Paper for AARE 1998 Symposium (Adelaide Nov29-Dec 3)

What are the factors that motivate mature-age students to commence mainstream tertiary mathematics courses and to make subsequent course-related decisions to persist, modify or drop-out of their courses? How effective are older students in utilising the opportunities for tertiary participation in mainstream mathematics courses and how do institutions respond to their specific needs? These questions formed the framework for a three year semi-longitudinal study. The study is now in its second year and comprised four phases:

• determining relevant factors to explore
• determining enrolment patterns of mature-age mathematics students
• a large scale quantitative survey across five universities
• a longitudinal in-depth qualitative study of a smaller sample of mature age mathematics/science students. Within this fourth phase of the study four data gathering methods were adopted.

In this paper the first three phases of the study are described where methodological issues are discussed and some preliminary results presented. Survey findings from two of the 26 mature-age students who participated in the in-depth component of the study are presented. These two students are the subject of focus in Leder (1998) and Forgasz (1998b) where the fourth phase of the study is discussed in detail.

In Australia, as in many other countries, various policy initiatives encourage young people to proceed to tertiary education. Those who appear to have taken most advantage of the opportunity proportionately are women and older students generally. Coupled with demographic factors such as an aging population, and the restructuring of our economies (with the greater emphasis on Information Technology), certainly few adults are now immune from the need for retraining and upgrading their skills and knowledge (Thomas, 1992). While the specific role of tertiary mathematical learning in the restructuring of the workforce is not clear, it remains a key component of first year tertiary courses that lead to career opportunities in the Informational Technology and related Science disciplines.

In 1995 the Higher Education Council reported on the continued inequities in the tertiary education sector in relation to the lower participation of women in non-traditional fields and the socially disadvantaged generally. For mathematics in particular, it has been recognised for some time that participation rates at all levels are not equitably distributed among groups within populations (see Leder & Forgasz, 1998). Higher participation rates in optional school-level mathematics courses for students from higher socio-economic backgrounds (Ainley, Robinson, Harvey-Beavis, Elsworth & Fleming, 1994; Teese, Davies Charleton & Polesel, 1996), continues to be a critical filter to many career opportunities. Almost without exception females are less likely than males generally to study the most demanding mathematics courses offered and to persist with mathematics to the highest degree levels (Leder, Forgasz & Solar, 1996). In Australia, ethnicity/cultural background is another common grouping category of disadvantage (see Yates & Leder, 1996). The question arises, are these social and cultural factors continuing to be reproduced at the tertiary level when adults return to further their qualifications, knowledge and skills, or are they diminishing with the increased flexibility shown by tertiary institutions in their entry requirements? Are other issues emerging?

Much of the research on factors contributing to differential participation rates in mathematics courses have centred on school-aged children (Forgasz, 1996). Using a variety of methods and theoretical perspectives, levels of participation and success in mathematics continues to be shown to be contingent upon a complex interaction of cognitive, affective, environmental and socio-economic factors (e.g. Leder, 1992; Leder, Forgasz & Solar, 1996). Positive attitudes and beliefs about mathematics when coupled with higher socio-economic background are associated with greater participation among both males and females (Lamb, 1997).

Comparable research on factors influencing participation rates and learning outcomes in mathematics at the tertiary level is still in its infancy though it has been drawing greater interest as mathematics enrolments have declined, or at best, remained stable in Australia as elsewhere (Jorgensen, 1997). Findings from a recent Australian study of first year tertiary mathematics students across five universities found that the most powerful factor motivating students to enrol in first year mathematics was that it was a pre-requisite to a mathematics or non-mathematics course or subject the following year. A far less influential factor was an actual liking for the subject (Forgasz & Leder, 1998).

In the Forgasz & Leder (1998) study, the group who stood out as having more functional attitudes and motivations towards their studies were the mature-age students. Such findings are consistent with more general data on the relative success of older compared to younger students at the tertiary level. For example, students enrolled in higher education institutions in 1993, and who were aged 29 years of age or over, generally passed a higher proportion of their units than younger students (Higher Education Series, 1995). As Arts and Education faculties have tended to attract the bulk of mature-age students (Hore & West, 1980), particularly women (Thomas, 1992; West & Boon, 1980), this is where research attention on mature-age students has, until recently, been focused.

Other recent Australian studies that have explored issues concerning mature-age students and tertiary mathematics have included the investigation of the success of bridging mathematics courses (FitzSimons. 1994) and the level of congruence between the learning needs of recent school leavers and mature-age students beginning tertiary studies (Pierce, 1995). No systematic research appears to have yet emerged that represents a comprehensive, longitudinal study of male and female students returning to study mainstream tertiary-level mathematics courses.

To understand better the different pathways of mature-age students enrolled in tertiary mathematics courses it was appropriate to collect biographical data and investigate their experience of the learning environment through focussing on previously held beliefs and developing perceptions.

Despite the almost universal preoccupation of governments with the annual collection of educational enrolment data, finding out exactly how many students enrol in particular disciplines such as tertiary mathematics courses is no easy matter. "(M)uch of the readily available statistical information aggregates the whole of science and therefore tends to mask trends in individual disciplines" (Australian Academy of Science, 1993, p.4). Our own investigations of both published and unpublished enrolment data with respect to individual disciplines, however, suggests that the aggregated data probably represents the limit to the accuracy of the Department of Employment, Education, Training and Youth Affairs (DEETYA) data. For example purchased DEETYA enrolment data for 1996 indicated two of our participating institutions did not officially have any students majoring in undergraduate mathematics, a fact we knew to be incorrect. It would appear that the national data under-estimates the actual number of students studying and majoring in mathematics. Furthermore, Cobbin (1995) drew attention to discrepancies in the finer level of coding (e.g. enrolments in Applied or Pure mathematics).

Other factors emerged that caution against the use of the DEETYA data for determining longer term enrolment trends across disciplines. For instance, amalgamations of institutions previously regarded as part of a "two-tiered" system means that university entry does not have exactly the same meaning or significance as it did two decades ago in terms of eliteness or link to careers. This change in government policy has led, in part, to the greater number of females now reported to be continuing on to tertiary education (e.g. education and nursing, traditionally female occupations). Annual Victorian Tertiary Admissions Centre data (1988-1996) also show that there have been numerous course and discipline name changes, collapsing and splitting up of courses and disciplines, and an explosion in the number of double degrees now offered that have usually in the past attracted separate enrolments (e.g. Arts and Science). All these factors, while probably geared to better cater for students through greater flexibility and diversified courses, have created a mine field for those interested in tracking annual enrolment trends across the different disciplines. Consistent with current theoretical developments, comparing the past with the present is problematic. Placing the data collected from the mathematics students in our study within a larger national context proved to be not possible.

What we do know is that in recent years there has been a substantial increase in enrolments in Australian higher education (HE) institutions. In the period from 1990 to 1996, (a period that is reasonably comparable as it includes all HE institutions funded by the Commonwealth Government), DEETYA data reveal an overall 30% increase and a slightly higher growth rate of 34% for females generally (Higher Education Students. Time Series Tables, 1996 and see Leder & Forgasz, 1998 for further details).

DEETYA data also show that this growth in enrolment was not uniform across all age cohorts. In 1990 students aged less than 19 years represented 44% of commencing enrolments compared to just 36% in 1996. These figures were due mainly to growth in the 20-24 years age cohort which can be explained, in part, by an increase in overseas student enrolment. Since 1995, this enrolment growth in mature-age students has declined in strength (Figure 1).

Figure 1: Annual growth rates in higher education enrolments for commencing Bachelor degree students by age cohort (Source: Selected Higher Education Student Statistics, DEETYA, 1996).

Not surprisingly, national data to determine whether these age cohort patterns are evident across the broad fields of study are not readily available. Recent Victorian figures, at least, show that there was a drop in applications by mature-age students to science courses in the period 1994-1996 which cannot be explained by demographic factors (Report of Ministerial Committee of Advice to Minister for Tertiary Education and Training, 1997). Together, the data suggest that a major factor(s) in the mid 1990s has diminished what might have been a far greater growth boom in adults returning to tertiary study. One conjecture is that the increase in the Higher Education Contribution fee and the different fee scales for disciplines discussed in 1996 and introduced in 1997 may be contributing factors.

The 1996 DEETYA enrolment data continue to show that the bulk of mature-age students (both male and female) are less attracted to the Sciences than the Humanities and Business disciplines and that the lower enrolment of females in the Sciences generally is even more accentuated among mature-age students (Table 1).

In an attempt to obtain more precise mathematics enrolment details for 1996 and 1997 we wrote to Australia's 38 Higher Education institutions. Twenty-three institutions, representing 40% of the national higher education enrolments, supplied us with information, of which 15 replied with information in the requested format. A summary of our findings were as follows (see Leder, Forgasz, & Brew, 1998 for further details).

• more males than females studied at least one first year mathematics subject.
• a higher proportion of males than females continued with a mathematics subject from first to second year, but
• a higher proportion of females than males continued with a mathematics subject from second to third year, particularly mature-age female students.
• for both males and females, the attrition rate from first to second year, and from second to third year, was higher for younger students than for mature age students.

Written feedback from these universities on how they coded students for DEETYA also shed further light on the reasons for the acute inaccuracies in the national mathematics enrolment data. For example:

To learn more about the students actually enrolled in mathematics courses, and in particular to identify variables critical to students decisions to study tertiary mathematics, we administered a large scale survey to first year students enrolled in mathematics courses at five Australian universities. This questionnaire was derived from an earlier stage of a related study (Forgasz, 1998a and is discussed in more detail in Forgasz & Leder, 1998). Our sample comprised just over 800 students. Of these, approximately 40% were female, 12% were mature-age students (of these 31% were female), and just under 40% were NESB students, defined in our study as students for whom English was not the language of preference at home.

There were three groups of variables on which comparisons were made between the school leavers (SL) and the mature-age (MA) students detailed findings can be found in Leder and Forgasz, 1998).

• Personal characteristics
• Beliefs and attitudes
• Perceptions of the learning environment

There was evidence to indicate that the MA students generally came from lower socio-economic backgrounds compared to SL based on their parents' educational backgrounds (tertiary educated father: MA=38%, SL=52%; tertiary educated mother : MA=28%, SL-39%). Furthermore, a greater number of MA students received the means tested Austudy (52%) compared to recent SL (21%) though this reflects, in part, the greater eligibility of students' with a work history to obtain financial assistance. One third of the MA students did indicate that their reason for not continuing directly from school to their current course was due to having to support themselves, compared to just 9% for the recent SL. Of interest was that very few MA students (7%) indicated they originally had no intention to go to university. Instead, other common reasons given by MA students for not pursuing their current course directly following school was due to having studied at another tertiary institution (33%) and also not having decided on a career (23%).

In terms of beliefs and attitudes towards study, there were very few statistically significant differences between the MA and SL yet some key differences did emerge. MA students were more likely to attribute success to hard work than were SL. Ironically a much higher proportion of SL compared to MA students stated that they were studying mathematics because they believed they were good at it but MA students were more likely to be enjoying their mathematical studies at university. This was in contrast to MA not having enjoyed mathematics at school as much as SL.

In terms of their mathematical learning environment, MA students were more positive. MA found their course more challenging, interesting and useful than SL and with specific references to teaching, MA students were also more likely than SL to believe they were being well taught, that the lectures were less boring, and that the lectures were more approachable. SL, in this sample, were clearly less satisfied with their mathematical studies, and as they were more likely than MA students to indicate that their mathematics course involved too much work, were perhaps more resentful of the time taken up by study.

To provide further context in which to consider some of the results of the indepth component of the study (Phase 4), the profiles of just two of the participating students is presented below from data extracted from the survey alone (Table 2). In Forgasz (1998b) and Leder (1998) these two students are expanded upon utilising the rich data sources obtained through the qualitative component of the study. In the papers presented by Leder

(1998) and Forgasz (1998b) this data becomes quickly superseded highlighting the limitations of survey data for understanding the motivations of students and their experience of university life.

The two students in focus participated fully in all aspects of the research study. They were chosen as they both clearly had adult responsibilities in terms of family. They were also chosen because they both spoke about their family responsibilities in relation to their study in the context of resistance to traditional gender stereotype roles. Ann, in fact, was one of only two women who completed the survey who had children and the only mature-age woman to have children. Ann and Howard also both completed the beeper study in the same week (see phase 4 below and Leder, 1998), which also provided the interesting opportunity to compare two students' activities in time. They had also both studied before at a tertiary institution and a substantial proportion of the sample of mature-age students (33%) fell into this category.

From the survey data Ann was a full time, Australian born, 38 year old student. She was married with three children and lived in her own home. Her reasons for not proceeding directly from school to university included not having decided on a career, wanted a break from formal studies, family influence, and she needed to work to support herself. Ann attended a metropolitan government coeducation school and was the youngest of three children. Her reasons for returning to study included wanting to continue to learn, to enhance her career prospects and also always wanted to return. At school, Ann did not study the most demanding mathematics, she obtained a below average score though said she enjoyed school mathematics. At the time she completed the survey she was only enjoying university mathematics sometimes. She had enrolled in mathematics at university because it was a pre-requisite to a non-mathematics subject in her second year but indicated she would have still enrolled had it not been compulsory. She definitely did not think she would be dropping out of her mathematics subject. Ann thought she was an average student in mathematics but expected to obtain an above average mark for her semester examination. She would attribute success in her mathematics course most strongly to an easy examination (task) but also to her ability, effort, and some luck. Similarly she would attribute her failure mostly to a hard examination and bad luck, but not to lack of ability or effort. On her learning environment, Ann was finding her mathematical studies challenging and interesting though the lectures were boring and she was unsure whether she really understood the work. Despite this she found the staff approachable and helpful (Table 2).

From the survey data Howard was a full time, Australian born, 26 year old student who was studying at a different university to Ann. Howard had one child and indicated his marital status was "Other". Like Ann, he had attended a coeducational government school but in a non-metropolitan area. Both parents were tertiary educated. Howard was the oldest of three siblings. His wish to travel and to have a break from formal study were important reasons for the delay between leaving school and embarking on his current course. His reasons for returning to study included wanting to continue to learn, to enhance his career prospects and dissatisfaction with his current situation. Howard obtained an above average score for mathematics at school, he enjoyed school mathematics as he was currently doing at university. He had enrolled in mathematics at university because it was a pre-requisite to another maths subject in his second year and because he liked the subject. He definitely did not think he would be dropping out of his mathematics subject. Howard considered himself to be an above average mathematics student and expected to obtain an excellent grade for the semester. He would attribute success in his mathematics course equally to effort and ability but not to an easy examination (task) or luck. He did not respond to questions that suggested the possibility of failure. On his learning environment, Howard was finding his mathematical studies challenging and interesting but unlike Ann, the lectures were well taught and he understood the work. He also found staff approachable (Table 2).

Phase 4: A longitudinal in-depth qualitative study of a smaller sample of mature age mathematics/science students. Within this phase of the study four data gathering methods were adopted.

Turning now to the more sustained and open-ended measures we used following the administration of the survey instrument. At the time the students completed the questionnaires the opportunity was made for mature-age students in the sample to provide us with a way of contacting them for further follow up. Approximately 50 students indicated inital interest in further participation. Twenty-six students finally participated in the follow-up component of the study which involved four different types of measures:

• one-to-one hour interviews - to obtain further background information on what were the important factors that led the students to return to tertiary study and what was their experience of university life (see Forgasz, 1998b).
• regular e-mail contact - this was to find out on a regular basis how the students were progressing with their studies and what events they perceived were shaping their ability to maintain their commitment to their studies (see Forgasz, 1998b).
• Tag for the day - this involved meeting individually with the students on their respective campus and to attend some of their normal classes. The aim was to gain our own impressions of their learning environment which they had described in their interview and in the regular e-mail contact. (see Forgasz, 1998b).
• A beeper study that investigated the daily routine of the students over six consecutive days during semester. This part of the study aimed to help us understand better how mature-age students juggle their adult responsibilities with their study commitments by creating a temporary window into their daily lives (see Leder, 1998).

Our attempts to map patterns of tertiary enrolment within the mathematics discipline and in relation to mature-age enrolment generally have proved to be difficult. The national enrolment data is dubious and it is interesting that how infrequently is there any reference made publicly to the extent of possible inaccuracy of the data. All to often, the face value of the figures appears to be accepted. Our own attempts to develop a data base from individual university enrolment data just emphasised the difficulties inherent in making sense of tertiary mathematics enrolment data.

The reported survey findings from first year mathematics students across five universities did show that mature-age students are enrolling in mathematics courses and in general are finding the learning environment more favourable than school leavers.

The survey data from the two students presented reveal them to be interesting students for comparison. To some extent their responses epitomise the traditional gender stereo-types associated with mathematical learning (e.g. school mathematics experience, perception of self in relation to mathematics; factors attributed to success and intentions for further mathematics study). They are similar in terms of having family responsibilities and being highly motivated. In Leder (1998) and Forgasz (1998b) the more personal lives of Ann and Howard are compared and inter-woven with how they maintain their study commitments.