Recent reports on mathematics education in English secondary schools have consistently expressed concern about students' performance and enjoyment as well as their progression into studying mathematics post-16 (Smith, 2004; Ofsted, 2006, 2008a; Royal Society, 2008, 2010; Vorderman et al, 2011). Too often students were expected to follow rules and procedures without mastering underlying concepts and connections, and hence without developing their mathematical understanding (Ofsted 2008a). Boaler (2008a) provides evidence for the introduction of Complex Instruction (CI) as an effective alternative approach to teaching and learning mathematics. The CI pedagogy combines rich mathematical tasks and instructional strategies that foster collaborative group work and problem solving. The approach emphasises effort over ‘ability' and challenges beliefs that only some students can do mathematics and that they should be taught in ‘ability' groups. This thesis explores factors which facilitate or militate against the adoption of such an approach by drawing upon Stigler and Hiebert's (1999) concept of a ‘cultural script' and Dweck's (2000) ‘theory of self and others'. It aims to build a better understanding of what influences teaching in mathematics classrooms in order to inform teacher development. The study combines quantitative and qualitative methods through the use of questionnaires, interviews and a reflective research journal over a two year period and includes: Secondary analysis of interviews with 20 teachers in schools with high numbers of students studying mathematics post-16; Course evaluations from 27 teachers attending a workshop on CI and interviews with a sample who were willing to use the approach; Pre and post study interviews with a lead mathematics teacher at two contrasting schools; one using CI with mixed ability groups and the other not. Questionnaires completed by 221 Year 7 students and their mathematics teachers at the two contrasting schools. Open coding analysis of the teacher interviews was used to produce themes. The questionnaires were statistically analysed to explore teachers' and students' frameworks of intelligence and personality in relation to learning and performance goals in mathematics. The findings support the notion of a ‘dominant cultural script' for teaching mathematics in English secondary schools. Teachers refer to ‘expected national norms', where the expectations are driven by their understanding of National Strategy/Ofsted guidelines and the judgements upon them are based upon students' exam performance. This performance goal orientated model, coupled with teachers' anxieties about unacceptable behaviour in the classroom together with concerns about finding time to plan and resource a different approach, offers strong reasons for teachers' reluctance to change. The findings demonstrate that the teachers using CI still adhered, to some extent, to aspects of the ‘dominant cultural script'. They felt vulnerable in terms of examination results and inspection. The extent to which they deviated from the ‘script' was contingent upon factors such as having a strong supportive department with collaborative sharing of resources; seeing students as actively involved in the learning process and continuing professional development opportunities both within their schools and with university departments of education. Whilst these teachers, though mindful of exam performance and inspection, held other beliefs and goals for their students, these were not necessarily shared by the students. A high proportion of students, particularly amongst the lowest attaining students and girls, were found to hold fixed frameworks of intelligence and personality coupled with a preference for performance over challenge in mathematics. Dweck (2000) suggests that having such beliefs is unlikely to lead to mastery orientated qualities in students, which are the key to improvement in progress. Hence, given a dominant script for teaching mathematics which also emphasises performance goals, the likelihood of all students achieving their full potential in mathematics in such a climate is jeopardised.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:554569 |
| Date | January 2012 |
| Creators | Altendorff, Lorraine Elizabeth |
| Publisher | University of Sussex |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://sro.sussex.ac.uk/id/eprint/39646/ |
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