Beliefs are the views that we hold about the world that are not verifiable or that have not been proven. Teaching is a complex undertaking that cannot be fully theorised, it is reasonable to expect that teachers have beliefs about teaching and learning. How do these beliefs influence classroom practice?

A strand of research in education is concerned with the relationship between teachers’ beliefs and their practices. An example, from my own field of mathematics education and one which has been influential, is by Paul Ernest [1]. Ernest proposes that the way in which mathematics teachers teach is influenced by their beliefs about: a) the most effective ways of teaching mathematics and b) the nature of mathematics. Practice and pedagogy are based on views about the psychology of learning and about the epistemology and ontology of mathematics.

For example, if a teacher believes that mathematics is learnt most effectively through transmission methods, drawing on a behaviourist view of learning. And if, in addition, they believe that mathematics is a fixed body of knowledge with logically-related structures and entities, then the teacher is most likely to teach in a traditional teacher-centred way. In other words, the teacher demonstrates and explains mathematical methods and approaches and students learn by practice and memorisation.

On the other hand, according to Ernest, if a teacher believes that learning mathematics takes place most effectively through pupils experiencing mathematical processes, constructing knowledge, socially and collaboratively. And if they believe mathematics to be dynamic, of interrelated and connected ideas, and provides the tools to solve problems both within mathematics and in the real world. Then, the teacher is more like to teach in student-centred ways, using collaborative investigation and problem-solving approaches.

This theoretical relationship between beliefs and practices is a popular way of trying to understand how teachers teach and how teaching might change. But there are two related problems with the theory. The first is there is little evidence from psychology or philosophy that the link between ‘belief’ and action is straightforward. Second, empirical studies in mathematics education show that the relationship between beliefs and practices is complex. Research generally reveals that mathematics teaching is traditional and teacher-centred, despite some teachers espousing beliefs in student-centred approaches.

Yet the relationship between teacher thinking and practice is important in understanding how to improve teaching and learning, and in knowing how to design professional development. I believe, therefore, it is time to look at new ways of understanding the relationship between teacher thinking, practice and pedagogy.

It has to be acknowledged, that beliefs about learning, teaching and subject matter are significant and do have a role. However, it is my view that a different kind of belief has greater impact on teachers’ practices. This belief is based on teachers’ assessment of how successful they will be using a a teaching approach. Human beings assess the situations they meet, at the same time they assess the resources they have and imagine a response to the situation. The imagined response is a cognitive rehearsal of the actions the individual is about to carry out. We use self-referential beliefs to guide our actions.

If the activity is something we do regularly, then we learn a set of routine responses; our responses become almost automated. In complex environments, like teaching, we develop a set of heuristic responses (see Phil Wood’s blog).

Theory about human agency and self-referential belief has been developed by Albert Bandura [2]. Bandura describes *self-efficacy *as a *forward-oriented *belief: a belief in the extent to which we will be successful in an activity. It is a negotiation of our resources, an assessment of the situation and guides us to make decisions about the actions we take. Self-efficacy beliefs are more useful than general beliefs in explaining the relationship between teachers’ thinking and practices. Although research in this area is in its infancy, it is an interesting line of inquiry and one which is likely to lead to a better understanding of the relationship between thinking and practice.

What is the relationship between *beliefs*, as characterised by Ernest, and *self-efficacy* beliefs?

Beliefs are memory resources, they are constructs and organisations of memory which we give value to and prioritise. Beliefs allow is to make decisions in complex and ill-defined situations [3]. Beliefs are used to inform our decisions. However, responses in the classroom are of an immediate nature, ones which require tactical rather than strategic decisions. The resources used by teachers are based on specific practical knowledge. Beliefs about teaching and learning are more general and strategic.

It is generally accepted that teachers acquire practical knowledge through observational learning processes. Dan Lortie [4] describes teaching as an *apprenticeship of observation*. According to Bandura the observational learning process is a major contributor to the formation of behaviour more generally. It is evident from historical analysis of mathematics pedagogy that mathematics has been (and continues to be) predominantly traditional and teacher-centred. Observational learning explains why these practices are sustained. The practices that are modelled and passed on through generations are traditional in character. If a teacher believes in student-centred approaches, then unless they have observed such an approach being taught effectively then it is more likely they will teach using more traditional teacher-centred approaches.

Self-efficacy beliefs and the practices teachers observe are influential on the way teachers teach. This is not to say that general beliefs about teaching and learning do not have a role, but they are subordinate to self-efficacy beliefs. The complex relationship between the two is something I look forward to researching further.

[1] Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. In P. Ernest (Ed.), *Mathematics teaching: The state of the art* (pp. 249–254). London: Falmer Press.

[2] Bandura, A. (1997). *Self-efficacy: The exercise of control*. New York: W.H. Freeman.

[3] Nespor, J. (1987). The role of beliefs in the practice of teaching. *Journal of Curriculum Studies*, *19*, 317–328.

[4] Lortie, D. C. (2002). *Schoolteacher* (2nd ed.). Chicago and London: The University of Chicago Press.

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