Teaching and Learning Research Programme - Widening Participation

Keeping Open the Door to Mathematically Demanding Programmes in Further and Higher Education - it's a question of 'value'

Introduction/summary

This project aimed to better understand how to extend and improve learning in mathematics, especially by those 'on the edge' of further participation. Our study surveyed students by large-scale questionnaire and by a series of interviews as they progressed through their AS year. We also studied contrasting Programmes and pedagogies. We conclude that Programme and pedagogy can make significant differences to learning outcomes for these students, in terms of drop-out and the disposition to continue to study mathematics, sometimes despite injurious policy and institutional influences.

Key findings and implications for policy

Programmes can make significant differences to participation, including drop out, and to the value students attach to mathematics: so programmes should be engineered appropriately to engage students in uses of mathematics, e.g. via substantial mathematical modelling tasks assessed through coursework.

'Connectionist' teaching practices can make a significant difference to students' dispositions towards mathematics, and understanding, especially for students who start with lower GCSE grades: so if policy seeks to include more students in mathematics, and outcomes such as understanding and disposition, then more connectionist teaching should be valued and encouraged.

A culture of 'performativity' in Colleges can reinforce transmissionist, teacher-centred, teaching to the test that can be damaging to learners: policy could reduce the pressure to teach to the test by giving value to learning outcomes involving deep understanding, and dispositions to study mathematics more.

Research process and results

The study sought to find out (i) how learners' engagement in different teaching and learning practices can develop a mathematical disposition or identity, and (ii) how teaching and learning practices are shaped by institutional and policy cultures.

A large sample questionnaire survey of students' dispositions and performance was conducted on three occasions, early in the AS course, at the end of the year of study before the AS exams, and in the second year of college when AS results were known and university subject decisions were being made. The sample had sufficient numbers of students following two contrasting Programmes, 'traditional' AS Mathematics, and the AS 'Uses of Mathematics', which was designed to widen participation in mathematical studies. Instruments were specially constructed to measure students' self-efficacy with mathematics, their disposition to study more mathematics in HE in the future, and to measure the degree of 'transmissionism' of teachers' self-reported, pedagogic practices. As a result we find the effect of Programme and pedagogy on students' learning outcomes.

This data was supplemented by case studies in five 6th form FE Colleges, where we observed lessons, interviewed teachers and managers, and interviewed a select group of over 40 students on up to four occasions. The students' interviews tracked their view of mathematics and their aspirations for higher education and their future generally. The case studies sought to develop insights into learning and teaching processes and explanations for survey results. The result was explanations and insights into how different pedagogies come about, and how they influence learners' participation and identities.

The survey analysis reveals for instance, that the 'Uses of Mathematics' programme encourages more students with lower grades to persist and to pass at AS level than 'traditional' programmes (though this is a terminal maths exam at present). These students also have a stronger view of mathematics as a 'use' value, whereas it appears to students on traditional courses solely as a means of exchange, or currency with which to gain access to certain university or career options, in some cases literally to 'become a success' with a lucrative future.

Students, teachers and College management are acutely aware of the currency of qualifications and grades and all make strategic choices on this basis: to opt out of maths in favour of other courses, to teach to the test, or restrict course-choices or even close courses that do not add value appropriately. The key narrative for students is 'when troubles come' (e.g. maths grades) then either 'aspirations adjust' or extra reserves are required to 'stay on course'.

Addressing 'value' of mathematics is perhaps where policy can intervene, but where interventions are likely to have perhaps unintended and even malign effects. For instance many students are steered away from mathematics options at present because Colleges judge that they will not get the reward required.

Additionally, teachers may broaden their pedagogic approaches if 'teaching to the test' is seen not to be rewarding: assessments that require more understanding or evaluations of students' dispositions to further study are therefore worth exploration.

We found a few case studies where strongly connectionist teaching made a real difference to students with weak mathematical background studying the traditional programme. The ideal case involved teaching that made processes of 'deep learning' visible. The classroom was 'social', thus encouraging communication with and about mathematics, ensuring that procedural mathematical rules are under-pinned by conceptual understanding, and reasoning. Close analysis of classroom practices reveals how learners are thereby engaged in mathematics as a collective, joint activity, and how positive dispositions to mathematics can come to be formed: there are implications for developing expertise in mathematics teaching here, but still, the teachers' values are critical.