The use of drama in mathematics teacher education

In the final week of my teacher training course in 2001, there was an ‘options’ day, in which a range of workshops were available for trainee teachers to choose from. I decided to attend the forum theatre workshop. I self-consciously entered the room where the workshop was to be held. The workshop leader, as I recall, asked me what subject I taught. I said, “mathematics.” And he looked at me as if to say, “you’re in the wrong room mate.” I looked around the room at the punctual trainee teachers, they were mostly prospective English teachers, history teachers and even a science teacher. But the initial impression was that for a mathematics teacher to be in a forum theatre workshop was beyond the pale. That I must have made a mistake – got the wrong room.

It wasn’t a mistake, I wanted to be there. I was not sure why. Maybe I just wanted to experiment with the teaching of maths.

What is forum theatre? The Drama Resource website describes it exactly how I remembered it being explained to me:

A technique pioneered by Brazilian radical Augusto Boal. A play or scene, usually indicating some kind of oppression, is shown twice. During the replay, any member of the audience (‘spect-actor’) is allowed to shout ‘Stop!’, step forward and take the place of one of the oppressed characters, showing how they could change the situation to enable a different outcome. Several alternatives may be explored by different spect-actors. The other actors remain in character, improvising their responses. A facilitator (Joker) is necessary to enable communication between the players and the audience.

The strategy breaks through the barrier between performers and audience, putting them on an equal footing. It enables participants to try out courses of action which could be applicable to their everyday lives. Originally the technique was developed by Boal as a political tool for change (part of the Theatre of the Oppressed), but has been widely adapted for use in educational contexts.

I started to use an adapted technique with a trainee teacher who was having difficulty last year. Yes, I suppose you could just call it role-play and that’s what it was. The trainee and me acting out teaching moments, rewinding and replaying situations. I was coaching him in his technique of classroom performance. But drama helped us try things out and develop some mastery experience (see Bandura, 1997 for conceptualizations of the development of confidence and self-efficacy through a ‘enactive mastery’ experience).

This summer I began thinking more about the use forum theatre with the trainee mathematics teachers in their faculty sessions. During the last five years, I had waded through lots of theory and engaged them in a meta-narrative of their (social) psychological processes as they learned to be teachers. This was all abstract. And it did not allow them to build their practice and their self-efficacy in aspects of their practice in the faculty. The theoretical felt far too abstracted from the experience they would have in the classroom.

So, for the first two days of the induction programme this week, I have been using a form of forum theatre in order that they can really think about what is going on in the classroom, by acting out the parts. We have a mini lesson in the faculty session. We crowd source ideas for the mathematics topic to be taught, the age of the learners and their context. There is a teacher and six students. I am the facilitator and the rest of the trainees not taking part are potentially ‘spect-actors’. After the first two days it’s more role play than forum theatre, but I imagine we will progress. At least the principles of forum theatre gives me an idea of where we are going. I, rather than just being a facilitator, act as a kind of coach, giving some advice to the volunteer teacher. Again, I imagine this will change – the group will become more self-sufficient and will be able to use the forum theatre technique to help plan and evaluate teaching.

During the first day there were immense preoccupations with classroom management and behaviour, both from the acting teacher and the acting pupils. The scenario was one in which they were supposedly 11 and 12 year-olds in their first maths lesson in big school. One of the girls at the back shouted out, “How old are you miss?”. “Really?” I asked. There was then debate about the behaviour of year sevens in their first maths lesson in secondary school. We did three mini-forum lessons on the first day. There was not much on mathematics (all rather procedural) or on the psychology of mathematics learning. It was all about classroom management. It was role playing how the teacher might establish and maintain a productive and classroom environment.

We had time for one mini forum lesson on day two. In this one we went more into the nature of mathematics and getting children to think about the concept and meaning of area. Those playing the members of the class also constructed biographies so that their behaviour and attitudes to mathematics had a background and history.

Tomorrow, we have two two-hour sessions. The theme of these are lesson planning and lesson observation. I will use forum theatre to illustrate how planning works based on my theory of teacher decision making and what they might attend to in a lesson.

So more to follow.

References

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

 

 

The problem of behaviour in schools: initial thoughts on the Bennett Report

This is a quick response to the following report:

https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/602487/Tom_Bennett_Independent_Review_of_Behaviour_in_Schools.pdf

A review group was commissioned in 2015 by the then Secretary of State for Education, Nicky Morgan MP, to look at content in initial teacher education. The group was chaired by independent education expert Tom Bennett. This report on behaviour in schools is an adjunct to that work.

The premise of the report is that attention to behaviour in schools has been relatively neglected. The report, after the weighing-up of selected evidence, concludes that “There is sufficient evidence to suggest that there is enough of a problem nationally with behaviour for it to be a matter of concern” (p. 21). It goes on to characterise ‘bad’ behaviour as “…behaviour that detracts from the academic and social success of the school community, along with behaviour that diminishes the dignity of staff or students (for example harassment or name-calling)” (p. 22).

There is careful consideration of whether insisting on good behaviour is oppressive. It links good behaviour with the characteristics of self-restraint and self-regulation. That to be free we have to learn to master these abilities.

There is no examination of the social, anthropological and sociological processes through which a child learns to behave well, as an effective learner and scholar, and with due respect to peers and adults. However, the means are implied in the characterisation of the features of effective schools.

The features of effective schools include: strong and effective leadership which  communicates a clear vision. I assume that this vision is a view of the culture of the school in terms of observable good behaviours. This implies a high level of conformity, but as Bennett stresses in this report this compliance does not amount to oppression.

There is a clear link made between ‘good’ behaviour and performance in examination results. I imagine the assumption is that if school leaders and managers can observe  good behaviour and that examination success is achieved, this is evidence enough of school effectiveness. I think bigger questions about the purpose of education need to be addressed here.

The pracitices underpinning the school-level approach include a full commitment and belief in the systems of behaviour management; a commitment to its consistent implementation; attention to detail in its application and that routines and rules are practiced and emphasised.

The establishment and repitition of routines appear at the heart of Bennett’s effective behaviour management process. This is consistent with a behvarioust view of learning. It is a conditioning process in which behavioural models are presented and a system of sanctions are used to ensure that pupils develop automatic responses in situations in the school. This create social norms within the school.

At some point, someone has to decide what behaviour is appropriate in order to construct a routine for the school. Someone, presumably, has to decide that there is a particular way in which pupils must move about the school and how they respond in lessons. The difficulty is in finding the limits to this programming: in which aspects does behaviour have to be legitimised and programmed? Where do individuals have the opportunity to act of their own volition and exercise agency and control?

It begs the same question that is raised at the beginning of the report, is this oppressive? Tom Bennett is rightly sensitive about this issue. I am not assured that has been answered fully. It is necessary to consider it in developmental terms: the appropriate level of behavioural control and whether this is compatible with human development. This report does not address this critical concern.

There is limited evidence that compliance in this way necessarily leads to the development of self-regulation. Self-regulation is developed through exercising agency and constructing our own models of behavioural response . We have to be very careful that we do not suppress this in a highly compliant setting. That would amount to oppression, to the extent that it is an abuse of human rights.

Teachers, especially trainees, must have the opportunity to develop a profound understanding of a range of disciplines that underpin children’s and young people’s developmental processes. It is inadequate, as teacher preparation, to present behavioural management as the effective implementation of desired models, routines and processes. These are necessary but a long way short of sufficient.

For many children the desired behaviours that are encouraged in a school are highly consistent with their social and cultural experience. This is the essence of what is lazily referred to as ‘normal’ behaviour. It is also consistent with what this report refers to as ‘good’ behaviour. Many schools centre around the British middle class; British middle class teachers enacting British middle class values and norms. To comply with this is manageable for many students even from diverse ethnic and cultural backgrounds. And even from different social classes. But for many reasons a significant proportion of children in our schools find it harder to comply. The social norms, the cutural context, the physicality and the cognitive demands are incompatible in so many ways. Often the the underlying reason for their non-conformity (‘bad’ behaviour) is undiagnosed, they are not recognised in an official sense as having a special educational need. It is unsurprising that students, whether they are recognised as having specific needs or not, or that they are from particular socio-economic and ethnic groups, become excluded. Whether that is a formal or informal exclusion.

The answer to this, in this report, is to be robust in ensuring that these pupils observe and accept the models of acceptable behaviour. It is suggested that, and alluded to, in the introduction of this report that we have not been doing this well enough. That teacher educators have not been making the simple truths of behaviour management more plain.

I am afraid that this, and the underlying premise of the report, are an oversimplication of the problems teachers and schools face in respect to pupils’ behaviour. It does not recognise the delicate balance of emotion, motivation, cognition and behaviour. Bandura has been a key contributor in the identification of the sophisticated reciprocity between social environment, cognition and behaviour. That in order to act in a particular way we have to have both knowledge, i.e. models of behaviour, and the belief that we are going to be successful. We need a supportive environment in which we develop confidence in our behaviours. We need to have faith that compliance will lead us to success. This is not just in an artificial sense such as being successful in examinations, it also needs to be related to deeper human fulfilment.

As part of their development, children need to have confidence to adapt and deviate from norms.

It is less effective, and often not effective at all, if we are presented with models of behaviour, with external motivations to comply, such as rewards and punishments. For many children it works for them, that’s how schools traditionally work. But for a significant proportion it simply does not foster self-regulation (as Bandura would call it, self-efficacy). It will work for some schools, it will not work for all schools and it will especially not work for schools in particular contexts.

What this report does is emphasise a traditional model of behaviour management and it suggests that if it is done more strictly, with greater attention and more seriously, then behaviour will improve. What I am saying is that this model is obsolete, it is of the past. We need to be moving forward.

There has never been a more important time, we need progressive and more sophisticated approaches to behaviour management. It is a complex and difficult world that children are growing up in. There are more challenges for them than for the previous couple of generations. We need to foster students’ capacity to live together and solve some of society’s problems (I don’t think Tom Bennett and I disagree on this, it’s just the means). For this they need knowledge, confidence, character, communication skills, problem-solving skills and reasoning skills.

To do this effectively, schools cannot be rigid and austere institutions of the past. They need the capacity to innovate in practice, they need to encourage curiosity, they need to be inclusive. This needs to be underpinned by a system of values, principles, flexibility and age-appropriate democratic participation. Teachers need to have a deep and critical understanding of disciplinary knowledge as well as in psychology, anthropology and sociology, at least.

Reference

Bandura, A. (1997). Self-efficacy: The exercise of control. W.H. Freeman.

An investigation of culture and habitus in teaching

A surprisingly popular blog post I wrote was on cultural scripts in teaching. I want to develop the ideas from that here in the form of a public writing experiment. To inform the theoretical considerations, I draw on observations from the research I have been doing with Underground Mathematics looking at how teachers incorporate new tasks and activities into their teaching. This is in the context of A Level mathematics in England. The understanding of the impact of culture and habitus in teaching could be helpful in a wider range of teaching and contexts. Culture and habitus in teaching are ideas that have not been given a great deal of attention, the emphasis has been on a) how teacher thinking impacts on their teaching and b) what practices result in greater learning gains? Culture and habitus do not replace these ideas, but I think give us much better understanding of why teachers teach in the way they do.

The following is an investigation of ideas that will be a component of a future publication. I share it here for discussion and comment.

What is culture?

The idea of culture comes to us as a critique of evolutionism. Anthropologists rejected the idea that all human societies progressed through the same stages of development. From a social evolutionary perspective different groups must pass through the same developmental stages. Franz Boas was a foundational thinker in the development of modern cultural anthropology. He argued that the world was populated by distinct cultures.

There has been an emphasis on behaviours, artefacts and symbols: the external actions and symbollism. For example, Meade (1953, p. 22, cited in Prinz, 2016) says culture “is the total shared, learned behavior of a society or a subgroup.” More recently there has been a turn to meaning and semiotics, “an historically transmitted pattern of meanings embodied in symbols” Geertz (1973, p. 89). It is these ideas that are fundamental to my discussion later.

There is a complex and rich sense of what culture means, almost defying definition. The moment one becomes specific the general sense is lost. And if the idea is too general then it becomes unusable. The following idea gives a sense of the issues:

…most definitions characterize culture as something that is widely shared by members of a social group and shared in virtue of belonging to that group. As stated, this formulation is too general to be sufficient (a widespread influenza outbreak would qualify as cultural). Thus, this formulation must be refined by offering a specific account of what kind of shared items qualify as cultural, and what kind of transmission qualifies as social. (Prinz, 2016).

Overall, culture means shared behaviours within a group. In my previous post on international comparisons in mathematics education, the international comparisons of teaching practice relied on the idea of distinct cultural practices in the different countries studied. Cultural anthropology provides the basis for making this assumption.

Habitus and habits

As an individual many of our habits are idiosyncratic, they are ours. The original meaning of habit was how a person holds themselves, their demeanour. This has developed to include apparel, then on to dispositions, behaviours and ways of doing things. “A settled disposition or tendency to act in a certain way, esp. one acquired by frequent repetition of the same act until it becomes almost or quite involuntary; a settled practice, custom, usage; a customary way or manner of acting” (OED Online, 2016). According to Camic ‘the term “habit” generally denominates a more or less self-actuating disposition or tendency to engage in a previously adopted or acquired form of action’ (Camic, 1986, p. 1044).

Pierre Bourdieu argued that habits are not idiosyncratic, especially in the context of professional practice. Bourdieu’s concept of habitus represents culturally acquired habits. Habitus is developed socially which result in enduring patterns of behaviour (Bourdieu, 1984). Habitus represents a socially acquired cultural basis for routines and patterns of behaviour.

This then is the basis of my discussion, that habits (habitus) is a cultural phenomenon, I look at this in the context of teaching, developing from extant ideas about the nature of teaching, practice and pedagogy.

Theories of teaching

Teachers’ beliefs

The tradition of theorising pedagogy and practice emerged from psychology (this is looking from the perspective UK and the USA in particular). Firstly, behaviourism explained behaviour as a consequence of external stimuli and behaviours are developed through reinforcement. While this was a dominant theory of learning, it does not adequately explain how teachers learn to teach and the practices they use. Later, theories of practice evolved around constructivist views of learning. We are talking about Vygotsky and Piaget. In simple terms individuals construct a view of objects and actions. This sort of cognitive functioning was absent in behaviourism. Within constructivism people have agency which contrasts with the behaviourist model, where agency is a kind of random action that is disciplined through reinforcing responses.

The dominant explanation of pedagogy and practice since the 1970s has been influenced by constructivism but in a particular form. Teachers’ views about practice that ultimately guide their actions are described as ‘beliefs’. Paul Ernest (1989) proposed that in mathematics teaching, the way teachers teach is based on their belief about the most effective way of way of teaching and learning and their beliefs about mathematics. I have a previous blog post on this.

While there has been extensive research on the relationships between teachers’ beliefs and practices, a consistent link between beliefs and practices has not been found. It is frequently observed that enacted beliefs (what is observed in the classroom) is different to what teachers say they believe in, their espoused beliefs. Ernest explained this difference as the effect of social context, meaning that teachers do not have full agency. They may believe that teaching and learning takes place in a particular way, but the way in which they teach is influenced by the expectation placed on them by the students, parents, colleagues, the schools’ leadership and policy expectations.

Situated cognition

In the 1990s more attention was given to the social aspects of learning. That people learn to adopt cultural practices as they become part of a discourse community. Jean Lave and Etienne Wenger (1991) suggested that professional communities have a dominant discourse, including language as well as practice. There are, in discourse communities, legitimised language, grammar and behaviours. As we become part of a discourse community we learn what they are and the extent to which they can be deviated from.

In my role in initial teacher education, at the University of Cambridge Faculty of Education, I am well aware of the socialisation that trainee teachers experience as they train in our partner schools. They learn the dominant forms of practice and some develop the confidence to subvert and extend existing practice. They also learn the routines of practices and language forms that teachers use to talk about their work, the progress of students and in describing learning. This is within the constraints of policy and accountability, these factors in addition to the disciplining character of social interactions normalise behaviours. As individuals we still maintain a degree of agency and configure these performances to our own preferences. While there are characteristics of what we do that are consistent with a dominant form, each of us acts in an individual way.

In the last three years I have increasingly discussed this with trainees. It is important to understand the socialisation process that we need to undertake in order to enter professional practice. I sometimes wonder what trainee teachers think the learning process is, whether they see it as the acquisition of skills, which is only partly true, or whether they see learning to teach as socialisation. I think the former is the more likely explanation based on my questioning at interview and in the early part of the course. So to understand social learning, to understand your own learning as social learning is valuable in understanding your progress. You understand why it is necessary to observe teaching, as well as interactions with pupils and colleagues and the exchanges that happen in staff-rooms and corridors. While it is easy to understand the idea of situated cognition and social learning, the processes in which this takes place is a little more demanding. To explain this I am going to draw on the ideas of social cognitive theory, self-efficacy, reflexivity and observational learning.

Social Cognitive Theory, self-efficacy and reflexivity.

A more in-depth explanation of social cognitive theory (Bandura, 1997) is available in a previous post, here I am just going to recall a few key points. The important point about social cognitive theory is that it integrates the social aspects of learning and learning through the acquisition of knowledge. Within social cognitive theory is the construct of self-efficacy and vicarious (observational) learning.

Self-efficacy is a self-assessment or self-belief. When doing something new we consider the situation and consciously construct an approach, we plan for the situation. We also assess how successful we will be. Self-efficacy is partially dependent on knowledge but importantly it is dependent on the belief the individual has in being able to apply existing knowledge to a novel context. Teaching self-efficacy is the belief a teacher has that, as a result of the teaching approaches used, students will make progress in their class.

Self-efficacy is a useful construct as it operationalises knowledge, it connects affective aspects with knowledge. It is not just knowledge and skill but the belief an individual has in being successful in a context. It explains then why, when teachers are tired or stressed, they generally become less effective even though their subject and pedagogical knowledge is still intact.

The second aspect of social cognitive theory vicarious learning. It was Miller and Dollard (1941) who highlighted the vicarious nature of learning. While they referred to imitation, they did not mean that we learn by copying precisely what others do, we adapt observed behaviour as part of the process of vicarious or observational learning. This was famously demonstrated in Bandura’s Bobo Doll Experiment, in which children observed adults engaged in violent behaviour toward a Bobo doll. The children were then observed to imitate the modelled behaviour but also, and importantly, they introduced novel behaviours.

Lortie’ (2002) aphorism that learning to teach is based on an apprenticeship of observation is a significant acknowledgement of vicarious learning processes in teaching. We spend hours, as students in classrooms, observing teachers and then, but to a lesser extent, as trainee teachers on a one-year training programme. Observational learning is an essential part of cultural transmission.

Social cognitive theory involves both self-efficacy, a cognitive and affective basis for the formation of behaviour, and observational learning. In this frame we can see a reflexive dimension of behaviour formation. There is continuity from existing established practices that are communicated vicariously, at the same time the individual can adapt and personalise the existing practices.

Automaticity and routinization: the basis of habitus

Malcolm Gladwell’s (2009) claim in Outliers, that we need 10,000 hours to achieve mastery in a particular human endeavour or profession, is something of a ponderous assertion in the context of learning. I think what Gladwell is really trying to get at is the point at which a learner no longer has to consciously think about what they are doing in their professional role or in a field of endeavour. Many skills once learnt can be carried out efficiently by drawing on established patterns of behaviour that exist in our long term memories. What Gladwell probably means is that 10,000 hours is necessary to develop professional habitus.

According to Bandura, once we have become self-efficacious in a domain of activity our actions become routinised and we do not need to mentally model each of our actions in advance, we can draw on scripts and patterns that we have already become confident with. This is equivalent to Bourdieu’s notion of habitus but a professional and occupational context.

This makes sense from the perspective of neurophysiology and in human evolutionary terms. Our working memory capacity is limited and conscious reasoning uses up a lot of energy. It is natural that we preserve our bodily resources for times when we are under threat or when we really need to think through a problem. To do this all the time is simply too demanding, we have to rely on established patterns of behaviour most of the time and respond almost intuitively. Human beings are animals capable of reasoning but only a limited amount of our behaviour is guided by conscious reasoning (Johnson-Laird, 2009).

When I observe trainee teachers, they have to consciously think about most of what they do. This is very demanding, it can be and often is stressful (Chaplain, 2008) and is certainly very tiring. This is a result of the demand for conscious reasoning in preparation for action in the classroom and in the school milieu. What is more, without actually carrying out an action, it is impossible to know the outcome, the contexts of classrooms and schools are complex and predicting the consequences of certain actions is also impossible. In this analysis, it can be seen how important the role of the school-based mentor is, an experienced teacher who can help guide, construct and evaluate the trainee’s proposed actions.

As the trainee’s self-efficacy develops they exhibit routinized action, in which they have greater confidence in the outcome. They know what to expect. Leinhardt (1988) describes experienced teachers’ cognition as situated in the context and relying on almost automatic responses based on heuristic thinking. How I understand this is that teachers are able to recall patterns of pedagogical behaviour in long term memory they match these to the situations they meet and probabilistically evaluate as an appropriate response. Action is contingent, a teacher encounters a situation and is able to adapt and reconstruct a previous response. Teacher cognition is based on rule-of-thumb and the heuristic use of previous actions that are in long-term memory – it happens in an instance.

Let me now return to culture and habit more directly. Observational learning alludes to a cultural impact on practice, that cultures of teaching are transmitted through observational means. The development of routinization, automaticity and the use of heuristics as self-efficacy develops underpins the formation of teaching habits. In the next section I consider how these aspects connect together.

Conservatism

Roger Scruton’s (2001) idea of conservatism rests on the value of, and indeed social capital of, customs, traditions, institutions and laws. There is value in such things as ‘constants’. Quinton Hogg went as far as saying,  “Conservatism is not so much a philosophy as an attitude, a constant force, performing a timeless function in the development of a free society, and corresponding to a deep and permanent requirement of human nature itself” (Hogg, 1959). Although I identify myself with the left of politics, I can’t help but to find myself in agreement. Especially when we locate the political and philosophical ideas of conservatism in the context of state schools and classrooms. And in my experience as a school teacher, I was as much a conservative as Scruton and Hogg. Indeed schools are conservative institutions and the practices observed there are conservative and teachers, by-and-large, are conservative. All this with a little ‘c’.

This has not always been so true, not to the extent that it has been since the late 1980s and increasingly so over time. In the 1960s in England there was a widespread progressive movement, with attempts to break away from traditional schooling and to responding to new thinking about learning and development. But still at the core were conservative curricula and practices. Similarly in the US where traditional teaching, like in England, followed patterns of practice where teachers explained and demonstrated followed by students engaging in practice or exercise. A time-honoured tradition that goes back to the grammar schools of sixteenth century England, at least. Larry Cuban, a historian of public education in the US, observed the traditional teacher-centred teaching had been there in perpetuity through a century or more of public education. Yet the progressive movements of the 1960s did not, according to Cuban (1993), significantly unhinge conservatism in schools. He observed what he described as “teacher-centred progressivism”, the essence of which are the traditional routines but with progressive features such as tables set out in groups – indicative of dialogic approaches – rather than desks and tables in rows for the traditional didactic approach. The same can be observed in England’s state schools, the mainstay of practice is traditional routine and conservative pedagogy, but with superficial ‘progressivism’. The traditional nub has proved to be impervious to fundamental change.

It was Cuban’s view that the perpetuity of pedagogical conservatism is down to day-to-day practical demands on teachers. State schools in the UK and US are resource-constrained, a secondary school teacher needs to be able to keep a class of students busy, they need to be able to maintain standards of behaviour. They may have six, seven or eight classes each week, each with up to 30 or more students, some of whom – because school is mandatory – will not want to be there. Naturally then, the most efficient pedagogy is a traditional teacher-centred approach. The teacher explains and demonstrates a central idea or method, then students work at a similar pace with the express aim of becoming more proficient in what is being taught. The work is routine enough to keep the students busy and the teacher can assess progress by observing how far students have worked through the task and how accurate their answers are.

While others have attributed the actions of the teacher and the pedagogy that is formed as a function of teachers’ beliefs about what is effective teaching and learning (see previous blog) , the practical explanation above is the more likely explanation. It is also an explanation that Stigler and Hiebert drew on in the analysis of eighth-grade mathematics classrooms in Germany, Japan and USA in 1995. They saw pedagogy as culturally distinct: there was more variation in practice between countries than there was within them. They saw pedagogy as following a cultural script, established routines within which teachers and students knew what was expected and what was likely to happen. This is similar to Hogg’s conservatism -“a constant force” based on institution, tradition and rules. While it corresponds “…to a deep and permanent requirement of human nature itself”, its permanence and constitutionality is much over stated and my view, like Arendt (2006) for example, is that there is a fundamental tension and dialect between progressivism and conservatism; between tradition and future. Or in Archer’s (2012) terms between structure (and culture) and individuality, that is between the self and the social, cultural and institutional context in which we act. It is on this I will finish, but before so doing, I want to consider very briefly why schools and classroom practice are generally conservative.

I left school in 1980 and did not set foot in a state school until 2000. I had an overwhelming sense that schools had become more conservative, I didn’t understand why. My expectation, based on a naive assumption that progress meant more progressivism, was that schools would be more progressive. Schools had in fact become more conservative. In the last few years I have been working on a hypothesis that helps me understand why. It was my initial view that this phenomenon was a consequence of policy, latterly I have expanded this to consider that a key influence on school culture is political economy at national and global level. I wrote about political economy in education in a previous blog. It is from this analysis, I show that the shift from liberal state interventionism to neoliberalism in the late 1970s had a profound influence on the nature of teachers’ work. Teachers’ jobs became more demanding and their teaching subject to greater scrutiny. The appearance of performativtiy (Ball, 2003), where teachers are frequently observed in a high-stakes accountability context, leads to the normalisation of practice. It leads to greater conservatism in the classroom. The reason for this can be explained through social cognitive theory. This more intense professional experience leads to higher levels of anxiety, this reduces self-efficacy and teachers are more likely to sustain conservative practices than to innovate. This is ironic since some of the policy -led reforms were supposed to be progressive, but in accountability contexts the opposite is achieved because of the impact on teachers’ levels of stress.

The cultural dimensions of teaching: structure, culture and agency

I have developed the idea that teaching is a cultural act. That pedagogy follows cultural scripts that participants (teachers, students and even parents) recognise and within which they can predict actions and responses. Teaching is not just a matter of imitating the practices of  previous generations and unthinkingly doing the same as was done in classrooms of previous decades. Yet there is a recognisable cultural and historical constancy. As actors in contexts, as teachers in schools we have agency, but behaviours in such institutions are not expressions of teachers’ preferences. Their preferences and individualism transact with cultural practices and scripts to form actions that are personal but culturally consistent. There is a further dimension: structures. Here, I have talked about the defining factors of institutions on cultural practices. It is the interaction and transaction between structure, culture and agency that shapes individual thinking and action through a process of reflexivity (Archer, 2012).

Taking the English context, the normalising effects of high-stakes accountability in a neoliberal setting, are likely to diminish innovation. As a consequence, there is a tendency to sustain more traditional forms of teaching. Interestingly activist groups have appeared to argue for a new conservatism. For me this is not critical enough, conservatism in teaching is merely a feature rather than a philosophy of education.

References

Archer, M. S. (2012). The reflexive imperative in late modernity. Cambridge: Cambridge University Press.

Arendt, H. (2006). Between past and future: eight exercises in political thought. New York: Penguin Books.

Ball, S. J. (2003). The teacher’s soul and the terrors of performativity. Journal of Education Policy, 18(2), 215–228. https://doi.org/10.1080/0268093022000043065

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

Bourdieu, P. (1984). Distinction: a social critique of the judgement of taste. Cambridge, Mass: Harvard University Press.

Camic, C. (1986). The Matter of Habit. American Journal of Sociology, 91(5), 1039–1087. https://doi.org/10.1086/228386

Chaplain, R. P. (2008). Stress and psychological distress among trainee secondary teachers in England. Educational Psychology, 28(2), 195–209. https://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.

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.

Geertz, C. (1973). Interpretation of Cultures. New York: Basic Books.
“habit, n.” OED Online. Oxford University Press, December 2016. Web. 10 February 2017.

Gladwell, M. (2009). Outliers: the story of success. London: Penguin Books.

Quintin Hogg Hailsham of St. Marylebone. (1947). The case for conservatism. West Drayton: Penguin.

Johnson-Laird, P. N. (2009). How we reason. Oxford, New York: Oxford University Press.

Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge: Cambridge University Press.

Leinhardt, G. (1988). Situated knowledge and expertise in teaching. In J. Calderhead (Ed.), Teachers’ professional learning (pp. 146–168). London: Falmer Press.

Miller, N. E., & Dollard, J. (1941). Social learning and imitation. New Haven, NJ: Yale University Press.

Prinz, J. (2016). Culture and Cognitive Science. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Fall 2016). Metaphysics Research Lab, Stanford University. Retrieved from https://plato.stanford.edu/archives/fall2016/entries/culture-cogsci/

Scruton, R. (2001). The meaning of conservatism (3. ed). Basingstoke, Hampshire: Palgrave.

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.

Welcome to the teaching profession

This is my fourth year leading the secondary mathematics initial teacher education programme in Cambridge. It is fifteen years since I trained to be a teacher in Sheffield. With the research I have been doing on teachers’ professional learning, I have had some time to think and reflect on my own teaching and what is involved in learning to be a teacher.

In part I write this as a ‘welcome’ – a welcome to the profession. Also I offer, to those embarking on a teaching career,  some advice on how to cope with the training year and prepare for their teaching career.

Teaching should be regarded with no less respect than any other profession, for example, doctors, accountants, engineers and lawyers. And I can’t help myself but get angry if anyone tries to undermine the professional standing of teachers. So my first piece of advice: be very proud of the profession that you are about to become part of.

But we have to face realities, the profession is at a point of crisis, pay and conditions have been undermined, the nature of the work has intensified and become focussed on a narrow set of measures. The recruitment and retention of teachers is in a poor state. Do not let this deter you though, for with these challenges comes the possibility of renewal and regeneration. Though they be challenging times, they are times of personal and collective opportunity.

But your focus will be on the present. You will be well aware that the one-year Postgraduate Certificate in Education (PGCE) is very demanding. What I want to do here is explain why and offer some tips and things for you to think about in order to try and make it manageable.

What is it like learning to be a teacher?

Working as a professional in the public sector is an important role and one which comes with a great deal of responsibility. Teachers have the chance to make a considerable difference to people’s lives. While they cannot always mitigate for the disadvantages that are a result of the deep inequalities in our society, they have it within their powers to potentially change young people’s lives.

You will be enthused, no doubt as I was and still am, about the possibility of being transformative and imbued with a passion for and a deep knowledge of your subject.

When I began my PGCE course, I was brimming with ideas of how to enthuse learners and explain the concepts, ideas and processes in my subject. However, I found that there was so much more to it than expressing my originality and communicating my knowledge passionately. Frustratingly, I had to learn how to do this within the structures and culture of the education system and the particular school I was placed at. What I found hard was tempering my individuality and originality to comply with and be consistent with the norms that existed in the school. Indeed, for my first placement I avoided this altogether. I forged my own path and failed. During my second placement, however, I was much wiser.

It is important to recognise the consequences of schools’ limited budgets and resources (it’s a shame that it took me so long). Teachers are working under incredible time and resource pressures; they are doing their very best with limited resources. There is not the time to deal perfectly with each pupil or to create perfect lessons. Often a full-time teacher is teaching up to 23 out of 25 lessons a week. There is little time to create bespoke and wonderful learning experiences for each classroom encounter. There is limited time to support individual pupils, parents and the community.

Under these constraints, schools and teachers find ways of making it work. They establish working systems and routines for lessons and around the school. As you learn to be a teacher you learn these established and tacit ways of working, what I describe as the structures and culture of education. As you gain experience as a teacher, you learn to assert your individuality within the structures and culture.

This is demanding. It is emotionally and mentally demanding. You do not have the kind of personal freedom or agency that you may be used to. It can test your well-being to the limit, you have to try and plan your lessons within a system for which the rules of engagement are not explicitly explained. They are implicit and tacit rules and often rationality is not obvious and can seem opaque. My advice is to be patient with yourself. As you observe experienced colleagues in and out the classroom, ask yourself what do they do to make the job easier for themselves and learn from them. It takes time in school to become acculturated to the way-of-(professional)life. But try to give yourself opportunities, even if it be a part of a lesson, to experiment with your own ideas. It gives you a chance to express yourself. As you develop you will become more comfortable as you become familiar with the culture of schools and the tacit rules and routines that exist.

Taking care of your mental health

You see how demanding this is. I have not even talked about the major concern of every trainee, that is managing behaviour. I will come to this. But before doing so, I want to talk about your mental health; this is really important. For many beginning teacher training, their expectations are high, they quite naturally want to be the best teacher they can be and make an impact. As I have described, the context in which professional learning takes place, because of the predominance of cultural practices and tacit rules and knowledge, is so much different from undergraduate learning, where the learning is around theory rather than learning ‘practice’. This means that you learn information and means of reconstructing that information to pass examinations. If you learn this process effectively you can be successful in examinations. In learning to teach there is no such process, it is more about absorbing the tacit rules and culture of schools. As an individual you have less control, it is therefore emotionally and mentally demanding. My advice is, as soon as you feel your levels of anxiety or stress levels get to a point at which you feel you are not your normal self, then get advice. Most universities have plenty of help available. If at any time during your training you feel that your mental health is being undermined, seek professional advice.

Don’t be too hard on yourself if you find you need help, especially if this is the first time. People often learn a great deal about themselves during phases of their lives when they experience extraordinary emotional and mental challenge. It is for this reason that learning to teach is such a powerful experience; often you learn so much about yourself.

Will the pupils behave?

All trainees worry about this. It is a supreme test of the self. A test of whether you can ‘control’ a class of young people. There is so much written about various techniques: using your body language, your voice, and the use of rewards and sanctions. There will be plenty of advice on managing behaviour and motivating children to make the most of their learning. The most important factor is self-belief (more technically I talk about self-efficay). It is the belief a teacher has in their capacity to maintain order in the classroom, it involves having good relationships with individuals as well as understanding what behaviours need to be addressed and what should be ignored.

Developing self-efficacy or confidence in managing behaviour takes practice and experience and needs time to observe experienced colleagues. It involves trying out techniques and getting to know individual pupils. Some trainees come along having had some experience that has helped them with this, for others it takes longer. You will make mistakes early on but colleagues are supportive and pupils quickly forget. So again, be patient with yourself, observe experienced teachers, read about theory and practice and learn in the classroom. Most of all don’t worry. Worry undermines your self-belief. 

Theory, research and assignments

This can feel like a chore, especially for maths and science trainees. No matter how much you might love social sciences going into it, having to read theory and carry out small-scale research can feel like an additional hoop to jump through. However, it is this engagement that maintains teaching as a profession. Of course you can learn to teach without this, and you can become a very effective teacher. But as a profession, we should strive to engage in scholarship: for teachers to have an understanding of the underlying disciplines of philosophy, anthropology, sociology and psychology. Teachers also need to be familiar with subject specific research. There is a lot said about the use of evidence in education, but teachers need to have a deeper understanding of what we mean by evidence, how educational research is undertaken and how to decide on what to incorporate into practice. The PGCE provides a very brief introduction to these things. It can take years of further reading and reflection to develop this to a point where you can effectively apply scholarship to your teaching. Having come accross Vygotsky as a trainee and understood some of the basic ideas, it was still a few years before I could really make sense of the implications of his work.

During the PGCE there is opportunity to begin a scholarly journey, to get a sense of the range and scope of thinking in educational research and to begin to develop your own scholarship. The PGCE is too short to really go beyond this and we should really make teacher training last longer. Compare it to the period of a time a medical practitioner spends learning about underlying theory.

Professional solidarity

One of the pressing issues for those entering the profession is the policy context under which you will work. Not only is it difficult to recruit teachers to the profession to work in certain parts of England, it is difficult to recruit people to train to teach some subjects, like for example Maths and Physics, and it is increasingly difficult to retain teachers. You are new to the profession, enthused and feeling that you have the power to change things, but there are teachers a few years down the line who are leaving, fed up with workload and the culture of performativity. Clearly I do not want to put you off, but I do want to equip you with insights into the context in which you plan to make what will hopefully be a long career. You need to know what is happening and what you can do about it.

Since the 1970s state education has increasingly moved away from being a public service, owned and accountable to the communities that schools serve. It began with changes to the way school funding was managed, then came the introduction of City Technology Colleges, then Academies, the introduction of OfSTED in 1992 and finally with schools being run by Multi-Academy Trusts. Local Authorities have very little involvement in the local provision of education. In this time successive governments have expected more from the profession and the intensity of teachers’ work has increased. We are also at the stage where performance related pay is likely to be implemented more widely. Teachers are having to work harder than the previous generation and working longer hours to try and deliver unrealistic targets that do not adequately quantify the work of the school, the teachers and pupils.

It is important that new teachers challenge the direction in which schools policy is going. Well not straight away, but part of your preparation should be to start to network and organise, in order prepare to challenge centralised accountability and redress the diminishment of community ownership. Don’t expect policy makers to do this for you. It is a professional responsibility to act collectively to challenge inappropriate government reforms. It is time to think and act collectively, and foster professional solidarity and activism, much like the junior doctors have done. So make sure you join a teaching union.  Together we can create a community-owned school system which is accountable to that community. But it needs us all to stand together and decide on how we want schools to run and decide together what the purpose of education should be.

Have a great year.

 

 

 

 

 

 

 

The College of Teaching: please don’t get the decorators in while the house is burning down

Congratulations to Dame Alison Peacock on her appointment as the first CEO of the College of Teaching. She has done an impressive job in championing assessment for learning in schools.

Broadly I am in favour of the formation of professional bodies, I believe they have the potential to support and develop the professional esteem of teachers.

However, I do have major reservations.

The problem is that since the 1970s there has been a steady move away from a publicly-owned state education system. While the discourse was being established back then, the process has gathered pace since 1988 with Local Management of Schools, then City Technology Colleges, then Academisation and PFI through the noughties. We are in the final stretch now, with the full-scale outsourcing of public and community education to academy chains and free schools. Schools are no longer public and community assets, they are now there for corporations to expand their capital through the acquisition of public assets and the state subsidy of their operations.

The impact of this on teachers is to intensify their work: longer working hours, reduced pay and worsening conditions. Karl Marx clearly explained how businesses accumulate capital by extracting surplus value from the workforce. And of course this is what teachers have experienced increasingly over the last ten or more years. First it was through the intensification of work under New Labour, then came restraint on wage growth, the undermining of collective bargaining and partial introduction of performance related pay. In a public or community-owned service this would not have happened.

The College of Teaching has been established with noblest of intentions and through the hard work of many committed people. I respect this unreservedly. I also respect the aims of the College to promote the best in professional development and promote the professional standing of teachers.

But none of this can be achieved unless schools and the education service are restored to being publicly and community owned, and accountable to their communities. If privatisation is allowed to continue, the teaching profession will be permanently atomised, subject to the vagaries of business and corporations, as we are increasingly seeing in Charter schools in the USA.

In the current economic climate corporate profit is hard to maintain, unless the business has an effective monopoly, like Google or Apple, or if you have a state subsidised-business, for example, Virgin Trains or G4S. There are powerful forces looking for business and our state education system is vulnerable to these.

I hope therefore that Alison Peacock and the Trustees of the College of Teaching recognise what is at stake here. All stakeholders in education, including headteachers, teachers, parents, governors, students, pupils and academics, need to organise and mobilise to to stop privatisation. I hope that the College of Teaching will soon make it clear that they are unequivocally opposed to moves to take education away from public ownership.

If the College of Teaching becomes fixated on professional development and ignores what is happening to our education system, then we will not have a profession to develop. And that is why I caution against getting stuck in to designing state-of-the-art decor when the house is being set alight by neoliberal arsonists.

 

 

Social cognitive theory

This blog post provides a summary of social cognitive theory. It begins with some background. I then move on to look at Bandura’s formulation of Social Cognitive Theory and finally I look at how the sub-component of self-efficacy can be used to evaluate professional learning

The origins of Social Cognitive Theory

Social cognitive theory has its origins in the work of William James (1891). James suggests the concept of the ‘social self’ as a constituent part of the ‘self’.

A man’s Social Self is the recognition which he gets from his mates. We are not only gregarious animals, liking to be in sight of our fellows, but we have an innate propensity to get ourselves noticed, and noticed favorably, by our kind (p. 294).

This perhaps marks the beginning of the study of the individual and their social environmental interactions. Alfred Adler developed this further, introducing the idea of ‘drive’ and suggested behaviour is purposeful and motivated by goals. With individual perception of and attitude toward the social environment influencing behaviour. And, importantly, a person’s thoughts, feelings and behaviours are transactions with one’s physical and social environments. Adler essentially recognised fundamental links between social environment, individual thinking, affect, motivation and behaviour.

Behaviourism has been influential in the development of social cognitive theory. This perhaps explains why social cognitive theory has not been popular in educational research: social cognitive theory has been referred to as radical behaviourism. Behaviourism is widely rejected in education out of preference for constructivist learning theories or situated learning theories. However, it is important in understanding social cognitive theory, to reflect on behaviourist theory. John Watson’s behavioural theory (circa 1913) considered behaviour as explicable by observable acts. Human behaviour is seen as a result of the action of an external stimulus (S) resulting in a response (R). This can be symbolised, S → R. This makes the individual a passive component in the formation of behaviour, but the simple stimulus-response model was very influential. Subsequent theorists have highlighted individual thinking as a factor in the stimulus-response model. Tolman suggested cognition had a mediating role in the stimulus-response model (see, for example, Tolman, 1932). The S→R scheme therefore becomes mediated by cognitive processes as shown in Figure 1.

Figure 1 Tolman’s proposed relationship between stimulus response and cognition. S represents a stimulus, R the response and C cognition.

This can also be thought of as behaviour (B) being some function of, their thinking and personal characteristics (P) and the environment or context (E). And can be represented thus:

I will return to this relationship when I discuss Bandura’s formulation of social cognitive theory, in the next section.

<But, it is the work of Miller and Dollard that really marks the beginning of social cognitive theory. Central to their social cognitive theory is the idea that if individuals are driven to learn a behaviour, that behaviour is learned thorough observation (Miller & Dollard, 1941).

Social cognitive theory has been developed further and the following have been identified as the principle features of the approach:

  • People learn by observing others
  • Learning is an internal process that may or may not change behaviour
  • People behave in certain ways to reach goals
  • Behavior is self-directed (as opposed to the behaviorist thought that behavior is determined by environment)
  • Reinforcement and punishment have unpredictable and indirect effects on both behavior and learning (Ormrod, 2006).

Social cognitive theory has been influential; the theory has been applied to clinical psychology by Julian Rotter. He developed the ideas of behaviour potential, expectancy and locus of control. Robert Sears applied the approach to explain socialisation processes and how children internalise the values, attitudes and behaviours of a culture. Walter Mischel investigated how new experiences effect the individual. Ronal Akers applied social cognitive theory to criminology. But perhaps the most influential social cognitive theorist, in recent times, has been Albert Bandura. It his interpretation and application of social cognitive theory that I shall discuss in the next section.

Bandura’s social cognitive theory

Albert Bandura’s work on social cognitive theory began in the 1950s and culminated in numerous journal articles and a book Social cognitive theory (Bandura, 1977). Bandura’s project has been to develop a core theory of social learning and pursue empirical evidence and applications in health, criminology, therapy, sport, business and education. Like earlier developments of social cognitive theory the cornerstone of Bandura’s conception is imitative and observational learning. The importance of observational and imitative learning has, in education, been afforded lesser regard because of its associations with behaviourist perspectives on learning. Moreover, we have endeavoured to offer the learner greater agency and this appears at odds with the idea of learning through imitation. However, as I shall describe shortly social cognitive theory does afford agency as a result of the way in which observed behaviours are imitated, modelled and formed to be behaviours; it is not a non-agent behaviourist perspective.

Triadic causality and reciprocal determinism

Bandura (1977) begins by explaining the idea of triadic causality or reciprocal determinism, which is a central feature of social cognitive theory. Bandura takes the relationship suggested by Tolman:

This suggests behaviour (B) is a function of personal characteristics (P), for example, thinking and beliefs and the environment or context (E). Bandura theorised a greater level of interaction between these variables. At first suggesting a relationship signified in the following:

Immediately Bandura develops this further, producing a three-way connection between the social and environmental context (E), the individual—their thinking and personal characteristics (P) and the individual’s behaviour (B) (see Figure 1).

Personal and environmental factors do not function as independent determinants, rather they determine each other. Nor can “persons” be considered causes independent of their behavior. It is largely through their actions that people produce the environmental conditions that affect their behavior in a reciprocal fashion. The experiences generated by behavior also partly determine what a person becomes and can do which in turn, affects subsequent behavior (Bandura, 1977, p. 9).

Figure 2 Reciprocal determinism (Bandura, 1977, p. 10), B signifies behaviour, P the person and E the environment.

In such a way then, the social context influences the individual’s behaviour and thinking. This is largely consistent with sociological perspectives of the formation of behaviour: how we think and behave is influenced by the social, environmental and contextual setting and can be seen as the individual responding to prevailing norms and modes of behaviour. At the same time thinking and behaviour influence the social setting and environmental context. In the next section I will describe the ways in which behaviours are learned.

The formation of behavior

The cornerstone of social cognitive theory is learning through observation and modelling. Bandura argued that most human behaviour is learnt this way, people cannot simply construct novel behaviours based on their own experiences.

[F]rom observing others[,] one forms an idea of how new behaviors are performed, and on later occasions this coded information serves as a guide for action. Because people can learn from example what to do, at least in an approximate form, before performing any behavior, they are spared needless error (Bandura, 1977, p. 22).

The ‘coded-information’ is consistent with the conception of mental models proposed by Johnson-Laird’s (1983). Models are mental symbolizations of the external world and are the building blocks with which we reason and make decisions.

Bandura goes on to detail observational learning sub-processes; these have remained central, for a number of years, to social cognitive theory. These sub-processes consider aspects of attention, retention, production processes and motivation. In terms of attentional processes, Bandura stresses that individuals do not learn through observation unless they ‘…attend to and perceive accurately, the significant features of the modelled behavior’ (1977, p. 24). Similarly, from the perspective of retentional processes, observed behaviours will not have much influence unless a person remembers what they observed. The production
process involve the conversion of the symbolic codification of observed behaviours into action and finally the motivation processes address how, out of the numerous behaviours observed and symbolically retained, certain behaviours are constructed and enacted. I shall now consider each of these processes in a little more detail in order to unpick the nature of observational learning from Bandura’s perspective. A summary of this process is presented in Figure 3.

The attentional processes govern what behaviours are observed and what the observer attends to. Children may require simple tasks, that are salient and conspicuous to promote attention, while the more mature learner can force their attention to observe behaviours that are less conspicuous. The attentional processes are affected by the kinds of behaviour observed and also by observer determinants which may include prior knowledge, preconceptions and cognitive skill, these will have an impact on levels of attention. One other aspect of attention is the functional value of the modelled behaviour; it is more likely that a behaviour which has perceived value will command greater attention by the observer.

Once a modelled behaviour has been attended to, the next process involves retention this ‘…involves the active transformation and restructuring of information about events’ (Bandura, 1986, p. 56). According to social cognitive theory there are two representational systems: imaginal and verbal (p.56). An imaginal representation is an abstraction of an event rather than a visual image. A verbal construction can be understood by considering the way in which geographical directions are communicated; as a series of right and left turns. In this way, behaviours are coded as linguistic instructions. Bandura suggests that these two representational systems are difficult in reality to distinguish and separate.

The next stage of the process is production. This sub-process involves the transfer of observed behaviour, that has been retained mentally, into the construction of a future behaviour. It is the process through which mental representations of behaviours are developed as possible courses of action. This involves the organisation of elements of representations, spatially and temporally into an arrangement consistent with the perceived activity. This process is influenced by matching thoughts and representations to the situation at hand and is also influenced by the individual’s skills and abilities.

The final sub-process, motivation, involves choosing a course of action or behaviour from the range of possible constructions. This is related to internal and external motivations and the degree of effort that one might perceive necessary to expend.

From the perspective of social cognitive theory, thinking influences behaviour by the enactment of mental models. However, as has already been explained, the mental models constructed from the observation of behaviour are not simply re-enacted: this is not direct imitation. Individuals, according to Bandura (1977), reconstruct mental models in order to create a behaviour that they believe is most suitable for a given situation. There is a self-regulative dimension to this production process. A person, from the perspective of social cognitive theory, can construct a behaviour based on the perceived likelihood of success with that behaviour. Self-efficacy is an important theoretical aspect of social cognitive theory and is used to account for the self-regulative aspects of behaviour. It is defined as a self-reflective belief that a person has in the extent to which they believe they will be successful in a particular activity or domain. Bandura presents a range of evidence demonstrating a relationship between self-efficacy and underlying skill (1997, p. 37).

Self-efficacy and teaching

Bandura considers self-efficacy to be of particular importance in understanding the cognitive and social dimensions of behaviour. This led to the book Self-efficacy: the exercise of control in 1997. Bandura suggests in the preface:

Much contemporary theorizing depicts people as onloooking hosts of internal mechanisms or orchestrated by external events. They are stripped of any agency. People are proactive, aspiring organisms who have a hand in shaping their own lives and the social systems that organize, guide and regulate the affairs of their society (Bandura, 1997, p. vii).

Bandura goes on to define self-efficacy. ‘Perceived self-efficacy refers to beliefs in one’s capabilities to organise and execute the courses of action required to produce given attainments [Bandura’s emphasis]’ (1997, p. 3). While Bandura considers self-efficacy in a wide range of human activity including medicine and health, sport and organizations he also looks specifically at teachers’ perceived self-efficacy. He suggests teachers’ beliefs in their teaching or instructional efficacy contributes to students’ determination of their intellectual capabilities (p. 240). Bandura refers to the study by Gibson and Dembo (1984) in which teachers’ efficacy beliefs were measured in respect to teaching difficult students. They found that the higher efficacy teachers gave more time to academic activities and provided students with more guidance than low efficacy teachers. Lower efficacy teachers also spent more time on non-academic activities and were likely to criticise students for their failures (Bandura, 1997, pp. 240–241). Bandura also draws on evidence from research into student teachers’ efficacy (Saklofske, Michayluk, & Randhawa, 1988) which revealed that those with a higher sense of efficacy were more adept at presenting lesson plans, offered more effective approaches to questioning and were better able to manage their classrooms effectively (Bandura, 1997, p. 241). In terms of practising teachers it has been found that higher levels of teaching efficacy also relates to the way in which teachers view the educational process. Low instructional efficacy teachers are more pessimistic about student motivation and believe in strict classroom regulation and rely on extrinsic inducements and negative sanctions to get students to study (Woolfolk & Hoy, 1990; Woolfolk, Rosoff, & Hoy, 1990 cited in, Bandura, 1997, p. 241). In a later section I shall describe further work that has been done on developing scales for measuring teaching efficacy as well as other studies where teaching efficacy has been related to student achievement and teachers’ propensity to experiment, innovate and sustain changes in their practice. These findings suggest that attention needs to be given to how self-efficacy can be developed as part of teachers’ professional learning. In the next section I want to present what Bandura considers to be the sources of self-efficacy more generally.

Sources of self-efficacy

Bandura proposes four sources of self-efficacy: enactive mastery experiences, vicarious experience, verbal persuasion and physiological and affective states (Bandura, 1997, pp. 79–113). Enactive mastery experiences offer the most powerful sources of self-efficacy beliefs. If we are successful in something our efficacy will increase, if we fail it will be undermined. Easy successes beget an expectation of quick results but can lead to being easily discouraged by failure (1997, p. 80). Self-efficacy can also be developed through vicarious experience, this provides an alternative and complementary source where individuals assess their own abilities and capabilities based on the attainments and successes of others. Bandura illustrates the process:

More often in everyday life, people compare themselves to a particular associate in similar situations, such as classmates, work associates, competitors, or people in other settings engaged in similar endeavours (Bandura, 1997, p. 87).

Comparing our performances with others leads to increases in self-efficacy; if we believe we can be realistically more effective than the person observed.

A further but weaker source of self-efficacy is through verbal persuasion. If an individual is persuaded that they have the abilities and capacities to achieve a particular level of success this will have an influence on whether the outcome of their performance is successful. However, if the persuasion is unrealistic then this can undermine the individual performance and also discredit the persuader (Bandura, 1997, p. 101).

Finally physiological and affective states have an effect on self-efficacy. If we feel ill or we are in a bad mood this will have an impact in the extent that we believe we will be successful. This according Bandura is especially relevant in areas related to ‘physical accomplishments, health functioning and coping with stressors’ (1997, p. 106). This is particularly important in teaching in which high levels of stress are often experienced. As a consequence, self-efficacy can be enhanced by improving physical status, reducing levels of stress and correcting misinterpretations of bodily states. Effectively, improving our physical condition and the way in which stress is dealt with as well as having an improved understanding of our physical self.

In this section I have summarised the idea of self-efficacy and how self-efficacy is developed through mastery, vicarious experience, verbal persuasion and physical an affective states. I will now look in more detail at teaching self-efficacy and its measure. I illustrate this by revisiting one aspect of the exploratory study I referred to earlier, this was a small-scale piece of research looking at how self-efficacy can be used to evaluate professional development.

Operationalizing social cognitive theory: teaching self-efficacy scales

A teacher’s self-efficacy beliefs (TSE) have been defined as ‘[a] judgment of his or her capabilities to bring about desired outcomes of student engagement and learning, even among those students who may be difficult or unmotivated’ (Tschannen-Moran & Woolfolk Hoy, 2001, p. 783). While TSE emerges from strong theoretical ground, its validity has also been demonstrated empirically and it has been shown to be related to other important factors. For example, TSE is related to student achievement (Allinder, 1994; Ashton & Webb, 1986; Tschannen-Moran, Hoy, & Hoy, 1998). In addition, it has been shown to be related to teachers’ willingness to experiment with and adopt new practices (Berman, McLaughlin, Bass-Golod, Pauly, & Zellman, 1977; Guskey, 1988; Stein & Wang, 1988). These present useful findings, as measures of TSE can also indicate levels of student achievement and teachers’ capacity to develop their practice.

TSE is potentially, a powerful measure but it has not been widely used in the evaluation of PD. However, Ross and Bruce (2007) conducted a randomized field trial using measures of TSE with grade six mathematics teachers (n=106) in the USA. It was shown that the PD had an effect on TSE. Karimi (2011) evaluated the effects of PD on EFL (English as a foreign language) teachers’ efficacy finding the PD had a positive effect on TSE. The reason for the limited number of PD evaluations using TSE is that this aspect of PD research is in its infancy. Desimone (2009) argues that PD evaluation is underdeveloped—there is a need for more empirically valid methods—previous studies have relied on ‘…teacher satisfaction, attitude change or commitment to innovation rather than its results…’ (p.181). TSE presents a suitable construct that goes beyond attitude change and commitment to change, it has the potential to measure the effects of PD on student achievement, albeit indirectly.

Much work has been done in recent years in developing TSE instruments. Tschannen-Moran and Woolfolk Hoy (2001) developed the Teaching Self-Efficacy Scale (TSES). This instrument is often regarded as a standard. They tested the validity of the scale by comparing it with other measures of TSE and found high levels of correlation. They also identified three factors: efficacy for instructional strategies; efficacy for classroom management and efficacy for student engagement. Efficacy for instructional strategies includes items relating to assessment, questioning, providing explanations and differentiation. Efficacy for classroom management has items relating to the control of student behaviour, establishing classroom rules, getting students to follow them and dealing with challenging behaviour. Efficacy for student engagement is concerned with motivating students from different backgrounds and encouraging them to value learning and to think critically and be creative. The TSES instrument was used by Ross and Bruce (2007) and Karimi (2011) in their evaluations of PD. While the development, validity and reliability work for the TSES had been carried out in the USA, the instrument has been shown to be valid across culturally diverse settings (Klassen et al., 2009).

Notes

The source of this historical perspective on social cognitive theory has been guided by Stone, D. (1998) Social Cognitive Theory, unpublished manuscript [http://mrspettyjohn.pbworks.com/f/SocialCognitiveTheory.pdf, accessed 20/6/2012] and Bachar, K. J. (n.d.) An overview of social cognitive theory, unpublished manuscript, [http://www.u.arizona.edu/~sexasslt/arpep/pdfs/sociallearningtheoryadhs.pdf, accessed 20/6/2012]

References

Allinder, R. M. (1994). The relationship between efficacy and the instructional practices of special education teachers and consultants. Teacher Education and Special Education: The Journal of the Teacher Education Division of the Council for Exceptional Children, 17(2), 86–95. http://doi.org/10.1177/088840649401700203

Ashton, P. T., & Webb, R. B. (1986). Making a difference: Teachers’ sense of efficacy and student achievement. White Plains, NY: Longman.

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.

Berman, P., McLaughlin, M. W., Bass-Golod, G., Pauly, E., & Zellman, G. L. (1977). Federal programs supporting educational change, Vol. VII: Factors affecting implementation and continuation. Santa Monica, CA: The Rand Corporation.

Gibson, S., & Dembo, M. H. (1984). Teacher efficacy: A construct validation. Journal of Educational Psychology, 76(4), 569–582. http://doi.org/10.1037/0022-0663.76.4.569

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Concerns about the Prevent Strategy from the perspective of the teacher educator

The following I wrote for a discussion at the University of Cambridge, Senate House 9 May 2016. It sets out my concerns about the Prevent Strategy.

A good proportion of my teaching in the Faculty of Education involves lecturing on the Post Graduate Certificate of Education (PGCE). This is a one-year masters-level programme for trainee school teachers working in the state sector. It leads to Qualified Teacher Status. The programme is run as a partnership involving the Faculty of Education and local partner schools.

This year I have had involvement in the Prevent Strategy training for the first time. A specialist police officer presented to the 200 trainee secondary teachers in the auditorium at Homerton College. They explained how Prevent was part of the government’s counter terrorism strategy and its importance in reducing radicalisation and terrorism. Case studies were used to illustrate how vulnerable young people may be attracted to extremist groups such as those associated with the Islamic faith and those right wing extremists who apparently go to football matches to recruit dissatisfied and dislocated youth.

The narrative presented (and there was no indication whether the case studies were real or illustrative) is that early intervention can combat extremist associations, can encourage young people to realign extremist thoughts and lead to them having a much happier life. The presentation went on to show how intervention had saved these youngsters and encouraged them to a better life without extremists or extremist views. The police officer explained that she believed absolutely in the efficacy of the Prevent Strategy.

After the police officer’s presentation, I spoke with a group of twenty trainee teachers. Many of them accepted the strategy uncritically. The general view was that it was a good idea in order to reduce the risk of terrorism. They accepted that extreme views held by young people might lead to them becoming violent terrorists. The widely held view among this group of twenty was that it was worth intervening and notifying the appropriate authorities if it reduced radicalisation that led to terrorism.

I spent time with them deconstructing the Prevent strategy, while reminding them that they have a legal duty to implement it in schools. First we considered the risks associated with terrorism in the UK, we used data to show that more deaths occur annually in the UK as a result of encounters with items of furniture in the home than they do as a result of terrorism [1]. Why is it we do not have a furniture safety strategy? We then considered what motives the government might have in bringing in legislation that raises anxiety and fear about particular groups? We also considered research about extremism, radicalisation and terrorism, in particular the unsubstantiated claim that there is a conveyor belt from extremist thought to terrorist act. We spent almost an hour discussing the issues.

In spite of this critique, I reminded them of their legal duty to implement the Prevent strategy.

Even though we spent time discussing and thinking about the implications of this strategy and the importance of freedom of expression, these teachers will go on to work in state secondary schools.

State schools have, over the last twenty years, become increasingly subject to centralised control through the reporting of progress data and through punitive inspection by the Office for Standards in Education. Foucault would have described this in terms of surveillance and discipline. As such our state schools have become socially conservative. Teachers can find they have limited autonomy to act critically in implementing policy and legislation.

What I fear then most of all is that through implementing the Prevent strategy in the context of initial teacher education, not only are we in danger of undermining free speech within the university, but also we help perpetuate and promote socially divisive behaviours and action through our complicity. We will be sending young teachers in the profession who will be obliged to single out any child who they suspect might have extremist views. We have to be aware of the University’s role in this.

I therefore ask that we think very carefully about how we implement the Prevent strategy, because if we simply comply with it, not only do we undermine a fundamental academic right to freedom of expression, but, like in the example of initial teacher education, we can end up contributing to divisive behaviours in schools and perpetuating fear and mistrust in society. Ideally I would like to see the University and Colleges robustly challenge the Prevent Strategy.

[1] Estimates of risk of death from terrorism come from http://www.countercurrents.org/polya160914.htm as 1 in 15.8 million compared with accidental deaths in the home (around 6000 per year) http://www.rospa.com/home-safety/advice/general/facts-and-figures/ as 1 in 10200. If say 5 of those deaths involve furniture in the home, the risk is approximately 1 in 12.2 million (see http://www.hassandlass.org.uk in support of this estimate). It is crude but it illustrates the risk order of magnitude.

Teachers’ beliefs about teaching and learning: their influence on practice

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.

The science bit: a social cognitive theory perspective on traditional teaching

I want to input some psychology into the issue I wrote about in my previous post. I will draw on theory developed by psychologist Albert Bandura.

Bandura developed social cognitive theory which integrates social and cognitive aspects of learning and behaviour. There are two key ideas in social cognitive theory: observational (or vicarious) learning and self-efficacy. A little bit about these:

Observational learning

Bandura argues that much human behaviour is learnt through observation of others’ behaviour. He argues that it is impossible for people to learn everything through trial and error. Human beings rely very much on observing modelled behaviour, we then have a blueprint on how to act in similar situations. It is not just imitation, people think about and construct their own behaviour prior to acting.

Bandura makes the distinction between novice and expert behaviour. As novices people have to think carefully about their actions. Expertise is characterised by habituation and routinised behaviour. Once we have become competent in an domain of activity, we do not consciously analyse and reason in response to stimuli. People have heuristics or mental models that they can apply in situations. From a cognitive neurophysiological perspective, working memory has only limited capacity, people therefore are almost hard-wired to limit the use of working memory. We therefore need to act based on models that we recall from our long-term memory, without consciously reasoning about everything we do.

Becoming competent in something like teaching requires that we have opportunity to observe and accumulate knowledge for potential use as models. However, action and behaviour are not simply about mustering mental models from resources in long-term memory. As we become competent we have to make strategic assessments about the likelihood of success with a particular courses of action. Or the level of attainment we are likely to achieve. This leads me on to the next aspect of social cognitive theory: self-efficacy.

Self-efficacy

Self-efficacy is a very useful idea developed by Bandura. It is a forward-oriented belief, that is, a belief about the outcome of future events, and it is a belief an individual has in their ability to be successful or achieve a certain attainment in a domain of activity.

When we come to do something we are not familiar with, we are making assessments about the extent to which we will be successful. If he we have knowledge and skill in something related then it is likely that we will have a degree of self-efficacy. But self-efficacy is not necessarily transferable between domains.

Self-efficacy is dependent on the individual, their knowledge and skills and the task itself. Experimental studies show that self-efficacy is strongly linked to outcomes. In most situations it is a better predictor of success than knowledge or other psychological factors such as personality. This is because it takes into account the individuals strategic assessment of the situation at hand.

According to Bandura there are four sources of self-efficacy: enactive mastery experience, vicarious experience, verbal persuasion, and physiological and affective states.

  • Enactive mastery experience – this is most powerful source of self-efficacy. It is developed through experience and being successful. However, it is not just based on successful outcomes, it is closely related to an awareness and evaluation of the strategies and approach used to achieve the outcomes. To develop self-efficacy, success has to be related to process. It goes beyond practice-makes-perfect.
  • Vicarious experience – We can develop self-efficacy by observing someone we relate to or that we think is similar to our own potential performance level. By observing a competent other with these features we can develop self-efficacy in this way.
  • Verbal persuasion – a much weaker source of self-efficacy. We can persuade and encourage someone to do something effectively.
  • Physiological and affective states – if we are tired, ill or a stressed then our self-efficacy is undermined.

How does observational learning and self-efficacy help understand why teachers tend to teach in traditional teacher-centred ways?

Trainee teachers observe experienced teachers and recall the approaches of their own teachers. In their early ventures into the classroom they try out approaches. The cognitive demand, at this stage, is quite high. The management of stress and anxiety is important. Effectively then, through training they develop self-efficacy in teaching, through enactive mastery experience. A reflective component is important, because self-efficacy is related to the strategies used as much as the successful outcomes achieved.

One of the main concerns of teachers is managing the classroom and pupil behaviour, this becomes something of a focus in the early years of teaching. Until the point at which a teacher believes they have become competent. This is the point at which they have acquired a level of self-efficacy. This is the point at which teachers no longer need to analyse and rationalise or consciously reason every aspect of what they do. Many things become routinised and knowledge is heuristically stored as a set of possible behavioural responses to the situation at hand.

This allows me to explain the prevalence of traditional or teacher-centred practices: which I characterise as featuring a teacher explanation, demonstration or instruction, followed by student practice involving a defined task and finally a review or teacher assessment. For the reasons I discussed in my previous post, it is the practical demands that tend to mould practice into historical forms that reflect the institutional and resource-limited constraints of a state-funded school. The traditional teacher-centred routines represent an efficient solution to the demands of the teachers’ role, the constraints of the institution and the expectation of students, colleagues and parents.

Further reading

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

Why we teach in traditional teacher-centred ways

The way we teach is learnt through the observation – as pupils – of our own teachers and through the observation of experienced teachers. The profession is based on what Dan Lortie described as an apprenticeship of observation [1].

It explains why Larry Cuban [2] found, in his historical analysis of classroom practice in the US, that patterns of practice and pedagogy are sustained through generations of teachers.

As we began comparative studies of practice in different countries in the 1990s, there was further confirmation of this. It was evident that there were cultural similarities in teaching practice. Stigler and Hiebert [3] recognised similar teaching practices within the countries they observed.

This is not to say teachers are dumb-ass automatons who simply imitate established practices. No, because in spite of observations of similarities in practice there are individual variations. We adapt and personalise what we see. Yet, there are still common features; common patterns of dialogue and organisation in lessons. Much like learning language, learning to teach is like learning vocabulary and grammar and developing the confidence to express oneself individually in a way that others can understand.

This last point is important – being understood – Stigler and Hiebert [3] began to consider why cultural scripts were followed in classrooms. They made a simple but insightful observation, that it enabled classes to be smooth running. Classes work largely because teachers and pupils know the rules, the grammar, the patterns and the expectations.

Larry Cuban [4] came to very similar conclusions about cultural and historical practices. But he also makes one further mundane but important observation about practice. That is, it is the demands of the role of teaching, as well as the institutional demands that are the defining aspect of the character of teaching. He puts it as follows:

Within the age-graded school, the classroom itself was (and is) a crowded setting where teachers must manage 25 or more students (50 to 70 a century ago) of approximately the same age (but not necessarily the same interests, motivation, or prior experiences) who involuntarily spend—depending upon grade level—from one to five hours a day in the same room. Those in the community who hired teachers expected them to maintain control of the students, teach a prescribed course of study, capture student interest in the academic content and skills, diversify their instruction to match differences among students, and display tangible evidence that students have performed satisfactorily.

Not an easy task to meet those social expectations and manage a crowd of 5- or 15-year-olds who have to be in school. Within a room no larger than 600 square feet a half-century-ago (now a third larger), teachers and students communicate often (up to a thousand interactions a day in elementary classrooms). Within these schools and classroom settings, teachers have learned to ration their time and energy to cope with conflicting an multiple societal and political demands by using certain teaching practices that have proved over time to be simple, resilient, and efficient solutions in dealing with large numbers in a small space for extended periods of time [5].

And here is the point.

It is not through concious thought, nor through identifying the most effective means of learning that establishes the way we teach. Teaching is a cultural act that is passed on through generations, it is characterised by routines and dialogue that ensure the class runs smoothly. It is teacher-centred and traditional not because that is better or worse than other approaches to teaching. This does not enter into it. It is a practical solution that has evolved and been refined over generations. To understand this is the beginning to understanding how we develop teaching and learning.

Notes

  1. Dan C. Lortie, Schoolteacher, 2nd ed. (Chicago and London: The University of Chicago Press, 2002).
  2. Larry Cuban, How Teachers Taught: Constancy and Change in American Classrooms, 1890-1990, 2nd ed. (New York: Teachers College Press, 1993).
  3. James W. Stigler and James Hiebert, The Teaching Gap: Best Ideas from the World’s Teachers for Improving Education in the Classroom (New York: Free Press, 1999).
  4. Larry Cuban, Hugging the Middle: How Teachers Teach in an Era of Testing and Accountability (New York: Teachers College Press, 2009).
  5. Cuban, Hugging the Middle. pp. 10-11