Incentivising student enrolments in secondary mathematics courses: is a 10% bonus enough?

Abstract

This replicated research project [see Hine, G. S. C. (2019). Reasons why I didn’t enrol in a higher-level mathematics course: Listening to the voice of Australian senior secondary students. Research in Mathematics Education, 21(3), 295–313. https://doi.org/10.1080/14794802.2019.15999982019] explored the reasons why senior secondary (i.e. Year 11 and Year 12) students elected not to enrol in a higher-level mathematics course. For this project, all senior secondary Australian Tertiary Admissions Ranking (ATAR) students within Western Australian schools (aged 17–18 years) were invited to participate in an anonymous, online survey comprised predominantly of qualitative items. The researcher analysed 1633 ATAR students’ perspectives of enrolments in mathematics courses, according to a symbolic interactionist paradigm. Reasons included the extent to which students feel higher-level courses are too challenging, time-consuming, not required for university nor future life, and requiring more effort and stress to complete than lower-level mathematics courses. Especially outlined is the extent to which participants feel a 10% bonus is a sufficient incentive to increase higher-level course enrolments, an extension of the original project. Participants indicated a range of responses either supporting or opposing this incentive. While approximately 47% of participants agree that the incentive is sufficient, a small proportion of these supporters offer their agreement conditionally. Within the proportion asserting the incentive is insufficient, a majority of participants suggested that a higher percentage bonus should be offered to students enrolled in Mathematics Specialist.

KEYWORDS:

• Secondary mathematics enrolments
• senior secondary mathematics
• senior secondary student participation

1. Introduction

The importance of studying higher-level mathematics courses at secondary school has been highlighted by scholars for various reasons. Prominent amongst these reasons is the need for students to learn key interdisciplinary knowledge required for other courses, including science, technology and engineering (Ker, 2013), and more broadly, for countries to produce a scientifically literate and economically competitive workforce (Australian Academy of Science, 2006; Chinnappan et al., 2007; Hine et al., 2016). Despite this acknowledged importance, a review of international literature indicates that student enrolments in mathematics courses in the final years of secondary school have been persistently low or declining for some time (Arnoux et al., 2009; Brown et al., 2008; Hogden et al., 2010; National Commission on Mathematics and Science Teaching, 2000; O’Meara et al., 2020; Smith, 2017). This trend has also been reported in an Australian context for many years (e.g. Barrington & Evans, 2014; Easey, 2019; Kennedy et al., 2014; Wilson & Mack, 2014), prompting researchers to explore correlations between participation rates in secondary mathematics courses and future success at the university (Hine et al., 2015), and in other sciences such as physics (Chinnappan et al.; Kennedy et al., 2014; Ker, 2013).

Past research has designated many factors impacting on decisions regarding the elective study of mathematics. Most commentators report on features considered inherent to the individual student, such as prior achievement, expectations of success, self-efficacy, subjective task value (interest, enjoyment, attainment value), perceived difficulty, and affective response (e.g. Brown et al., 2008; Easey, 2019; Hine, 2019; Kaleva et al., 2019; Kennedy et al., 2014; McPhan et al., 2008; Noyes & Adkins, 2016; Prieto & Dugar, 2017; Sikora & Pitt, 2019). However, these individual perceptions do not develop in isolated instances; rather, they tend to be heavily influenced by the people with whom students spend most time in their immediate environment (Gemici et al., 2014). For example, family influences, teacher and peer advice were frequently cited reasons by students who chose intermediate and specialist mathematics courses (Kirkham et al., 2020). Many students may not appreciate the importance of mathematics in their future careers (Kaleva et al., 2019), and yet there is evidence that such perceptions of usefulness are critical in the decisions made to study basic versus advanced level mathematics (Kaleva et al., 2019; Kirkham et al., 2020). In addition, the removal of mathematics pre-requisites for many Australian degree programmes (UAC, 2017) and increasing options of university bridging courses may have resulted in students perceiving higher-level mathematics as having low utility value, or even unnecessary if there is an option to ‘catch up’ once at university. Policy changes on how secondary school results are calculated and reported have resulted in students ‘playing the system’ to maximise their final year results (Hine, 2019; Kirkham et al., 2020; Wilkie & Tan, 2019).

In response to declining enrolments in higher-level mathematics courses, initiatives within and outside Australia have been introduced to encourage students to enrol in such courses (Jennings, 2014; O’Meara et al., 2020). For instance, O’Meara et al. conducted a national study on the introduction of a bonus points initiative (BPI) in 2012 for students in Ireland. For the BPI, students are awarded additional credit in their upper post-primary school state examination results if they achieve a passing grade in a higher-level mathematics course. These authors noted that while the numbers enrolling in higher-level mathematics have steadily increased, there have been some associated concerns. Notably, many students who are incapable of performing to the requisite standard are now opting for the higher-level paper which has resulted in the difficulty of the examination paper and the marking schemes to be adjusted accordingly. Several Australian researchers have commented on how the national trend of declining enrolments in higher-level courses appears to have been reversed in Queensland due to a BPI offered to students (Jennings, 2014; Maltas & Prescott, 2014). For instance, the Queensland Curriculum and Assessment Authority (QCAA, 2010, 2015) reported that, from 2010 to 2015, enrolments in the Mathematics C course increased for both Year 11 students (25%) and Year 12 students (22%). In Western Australia (WA), a BPI was introduced in 2017, which meant students completing either or both Mathematics Methods (MAM) and Mathematics Specialist (MAS) courses received a 10% bonus of their final scaled score in those courses (TISC, 2016). The researcher sought the student voice in 2016 with regards to why they felt senior secondary students elected not to enrol in higher-level courses (see Hine, 2019), as no such data were available in WA. Since then, the researcher replicated that study with one change; namely, to explore the extent to which students feel the BPI (i.e. a 10% bonus) is a sufficient incentive for students to enrol in higher-level courses. Longitudinal data on course enrolments for Mathematics Applications (MAA), MAM, and MAS courses in WA indicate that from the period 2016–2020 enrolments have remained consistent, with little variation (SCSA, 2017; 2020, 2021a). These data suggest that the BPI has not influenced the number of enrolments for the indicated courses. The significance of this study rests upon the extent to which students’ perceptions can shed light on current enrolments in WA ATAR courses, especially with regard to the introduction of a BPI.

2. Research aim

The aim of this project was to investigate the perceptions of Year 11 and Year 12 Australian Tertiary Admissions Ranking (ATAR) students in WA secondary schools regarding declining student enrolments in higher-level mathematics courses. The overarching question to be explored was:

What are the factors senior secondary students believe contribute to the declining enrolments in higher-level mathematics courses in WA schools?

The two sub-questions were:

1. What are the reasons Year 11 and Year 12 ATAR students feel senior secondary students do not enrol in higher-level mathematics courses?

2. To what extent is the 10% bonus offered to MAM and MAS students a sufficient incentive for senior secondary students to enrol in those courses?

The ATAR is a percentile score that denotes Australian students’ academic ranking relative to their peers upon secondary education completion. This score is used to predict a student’s suitability for particular university courses, and ultimately, for university entrance. In WA, Year 12 students can take as many as six (but no fewer than four) subjects that can be counted towards the Tertiary Entrance Aggregate (TEA). Since 2008, the TEA has been calculated by adding any student’s best four scaled subject scores, plus a 10% bonus of a student’s best Language Other Than English (LOTE) scaled score. The calculated TEA is then converted to an Australian Tertiary Admissions Ranking (ATAR), which can range from 0 to 99.95 (in increments of 0.05) and reports the ranking position of any student relative to all other students. According to the Tertiary Institutions Service Centre (TISC), the ATAR takes into account the number of students who sit the Western Australian Certificate of Education (WACE) examinations in any year, as well as the number of people of Year 12 school-leaving age in the total population (TISC, 2016). While mathematics is mandatory across Australia up until the end of Year 10 (15 years of age), it is not required for senior secondary school completion in some states and territories including WA, New South Wales, and Victoria.

3. Research design

3.1. Theoretical perspective

The theoretical perspective informing the methodology of this study was symbolic interactionism, mirroring that of the initial study (see Hine, 2019). According to Berg (2007), symbolic interactionists seek to understand the meanings people intrinsically attach to objects, events and phenomena. These elements themselves do not possess meaning; rather, meaning is conferred on the elements by and through human interaction (Berg). For this study, the meanings Year 11 and Year 12 students conferred upon the mathematical courses they (and their fellow students) elected to undertake or not undertake were sought and analysed by the researcher. In doing so, and consistent with a symbolic interactionist paradigm, students’ perceptions of enrolments in mathematics courses were taken exclusively from the perspective of those people being studied, i.e. Year 11 and Year 12 students participating in senior secondary mathematics courses. The analytical framework and presentation of data captured the essence of meanings intrinsically attached by participants to the socially constructed phenomenon under investigation, principally: students’ perceptions as to why senior secondary students elect not to enrol in higher-level mathematics courses.

3.1.1. Methodology

This interpretive study predominantly used qualitative research methods to gather and analyse data about why Year 11 and Year 12 ATAR students feel senior secondary students do not enrol in higher-level mathematics courses. All Year 11 and Year 12 ATAR students in WA secondary schools were invited to participate in the study. By completing a single anonymous online survey comprising 12 five-point, Likert scale items (Q3) and three open qualitative questions (Q4-Q6), 1612 Participants registered their perceptions. The origin of the survey items was twofold; these were developed from the findings of two previous studies (Hine, 2018; 2019) as well as from current literature (Barrington & Evans, 2014; Kennedy et al., 2014; Wilson & Mack, 2014). Participants completed the 12-item, Likert scale question by indicating the extent to which they felt senior secondary students did not enrol in a higher mathematics course (1 = Strongly Disagree, 2 = Disagree, 3 = Undecided, 4 = Agree, 5 = Strongly Agree). The subsequent three open-ended questions asked participants to (i) elaborate on their responses to the Likert scale items, (ii) comment on whether they felt the 10% bonus was enough to attract Year 11 and Year 12 students to undertake a higher mathematics course, and (iii) to make any further comments regarding why they felt senior secondary students did not enrol in a higher mathematics course. Additional demographic information of participants was obtained through a series of closed questions regarding gender (e.g. Male, Female), year level (e.g. Year 11, Year 12), the mathematics courses currently enrolled in (e.g. Applications, Methods, Specialist), type of school (e.g. secondary 7-12), gender composition of school (e.g. co-educational), and location of school (e.g. metropolitan, regional). The survey items have been included in Appendix 1.

3.2. Method

3.2.1. Participants

In WA, there were 198 secondary schools (39 Catholic, 61 Independent, 98 Government) offering ATAR mathematics courses to Year 11 and 12 students (aged 17–18 years) in 2021. These courses are MAA, MAM, and MAS (SCSA, 2021b) (see Appendix 2 for the description, structure and content of these courses). For this study, the term ‘higher-level’ courses apply for MAM and MAS if the participants only studied (or referred to others studying) MAA, and MAS if the participants only studied (or referred to others studying) MAM. In WA, if a student enrols in the highest-level mathematics course (i.e. MAS) then they must also enrol in MAM. The Principals of these purposively sampled schools were contacted to give their permission for students to participate in the research, and a total of 40 principals gave their permission. Subsequently, 1616 students from 40 schools participated in the research. While the number of schools participating in the study is precise (40/198 = 20%), the number of potential student participants is markedly more difficult to calculate. With reference to an annual report of candidates sitting for a specific number of ATAR course examinations in 2021, there may have been as many as 28 000 Year 11 and Year 12 students who could have participated in the study in that year (SCSA, 2021c, 2021d). Participants’ demographic information (see Tables 1–3) indicate that data represent a cross-section of WA secondary students with regard to gender, school location (metropolitan and regional) and composition (co-educational and single gender), educational sector (Catholic, Government and Independent) and mathematics course(s) undertaken (MAA, MAM and MAS). Despite the heterogeneity provided by this cross-section, there appears to be some underrepresentation in the total number of responses from single-gender schools.

3.2.2. Data analysis

Using an analytical framework devised by Miles and Huberman (1994), the researcher examined the three open-ended questions for themes, patterns and shared perspectives. This framework comprises four key steps: data collection, data reduction, data display, and conclusion drawing/verification. Within each of these steps, the researcher carried out the following operations: coding, memoing, and developing propositions (Miles & Huberman, 1994).

For the operation of coding, data were analysed according to a content analysis process (Berg, 2007), and according to a coding protocol developed in previous studies (see Hine et al., 2016; 2019). As Question 5 was the only additional question from those previous studies, the codes for this interrogative were inductively derived using a content analysis process. Inter-rater (or coding) reliability was checked by a research assistant and confirmed at an accuracy rate of 84% on 98% of codes (Miles & Huberman, 1994). The researcher used the second operation of memoing to synthesize coded data so that they formed a recognizable cluster of conceptual information, e.g. The 10% Bonus is Sufficient. As the coding process progressed, memoing was also used to record any salient, emerging thoughts of the researcher. The final operation required the researcher to develop propositions (or key findings) from clusters of information regarding students’ perceptions, cross-check the veracity of those propositions against the original data, and drew conclusions about the research questions.

4. Results

The number of participants registering a scale rating (i.e. 1–5) and the weighted mean for each question item have been included, for each of the 12 Likert scale items (see Appendix 1). Within Table 4, a higher weighted mean represents stronger agreement with the question item, while a lower weighted mean represents stronger disagreement. The three items with the highest means (in descending order) were Not Needed for University Entrance, Higher Mathematics Not Scaled, and Other Courses More Viable/Attractive. In ascending order, the items Dislike the Teachers, Timetabling Constraints, and Compulsory Subject Selections registered the lowest means, respectively.

Table 1. Summary of participants’ demographic data (by gender and year level).

	Year 11	Year 12	Total
Male	448	393	841
Female	394	321	715
Non-binary/third gender	22	11	33
Prefer not to say	19	8	27

Table 2. Summary of participants’ demographic data (by school location and composition).

	Metropolitan	Regional	Total
Coeducational	1151	460	1362
Single Gender	254	0^a	254

^a N.B. There are no single-gender regional schools in WA.

Table 3 . Summary of participants’ demographic data (by mathematics course, year and gender).

	Male	Female	NB/TG	PNTS	Total
11 Applications	241	271	10	17	539
12 Applications	240	253	5	6	504
Applications	481	524	15	23	1043
11 Methods	129	98	9	4	240
12 Methods	90	53	3	1	147
Methods	219	151	12	5	387
11 Specialist	76	22	3	11	112
12 Specialist	62	14	3	8	87
Specialist	138	36	6	19	189

Table 4. Responses to Likert scale question items (Question 3).

Question Item	1	2	3	4	5	Weighted mean
Not needed for university entrance	31	61	160	311	1052	4.43
Higher mathematics not scaled	54	131	293	575	559	3.90
Other courses more viable/attractive	122	277	466	543	206	3.27
Maximise ATAR without higher maths	114	281	567	453	200	3.22
Dissatisfaction with mathematics	182	368	354	468	243	3.14
Gender-related issues	261	362	463	427	102	2.85
Friends doing the same courses	358	337	423	351	140	2.73
Lack of qualified staff	337	370	521	225	158	2.69
Not offered at our school	408	411	422	251	120	2.54
Compulsory subject selections	525	466	357	205	57	2.25
Timetabling constraints	881	343	194	115	76	1.85
Dislike the teachers	1242	168	115	36	47	1.43

Table 5. Summary of extended answer questions (responses to Questions 4 and 6).

Key themes	Q4	Q6	Total
Dissatisfaction with mathematics	363	862	1225
Other courses are more viable/more attractive	316	611	927
Mathematics is not needed	170	252	422
Scaling of mathematics courses	42	21	63
Mathematics is needed for university entrance	34	8	42

Table 6. Summary of extended answer questions (responses to Question 5).

Key themes	Q4
Yes the 10% bonus is sufficient	664
No the 10% bonus is insufficient	586
Unsure whether the 10% bonus is sufficient	160

The qualitative responses for Survey Questions 4 and 6, and Survey Question 5 (see Appendix 1), have been summarized in Tables 5 and 6, respectively. Using a content analysis process (see Data Analysis), responses were coded into first-level themes (broadest themes), second-level themes (more specific), and in some cases, third-level themes (most specific). Any third-level theme generated acts as a sub-set of a second-level theme, which in turn is a sub-set of a first-level theme. A full listing of derived codes has been included in Appendix 2. Students’ responses to Question 4–6 sometimes comprised more than one code, and some students did not provide a response to any or all of these questions. From responses to Survey Questions 4 and 6, the first-level themes mentioned most frequently were Dissatisfaction with Mathematics (Q4 = 363/1612; Q6 = 862/1612), Other Courses are More Viable or More Attractive (Q4 = 315/1612; Q6 = 611/1612), and Mathematics is Not Needed (Q4 = 170/1612; Q6 = 252/1612). These responses will now be explored.

4.1. Dissatisfaction with mathematics

Following a first-level analysis, six second-level themes were created where those most frequently mentioned by students were: Higher-Level Courses are Too Challenging (Q4 = 154/363; Q6 = 438/862), an Expressed Lack of Interest or Enjoyment in Mathematics (108/363; 173/862), and a Lack of Confidence to Study a Higher-Level Mathematics Course (34/363; 146/862).

4.1.1. Higher-level courses are too challenging

Within this theme, two third-level themes were developed: Discrepancy between Complexity and Workload of Methods and Applications Courses (53/154; 55/438), and an Acknowledged Mismatch Between Effort and Reward (19/154; 58/438). For the most part, those students who underscored a perceived discrepancy between the MAM and MAA courses drew attention to the complexity of concepts studied, time spent studying these concepts, and overall scaling outcomes for both courses. For instance, one student noted:

I think that the difference between applications courses and methods courses is too large. The difference between the boosted scale of methods courses compared with the decreased scale of applications courses is too different. If a student wants to pursue higher maths they are punished for choosing applications over methods or specialist courses. I believe the scaling for methods is attractive to students, but the difficulty of the course pushes students completing other advanced courses to do applications or a simpler maths course.

Almost as a corollary of the first theme, were students who acknowledged that the effort invested in taking a higher-level course was not rewarded in the shorter (i.e. for topic/chapter tests) or longer term (final examination, final course mark). Herein, a typical comment:

I believe the reasons behind the lack of higher-level maths students is due to the amount of effort students have to put in just to pass the subject. It is not satisfying for students to put effort in and only receive a 50% on a test. I believe there needs to be some kind of better scaling as the majority of people possible of studying Methods are deterred because there is no perceived achievement or reward for their work because psychologically a 50% isn't a satisfying mark.

For these two third-level themes, a summary of findings indicates that students feel the higher-level courses are too challenging due to the complex nature of the content presented, coupled with an insufficient incentive to make those courses attractive study options.

4.1.2. An expressed lack of interest or enjoyment in mathematics

Of those students who expressed a dissatisfaction with mathematics, approximately 30% (Q4) and 50% (Q6) supported their claim with an expressed lack of interest or enjoyment in mathematics. Some collective testimony includes:

Most students I know don't particularly enjoy mathematics, as such when they get the chance to replace it with something they find more interesting they are bound to choose it over maths.

Some students do find it boring and don't see the point in learning all of this as they don't see how it can be useful in the future.

They don't like the subject as it is less about practical learning and more about solving boring sums.

Overall, such expressions of dissatisfaction were substantiated with claims that higher-level courses appear too complex, impractical, unnecessary for future endeavours (including university), less enjoyable than other courses of study, and uninteresting.

4.1.3. A lack of confidence to study a higher-level mathematics course

Approximately 9% (Q4) and 16% (Q6) of students claiming to be dissatisfied with mathematics cited a lack of confidence as a factor stymying enrolments in higher-level courses. For example, one Year 11 student offered ‘Students hold a misconception that, in order to do Methods, they have to be “really smart” which is untrue’. Another Year 11 student concurred with this sentiment, stating:

I think a reason they might dislike maths is because they feel they aren't very good at it. Personally, I find dissatisfaction of courses often arises from a lack of confidence or decent grades in the subject. In addition, maths is a very hard subject - they might feel it will drag their ATAR score down instead of bring it up. Maybe if more students felt like they were decent at maths there would be more students in courses?

Common responses indicated both the complexity of higher-level courses and a lack of confidence to succeed therein, as well as an entrenched lack of confidence stemming from mathematics classes in previous years.

4.2. Other courses are more viable or more attractive

Two second-level themes were created following a first-level analysis. These themes and the frequency of their mention were as follows: Taking a Lower-Level Mathematics Course to Maximise Other Opportunities (Q4 = 168/315; Q6 = 279/611), and Taking a Lower-Level Mathematics Course Requires Less Effort and Stress (Q4 = 113/315; Q6 = 293/611).

4.2.1. Taking a lower-level mathematics course to maximise other opportunities

Two third-level themes were created to lend further specificity to students’ responses. First, a significant proportion of students (Q4 = 84/168; Q6 = 201/279) offered a response themed as Taking a Lower Mathematics Course Requires Less Time for Mathematics Study, and to Set Aside More Time to Successfully Complete Other ATAR Courses. To illustrate, a common response for this theme is provided by a Year 12 student avowed:

Yes, because students are preoccupied by their other ATAR subjects. I would of [sic] preferred to choose a math like methods but I cannot prefer to dedicate more time to it, choosing applications means I can achieve high marks and not spend as much time on math.

To a lesser extent, students provided responses themed as Taking a Lower Mathematics Course Increases their ATAR/Acceptance into their Desired University Course. For instance, one Year 11 student shared ‘You can get a higher average score in App[lication]s and it isn't as much work and stress. Easier to understand’. In accord with this statement, another student drew attention to the 10% incentive for taking a higher-level course: ‘It is far easier to do a lower mathematics course then[sic] to do a higher mathematics course, and even with the percentage bonus, they will score higher in a lower course’.

4.2.2. Taking a lower-level mathematics course requires less effort and stress

Following a second-level analysis, another two third-level themes were developed: Taking a Lower Mathematics Course Requires Less Effort (incl. for success); and Taking a Lower Mathematics Course is Less Stressful (Q4 = 32/113; Q6 = 120/293). For the former theme, a majority of students (Q4 = 81/113; Q6 = 173/293) intimated that either a higher-level course required too much effort and insufficient success, or a lower-level course demanded much less effort for greater success. For example, a Year 12 student noted: ‘Students do not particularly choose higher mathematics as other subjects are harder and require more attention. It is easier to choose an easier mathematics so it is easier to juggle other subjects that are equally demanding’. For the latter theme, a comparatively smaller proportion of students shared that taking a lower-level mathematics course requires less stress than undertaking a higher-level course would. To illustrate, a Year 11 student explained:

I chose to do Applications even though I was recommended for Methods and Specialist because I didn't want too much stress, and I wanted at least one subject that I found easy and did well in. It was better for my mental health - I knew that I could do well with minimal effort, so that I could focus on more challenging subjects for me, like Politics and Law and Literature.

This explanation, in particular, was echoed among other students who, despite claiming to be capable or recommended to undertake a higher-level mathematics course, opted for a lower course to reduce the stress of a heavy scholastic workload.

4.3. Mathematics is not needed

Within this first-level theme, two second-level themes were generated: Mathematics is Not Needed for University (Q4 = 102/170; Q6 = 107/252), and Mathematics is Not Needed for My Life or Career (Q4 = 68/170; Q6 = 145/252). For the former theme, students typically grounded their assertions in university pre-requisites or recommended courses of study for certain university degrees. Some assertions included:

Most courses at university don’t have the prerequisite for mathematics and if maths is involved in the course, the University will teach it.

It’s pretty hard, and only really leads to engineering.

A higher mathematics course does not seem relevant to many university degrees and pathways, so I think people don't choose to put in the extra work when they will probably not use the maths they learn again after they leave school.

For those students who claimed mathematics would not be needed for their life or career, a majority decried the applicability or necessity of studying a higher-level course in place of a lower or even non-ATAR mathematics course. To illustrate:

The majority of jobs require basic math and not higher-level maths. Doing Methods and Specialists are needed for rare jobs that require higher knowledge. People are just trying to graduate.

Many kids are more oriented to English, science or humanities-based subjects and do not wish to pursue a career or study a course requiring math.

The maths that we are learning in the classes seems to be extremely unrelatable as many of the things we are learning we can't see where we would need this in real-life situations or even jobs unless if you become a mathematician.

4.4. The 10% bonus is sufficient

When asked if the 10% bonus was a sufficient incentive to attract students to a higher-level course, approximately 47% of the participants (664/1410) agreed that it was. Of these participants, 325 answered ‘Yes’ or an equivalent response. The remaining affirmative responses were analysed further to develop second-level themes, where three themes became prominent. First, a number of students (101/664) asserted that the bonus was a sufficient incentive to maximise the ATAR score. For instance, one Year 12 student mentioned ‘Yes, because 10% adds a significant amount to a student’s ATAR and gives motivation for students who study the course’. Second, 74 students expressed that the bonus was a sufficient reward for the workload and complexity of a higher-level course. Commonly registered comments from students included ‘Yes, because receiving a bonus would make students more likely to feel that studying maths is ‘worth it’, when it can be tedious and difficult for some people’, and ‘Yes, as they are dealing with complex mathematics that deserve compensation’. Third, 73 students stated that the bonus was sufficient to attract them to undertake the MAM course. However, a vast majority of these students (62/73) conceded that the bonus was insufficient to attract them to study MAS.

4.5. The 10% bonus is insufficient

Approximately 42% of participants (586/1410) stated the 10% bonus was an insufficient incentive to enrol in a higher-level mathematics course. Of these participants, 171 answered ‘No’ or an equivalent response, without further explanation. A number of second-level themes were developed from the 415 remaining negative responses, and three themes received frequent mention. First, 110 students described how they chose to enrol in MAA instead of MAM, due to the bonus seeming an insufficient incentive. A commonly-registered sentiment was shared by a Year 12 student:

No, I used to do Mathematics Methods and I found it incredibly difficult, now that I do App[lication]s I am doing much better in it and am getting a higher score compared to when I did Methods (including the bonus). Basically, I believe that the increased difficulty of Methods and Specialist is not worth the 10% bonus.

Another 97 students averred that the bonus is insufficient for the workload and complexity of a higher-level course. In particular, one student stated ‘No, I believe the benefits of the 10% bonus are outweighed by the amount of effort that must be put into methods in order to get a decent 10% bonus’. Third, and in accordance with a previous finding, 73 students described how the bonus was insufficient for the MAS course (62 of these students felt that the bonus was sufficient for MAM).

5. Discussion

The focus of this study was twofold, with the first sub-question exploring the reasons Year 11 and Year 12 ATAR students feel senior secondary students do not enrol in higher-level mathematics courses. Student testimony pointed to a range of reasons, including a general dissatisfaction towards mathematics, and the viability or attractiveness of other courses. Such testimony is indicative of students’ negative attitudes towards mathematics, as well as providing insight into their shorter- and longer-term goals for further study or career prospects. First, and in line with past research efforts, ‘dissatisfied’ students described how higher-level courses are too challenging, unenjoyable and uninteresting, and that they generally lack confidence to success in these courses (Brown et al., 2008; Easey, 2019; Hine, 2019; Kennedy et al., 2014; McPhan et al., 2008; Noyes & Adkins, 2016; Prieto & Dugar, 2017; Sikora & Pitt, 2019). In addition, a proportion of students feel that the discrepancy in workload and complexity of the MAM and MAA courses is too pronounced and that the effort put forth in taking a higher-level course (e.g. MAM) is unrewarded. For these students, a commonly-registered suggestion was for the implementation of a course positioned between MAM and MAA courses in terms of workload and complexity (or as two students posited, a ‘Methications’ course).

Second, students outlined that other courses (including lower-level mathematics courses) are more viable or attractive to undertake than higher-level mathematics courses. In particular, there appears to be a tendency for students to ‘play the system’ and maximise their final score with lower courses. Such a finding also supports previous research suggesting that final results attained at the secondary school level act as an endpoint for students (Hine, 2018; Hogden et al., 2010; Kirkham et al., 2020; MANSW, 2014; Wilkie & Tan, 2019). At the same time, other students taking a lower-level course highlight how lower-level courses require less time, effort and stress to complete successfully. In these instances, students are adopting a balanced approach towards their studies where the amount of time apportioned to all courses undertaken is similar, and the possibility of compromising a healthy lifestyle (e.g. avoiding unnecessary stress) is minimized. Data from Survey Questions 3, 4 and 5 indicate strongly that students acknowledge that a higher-level mathematics course is unnecessary for tertiary entrance, reinforcing previous findings (Hine, 2019; Kaleva et al., 2019; Kirkham et al., 2020). Most described how their desired course required little or no secondary mathematics, and that if it did, a tertiary enabling course (e.g. a ‘bridging course’) was a more viable option.

The second sub-question examined the extent to which the 10% bonus offered to MAM and MAS students is a sufficient incentive for senior secondary students to enrol in those courses. Nearly half of the students answering this question felt the 10% bonus was sufficient (47%), with 42% expressing that this incentive was insufficient and 11% were unsure. Consistent with findings from Questions 4 and 5, students tended to anchor their respondents with statements of course complexity, workload, and associated effort, time and stress. However, irrespective of which response students offered for Question 5 (viz. ‘Yes, ‘No’, ‘Unsure’), they seemed unified in comments about the MAS course. That is, students expressed unequivocally that the 10% was an insufficient incentive to attract enrolments for the MAS course, and that it should be greater.

6. Conclusion

This research engaged the student voice in determining reasons why WA senior secondary students elect not to undertake higher-level mathematics courses. At the same time, student opinions were sought regarding a recently introduced incentive in WA and whether they felt such an incentive was sufficient in attracting enrolments. With symbolic interactionism as the theoretical perspective, the researcher was able to discern meanings students conferred upon the mathematical courses they (and their fellow students) elected to undertake or not undertake. Consistent with findings of past research, students elect not to study a higher-level mathematics course largely due to ascribed meanings of low subjective task value, perceived difficulty, low self-confidence and expectations of success, and poor prior achievement. Moreover, many students justified decisions to enrol in lower-level courses for reasons of lifestyle, to maximise their final score, and that mathematics was not required for university entrance. While the 10% BPI has been offered to WA students since 2017, surveyed respondents appeared divided on the matter with only a slight majority communicating the incentive is a sufficient reward. Taken in conjunction with the relatively unchanged enrolment pattern for MAA, MAM and MAS courses from 2016 to 2020, it appears that the BPI in WA had not had the same effect on student enrolments as initiatives introduced elsewhere.

Disclosure statement

No potential conflict of interest was reported by the author.

Appendices

Appendix 1. Survey items

• 1. After having read the Information Sheet, do you give your informed consent to participate in this research project? Yes No

• 2. Please indicate:

  • (a) your gender: Male Female Third Gender/Non-Binary Prefer Not to Say

  • (b) what year level you are in: Year 11 Year 12

  • (c) the mathematics courses you are currently studying: Mathematics Applications Mathematics Methods Mathematics Specialist

  • (d) the type of school you attend: K-12 4–12 5–12 7–12 11–12

  • (e) the gender composition of your school: Coeducational All Boys All Girls

  • (f) the location of your school: Metropolitan Country

• 3. Respond to the following items by indicating a number 1, 2, 3, 4, or 5 that represents your opinion (1 = completely disagree, 2 = slightly disagree, 3 = neutral, 4 = slightly agree, 5 = completely agree).

From your experience as a mathematics student why do you feel that Year 11 and Year 12 students do not choose to study higher-level mathematics courses?

Table

(a) Dissatisfaction with mathematics	1	2	3	4	5
(b) Not needed for university entrance	1	2	3	4	5
(c) ATAR can be maximised by studying 1 mathematics course	1	2	3	4	5
(d) Other courses of study are more attractive	1	2	3	4	5
(e) Gender-related issues	1	2	3	4	5
(f) Timetabling constraints	1	2	3	4	5
(g) Compulsory subject selections	1	2	3	4	5
(h) Not offered at our school	1	2	3	4	5
(i) Lack of qualified staff	1	2	3	4	5
(j) Higher mathematics courses are not scaled enough	1	2	3	4	5
(k) Their friends are doing the same course(s) as them	1	2	3	4	5
(l) They do not like the teachers who take higher mathematics courses	1	2	3	4	5
(m) They have been advised not to take these courses	1	2	3	4	5

1. Can you elaborate on any of the items from Question 3? Please include your responses below.

2. Do you think that a 10% bonus is sufficient to attract ATAR students to take either or both Mathematics Methods and Mathematics Specialist courses. Please explain your response.

3. Are there other reasons you feel Year 11 and Year 12 students do not choose to study higher-level mathematics courses?

Appendix 2. Summary of ATAR mathematics courses (WA)

Table

Year 11 Mathematics Applications	Year 12 Mathematics Applications
Unit 1Topic 1.1 Consumer arithmetic (20 h)Topic 1.2 Algebra and matrices (15 h)Topic 1.3 Shape and measurement (20 h)Unit 2Topic 2.1 Univariate data analysis and the statistical investigation process (25 h)Topic 2.2 Applications of trigonometry (10 h)Topic 2.3 Linear equations and their graphs (20 h)	Unit 3Topic 3.1 Bivariate data analysis (20 h)Topic 3.2 Growth and decay in sequences (15 h)Topic 3.3 Graphs and networks (20 h)Unit 4Topic 4.1 Time series analysis (15 h)Topic 4.2 Loans, investments and annuities (20 h)Topic 4.3 Networks and decision mathematics (20 h)
Year 11 Mathematics Methods	Year 12 Mathematics Methods
Unit 1Topic 1.1 Functions and their graphs (22 h)Topic 1.2 Trigonometric functions (15 h)Topic 1.3 Counting and probability (18 h)Unit 2Topic 2.1 Exponential functions (10 h)Topic 2.2 Arithmetic and geometric sequences and series (15 h)Topic 2.3 Introduction to differential calculus (30 h)	Unit 3Topic 3.1 Further differentiation and applications (20 h)Topic 3.2 Integrals (20 h) Discrete random variables and networks (15 h)Unit 4Topic 4.1 The logarithmic function (18 h)Topic 4.2 Continuous random variables and the normal distribution (15 h)Topic 4.3 Interval estimates for proportions (22 h)
Year 11 Mathematics Specialist	Year 12 Mathematics Specialist
Unit 1Topic 1.1 Combinatorics (11 h)Topic 1.2 Vectors in the plane (22 h)Topic 1.3 Geometry (22 h)Unit 2Topic 2.1 Trigonometry (16 h)Topic 2.2 Matrices (19 h)Topic 2.3 Real and complex numbers (20 h)	Unit 3Topic 3.1 Complex numbers (18 h)Topic 3.2 Functions and sketching graphs (16 h)Topic 3.3 Vectors in three dimensions (21 h)Unit 4Topic 4.1 Integration and application of integration (20 h)Topic 4.2 Rates of change and differential equations (20 h)Topic 4.3 Statistical inference (15 h)

Table

Question	First-level themes	Second-level themes	Third-level themes
4 and 6	Dissatisfaction with Mathematics	Higher-Level Courses are Too Challenging	Discrepancy between Complexity and Workload of Methods and Applications Courses
			Acknowledged Mismatch Between Effort and Reward
		An Expressed Lack of Interest or Enjoyment in Mathematics	Taking a Lower-Level Mathematics Course to Maximise Other Opportunities
			Taking a Lower-Level Mathematics Course Requires Less Effort and Stress
		Lack of Confidence to Study a Higher-Level Mathematics Course
	Other Courses are More Viable/More Attractive	Taking a Lower-Level Mathematics Course to Maximise Other Opportunities	Taking a Lower Mathematics Course Requires Less Time for Mathematics Study
			Set Aside More Time to Successfully Complete Other ATAR Courses
		Taking a Lower-Level Mathematics Course Requires Less Effort and Stress	Taking a Lower Mathematics Course Requires Less Effort (incl. for success)
			Taking a Lower Mathematics Course is Less Stressful
	Mathematics is not Needed	Mathematics is Not Needed for University
		Mathematics is Not Needed for My Life or Career
	Higher Mathematics Courses are not Scaled Sufficiently	Higher Mathematics Courses are not Scaled Sufficiently
		Higher Mathematics Courses are Scaled Sufficiently
		MAA Should be Scaled the Same as MAM & MAS
	Mathematics is Needed for University Entrance
5	Yes the 10% Bonus is Sufficient	The Bonus is a Sufficient Reward	Sufficient Reward for MAM
			Sufficient Reward for MAS
			Sufficient Reward for both MAS/MAM
		The Bonus is Helpful	The Bonus is Helpful for Some Students
			The Bonus is Helpful for University Entrance
			The Bonus is Helpful for Scaling
			The Bonus is Helpful for ATAR
		The Bonus is Why I Chose MAM over MAA
	No the 10% Bonus is Insufficient	The Bonus is Insufficient for Scaling
		The Bonus is Insufficient for the Effort Put Forth	The Bonus is Insufficient for the Effort Put Forth in MAM
			The Bonus is Insufficient for the Effort Put Forth in MAS
			The Bonus is Insufficient for the Effort Put Forth in both MAM & MAS
			The Bonus is Insufficient to Help With University Entrance
		The Bonus is Too Great
		The Insufficient Bonus is Why I Chose MAA over MAM
	Unsure Whether the 10% Bonus is Sufficient