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A re-examination of Reflective practice as a viable frame for mathematics teacher education:

Is it Sustainable?

Tansy Hardy, Sheffield Hallam University

Una Hanley, Manchester Metropolitan University

Paper presented at the British Educational Research Association Annual Conference, Heriot-Watt University, Edinburgh 11-13 September 2003

Abstract: Within our professional practices in mathematics teacher education we have promoted the use of reflective practice as a conceptualisation of the formation of professional knowledge. This paradigm opens up practices in teaching and learning mathematics; from this teachers can establish what is possible, that is how practices might develop and change. This has also offered us a valid approach for our own researches which have interest in the production of knowledge and socio-political concerns. For some time we have had concerns about the sustainability of this paradigm within the competence-based descriptions of training that now pervade much of (particularly, primary) initial teacher education in the UK. It has been suggested that self reflection and examination of professional challenges and possibilities are at odds with a competence based model of training, that ITE students are necessarily preoccupied with the practical concerns of preparation and that a more critical way of working is best placed in teachers’ continuing development courses, for example, at Master’s level.
This raises questions about what, in particular, reflective practice and the development of reflective practitioners can offer mathematics teacher education, both pre-service and in-service. Also where and in what forms it is appropriate and possible for this paradigm to emerge within today’s technicist/rational discourse. We have drawn on teachers’ discussions of their own professional development in mathematics teaching and learning to consider the continuing relevance of reflective practice and the significance of teachers’ sense of agency and governance in mathematics teacher education.

Understandings of the formation of professional knowledge, those given through government policy and those formed within and through teacher education activities, affect not only the specification of teacher education courses but more profoundly, teachers’ sense of agency and governance. From this teachers establish what is possible, that is how practices might develop and change. Where school is documented as replicating inequity and division in society (Bourdieu and Passeron 1977), teachers’ sense of how professional knowledge and practices can be re-examined is of crucial importance in an ongoing project to stay alive to these divisive effects on learners.

This examination of the frame of reflective practice in teacher education is focused on the teaching and learning mathematics (in UK schools). This focus brings to our examination societal practices and assumptions about the subject itself, and about what it is to be a learner and a teacher of mathematics. These practices associated with cultural construction of school mathematics are often taken as given and common sense. For example, when mathematics is taken as having right and wrong answers, teachers’ interpretations of children’s mathematical activity is often seen in terms of correct answers and methods, errors and misconceptions. The learners themselves are attributed with ability (or a lack of it), with having the appropriate language (or not), with appropriate and inappropriate previous or out of school experiences and so on. The presentation of mathematics as a self-defining, internally-justifying subject outside of human creation is astonishingly persistent and contributes to many teachers' sense of disempowerment when considering how mathematics teaching practices might develop and change, particularly for those concerned to counter its significantly negative and often violent effects on learners’ construction of themselves.

Add to this that school mathematics in England and Wales is set in a landscape of an imposed National Numeracy Framework (DfEE 1999) with tightly defined teaching programmes, narrowly structured lessons and national training for all teachers in these curriculum changes. This strategy for change is regulated through tactics such as the publication of school results on national maths tests, regular school inspections and gradings, funding targeted tightly at standards and achievement in SATs in key test boundaries which relate to government-set targets.

This landscape motivates our interest in teachers' development of professional practices and a professional self which allows the possibility of challenging required patterns of practice and particularly of addressing the effects of the divisive norms of mathematics education.

Our work:

Understandings of the nature of reflective practice have been the concern of much of our researches and writing, and a vehicle for our own professional development feeding into our course design and teaching. We have both worked in universities where there was a documented commitment to deriving educational practices which were oriented towards the development of ‘reflective practitioners’. Course descriptions referred to models of developing professional practice that brought together theory and practice, where students work on one in the context of the other through reflection on aspects of their experience. These underpinnings are aimed to dislodge the segregation of university elements and school based elements of courses.
As tutors and researchers we have worked with strategies and exercises that centralise this bringing together of theory and practice in a reflexive move (e.g. Mason 2002). In these writings on a systematic approach to professional development, John Mason makes clear that reflection is more than ‘just thinking a bit’, that it involves the breaking of habitual thinking (as well as habitual responses).

Yet we all know that it takes more than the mechanical and superficial carrying out of tasks for most learning to take place. The student has to participate in an action, not merely go through the motions. So too with reflection, professional development, and research. Mason 2002 p.16

He also says that this is anything but straightforward and outlines particular exercises that are important to disturb and break out of existing frames of interpretation. One significant feature of our own teaching has been that the intentions and the benefits of such strategies are discussed explicitly and frequently with the students.

We have written about our explorations in working with such strategies in a variety of contexts and about the joys and difficulties we have experienced.

We have considered the role of written articulations and descriptions for students in initial teacher education (Hardy & Hanley 1995). We developed our teaching on a four-year undergraduate primary education degree course(1) to promote students’ articulation of their experience and knowledge of teaching, and of their concerns and awareness as part of their development of a reflective attitude. When the students arrived, we needed to convey some flavour of the complex ideas that permeated the course. They understood that they needed to develop as practitioners. We introduced the notion that in order to do so they must make connections between aspects of their continuing experience in their course at university and in school, and learn to talk and write about this in particular ways. Students were expected to learn to use professional language, for example, that employed in the UK National Curriculum and Primary Strategy documentation, when they described their planning and teaching in school. They also needed to become familiar with the language associated with analysis, of ‘being reflective’ and ‘being critical’.

With first year students we asked for reflective writing on themes drawn from university sessions and from school-based work we highlighted the need to describe the teaching that they had observed and their own teaching in the professional discourses that they had encountered. As the course progressed, we encouraged students to recognise that their writing should change, that they should move away from offering predominately narrative or over general accounts and begin to identify strands of concern. We also had specific strategies to help them consider and reconsider their writing, using tutor written feedback on their writing, and whole group verbal feedback. We invited students to read each other’s writing and give peers written and verbal feedback as well as contributing to whole group discussions arising from these readings.

The following extract taken from a piece written by a first year student in response to the prompt to relate her recent school observations to reading of government reports and curriculum guidance

In one school they took a very practical approach to the work providing the children with multi-link, peg boards with elastic bands, counting aids, shapes etc, allowing the children to work out the problems practically. Using this approach I noticed that the children had a greater understanding of the work they were doing and were able to understand the underlying mathematical concepts. Rather than constantly asking the teacher for help they could use mathematical equipment to work out their problems e.g.: in a year 4 class I observed a boy named Sam working on area, he was asked to find the area of a diamond/kite shape. He wasn’t sure what a kite shape was so went to the teacher, instead of the teacher telling him what to do she told him to look in a shape book. On finding the shape he made it on his pegboard using an elastic band then drew the shape on to spotty paper and could work out the areas…The children are given the choice of whether they need to use the equipment or work the problem out in their head.

As the Cockcroft report states, ‘Practical work is essential throughout the primary years ... for most children practical works provides the most effective means by which the understanding of maths can be developed’. It also states, which I found quite interesting when thinking back to my primary school experience of maths, ‘It is a mistake to suppose that there is any particular age at which children no longer need to use practical material’. (Cockcroft 1984 – our insertion)

On close examination this extract provides an example of possible characteristics of reflective writing. She gives a recognisable account of an incident that captures a moment that she sees as characterising this teacher’s practice. The teacher’s role and child’s response can be identified easily from her writing. She is selective about what to tell and produces a vivid description. (However, she has said that the children’s responses indicated greater understanding without describing what the children did to lead her to this interpretation.) She is alert to connections between her experience and the professional description of practical work. Through this she illustrates the issue she goes on to discuss (the role of practical work in children’s learning), an issue through which identifies her developing professional beliefs.

We should say that not all students at this early stage in the professional course were able to report with clarity and make connections between their experiences and the documentation they encountered. But, our examination of reflective writing did confirm the complexity that is involved in the development of professional knowledge and practice.

Over this period we collected students’ writing and our written responses and, from our re-examination of these writings, we found that articulation itself had an impact on students’ sense of their experiences and the meanings that they made of interactions in classroom scenarios. An interpretation is involved here and their written articulations, together with peer and tutor responses, can force attention on this interpretation and so open up these experiences to examination and reinterpretation and the questioning of the meanings attached to professional discourse.

We have also worked on concerns to diffuse the stagnating effect of a theory/practice polarisation on teachers’ investigations and have explored the possibility of explicitly inserting theory to add potency and rigour to Masters teachers' mathematics classroom researches (Hardy & Hanley 1997). In the context of a Master’s course, ‘Enquiring into the mathematics classroom’, we explored the possibility of inserting ‘theory’ to add potency and rigour to Masters teachers’ classroom researches (Hardy & Hanley 1997). We had found that theory/practice polarisation gave inappropriate frames and an inauthentic voice for thinking about the forming of professional knowledge and for working on the professional activity and life of a teacher. The example below gives an illustration of a successful bringing together of these.

Throughout sessions the process of anecdoting was used. Briefly, tellers and listeners are identified. The teller reviews an anecdote; the listener seeks resonance with her own experience. The listener also assists the teller in identifying where the significance of the moment lies. The teller may then consider systematically other incidents from her practice, consult relevant literature, tell and re-tell these anecdotes to colleagues, discussing similar experiences and seeking recognition.

Alongside anecdoting, we offered readings outlining others’ theoretical notions of teaching and learning of mathematics. For a particular session later in the course we gave out readings related Brousseau's notion of the didactic contract and Bateson's more generalised double bind (Mason 1988, Melin-Olsen 1987). These we intended to have a jarring effect, making over-familiar practice less familiar and so open to re-examination.

The students’ first task was to highlight a section from the readings that resonated strongly or jarred in some way with their sense of classroom dynamics. John Mason describes the ‘didactic contract’ as

‘...between teacher and pupil although it may never be explicit. The teacher’s task is to foster learning, but it is the pupil who must do the learning. …. Acceding to the pupil’s perspective reduces the potential for the pupil to learn; yet the teacher’s task is to establish conditions to help the student to learn. Put another way, the more the teacher is explicit about what behaviour is wanted, the less the opportunity the pupils have to come to it for themselves and make the underlying knowledge or understanding their own…To stay alive as a teacher, it is necessary to be aware of the variety of perspectives (that students and teachers have as to the nature of learning and the role of teachers) and the fact that they are very deeply rooted…I believe that it is important to be open to these dilemmas, to take opportunities to talk about them with colleagues, to try to become precise in our articulations, because then it is possible to unlock the blocked energy and exploit it positively’ Mason 1988 pp.168-9

We followed a discussion of highlighted sections by setting the task of jotting down an incident from their teaching over the coming week that contained within it some kind of double bind and bringing it to the next session for anecdoting.

Judith offered the following anecdote.

A lively, enthusiastic year 7 class ‘bounce’ into the classroom, buzzing with questions and answers for challenges from previous lessons. Kevin comes in two minutes later looking at the floor and walks up and down from the front to back of the classroom. Eventually he picks up a chair and drags it to the back of the classroom and sits on his own. I set a few questions for the class to occupy them and avoid too much attention on Kevin.

‘Kevin, what’s happened? I can see you are upset, what’s the problem?’
‘Nothing, nothing!’ came the forceful reply.
‘Kevin, let me help if I can - who do you want to sit next to?’
‘Nobody wants to sit next to me’
‘Why Kevin, why is that?’
‘I don’t know but I can’t do maths, french, anything’
We continued in this vein for a few minutes where I tried to be positive. Kevin had produced some excellent work in the last few lessons in percentages. He agreed to start afresh after a lot of praise.

The group worked together on the incident against the theoretical notions of double bind and didactic contract. The group was able to identify a range of interpretations of the incident in terms of the double binds in which the parties in the interaction were caught. For example for the teacher working with a mixed ability class:

I believe that confidence is important for all children to work successfully at mathematics. I am especially concerned that Special Needs kids develop this confidence. I want to help them break out of the demotivating failure cycle and break their self-image as failures and of maths as ‘too hard’. This would lead me to give separate (not too hard) work that they can succeed at. (In practice such tasks prove unengaging and being given this sort of work rarely boosts children’s confidence – rather it stigmatises.) At the same time I believe challenge is important and so think that they should ‘hang on’ with the rest of the class and that I should offer them the support they need to stay with the group and engage in this work.

Melin Olsen has said that the method of avoiding the double bind damaging effects is to loosen it by communicating at the metalevel as often as possible, thus releasing the contradictions that determine it. Some of the teachers in this group, by using such strategies to bring together theoretical notions and their practice, felt this double bind had been loosen to some extent. These strategies also offer the possibility of using the theory of others as ‘thinking tools’.

Bateson’s conception of…double bind is useful for a full understanding of learning behaviour ...what are being offered are thinking tools which help to understand the pupil’s predispositions for learning’ Melin Olsen, 1987 p.189-190

In earlier sessions it was striking that group members often approached readings and others’ anecdotes as problems to be solved and responses to readings were offered the form of attempted solutions. However, the double binds identified show a thinking differently and to some awareness of the social and power relations operating.

As with all our other teaching (as tutors who assess students work) we were caught up in a double bind ourselves; of being clear to students about what a reflective approach is, and of generating a desire in students to produce what we seem to desire of them. This could lead them to replicate the symptoms of reflection – rendered it in a technical form, a trainable behaviour.

Teacher and pupil are thus all the time busy inventing ever new forms of behaviour and interaction, which they hope can be in accordance with the contract, which are either interpretations of it or tolerable evasions. Melin-Olsen 1987 p.185

Whilst we said that the strategies we worked with contributed to lessen the immobilising effects this bind, we do find that unenergising replications and a sense of contradictions are astonishingly persistent in our students and teachers and discuss this aspect next in relation to the prevalent ‘competence-based’ descriptions of teacher education that we have worked with (or against) in the UK.

We found that theory/practice polarisation gives inappropriate frames and an inauthentic voice for thinking about the forming of professional knowledge and that teachers are able to value using sustained systematic reflection together with readings as a way of working on professional activity.

We have also explored methodological issues for our own professional development and practitioner research and discussed how practitioner research from systematic noticings (Mason 2002) can allow an authenicating account of the struggle for professional identity and growth (e.g. Hardy & Wilson 1996).

We remain aware, however, that in these higher education courses there remain obvious difficulties in linking school-based and institution-based parts of such courses. This reflective approach to teacher education was not necessarily well received by students, being variously seen as irrelevant, a distraction of the practical concerns of the classroom, or, not least, obscure. As we had pointed out, as tutors we are caught in a 'double bind' of being clear to students about what this reflective approach is, and so rendering it in a technical and trainable form of behaviour.

However, we have persevered in foregrounding reflective practice. We hold it of great value in our work. In knowledge terms this paradigm is fundamental to our attitude to mathematics teacher education. It implies more than just ‘doing’ and more than ‘thinking’. It does not relieve a practitioner of the responsibility to doing more. It insists on the acknowledgement of the social, situated nature of this professional practice, it insists on power relations and desires being seen as present. It offers tactics for valid generalising but warns of the provisionality that must be keep in mind.

An impetus for re-examination

In England and Wales an astoundingly detailed National Curriculum for Initial Teacher Training was introduced in 1998 and refined in 2003 (DfEE 1998, TTA 2003). This specifies the competences (referred to as ‘the standards’) that must be demonstrated for the award of qualified teacher status. This is often manifested through these ‘standards’ being ticked off in some audit file. Such documents become the embodiment of the technical-rationalist approach to teacher preparation and have particular ‘effects’ on the identity of beginning teachers. Beginners have always had to some extent ‘talk the talk and walk the walk’. However, this technicist approach sees teachers as ‘deliverers’ of the curriculum, and ‘the standards’ gives very little space to notions of intellectual growth. Beginners are constructed as the embodiment (or not!) of the subject knowledge and pedagogic knowledge itemised. A measure of beginner teacher development is determined by the ‘thickness of the file of evidence’ they amass throughout their training course (and become a material version of ‘the standards'; a fully ‘ticked off’ member of the profession.)

For ourselves as teacher educators, we find ourselves in some discomfort in living our professional lives with resultant remnants of what we have known as teacher education and our seeming impotence to intervene in the implementation of such regulatory policies. This seems particularly distressing for our work on primary mathematics education courses. In primary school ITE, policy requirements result in course specifications that are overwhelmingly full and technical; and what we have argued are key aspects of professional development are not only squeezed but purged from these course descriptions. This sense of loss, shared with other primary mathematics educators, is more that just whinging from ‘reactionary higher education’ as government education officials here have claimed. More personally, we suppose that our own reluctance to change may seem to others mostly nostalgic. This claim is hard to dismiss and we need to continue to examine our sense of loss and its place in our own teaching practices. However, over the years we have identified and explored a number of paradigms from which to consider the acquisition and development of professional knowledge. We remain clear that our considered preference for a paradigm would be other than the bullet-pointed competences of the National Curriculum for Initial Teacher Training of 1998 and 2003, and that this preference is more than harping back to the teaching of more youthful days.

And for teacher's sense of agency and the development of their professional knowledge? Working with a reflective practitioner based paradigm involves adopting a ‘critical’ perspective (for beginning teachers, practicing teachers and teacher educators), and involves a shift to consider not just ‘what knowledge?’ but ‘why this knowledge and for what purpose?’. Here teachers can ask, ‘Can I acquire an identity as a teacher outside of such assertively expressed and given descriptions? Is there another language relevant to my practice which will help me research my practice and my context?’

In the terms that we have set out in this paper these are key questions for all teachers of mathematics to be able to ask. In what terms if at all is it possible to ask such questions within a competence based model of professional development? This is the theme we move to expand next.

What forms of knowledge production are possible?

Expansion of this theme raises questions about the knowledge claims and the nature of the subjectivity and of the self ‘in ‘practice’ that are central to a competence based model of ITE. In focusing on practice and detailed technical aspects, what sense of a decision-making self is implied or possible? Can we function with a sense of fractured professional selves? To what extent as a practitioner do we need to recover a sense of ourselves as centred and not atomised as a subject, with purpose and agency? And if so, how is this to be achieved (to some extent)? In our re-examination it is important to remain of the re-emergence of such questions.

Given that ITE statutory requirements are overfull and technical McNally’s suggestion (McNally et al., 1997) that 'reflection' is a vehicle more appropriate to experienced teachers might seem to offer us a way out. However, it is important to be suspicious of this view. It can be seen to serve a technical induction paradigm for initial teacher education We have found that amongst the key features affecting the effectiveness of reflective work in any teacher education are the sustained, ongoing nature of the work and the support and focus offered by tutors and peers. It is clear that reflective practice is at odds with a competence based model of initial training with associated atomised goals attainable through short defined tasks. Here reflective work will be reduced to short, fragmentary 'gestures' that are likely to have little reportable effect. Despite these difficulties there is research reporting significant roles for reflective enquiry (often in the later stages of ITE). Una Hanley and Tony Brown (1996) suggest that reflective work can provide a forum in which students can reconstruct their own professional identities in relation to the professional discourses into which they come inducted. John Coldron and Robin Smith (1999) report students' appreciation of a substantial unit of work based around a reflective classroom based research enquiry in the final year of a 3 year initial teacher education course. There was evidence that this work contributed to the students’ move from a practical problem- solving attitude to their future professional work.

It would be unsurprising in an area that requires sustained engagement that tangible evidence of positive effects and appreciation of this way of working by students emerges more easily in the later stages.

This does not however lead to the assertion that it is effective at the later stages of professional formation alone

Disjoint competence based regimes of ITE can be seen to contribute to the prevalence of limited and habitualised concepts and discourses of what it is to develop professionally for beginning and more experienced. It seems unproductive to justify this narrowing only to argue for the need to challenge and break down such attitudes later in a teacher's professional life. Indeed there has been evidence of such competence based specifications filtering into conceptions of continuing professional development programmes.

Are there forms in which reflective practice can re-emerge?

However today, alternatives to the dominant competency discourse are unusual, under funded and are currently forced onto the periphery. Theory continues to be a dirty word for policy makers and teachers alike (Griffiths and Tann 1992).

The professional way of life that we have promoted is not easy to articulate or to act out. Students need to acquire unusual habits, for example to discuss their practice from a personal perspective, to articulate this precisely and to learn to analyse this. They also need to generate time and motivation to do this. They need to work on personal awareness, a sense of their own ‘voice’ as practitioners and suspend the belief that ‘getting it right’ is just a government document away. Adelman (1993) points out that for practitioner research to involve a sense of development(2), teachers not only need to acquire a researcher’s habits and a fine-tuned sense of their professional context. So for experienced teachers, practitioner research also needs to include tactics for theorising that practice, for example, this might involve engagement with tools from social and cultural theory to examine the social interactions of the classroom.

We have been thinking about whether the paradigm of reflective practice can offer something special and what would be the characteristics of valid uses of this paradigm. In our work on reflective practice we have found potent strategies and tactics that offer the possibility to break habits (never underestimate how hard this is!) and to think differently. There is the possibility to live with the contradictions and dilemmas that are so much part of our own teaching and learning, to avoid seeing these all as problems to be solved and to resist the search for an overly easy solution.

However, the context of the United Kingdom, reflective practice was never a dominant frame in teacher education but it was speakable. Now it feels muted, perhaps silenced through appropriation (and so do we) by a 'training' discourse. We have tried to ask seriously of ourselves and of our discipline why it holds such promise and attraction for us and why we find ourselves so aggrieved at its nearing demise. Perhaps if reflective practice has become an over familiar and so neutralised discourse, it is time to abandon our attachment and look elsewhere for some authentication of our professional selves, some other language to frame our professional values?

Some prevailing concerns and questions on agency and authority: inconclusion

As a conceptualisation of knowledge formation in professional practice we find a theory/practice polarisation gives an inappropriate frame and inauthentic voice for thinking about the forming of professional knowledge and for working on professional activity and life of teacher. So we draw on reflective practice. However, this theorisation will result in the privileging of particular forms of knowledge and engagement. It remains valuable to ask who gains from our working with reflective practice. Are we just producing knowledge in another form, still divisive, elitist, still driven by a privileging of theory and demeaning to teachers’ work?

All our experience shows that reflection is hard. Much that is produced is described as uninsightful and unprovoking. How can it be made more doable? It takes considerable time and effort. There is a double bind for us as teacher educators; that is, succumbing to demands of students for clarification and the pinning down of this hard and elusive thing. By this doing this, we might generate a desire and a possibility in students to replicate the symptoms of reflection. It becomes rendered in a technical form, a trainable behaviour. Can it be appreciated as rigorous and at the same time authenicating?

When discussing our work in teacher education we may be seen to describe teachers’ practice in terms of its practical concerns and lack of reflective spice. This may result in the rendering of professional practice into a hierarchy of categories and levels(3), a deficiency model of teachers’ meanings of their work. It would be valuable to continue to search for other terms in which professional knowledge and development can be described clearly, without a insinuation of lack or not yet good enough.

In more personal and more extreme terms, we ask is this version of professional growth and life no longer viable? Our persistence in referring to it may reveal our marginalisation in teacher education practices that dominant in the UK today. Is it timely to return to insistence on the central place of reflection not least as a challenge and disruption to an authoritarian ordering of education. Our re-examination of professional life finds that there remains a need for a place where the educator self lives with contradiction and multiplicities and opposing identifications that prevail.

Put differently, the privileging of teachers’ work along the lines Petrie delineates (...where the work of teachers (and the research they draw upon) remains at the level of optimizing efficient performances...) severely restricts any notion of teacher agency that argues for an open, dynamic, engaged course of action. .... Teachers themselves should see these reform efforts as important opportunities to develop and to frame ongoing critical strategies that not only challenge prevailing inequitable structural arrangements, but also probe their own complicity in those arrangements.

(Pignatelli 1993 p412)

Our willingness to accept and internalize questionable limits on what we can know about ourselves and how we might act as a natural or inevitable condition (Pignatelli 1993 p412)


1. This was a course for intending teachers of 5-11 year olds. All subject areas in the primary national curriculum are crammed into these courses, and all students take core units on the teaching and learning of mathematics. There are also one-year postgraduate courses available with the same aims

2. There is an implied ethical and value judgement in discussing ‘effective’ reflective practice or practitioner research in terms of ‘improvement’, ‘development’ and ‘growth’. There is not a simple or direct link between re-thinking, re-searching, acting differently and ‘improvement’.  We try to bear this in mind

3. This could be seen in the work of Carr and Kemmis describing reflection as technical,  strategic and  emancipatory, and Elliott’s seven levels of reflection.


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This document was added to the Education-line database on 11 May 2005