Mathematics education in New Zealand secondary schools: Are students studying less algebra?

Sarah Howell and Dr. Bronwyn Wood, Victoria University of Wellington

Mathematics education in New Zealand has received considerable attention in the past year,  as we seek to understand and combat declining maths achievement and a ‘slippage in expectations’. A Royal Society of New Zealand Expert Advisory Panel report documented just had bad things have become. Primary principals have been vocal in calling for more support to address the decline in performance.

While the prevailing focus of these concerns has been on primary schools, what is happening in secondary school maths, particularly in Years 11-13? This blog post, based on findings from Sarah’s Masters of Education dissertation, reveals the concerning decline in the number of students studying algebra, the gatekeeper to progression in mathematics.

Why is algebra so important?

A key question we set out to answer was what type of maths learning set students up well for future success in maths – in other words, what maths learning should not be left to chance? A set of ‘key standards’ (Figure 1) were identified through analysis of the research literature in Mathematics and Statistics education, the requirements of Aotearoa New Zealand universities’ for tertiary study involving Mathematics and Statistics, and the content of the NCEA Achievement Standards [AS].

For those not familiar with New Zealand’s NCEA system, assessment in the final three years of secondary school is broken up into modules (‘achievement standards’) that are each assessed separately. These standards span three ‘levels’ reflecting increasing sophistication in the learning being assessed. Some standards are externally assessed (e.g. through national examinations) and others are internally assessed within individual schools and monitored through national moderation processes. While the achievement standards are assessment and not curriculum specifications, schools typically structure their senior mathematics teaching around these standards, tackling one standard at a time. Schools have flexibility in which standards to offer and how to combine these standards to form courses of study, and students also have flexibility in which standards they actually want to be assessed against.

Figure 1: Our representation of the key standards for progression and pathways in Mathematics and Statistics.

A note on Figure 1: The arrows represent the contributing prior learning for each standard, not alternative pathways to reach the standard. The full names of the standards can be found here. AS1.2 (Algebra) has been shaded as our analysis suggested that it acts as ‘gatekeeper’ standard for progression in Mathematics.  

We coined the term ‘key standards’ for this research to represent the Achievement Standards in each of Mathematics and Statistics, which best support progression through the levels of NCEA and onto first year university study in these disciplines. The focus of this blog is on the maths (in particular algebra) standards but the analysis in the Masters dissertation includes both Mathematics and Statistics.

Analysis revealed that AS1.2 (Algebra) is one of these key standards but additionally acts as an important ‘gatekeeper’ in NCEA Mathematics progression. If students do not participate in this standard or perform well in this assessment, they will be highly unlikely to progress through an algebra and calculus pathway. As a result, this study paid particular attention to this Achievement Standard.

Algebra in decline

Our research examined the participation and success of NCEA maths students between 2013 and 2019 across Aotearoa New Zealand. We identified some concerning patterns for algebra and calculus in particular. One notable pattern was that Level 1 and 2 (Year 11 and 12) students were studying less algebra and calculus than in previous years. For example, fewer students from any school decile were sitting the Level 1 (Year 11) A.S1.2 (Algebra) in 2019 than in any previous year (see Figure 2). In addition, as Figure 2 shows, the decline in this achievement standard has been most steep in the higher decile schools (Deciles 10, and Deciles 7-9) since 2015. At its peak in 2015, Decile 10 students were almost 1.7 times more likely to be participating in AS 1.2 (Algebra) than in 2019. Decile ratings are used in New Zealand to classify schools based on the socio-economic status of the homes in their surrounding area, and so the differences in AS 1.2 (Algebra) uptake across decile ratings suggests that students attending schools in higher socio-economic areas are more likely to be accessing this important ‘gatekeeper’ mathematics standard.

Figure 2: Rates of participation of Year 11 students in AS1.2 (Algebra), 2013-2019.

All Level 1 and 2 NCEA Mathematics algebra and calculus Achievement Standards which are externally assessed had declined during this time period. In addition, patterns of inequity associated with school deciles persisted year after year, with lower decile schools far less likely than higher decile schools to offer the AS1.2 (Algebra) Achievement Standard

There is also a strong pattern associated with school decile that relates to achievement. For example, in the same Algebra Achievement Standard 1.2, (see Figure 3), not only do higher decile schools have higher pass rates (red line), but students attain many more merit and excellence grades (purple line).

Figure 3: Pass rates and rates of Merit and Excellence grades for Year 11 students against school deciles for AS1.2 (Algebra) in 2019.

If we combine the percentage of those who participated in the standard and attempted the exam, with pass rates, it paints a sobering picture for those at Decile One schools compared to their counterparts at Decile 10 schools. To illustrate this picture even further: If we had 1000 Year 11 students from each of the Decile One and Decile 10 schools in 2019,

  • For the Decile 10 schools, 436 students would pass AS1.2 (Algebra), with 300 of those students getting Merit or Excellence.
  • For the Decile One schools, only 199 would pass the standard, with 76 of those getting Merit or Excellence.

Why and how is this decline happening?

The reasons behind what we found are complex. One of the unique features of NCEA is the flexibility it allows schools and students to select the achievement standards they wish, especially in Mathematics and Statistics, where there are 43-60 credits available at each level. While some schools require students to participate in particular Achievement Standards, others are left up to the individual choice of students and/or their teachers (parents also play a role here). The potential exists for schools to not even offer the key standards, meaning students have no pathway to access the associated knowledge and skills for progression.

Teachers are often under pressure to ‘get students credits’ and therefore, for topics that students (or teachers) view as more difficult (which frequently includes externally assessed standards, such as Algebra), schools can decide to not offer these or offer alternative (arguably easier) standards instead. National data support this, with the average pass rate for externally assessed standards across all subjects being 78.4%, while the pass rate for internally assessed achievement standards is 84.7%. In addition, students are also less likely to participate in externally assessed standards with 2019 data showing that internal assessment now exceeds external assessment in a ratio of about 3:1.

The decline in the study of Algebra at Level 1 has significant implications for students and for New Zealand’s educational system. If students don’t do Algebra in Year 11, it is very difficult to pick this subject up in Year 12 or 13. Failing to secure a strong foundation in Mathematics also has significant impact on future tertiary education pathways, with growing concerns expressed by universities and polytechs that New Zealand students are not sufficiently maths literate for future study or that they may be locked out of future higher paying jobs.

Implications for policy

There is currently a review of NCEA underway to address some of the concerns raised in this study. The review includes a focus on well-being, equity, coherence, pathways and credibility for students and teachers alike. These changes are expected to be finalised by 2026. The changes indicate a much greater focus on progression of learning for students which will be challenging given that many schools have reduced their focus on teaching algebra. Equitable mathematics programmes across schools in different socio-economic communities will also be required. However, we owe it to our students to provide them with coherent and equitable pathways by offering them opportunities in maths that open rather than shut doors.

Sarah Howell has recently commenced PhD study at Victoria University of Wellington Te Herenga Waka, New Zealand. She is interested mathematics curriculum making in senior secondary schools in Aotearoa New Zealand. She has taught in secondary schools and universities and is currently teaching on the Foundation Studies course at Massey University Te Kunenga ki Pūrehuroa.

Dr. Bronwyn Wood is a Senior Lecturer in Education at Victoria University of Wellington Te Herenga Waka, New Zealand. Her research interests lie at the intersection of sociology, geography and education and centre on issues relating to youth participation, citizenship and education policy.  

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