Diamonds in a skull: Unpacking mathematics subject knowledge with students

Author(s):

Tony Cotton(presenting / submitting)

Conference:

ECER 2012

Network:

20. Research in Innovative Intercultural Learning Environments

Format:

Paper

Session Information

20 SES 03, Mathematics Teacher Practices

Parallel Paper Session
Joint Session with NW 24

Time:

2012-09-18

17:15-18:45

Room:

ESI 3 - Aula 2

Chair:

Raimonda Bruneviciute

Contribution

This paper describes the journey of a group of student teachers on a nationally funded project to support them in developing their skills in teaching mathematics. This group had self identified as having a ‘lack of confidence’ in their own mathematical subject knowledge and hoped that the project would boost their confidence as well as their practice. A series of experiential seminars supported them in developing both their subject knowledge and their pedagogical range. Drawing initially on Shulman’s work the paper investigates the way in which the student teachers’ views of themselves as mathematicians and mathematics teachers impacted on their developing identities as teachers, and in turn how this informed their future professional development.

Method

Tony Brown and his colleagues (Brown et al (2004) explored issues of identity among trainee teachers as they studied mathematics during their first year at University. They suggest that students are ‘interpellated by multiple discourses’ (p177) and in trying to identify with recognized constructions of mathematics and mathematics teaching and learning, they find it difficult to produce an identity of their own. The discussion of teacher subject knowledge and pedagogical practice was developed by Lee Shulman in 1986 with the introduction of his idea of pedagogical content knowledge. Shulman suggested that teachers draw on three forms of knowledge in order to teach effectively. The first is a ‘deep’ knowledge of the subject itself; secondly teachers need an understanding of the curriculum they are expected to teach; and thirdly they must be able to draw on an understanding of the range of pedagogical choices that are open to them which may support learners in coming to an understanding of the content. For Lacan, the construction of identity begins with a young child unaware of the social situation into which it has been born.

Expected Outcomes

Shulman’s notion of pedagogical knowledge is problematic if viewed as something which is fixed or can be attained. We cannot find ‘the most powerful’ ways of working with children – a better aim might be to find ways to give ourselves space to explore how effective our ways of working have been. More importantly Shulman’s triad does not allow us to focus on developing caring and respectful relationships with our learners. The idea of subject knowledge needs re-theorising to bring this to the fore. An alternative conception is offered: A conceptual understanding of the student and the student’s needs A conceptual understanding of the subject matter A conceptual understanding of teaching and learning environments I would suggest that the latter two areas coincide with Shulman’s content matter and pedagogical content knowledge with curricular knowledge replaced by a focus on the learner and their specific needs – perhaps the focus on care which the students found lacking in the models of pedagogical knowledge offered to them.

References

Brown, T., Jones, L. Bibby, B. (2004) Identifying with Mathematics in Initial Teacher Training in (Walshaw, M. Ed.) Mathematics Education within the Postmodern. P161-181.Greenwich, USA: Information Age Publishing Goulding, M., Rowland, T., Barber, B (2002) Does it matter? Primary Teacher Students’ Subject Knowledge in Mathematics in British Educational Research Journal. Volume 28 No. 5 October 2002. p689-705. Abingdon: Carfax Publishing Murphy, C. (2006) Why do we have to do this? Primary trainee teachers’ views of a subject knowledge audit in mathematics in British Educational Research Journal. Volume 28 No. 5 October 2002. p227-251. Abingdon: Carfax Publishing Shulman, L (1986) Those Who Understand: Knowledge growth in teaching Educational Researcher, 15, (2) 4-14 Training and Development Agency for Schools (2007) Professional Standards for Teachers London: Training and Development Agency for Schools

Author Information

Tony Cotton (presenting / submitting)

Tony Cotton Educational, United Kingdom

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