What’s the most effective way to train maths teachers?

Education policy has favoured school-based initial teacher education, with recruitment limits placed on some subjects on university-based programmes. In spite of increased challenges in the recruitment of teachers, Ministers in the Department for Education have been unrepentant and unrelenting in their attempt to diminish the role of universities in initial teacher education. This is in spite of evidence that attempts to steer training to school-led programmes has exacerbated the recruitment problem. (Education Select Committee, 2015).

Catch the standard

Government policy contrasts with the model proposed by McIntyre’s notion of reflective engagement between theory and practice. It favours an approach in which teaching is a craft-level undertaking, focussing on learning teaching skills through observing ‘great teachers’. (DfE, 2010) Rather than engagement with theory, teachers should implement practices based on evidence derived from large-scale experimental studies (Gibb, 2015a).

Little integration, little progress

Previous research in this area has considered the development of teacher knowledge, teachers’ beliefs and the development of teacher identity (Liljedahl, 2009). Thus professional learning has been seen in terms of the development of teacher cognition and their practices or in terms of their development and assimilation into a community of tacit knowledge and practices. Theory is limited because it doesn’t integrate these two aspects of professional learning. 

Does truth lie in doing?

My starting point here is within, or consistent with pragmatist philosophy. Knowledge is connected with action and in collective interpretation of that action in context (Biesta, 1994). Truth lies in doing. Which contrasts with a rationalist’s view of eternal abstract truths or from an empiricist’s experientially derived truths (Biesta, 2014). Yet pragmatic knowledge is informed by these positions but not dominated by either.

Behaviour emerges as a result of individual pragmatism.

Although Archer (1995) distances herself from pragmatism, her position, and hence her realist social theory approaches pragmatism (Kivinen & Piiroinen, 2006). While there are philosophical issues in linking Archer’s work with pragmatism, her theory from the pragmatist perspective provides a confirmatory framework for the theory I have been working on. Archer proposes that the behaviour of individuals and groups is formed as a reflexive process of structure and agency.  She states that individuals assess the physical and abstract structures (constraints, rules, regulations, physical limitations and social norms) and determine the extent to which they can exercise their agency or freewill (Archer, 1995). Thus, behaviour emerges as a result of individual pragmatism.

Is our teaching success based on our belief?

While Archer approaches the formation of behaviour and agentic action from a sociological perspective, Bandura (1977) emerges with a compatible theory from a social psychological perspective. For Bandura the agentic self-assessment process is through the construct of self-efficacy (Bandura, 1997). This he defines as the belief the individual has in the extent to which they will be successful. Self-efficacy has equivalence with Archer’s reflexivity.

Know who you are

Teacher identity has been increasingly recognised as a key aspect of teacher preparation (Beauchamp & Thomas, 2009). The concept of identity is related to self-efficacy and reflexivity: forming conceptions of self within a social context. It is also about performance and presence (Rodgers & Raider-Roth, 2006).

Taking further the pragmatist view, knowledge is developed through experience. I assume a social cognitive position, that much behaviour is learnt through observational processes. As Bandura explains, learning through trial and error is time-consuming and inefficient; whereas observational processes permit the transference of cultural and social practices. The relationship between knowledge and behaviour is facilitated through mental models constructed from observation and adapted through our imagination (Johnson-Laird, 1983). And, as I shall explain, moderated and mediated by reflexivity and self-efficacy.

Pedagogy is a formed within institutional and cultural contexts

Practice and pedagogy in teaching are cultural activities (Alexander, 2008; Chevallard, 1990; Cuban, 1993; Stigler & Hiebert, 1999) learnt and transmitted through generations of teachers through observation (Lortie, 2002). Thus, cultural and historical practices present defining structures over practice. Learning to teach involves developing agency within extant structures. Pedagogy is a formed within institutional and cultural contexts. Effectively pedagogy is a personal reflexive negotiation of institutional structures, policy, established practices and an expression of individual choice and agency. 

Do as I do

But it is important to recognise this process is a negotiation and not about individual agency alone. Trainees are learning to express their individuality within a pre-framed set of tacit rules and socially expressed norms. 

An experienced teacher develops stable sets of practice and responds to classroom situations without detailed analysis of the situation at hand (Leinhardt, 1988). Once competent an individual’s behaviour, within a context, follows routine patterns of behaviour within their self-efficacy beliefs (Bandura, 1997). For the trainee teacher – the novice practitioner – the process involves the development of practice and pedagogy through a reflexive negotiation of structure and agency and the development of self-efficacy in aspects of teaching. 

It’s the way maths as a subject is taught

This is related to knowledge. Shulman’s (1986) notion of pedagogic content knowledge (PCK) introduced the concept of knowledge in-action and that knowledge has subject specificity. This specificity is further developed by Ball and Bass (2000) ,as ‘mathematics knowledge for teaching’ (MKT). These concepts themselves represent cultural scripts as routines through which mathematical content and knowledge is operationalised into pedagogy. Effectively, it is the way in which something is taught.

Practice and pedagogy follow cultural scripts

This is the view of (Givvin, Hiebert, Jacobs, Hollingsworth, & Gallimore, 2005; Stigler & Hiebert, 1999). Historical analysis in the US reveals that practices tend to be teacher-centred and traditional on account of the practical demands of the teacher (Cuban, 1993, 2009). This is consistent with secondary teaching approaches in England (Ofsted, 2008, 2012). The emphasis is on teacher demonstration and explanation, followed by student practice, followed by review. The predominant practices do not take account of contemporary learning theory. Indeed analysis of PCK reveals traditional teacher-centred approaches (Meredith, 1993, 1995). 

Is there room for change?

In the context of the McIntyre’s model, the aim of initial teacher education in mathematics should be for broader pedagogic knowledge rather than simply perpetuating existing practices. It may even have to be recognised that cultural and historical practices may predominate.
To sum up, there are two components in the development of trainee mathematics teaching, teacher self-efficacy and mathematics knowledge for teaching. In a recent paper entitled: The impact of university teacher education programmes on the practice of pre-service mathematics teachers: a case study of a programme in England I integrate these ideas in the social cognitive theory of professional learning and relate them to the development of teacher identity. This I consider in two domains: the structural and organisational aspects of professional learning and the individual longitudinal development. To read more click here.

What is your view, or experience of mathematics teacher training?

Author Bio:

Steve Watson is a Lecturer in Mathematics Education in the Faculty of Education at the University of Cambridge.  He is a Fellow of Wolfson College and a former teacher of mathematics.

Further Reading

Archer, M. S. (1995). Realist social theory: The morphogenetic approach. Cambridge: Cambridge University Press.
Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 83–104). Westport, CT: Ablex.
Ball, S. J. (1987). The Micro-Politics of The School: Towards a Theory of School Organization. London: Methuen.
Bandura, A. (1977). Social learning theory. New Jersey: Prentice Hall.
Bandura, A. (1986). Social foundations of thought and action: A social cognitive theory. Englewood Cliffs; N.J.: Prentice-Hall.
Bandura, A. (1997). Self-efficacy: The exercise of control. New York: W.H. Freeman.
Biesta, G. J. J. (1994). Education as practical intersubjectivity: towards a critical-pragmatic understanding of education. Educational Theory, 44(3), 299–317. http://doi.org/10.1111/j.1741-5446.1994.00299.x
Biesta, G. J. J. (2014). Pragmatising the curriculum: bringing knowledge back into the curriculum conversation, but via pragmatism. The Curriculum Journal, 25(1), 29–49. http://doi.org/10.1080/09585176.2013.874954
Chaplain, R. P. (2008). Stress and psychological distress among trainee secondary teachers in England. Educational Psychology, 28(2), 195–209. http://doi.org/10.1080/01443410701491858
Cuban, L. (1993). How teachers taught: Constancy and change in American classrooms, 1890-1990 (2nd ed.). New York: Teachers College Press.
Cuban, L. (2009). Hugging the middle: How teachers teach in an era of testing and accountability. New York: Teachers College Press.
Department for Education and Science. (1972). Teacher education and Training: Report by a committee of inquiry appointed by the Secretary of State for Education and Science, under the chairmanship of Lord James of Rusholme (James Report). London: HMSO. Retrieved from http://www.educationengland.org.uk/documents/james/james00.html
DfE. (2010). The Importance of Teaching - The Schools White Paper 2010. London: DfE. Retrieved from https://www.education.gov.uk/publications/standard/publicationDetail/Page1/CM%207980
DfE. (2011). Teachers’ Standards: Guidance for school leaders, school staff and governing bodies (introduction updated June 2013). London: DfE. Retrieved from https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/208682/Teachers__Standards_2013.pdf
Education Select Committee. (2015). Oral evidence: Supply of Teachers (No. HC538).
Evans, E. D., & Tribble, M. (1986). Perceived Teaching Problems, Self-Efficacy, and Commitment to Teaching among Preservice Teachers. The Journal of Educational Research, 80(2), 81–85. http://doi.org/10.1080/00220671.1986.10885728
Gibb, N. (2015a, January). Reforming education through international evidence. Retrieved from https://www.gov.uk/government/speeches/nick-gibb-reforming-education-through-international-evidence
Gibb, N. (2015b, September). The importance of the teaching profession. ResearchEd Conference, London. Retrieved from https://www.gov.uk/government/speeches/nick-gibb-the-importance-of-the-teaching-profession
Givvin, K. B., Hiebert, J., Jacobs, J. K., Hollingsworth, H., & Gallimore, R. (2005). Are there national patterns of teaching? Evidence from the TIMSS 1999 video study. Comparative Education Review, 49(3), 311–343. http://doi.org/10.1086/cer.2005.49.issue-3
Gove, M. (2013, April). Speech to teachers and headteachers. National College for Teaching and Leadership. Retrieved from https://www.gov.uk/government/speeches/michael-gove-speech-to-teachers-and-headteachers-at-the-national-college-for-teaching-and-leadership
Liljedahl, P. (2009). Components of mathematics teacher education. In R. Even & D. L. Ball (Eds.), The professional education and development of teachers of mathematics. The 15th ICMI Study. (pp. 25–33). New York: Springer.
Lortie, D. C. (2002). Schoolteacher (2nd ed.). Chicago and London: The University of Chicago Press.

McIntyre, D. (1988). Designing a teacher education curriculum from research and theory on teacher knowledge. In J. Calderhead (Ed.), Teachers’ professional learning (pp. 97–114). London: The Falmer Press.
McIntyre, D. (1990). Ideas and principles guiding the internship scheme. In P. Benton (Ed.), The Oxford internship scheme: integration and partnership in Initial Teacher Education (pp. 17–34). London: Calouste Gulbenkian Foundation.
Meredith, A. (1993). Knowledge for teaching mathematics: some student teachers’ views. Journal of Education for Teaching, 19(3), 325–338. http://doi.org/10.1080/0260747930190308
Meredith, A. (1995). Terry’s learning: some limitations of Shulman’s pedagogical content knowledge. Cambridge Journal of Education, 25(2), 175–187. http://doi.org/10.1080/0305764950250205
Ofsted. (2008). Mathematics: Understanding the score. London: Office for Standards in Education.
Ofsted. (2012). Mathematics: Made to measure. London: Office for Standards in Education.
Rodgers, C. R., & Raider‐Roth, M. B. (2006). Presence in teaching. Teachers and Teaching, 12(3), 265–287. http://doi.org/10.1080/13450600500467548
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15, 4–14.
Stigler, J. W., & Hiebert, J. (1999). The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. New York: Free Press.
Tschannen-Moran, M., & Woolfolk Hoy, A. (2001). Teacher efficacy: capturing an elusive construct. Teaching and Teacher Education, 17(7), 783–805. http://doi.org/10.1016/S0742-051X(01)00036-1
Tschannen-Moran, M., & Woolfolk Hoy, A. E. (2007). The differential antecedents of self-efficacy beliefs of novice and experienced teachers. Teaching and Teacher Education, 23(6), 944–956. http://doi.org/10.1016/j.tate.2006.05.003
Vonk, J. H. C. (1989). Beginning teachers’ professional development and its implications for teacher education and training. The Irish Journal of Education / Iris Eireannach an Oideachais, 23(1), 5–21.
Watson, C. (2006). Narratives of practice and the construction of identity in teaching. Teachers and Teaching, 12(5), 509–526. http://doi.org/10.1080/13540600600832213
Watson, S. (Forthcoming). Teacher change in the context of professional development: a challenge to mathematics teachers’ beliefs or supporting teachers to meet the challenge of change?
Watson, S. (2013). Understanding mathematics teachers’ professional development from the perspective of social learning theory. In B. Ubuz, C. Haser, & M. A. Maiotti (Eds.), Proceedings of the 8th Congress of European Research in Mathematics Education (CERME-8), Antalya, Turkey (pp. 3287–3295). Ankara: PME.
Watson, S. (2014a). The impact of professional development on mathematics teachers’ beliefs and practices (Unpublished PhD Thesis). University of Nottingham, Nottingham.
Watson, S. (2014b). The impact of professional development on mathematics teachers’ beliefs and practices (eThesis). University of Nottingham. Retrieved from http://eprints.nottingham.ac.uk/27744/
Whitehead, J. (n.d.). The history of teacher training at the University (1879 - 2000). Retrieved from http://www.educ.cam.ac.uk/about/timeline/
Wilson, E. (2013). Building social capital in teacher education through university-school partnerships. In M. Evans (Ed.), Teacher education and pedagogy: theory, policy and practice (pp. 41–59). Cambridge: CUP.