Conclusions drawn based on the case study about learning mathematics

I believe that the findings resulted from the case study and summarized above reflect some of the experiences of mature non-specialist students observed in other institutes. I have highlighted below my findings and recommendations that I think could be transferable to other institutes of a similar status.

The majority of the literature reviewed in Chapter Two concerned pupils at secondary school level. The school experiences that learners have prior to joining university have an enormous impact on their learning at a higher level (Schoenfeld, 1992; Crawford, et al.,

1994; Carlson, 1999; Anthony, 2000; Cox, 2001; Parsons, 2005; Solomon, et al., 2011). Many of the mature participants in the in-depth and focus groups interviews, spoke candidly of the effect, positive or negative, of their earlier experiences on their current endeavor in the learning of mathematics. I conclude that recognizing and valuing a student’s prior knowledge and experience is an essential aspect of planning courses for mature students.

For many of the respondents (69% - 90%), pedagogy was very important for the successful learning of mathematics. Drawing on their experience the participants indicated that the length of the lecture and tutorial times compromised their learning (Section 5.2). They also believed that relationships with tutors played significant roles in affecting their learning (Section 5.2.3). The preferences of the students in my study were for a short lecture followed by a tutorial / workshop sessions of an unspecified but appropriate duration, where students would be given the opportunity to assimilate and construct knowledge and have open access to get the extra support they needed. The participants believed that such arrangements would allow them to discuss and share problem-solving techniques with colleagues (Section 5.2.2), thus allowing the learners to develop their identity as engagers in mathematics. The students pointed out that the pace was too fast and the teaching methods did not accommodate the learning styles they had developed at a pre-university level of learning. This suggests that it is essential to recognize the methods of the delivery of the mathematics module offered to mature non-specialist students at university level could be incompatible with the learning styles that some students felt they needed.

The length of the lecture, the teaching style and the pace of the lecture appeared more important to both the female and younger respondents than to their counterparts. In addition, this particular group of respondents also agreed that ‘regular class attendance

and seeking help at the early stage’ to be important in the learning of mathematics. Both

the male and younger respondents, more than their counterparts, agreed that the aptitude and motivation of the learner to be important for the learning of mathematics (Section 7.3). In addition, as pointed out by Coben (1996: 5) ‘teaching should proceed at a pace which suits the learners’’, in particular, the mature non-specialist students. As my investigation revealed the learning needs of different groups of mature non-specialist students must be recognised in order to put them on the road to developing their deep learning ability and the construction of mathematical skills.

Furthermore, some of the participants believed that putting together students following different main/principal areas of studies to do the same module had adversely affected their learning. The participants preferred to have their lectures within the context of their particular course and area of study. That is, each subject area should have a class of its own. The students believed that such provision would help them build their confidence and be continuously motivated in their learning activities. Based on this finding, as a module leader for the MA module I put to the Area Group Leader (AGL) this pedagogical case against the teaching of the Biomedical Science and Mathematics students jointly at Campus A. I was given permission to teach the two groups separately on a trial basis. In the autumn semester of the 2010/11 academic year, the MA module was offered to Mathematics students on one day while the Biomedical Science students were taught on two other days. The Business students doing the QM module at Campus B were not included in this arrangement as they were already taught separately from the rest of the two groups. After the introduction of the new grouping, the autumn semester overall pass rate for the MA module increased from 84% in 2009/10 to 92% in 2010/11(Module Log, 2010/11). Based on the evidence of the increment in the pass rate from the trial grouping of

the two course groups, it is now a policy for the Mathematics Cluster of the Faculty to provide the module separately for the non-specialist and specialist students. This suggests that if the right resource is made available to run small sized classes of similar subject area it is possible to improve the performances of mature non-specialist students doing mathematics as an ancillary subject.

The dissonance (Ajzen, 1988) between the social obligations of mature students and the requirements of a regular attendance of classes was also considered by the participants to adversely affecting their learning of mathematics. Just over half of the students covered in the study, 53%, had part-time jobs (Section 5.3) to help with present financial needs. The tension resulting from between these two situations – of attending classes on regular basis and of working during term time, put the students in a dilemma and sometimes forced them to compromise their class attendances. Furthermore, dominant discourses about mathematics had created a negative emotion within some of the students, forcing them to position themselves outside of mathematics, to lose their confidence and to disengage from learning mathematics, all of which subsequently affected their achievement in the subject. This indicates the importance that ought to be given to the multi-selves of the mature non- specialist students when designing a course and the recognition of the discourses about mathematics embraced by the learners.

Based on their past experiences of learning mathematics, some of the participants identified the importance of support made available for them when learning mathematics. The source of the support could be the learner’s social capital or the institute providing the teaching. The learners’ cultural background also played a significant role by providing a basis for positioning mathematics as an important subject to study. Moreover, over 70% of the respondents agreed with ‘studying mathematics will make me more employable and

help in my career’ and was agreed across the three combinations of the constructed

identities; gender, age and ethnicity (Section 7.2). The majority (61%) of the Biomedical Sciences students viewed mathematics to be a difficult subject, followed by Mathematics students (46%) and Business students (37%). So, more than half the Mathematics and Business students presumably did not consider it as difficult. Some of the participants perceived mathematics learning as hierarchical (Reid, et al., 1981; Brown, 2003) and the subject as a new language (Sousa, 2008) for which the learners had not been given enough time to learn. In line with deficit discourse where the learner is blamed for the low performance and failure as a lack of ability, some of the participants blamed themselves for lacking the prior knowledge in the hierarchical learning of mathematics as one of the factors affecting their learning. Many of the participants of the interviews and 89% of the respondents of the questionnaire pointed out that ‘understanding basic concepts’ was a strategy that they have found to be effective strategy in learning mathematics (Solomon, 2007a; CBI, 2008). If it becomes apparent to the students that the skills they gained from learning mathematics it will enhance their learning; but the social construction of mathematics as a difficult, hard and boring subject has a counter-effect on some students’ learning, creating a phobia of mathematics.

As pointed out earlier, when students elect a main subject they construct their identity around that subject. Shaw (1995:113) suggested that ‘When we choose subjects [here, mathematics] we are obliged to redefine ourselves and make a public statement about what sort of person we are or hope to be. It is perhaps the first significant choice of identity’. But when students are obliged to do a subject, for example mathematics, irrespective of their choice, they react by asking ‘why is mathematics important’ (Claire, one-to-one interview); or wish to have their own world ‘free of mathematics and nothing to do with it’

(Martha, one-to-one interview) and some even ‘run away from mathematics’ (Liz, focus Group A). I suggest that one way that could help students develop their knowledge of mathematics and build their confidence is running a bridging course during the summer or for a few weeks at the beginning of the academic year for mature non-specialist students, e.g., Biomedical Science students who join the course through widening participation schemes and prefer not to study mathematics. As (Solomon, et al., 2011) indicated the provision of bridging courses helps develop the normative identity of engagement with the subject.

Drawing on their experiences in pre-university education, the majority of the participants believed that the learners’ gender or ethnicity did not contribute to the learning of mathematics (Sections 7.2 & 7.3). However discursive practices that have their basis in cultural discourses that discount girls from mathematics, such as differential treatment of appreciation given to male students, biased responses and comments that marginalise girls, etc. and dominant discourses about mathematics that position mathematics as a subject only to a particular group of students could make mathematics to be gendered or ethnically biased. In agreement with a discourse of individuality (ability is related to individuals rather than to gender or other factors), some students believed that hard work, fostered by cultural background and ability that result from ‘practice-linked identity’ (Nasir, 2002), helped to facilitate the learning of mathematics. My data suggest that a large majority of the students who took part in the study believed that mathematics was not gendered; however a small minority of the mature non-specialists did believe that mathematics was gendered, a view supported by Francis (2000b) and Mendick (2005). The male students in the case study were more than three times as likely to believe that male students are more likely to be successful in mathematics than female students, a view that was opposed and

rejected by the majority of female respondents (Section 7.3). In addition, contrary to the belief that mathematics is an important subject (Cockcroft, 1982) the younger students believed that the value given to the learning of mathematics is overstated (Section 6.3). I believe recognition of the prevalent discourses about mathematics and the resulting discursive practises could help lecturers approach the teaching of mathematics in a way that benefits the majority of the different groups of the mature non-specialist students.

In conclusion, I suggest that my research has gone some significant way in answering the research questions by identifying the perceived factors that affect the learning of mature non-specialist students who have to do mathematics as ancillary subject. According to the students who participated in the research, the pedagogy; the learner’s attitudes, beliefs and perceptions; and the support available to them were perceived to affect their learning of mathematics. However the impact of each factor, as explained earlier is dependent on the constructs of the identities of the learners. The awareness about the existence of these perceived factors can help lecturers understand how students perceive and learn mathematics; and accordingly adjust their mode of delivery of the subject and the perceptions of the learners’ in order to minimize the problems that may arise in the learning processes. The findings of my research show the importance of understanding the wider needs of the complex lives of contemporary students to address the problematic nature of mathematics teaching and learning.