El futuro de Internet: una verdad anticipada

ing perspective

In this section, I bring the components of social learning theory together to consider mathematics teachers’ professional learning in the context of this research. I also integrate the issues identified in the previous chapter on the analysis of the PD materials. I began by examining assumptions presented in Chapter 1, about the prevalence of traditional teacher-centred teaching in secondary mathematics and examine this from a social learning theory perspective. Following this I consider professional development from a social learning theory perspective.

The ubiquity of teacher-centred teaching

OfSTED characterized traditional teacher-centred teaching approaches as follows: “In the secondary lessons [observed], the most prevalent style was

one where the teacher demonstrated a new mathematical method which pupils then practised” (OfSTED, 2008, p. 16). I use social learning the- ory to explain how this is sustained through observational learning and how self-efficacy explains why such practices are ubiquitous in secondary mathematics classrooms. This leads on to explaining how professional de- velopment might lead to change.

In the first part of this chapter, I explained how observational learning is a component of social learning theory and tells us that behaviours are learnt through observation. Teachers participate in an apprenticeship of observation (Lortie, 2002), as trainee and new-qualified teachers. They adopt “cultural scripts [that] are learned implicitly, through observation and participation” (Stigler and Hiebert, 1999, loc. 1102).

A further proposition from social learning theory is that where there is little or no motivation to do otherwise, behaviours becomes automatic or routinized. Much human behaviour once learnt does not require constant redesign—we do not have to rethink everything we do each time we do it. “After people develop adequate ways of managing situations that recur regularly, they act on their perceived efficacy without requiring continuing directive or reflective thought” (Bandura, 1997, p. 34). Once teachers have learnt to teach and have developed practices and approaches that permit them to function in their rˆole, they do not have to think about and plan every detail of every lesson and everything they do in each lesson. They have access to a range of behaviours and lesson patterns that simply work. Acting on “perceived efficacy” means that a teacher believes that those actions will be successful. Thus, routines of teacher-centred practice can be implemented reasonably reliably.

Leinhardt (1988) observed a number of lessons over a lengthy research career. She derived a similar theory of practice to that which I developed from social learning theory.

Situated knowledge can be seen as a form of expertise in which declarative knowledge is highly proceduralized and automatic and in which a highly efficient collection of heuristics exist for the solution of specific problems in teaching. This automation or resistance to change on the part of the teacher should not be perceived as a form of stubborn ignorance or authoritarian rigidity but as a response to consistency of the total situation and a desire to continue to employ expert-like solutions (Lein- hardt, 1988, p. 146).

This, although not from a social learning theory perspective, is consis- tent with Bandura’s proposition of developing behavioural routines that meet the needs and demands of situations that recur regularly. Leinhardt enriches this idea with the introduction of “heuristics”. Although teaching behaviours become ‘proceduralized’ and automated, teachers are not sim- ply automatons; they use patterns of previously used actions and classroom

behaviours to meet the needs of the classroom situation. Lienhardt sug- gested that by using ‘proceduralized’ and automatic knowledge, teachers are able to act in sophisticated ways but without having to think about, in detail, every action and response in their teaching.

Leinhardt’s heuristics are consistent with social learning theory. Ban- dura (1997) explained how observational learning can be a generative pro- cess, where observed behaviour can be used as a guide for action rather than something that it is directly imitated and replicated. Generativity in observational learning is consistent with Leinhardt’s notion of heuristics. The difference is that social learning theory goes on to attribute the sources of behaviour to observation.

So far I have provided support for the formation of patterns of practice, but why would these tend toward a teacher-centred approach? And, why should these practices be similar within a culture or within a country?

In order to answer these questions, I draw on the historical analysis of classrooms in the US carried out by Cuban (1993). An historical analysis is useful because it provides insight into the development of practice. Cuban explained the formations of particular patterns and approaches through this. For the second question I draw, once again, on the comparative study of practice carried out by Stigler and Hiebert (1999) but consider a retro- spective analysis of Stigler and Hiebert’s assumption that practice is similar within a culture or jurisdiction by (Givvin, Hiebert, Jacobs, Hollingsworth, and Gallimore, 2005). From this analysis I demonstrate that it is reason- able to assume that traditional teacher-centred practice is a default teach- ing style: that it is reasonable to assume that there are similarities within a culture and that observational learning offers an explanation why.

Cuban (1993) examined the practices and teaching patterns found in classrooms in the US between 1880 and 1990. His starting point is simi- lar to the observations made by Stigler and Hiebert (1999) that teaching followed similar approaches within a culture and seemed to remain largely unchanged over time.

Cuban’s (1993) study was located in the US, across all subject teaching and in both elementary and high school settings. So, how is this useful in the English context? The reason I view Cuban’s research as important is that he attempted to explain the similarities that might be observed in teaching within a culture. This explanation can be applied to the English context and be used to account for the similarities that are observed in English secondary mathematics classrooms. Cuban’s explanation, as I will justify, is not specific to context.

Cuban drew on a number of sources of evidence in his analysis: pho- tographs of teachers and students in class; textbooks; student recollections; teacher reports on how they taught; reports from journalists, administra- tors and others who visited classrooms; student writings school newspapers and yearbooks; research studies of teaching practices; and description of classroom architecture, room size, desk design and building size. He ac- knowledged the historian’s dilemma of selectivity of evidence (p. 13) but

“sought multiple and divergent sources representing . . . a number of dif- ferent settings” (p. 13). He gathered descriptions of 1200 classrooms in the period 1890 to 1990; he combined this with his broader data set and so claimed to have an “indirectly” derived picture of teaching practices in 7000 classrooms.

He acknowledged the difficulties in describing practice. “Anyone famil- iar with a classroom knows the kaleidoscope whirl that it is . . . How can I capture only one slice of this whirl after it has disappeared?” (Cuban, 1993, p. 14). Yet this is what he attempted to do, with a range of assembled sec- ondary evidence. In order to facilitate this Cuban adopted a framework for describing teaching using the idea of teacher-centred and student-centred practices. He characterized teacher-centred teaching as follows:

• Teacher talk exceeds student talk during instruction. • Instruction occurs frequently with the whole class; small-

group or individual instruction occurs less often. • Use of class time is largely determined by the teacher. • The teachers rely heavily upon the textbook to guide cur-

ricular and instructional decision making.

• The classroom furniture is usually arranged into rows of desks or chairs facing a chalkboard with a teacher’s desk nearby (Cuban, 1993, pp. 6-7).

Cuban’s justification for the prevalence of teacher-centred teaching pro- vides the most convincing argument for the prevalence of teacher-centred approaches to teaching because it is consistent with my own experience of teaching in English secondary schools.

Within these schools and classroom settings, teachers have learned to ration their time and energy to cope with conflicting and mul- tiple 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 (Cuban, 2009, p. 10-11).

This has the same underlying logic as posited by Leinhardt (1988) and also that which I derived from social learning theory. Teachers deploy a range of traditional teacher-centred teaching approaches as a result of the demands of the rˆole and as a result of constraints arising from having fi- nite resources in state-funded education. This also contains some implicit reference to what teachers might consider to be effective in teaching math- ematics. That is, the lesson runs smoothly and is well-managed. This means then, that the primary goal of teaching is not necessarily optimising learning but effective management of the classroom and behaviour. I am not saying that teachers do not value student learning, but there are often more pressing needs concerned with classroom management.

Cuban’s argument is related to Bandura’s proposition that “people de- velop adequate ways of managing situations that recur regularly” and act on their perceived efficacy (Bandura, 1997, p. 34). However, Cuban offered a deeper analysis of adequacy in practice. So taking Bandura’ theory and Cuban’s historical analysis together: within the demanding rˆole of teaching and the resource-constrained school institution, teachers have self-efficacy in traditional teacher-centred approaches and those practices will be ef- fective in managing classrooms and behaviour. They may not offer the optimal learning experience but they do allow lessons to run smoothly.

I think it is important to consider the rˆole of the student as a participant in classroom routines. Stigler and Hiebert considered students, as well as teachers, as following a cultural script:

. . . one of the reasons classrooms run as smoothly as they do is that students and teachers have the same script in their heads: they know what to expect and what rˆoles to play (Stigler and Hiebert, 1999, loc. 1121).

This reflects the idea of a didactical contract:

Then a relationship is formed which determines – explicitly to some extent, but mainly implicitly – what each partner, the teacher and the student, will have the responsibility for man- aging and, in some way or other, be responsible to the other person for. This system of reciprocal obligation resembles a contract. (Brousseau, 2002, p. 31).

Traditional teacher-centred teaching is a feature of an equilibrated sys- tem, where patterns of behaviour have been shaped over time and transmit- ted through observational processes through generations. This is largely a consequence of the constraints and demands of the job of teaching. Where primacy rests in teachers having smooth running classes and classrooms. It also rests on not having to think through every action in a lesson. This, in many ways, contradicts Schoenfeld’s (2010) assertion that ‘in-the-moment decision-making’ is influenced by goal orientation. From a social learning theory perspective, teachers’ in-the-moment decision making in classrooms is a result of having a range of mentally modelled actions gained through observational means, that have been rehearsed in the course of experience and that are ready to be deployed heuristically.

From my analysis here, social learning theory provides the more likely explanation of teachers’ actions and behaviours and hence my decision to use it for explaining professional learning in this research, but also as a potential overarching theory for reform-oriented professional development. My next consideration is how teachers might introduce new methods and approaches in a sustainable way.

A summary of the

social learning theory model of pro-

fessional development

In this section, I present a summary of the model of professional learn- ing based on social learning theory that I used in this research. I begin with the two components of social learning theory that I operationalised: observational learning and teacher self-efficacy.

Observational learning

In this research, I used observational learning as an explanation of how teachers (potentially) learnt new practices. It is important to have some process or mechanism by which new or alternative ideas are potentially implemented. I chose observational learning (as a component of social learning theory) as it offers a framework for analysis and explanation as part of a wider theory. It allowed me to focus in on aspects of individual learning. I looked at the observational processes that groups of teachers used in PD sessions and looked at how individual teachers translated these ideas into lessons. I used the observational sub-process of attention in order to analyse teacher behaviour in the PD sessions. In case studies of individual teachers, I considered how teachers took ideas presented in various parts of the PD, whether it be video examples of lessons or in printed lesson plans, and adapted them to their own classrooms. I was particularly interested in the generative aspect of observational learning and how teachers take and adapt an idea or alternative approach.

Teacher self-efficacy

The implementation of a new approach relies on teachers being efficacious in that approach. In this study I was interested in making assessments about initial levels of efficacy in the teaching of problem solving. I assumed the more willing teachers were to implement the approaches and ideas suggested in the PD, the more efficacious they were. I was also interested in understanding how teaching efficacy might be affected by the PD. I chose to look at this quantitatively using existing teacher efficacy instruments and a problem-solving specific instrument developed for this research. I also decided to look at individual changes by considering case studies of individual teachers. I elaborate on this in the next chapter.

I used the four sources of self-efficacy proposed by Bandura (1997) as analytic framework for the qualitative research, these are: mastery experi- ence, vicarious experience, verbal persuasion and affective and physiological states. The most important source of self-efficacy when using the PD ma- terials is through mastery experience, the chance to experience success in using the ideas in a lesson. It is likely that the other sources will also play a rˆole too. Vicarious experience might provide opportunities for de- veloping self-efficacy though watching the video examples or working with colleagues. Teachers, if they identify with another individual, assess their

effectiveness more positively as a result of observing another being success- ful in implementing the new approach.

Verbal persuasion is a weaker source of self-efficacy, but may encour- age teachers to try out ideas in the first instance which then leads to the development of mastery and in consequence self-efficacy in the approach. Finally, affective and physiological states can undermine self-efficacy—if stressed or ill, teachers will be less efficacious and this will limit the im- pact of new ideas. This is important since teaching can be highly stressful and a teacher is frequently faced with multiple and often competing de- mands on their time and energy. As such a stressful or demanding context is not conducive to reform because teachers tend to feel less confident in implementing new ideas.

Integrating the characteristics of effective PD with

so-

cial learning theory

Having summarised a model of professional learning using observational learning and teacher self-efficacy, I wanted to integrate the analytic frame- work I derived from previous research on professional development effec- tiveness, described in the previous chapter. I could therefore relate the findings of this research with existing research, at least in terms of the consensus of ideas and characteristics. For example, I considered the rˆole of PD leadership, collective participation etc. in relation to social learning theory and in terms of the data. In other words, I considered the impact of these characteristics and provided an explanatory analysis using social learning theory.

I consider each of the characteristics of effective PD (leadership; col- lective participation; engagement; time and coherence) and integrate them with social learning theory.

PD leadership

From a social learning theory perspective, leadership contributes in two areas. The first is in relation to observational learning processes. Using Bandura’s theory of observational sub-processes (attentional processes, re- tention processes, production processes and motivational processes), I con- sidered attentional processes and motivational processes as most relevant here. The PD leader has a rˆole in making the PD content relevant and salient to individual teachers and in encouraging them to try things out. Therefore, one aspect of PD leadership is in facilitating observational learn- ing.

The second contribution of leadership is in developing teacher self- efficacy. PD leaders can promote self-efficacy through verbal persuasion. While it is considered weaker than mastery experience or vicarious expe- rience, it contributes to teachers’ motivation to try the approaches out,

which in turn would lead to the development of self-efficacy through mas- tery experiences.

Collective participation

Prior research has claimed this to have a positive impact on the effec- tiveness of professional development (Back et al., 2009; Desimone et al., 2002; Stoll, Bolam, McMahon, Wallace, and Thomas, 2006). From a social learning theory perspective, collective participation contributes to teacher self-efficacy in terms of vicarious experience and verbal persuasion. Seeing a colleague try a new approach out in their classroom and being successful can be a source of self-efficacy. Although, if relationships were not strong in the mathematics department, this might have the opposite effect.

Bandura (1997) put vicarious experience in terms of “referential com- parisons” (p. 87), in other words, comparing your own performance with others or as “attribute similarity” (p. 98). In the latter a teacher would be looking to identify with a similar teacher as a model and a vicarious measure of the level of success.

Another source of self-efficacy in collective participation is through ver- bal persuasion i.e. supporting and encouraging each other. In a highly individual and competitive department self-efficacy could be undermined or if indeed relationships were poor and there was limited trust: there would be no recognition of similar attributes.

Collective participation, from a social learning theory perspective, is therefore a necessary but not sufficient condition for PD effectiveness. It is possible that collectivity could undermine effectiveness under certain conditions, like for instance if there were a lack of trust or if there were no existing collaborative culture.

I considered the effects of collective participation from the perspective of two efficacy sources: vicarious experience and verbal persuasion. I did not go into this in any great depth as I was particularly interested in ob- servational learning and teacher self-efficacy. I made assessments of how effectively departments collaborated and the culture of those departments as part the analysis of coherence characteristics (see below).

Engagement

In the previous chapter I used this term as a catch-all for a range of related factors which had been derived from prior research. These included:

• The PD was practical and related to classroom practice; • It involved experimenting with teaching and practice; • It involved active learning;

• It was of a ‘reform-type’ i.e. it did not involve teachers participating in a lecture-style programme.

From the viewpoint of social learning theory, the underlying connecting theme is that the PD offers opportunity to try things out, rehearse ideas and experiment. This is related to the strongest source of self-efficacy that of mastery experience. It also implies having models and ideas that can be