the *middle or lower achievement bands* in General Mathematics, Mathematical Methods or Specialist Mathematics, but *lower *than those of students in the *highest achievement band* in Mathematical Methods or Specialist Mathematics.

### Conclusion

There has been much debate about prerequisites for university mathematics and science courses, and whether mathematics should be compulsory in senior secondary school. Overall, our findings show that, while the majority of university students do pass their first-year biology, chemistry, mathematics and physics subjects, some groups perform better than others. This has implications for school subject choice, university admissions policies, and the support services provided to first-year students. ■

**Read the full report:**

*Performance in first year mathematics and science subjects in Australian universities: Does senior secondary mathematics background matter?* by Dr Julie McMillan and Dr Daniel Edwards, Australian Council for Educational Research, 2019.