How inclusive is year 12 mathematics?
This article examines year 12 students' attitudes to mathematics, their experience of the mathematics classroom and their views of teachers and their expectations of success, drawing from a longitudinal study of student achievement in Melbourne's northern suburbs. Despite a differentiated year 12 mathematics curriculum, there is evidence of inequity in students' experience of mathematics. Perceptions of mathematics classrooms and mathematics teachers, and expectations of success, vary according to subject, gender and social background. Implications for pedagogical and curriculum reform are discussed. The article is adapted from a paper of the same title presented to the 2011 MERGA Conference.
Mathematics is not a level playing field. Achievement gaps based on socioeconomic status (SES) are evident in early primary school and increase in magnitude throughout the school journey (ACARA, 2009). A case in point is DEECD's Northern Metropolitan Region (NMR), one of the poorest regions in Victoria. In 2007 the NMR's literacy and numeracy achievement levels were among the lowest in the state (DEECD, 2009). The region also had the lowest VCE study scores in Victoria and the lowest rate of transfer to university (Helme, Teese & Lamb, 2009).
In recognition of low student achievement levels, the NMR embarked on a major school improvement campaign in 2008 whose key initiative is the Achievement Improvement Zones (AiZ) project. The AiZ aims to improve literacy and numeracy levels across all schools in the region, focusing on leadership development, professional learning in numeracy and literacy, ongoing coaching and training and support from the region, department and education experts (DEECD, 2009).
A study is evaluating the impact of strategies to lift achievement within the NMR. The Raising Achievement in Public Schools (RAPS) project is synthesising data from a range of sources: NAPLAN data, student and teacher surveys and teacher interviews. Years 3, 5, 7 and 9 NAPLAN data will be monitored for a period of five years, with a focus on SES differences in achievement as students progress from one stage to the next.
Teacher surveys have been conducted in a sample of 10 primary and 10 secondary schools in the region to obtain a teacher perspective on the challenges of lifting student achievement and the strategies needed to achieve progress. Focus groups with teachers and leadership teams were undertaken in 2011 and a second wave of interviews is planned for 2013 to allow teachers to reflect on progress. Surveys have been completed with students in years 3, 5, 7, 9 and 12 in the 20 sample schools to obtain a student perspective on learning and achievement.
The current article looks at this evidence base as it relates to year 12 (final year) mathematics in the NMR, to see the extent to which nation-wide gaps in achievement are also reflected within the region itself. It finds that perceptions of mathematics classrooms and mathematics teachers, and expectations of success, vary according to subject, gender and social background. Implications for pedagogical and curriculum reform are discussed. This article is adapted from a paper presented to the 2011 MERGA Conference.
Previous phases of research in the NMR had already suggested how students' social background might be impacting on year 12 mathematics. The more academic subjects of Specialist Mathematics and Mathematical Methods contain higher proportions of students from higher-SES backgrounds: enrolment rates in Mathematical Methods are almost twice as high in the highest SES quintile as in the lowest, and for Specialist Mathematics this ratio exceeds 2:1 (Helme, Teese & Lamb, 2009).
In terms of academic achievement, Further Mathematics students in the highest SES quintile in NMR were more than twice as likely than their counterparts in the lowest SES quintile to achieve a study score above the defined average of 30. Similar patterns were evident in Mathematical Methods. For example, more than half the Mathematical Methods students in the lowest quintile of SES achieved scores below 24 (53 per cent), compared with 18 per cent of those in the highest SES quintile (Helme, Teese and Lamb 2009).
The 10 secondary schools investigated in the 2011 survey had a total enrolment of 1107 year 12 students, 841 of whom completed the survey. Questions canvassed their views of subject content and difficulty, quality of teaching, quality of classroom experience and their expectations of success. Students were also invited to contribute their ideas on how to improve mathematics and the way it is taught in their school. Students were additionally asked to nominate, for each parent separately, their highest level of school completed and their highest post-school qualification, in order to establish a measure of SES.
Survey results show that the students taking Specialist Mathematics and Mathematical Methods were the most likely to find the subject interesting and enjoyable, suggesting a better match between the content and pedagogy of these subjects and the needs of their clientele.
Children of tertiary-educated parents were more confident of success. When data for all mathematics subjects were combined, students from more highly educated homes were more likely than students from less well-educated homes to expect to do very well (25 per cent compared with 14 per cent). They are therefore better placed to achieve good results and enter tertiary education. Children of tertiary-educated parents were also more likely to attend larger schools that do not experience the serious staffing issues confronted by smaller, poorer schools in the NMR. It is noteworthy that four of the 10 schools in this study are no longer able to offer Specialist Mathematics classes.
Gender differences are characteristic of enrolment patterns in year 12 mathematics in Victoria. State-wide enrolment rates, derived from VCAA (2010) figures, indicate that participation in Further Mathematics is much the same for males and females, but that girls are less likely than boys to select Mathematical Methods (26.0 per cent compared with 37.4 per cent) and even less likely to enrol in Specialist Mathematics, where the enrolment rate of boys is more than double that of girls (13 per cent compared with 6.2 per cent). Teese, Lamb, Helme & Houghton (2006) found that year 12 girls perceived mathematics as less interesting, more difficult and less relevant to the real world than boys did.
This pattern was evident in the 2011 NMR survey: girls in Further Mathematics and Mathematical Methods were significantly less likely than boys to perceive mathematics as relevant and useful for the future. Also, female Further Mathematics students were significantly less likely than their male counterparts to agree that their teacher understands how they learn, significantly more likely to report that the pace of learning is too fast, and significantly less likely than their male counterparts to agree that they enjoy the subject.
In Further Mathematics there was no notable gender difference in students' expectations of success, but this was not the case for Mathematical Methods and Specialist Mathematics. Male Mathematical Methods students were more than three times more likely than their female counterparts to expect to do very well (29 per cent compared with 9 per cent; the corresponding percentages for Specialist Mathematics were 62 per cent and 40 per cent). Given that girls take Methods less frequently than boys, one might expect that those who enrol in the subject have at least as much confidence as their male peers. But they do not.
Recent Victorian data shows a significant decline in enrolment rates in the more demanding year 12 mathematics subjects. In 2011 enrolments in Mathematical Methods and Specialist Mathematics were, respectively, 17 per cent and 38 per cent lower than in 2001 (Dunn 2012). A worrying concern from a gender perspective is that enrolment rates in both these subjects have slipped more for girls than for boys, which means that an already significant gender gap is becoming wider.
It appears that, despite decades of research into gender differences and strategies for making mathematics more responsive to the needs of girls, there is still a great deal of work to be done.
The survey invited students to suggest ways to improve the teaching of mathematics. The most frequently mentioned suggestion concerned quality of teaching. Students asked for teachers who could speak and explain more clearly, and adapt their explanations to individual needs. They also called for teaching methods that were less dependent on textbooks and were more interactive.
Other feedback included better teaching at earlier year levels, more thorough preparation for year 12, and a slower pace of teaching in year 12. Students also asked for more enjoyable coursework and course content that has stronger links to real life situations. Students in all subjects expressed a desire for more 'hands-on' mathematics.
While students appear to have a good understanding of their needs as learners, these often clash with externally imposed demands and constraints. Teachers must complete the coursework in the time available and prepare their students for final examinations. They cannot slow the pace, diverge from the set curriculum or amend the content to suit students' needs and interests. This issue has been previously identified in low-SES schools, where the need to accommodate student diversity is the greatest (Helme, Lamb, & Teese, 2009; Teese, Lamb, & Helme, 2009).
Inequities in the experiences and outcomes of year 12 mathematics students cannot be overcome simply through the efforts of teachers in low-SES schools. School systems must also heed student feedback, reinvigorate the curriculum and provide enough trained teachers to ensure that all students have the opportunity to engage deeply with mathematics. What better time than now to review curriculum and pedagogy, in the current context of the development of the Australian mathematics curriculum? Otherwise, too many students will remain marginalised from mathematics and the rewards conferred by curriculum and pedagogy will continue to be inequitably distributed.
The study reported in this paper is part of a larger ongoing evaluation of intervention strategies for lifting student achievement in the Northern Metropolitan Region of Melbourne, funded by the Victorian Department of Education and Early Childhood Development (DEECD). The authors acknowledge Esther Doecke's invaluable assistance with data collection and analysis.
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Key Learning AreasMathematics