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Working as partners for classroom reform
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International Journal of Educational Development 28 (2008) 534–545 www.elsevier.com/locate/ijedudev
Working as partners for classroom reform Razia Fakir Mohammad, Brian Harlech-Jones The Aga Khan University, Institute for Educational Development, PO Box 13688, Karachi 75950, Pakistan
Abstract This paper discusses a partnership involving teachers and a teacher educator working together to develop teaching and learning practices in Pakistan. The partnership was established in response to the teachers’ need for support in developing their professional practices within the actual contexts and realities of their schools, after they had attended an in-service training course at a university. Providing case studies, the paper analyses the processes and outcomes of this co-learning partnership. The findings suggest that the collaborative process advances the understanding of teachers’ problems, resolves them on the spot, and provides teachers with the confidence and courage to transcend the constraints of their workplaces while developing professionally. r 2008 Elsevier Ltd. All rights reserved. Keywords: Collaboration; Teaching and learning; Teacher learning; In-service education; Reform
1. Introduction 1.1. Convential practices of teachers and researcher/ teacher educators In this paper, we show that even in the difficult and often discouraging circumstances of Pakistani schools and in spite of severely asymmetrical relationships, it is possible for teachers to change their practices and also improve the quality and outcomes of students’ learning when teacher educators and teachers work together on-site in partnership. Pakistani society is characterised by hierarchical structures in which respect is unidirectional: for example, from weak to strong, from poor to rich, Corresponding author. Tel.: +92 21 6347611;
fax: +92 21 6347616. E-mail address: [email protected] (R.F. Mohammad). 0738-0593/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijedudev.2008.01.006
from student to teacher, and from teacher to head teacher. Not surprisingly, most schools employ traditional modes of teaching that reflect these wider social practices. Students are expected to follow teachers passively, while teachers are compelled to follow the instructions of their school heads and other professional seniors, usually suppressing their individual potentials and eschewing creative thinking. External bodies impose curricula and set textbooks while, en route to the all-important examinations, teachers are expected to follow prescriptions without any deviations. As can be expected, the teaching of mathematics suffers from the same constraints. Generally, mathematics teachers do not appear to think about their tasks creatively or innovatively; they have taught the same rules in the same ways for many years because this is what they are required to do, and they seem to be prepared to go on doing so for the foreseeable future. The students’ achievements
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are graded according to their ability to define or to apply rules in the prescribed ways, with memorisation looming large in classroom practices. They rote-learn rules such as ‘Invert the divisor and multiply’, or ‘(a+b)2 ¼ a2+2ab+b2’ without understanding why they are doing so or what the rules might mean. Teachers, too, are usually evaluated according to their ability to follow traditional practices. Supervisors make their assessments without consultation with the teachers who are affected. Indeed, questioning authority is considered to be disrespectful and will probably adversely affect a teacher’s annual evaluation report. Similarly, teachers evaluate their own teaching from the external perspectives of their students’ success or behaviour. For example, silence in the classroom and the sight of students busily writing in their notebooks are regarded as evidence of good teaching, without reference to any other indicators of successful outcomes. Self-evidently, traditional teaching practices such as these do not encourage teachers to be active, creative, or innovative. Knowledge is regarded as an entity that emanates from the textbook rather than as something that is constructed by teachers or students themselves in the light of their personal backgrounds, emerging needs, experiences, and interactions with contexts. Many writers (for example, Freire, 1971; Skemp, 1976; Van Glaserfeld, 1994) question the effects of a traditional mode of learning that emphasises performance rather than reasoning. For instance, Van Glasersfeld (1994, p.17) states: Reinforcement fosters the repetition of what gets reinforced, regardless of the acting subject’s understanding of the problem that was posed, and of the inherent logic that distinguishes solutions from inadequate responses. Critiquing the traditional view of teaching, Freire (1971) employed the well-known image of children as empty vessels that are filled up with knowledge by the teacher. Similarly, Skemp posited that a traditional view of teaching promotes the practise of rote learning, in which learning is identified with repetition, which can be done without thinking: Certain actions are reinforced as a result of their outcomes, so learning follows action. And what is learnt is action: the cognitive element is small (1979: p.33).
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Thus, traditional learning practices do not encourage students to explore and extend their mathematical knowledge. In addition, the neverending routines of memorising rules and doing long calculations make mathematics a boring and difficult subject for most children. Finally, perhaps the most serious effect is that many students lose their confidence and self-esteem because, as a result of their inability to solve problems themselves, they depend on the teacher to tell them what to do. Unsurprisingly, most teacher-education institutions employ similar ‘top-down’ methods and approaches. Even when they are advocating more creative and innovative ideas and methods, the teacher educators’ approaches are likely to be formal and transmission based. For the teachersin-training, whether in pre-service or in-service courses, the medium is most of the message. The study on which this paper is based comprised part of the doctoral research of one of the authors of this paper (Mohammad, 2002) and focused on the researcher, who was also a teacher educator, working with teachers to facilitate change. The teachers who were the subjects of the research had attended in-service training courses at a university in Pakistan; before their involvement with the university, the teachers—isolated from practical and moral support in their schools—were rigidly constrained by the authority of their schools, taught for the ‘right answers’, and explained facts and rules rather than developing their students’ intellects and thinking abilities. As will be seen, when they widened their perspectives, these teachers felt that they needed support as they tried to develop their teaching in the face of the constraints of their workplaces. 2. Context of the study Although the majority of teacher-education institutions in Pakistan still employ ‘traditional’ approaches and practices, during recent years some institutions have undertaken conceptual shifts and have implemented more innovative methods. This is particularly true of the university at which this study was undertaken, where the approved perspective is learner centredness, which is based on the concept that teaching should accord with a child’s psychological and social orientations to classroom learning (cf. Ernest, 1991, 1994; Cobb et al., 1991; Jaworski, 1994). The teacher educators thus view teachers as facilitators who support and develop their students’
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thinking. In theory, then, teachers are expected both to set meaningful tasks for the students and to analyse the outcomes of the tasks in order to understand how the students construct meanings. Furthermore, teachers are expected to listen to the students, to understand their levels of thinking, and to help them to achieve common agreement about a concept. When teachers support and develop their students’ thinking capabilities in these ways, it is expected that the students will not only assume responsibility for their own learning but will also develop social responsibility. As discussed in Mohammad (2002) and in Mohammad and Harlech-Jones (2008), research suggests that the teachers’ experiences in the educational programmes at this university generally lead to significant changes in their understanding of what mathematics and/or science teaching could and should be. They also gain insights into the limitations of traditional approaches to teaching. However, in spite of the fact that the teachers who participated in this study developed favourable attitudes towards innovative teaching, to the extent that almost all of them considered it to be highly desirable, most of them were unable to make significant changes to their approaches because of conceptual and contextual constraints. Here, it is necessary to emphasise that the head teachers and colleagues in the schools to which these ‘refreshed’ teachers returned did not expect them to adopt new approaches to their teaching, and were certainly not sympathetic to their desires to implement changes. On the contrary, the heads and colleagues simply anticipated that the ‘refreshed’ teachers would return with the ability to be better implementers of the traditional methods. As a result, the teachers reentered work environments that were indifferent at best and sceptical, even antagonistic, at worst. Not surprisingly, this unhelpful environment resulted in significant discrepancies between their aspirations and practices (as discussed in Mohammad and Harlech-Jones, 2008), to the extent that they almost entirely abandoned their efforts to change their practices; inevitably, however, the clash between their desire for change and their failure to practise it generated further pressures and tensions. It was only when the teacher educator was present to support the ‘refreshed’ teachers, providing the only element of support in otherwise unsupportive workplaces, that they were actually able to translate aspects of their aspirations and new knowledge into improved practices.
It is also necessary to emphasise just how great was the gulf between the environment and experiences that the teachers enjoyed at the university on the one hand, and their work contexts on the other hand. While they were attending the in-service course at the university, they were removed from the problems that they faced in their schools; in addition, they enjoyed new and stimulating learning experiences in a comfortable, well facilitated, encouraging, and supportive environment. However, as discussed above, once they were back in their schools, they faced the same, unchanged conditions, which included an enervating lack of support as well as a rigorous emphasis on set routines. Clearly, teachers such as these cannot be effective change agents if they are set adrift without support in their work environments. Here we would add that reforms are more likely to be successful when they are integrated into a comprehensive plan for improvements across the whole system, with all involved agreeing on what is to be done and how. It is clear that if teacher educators are to help to liberate teachers from the constraints of their schools and to support the teachers as they work to effect the changes that they envisage, they (the teacher educators) need to be sensitive to, and understand, the true nature of the difficulties that face the teachers. Furthermore, teacher educators need to appreciate not only how the constraints affect the teachers’ ability to transfer knowledge and ideas from the university to the schoolroom, but also the effects that these constraints have on learning in the classrooms. However, although important, these matters are beyond the scope of this article, which deals only with onsite interventions by an individual teacher educator.
3. Theoretical framework In the study on which this paper is based, the researcher was also a teacher educator at the university at which the teachers—the participants in the study—had taken an in-service training course. After they had completed the course, the researcher partnered the teachers in their workplaces, supporting, encouraging, and dialoguing with them as they tried to implement what they had learned. The guiding principles behind the partnership between the teachers and the researcher/teacher
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educator were that dialogue and reflection on one’s actions would: Enable the participants to understand the realities and difficulties of practise, and Assist them to make improvements. These principles were adopted from the work of Wagner (1997), who used the term ‘co-learning agreement’ to refer to partnership and a dialogic relationship between the participants in research projects. In this partnership, the research is regarded as embodying a significantly interactive, social approach to the educational reform process. As Wagner states: In a co-learning agreement, researchers and practitioners are both participants in processes of education and systems of schooling. Both are engaged in action and reflection. By working together, each might learn something more about the world of the other. Of equal importance, however, each may learn something more about his or her world and its connection to institutions for schooling. (1997, p.16) From the above, it appears that the essential feature of the co-learning agreement is that all partners are learners. This means that teachers do not work under external control or imposed authority; rather they commit themselves to learn as equals with the researcher, with all parties sharing an agenda and respecting each other’s goals. Jaworski (2000, p.6) extends the perspective to apply specifically to the relationship between teachers and teacher educators, stating that, ‘A colearning partnership implies an explicit arrangement agreed between participants’. Here, it is important to recognise that the quality of the relationship is central to achieving a collaborative culture of learning; also, that a commitment to learning together fosters shared understanding through mutual dialogue, leading the participants to achieve ownership and confidence in creating knowledge. Similarly, in her study of collaborative partnerships between parents and teachers, Rogoff (2001) states that learning through collaboration requires respect for all of the participants’ ideas, views, and opinions. Differences in views are regarded as resources rather than stumbling blocks, and as enhanced opportunities for learning. Conflicts and differences of opinion should be dealt with by discussion and problem solving in trusting, nonjudgmental environments.
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Although teachers are often depicted as uncreative and passive, this literature suggests that teachers are (or can be) self-aware agents of their own learning, with the capacity to reflect. A culture of collaboration, focusing explicitly on nurturing teachers’ thinking and practices, can be promoted by both teachers and researchers or teacher educators committing themselves to learning. This commitment promotes mutual dialogue, the product of self-reflection and/or a trusting relationship. The result is that external control and authority over teachers’ learning are reduced, while responsibility for self-improvement intensifies. Thus the ideal situation, as depicted here, is one in which teacher and teacher educator relate to each other as equal partners in a symmetrical relationship, contributing each learning equally from the other. However, in most public schools in Pakistan, in the short- to medium term it would be difficult if not impossible to achieve this sort of relationship, because most teachers regard teacher educators and/or supervisors as professional superiors. This inclines the teachers to adopt attitudes of deference and dependence, and makes them less inclined to exercise initiative (Mohammad, 2004). Selfevidently, under these conditions teachers feel neither sufficiently autonomous nor adequately motivated to initiate or sustain their own professional development. Describing how, in these situations, teachers experience a lack of professional autonomy and have a sense of being isolated and powerless when it comes to promoting change, Frost and Durrant (2002, p.144) observe that, What really needs to be emphasised is not autonomy, but the capacity of individual teachers to make a real difference, in other words to exercise leadership and to experience the satisfaction of having a significant impact on professional practise and ultimately on the quality and outcomes of students’ learning. This is the thrust of our article—namely, that while ‘autonomy’ is unrealistic in such difficult contexts, it is possible for teachers to change their own practices and also improve ‘the quality and outcomes of students’ learning’. While these might be viewed as modest outcomes under more fortunate circumstances, they are considerable and significant advances in the situations that are depicted here.
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In the case studies that are presented here, we show that significant achievements were possible, given the context, even although the relationships between the teacher educator and the teachers were neither equal nor symmetrical. It is important to emphasise that a journey always begins with a single step—a step that is often made into uneven and ‘asymmetrical’ terrain. Through dialogue and support, and by reducing the distance between the participants, the teachers were able to translate some of their new aspirations and knowledge into practise. We wish to re-emphasise that, small as these achievements might appear to be within the overall constraints of a rigid and tradition-bound system, for the individuals concerned they were nevertheless substantial advances, opening windows into new possibilities. 4. The design of the study As already stated, the study on which this paper is based comprised part of the doctoral research of one of the authors of this paper (Mohammad, 2002) and focused on a researcher, who was also a teacher educator, working with teachers to facilitate change. It also examined processes and issues that are related to collaborative partnerships. The nature of this research was reflective and participatory, with the researcher having two roles. The first was as a teacher educator assisting teachers to convert their learning into practise. The second role, in the over-arching position of researcher, was to analyse processes of teacher development. As a teacher educator, the researcher supported the teachers in trying out new ideas and helped them to gain insights into their teaching. As a researcher, she investigated the processes by which the teachers developed their teaching in collaboration with her. 4.1. Data collection Three teachers collaborated in this study, which lasted for 12 weeks, during which the researcher met with each teacher at least once every week. The researcher adopted interpretive research methods, collecting data by audio-recorded conversations during pre- and post-observation meetings; making field notes during teaching sessions and while the participants discussed their learning with her; collecting the teachers’ written comments; and compiling her own reflective journal entries. During this period, the participants were involved in
planning lessons that embodied their new aims for effective teaching, as well as implementing their plans and reflecting on the outcomes and issues that arose. 4.2. Method of analysis Initial analysis entailed reading the data from visits to the teachers in their schools and, for each meeting, writing an analytical memo that described the collaborative work that had taken place, with particular reference to pre- and post-observations. For example, the data included descriptions of how the collaborators initiated their work, what the teachers said or did, how the researcher reacted, and ongoing observations about the limitations or successes. During the researcher’s scrutiny of these analytical memos, a wide range of examples, which provided evidence of the teacher’s learning were highlighted in tabulated form. Items were clustered together to form categories describing one or other aspect of the learning that was taking place. 5. Working together examples and outcomes In the section, from the wider set of findings we present case studies that are representative of the teachers’ learning. As will be seen, during the collaborative work in the schools, the teachers made concerted efforts to implement new ideas that reflected what they had learned during their course at the university. Analysis showed that, amongst other responses, the teachers were thinking through and modifying or re-modifying their lesson plans, analysing students’ responses, and improving their mathematical knowledge. Note: In these examples, whenever we refer to ‘the researcher’, it should be remembered that in the school contexts, the researcher was also a teacher educator. 5.1. Case study 1: developing a practical understanding of new strategies In this study, the teacher, named Sahib, initially intended to teach the topic ‘circles’ through a practical activity that he had learned during the in-service teacher education programme. However, for a variety of reasons, such as lack of time and the forthcoming examinations, he seemed to have decided to omit the practical activity and teach in
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a routine manner. His main concern was that developing conceptual understanding was unnecessary to pass examinations; as he said: I have to complete the syllabus before the final examination. A teacher does not need to bother about their [students’] learning; it depends on students how much they want to ‘absorb’. We check their memory and skills of drawing in the examination; conceptual clarification is not a basic requirement of the examination. If we ‘check’ [assess] their concepts, none of them will pass the examination. Sahib’s statement seemed to indicate that he adhered to a transmission view of teaching, despite his apparent appreciation of the value of practical activities. The teacher educator encouraged him to imagine himself in a teaching situation at a school with a more favourable environment. Under those conditions, how would he teach the lesson while incorporating a practical activity? Sahib responded, ‘I have not tried out any practical activity in teaching the topic previously, although I have always been thinking about teaching it differently’. It appeared that, although he had talked about it, Sahib had not considered actually integrating his new learning into his teaching practise. When the teacher educator asked him to give an example of a practical activity that could apply to the topic of the lesson, Sahib described an activity related to ‘circles’ that he had experienced during the university course, when the course participants were asked to stand at an equal distance from a fixed point holding a rope. Sahib said that this activity would not only be a practical demonstration of ‘circles’ but would encourage the students to explore the concept for themselves. However, he cautioned that, ‘I need a full period to take the students outside the classroom and to ask them to arrange themselves. Getting a rope is difficult, too. [After all this,] I do not think that any time will be left for written work.’ These words show how difficult Sahib found it to integrate an activity into his lesson; in particular, he thought that it would be difficult to obtain materials, as well as to find the time and space. His statement also shows how much he struggled to accept new ideas while his thinking was still largely rooted in the ‘traditional’ transmission view of teaching and learning. However, his collaboration
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with the researcher motivated him to try out a new method; as he said: As you are also here, I should try this method in the classroom and you can tell me how I can improve in the activity.’ From this point onwards, he thought more creatively, saying that he could ask the students to stretch out their arms to form a circle themselves. Sahib commented, ‘I could do this activity inside the classroom in the available space by calling some students. It could be a small circle, and if there is some space between them, I will tell them to imagine no gap. Later analysis of his teaching showed that his thinking did not stop where the discussion with the researcher ended. Sahib continued to reflect on new ideas and their practicality in the realities of the classroom. In evaluating his teaching, he acknowledged that the partnership had helped him to extend his thinking by accessing new ideas and activities, and by discussing how they might be applied: We always have previous experiences of learning and knowledge; they are all hidden in our minds. Thinking deliberately means bringing them out. It is difficult to think in isolation. When one talks with someone, he discloses many ideas to himself. However, that person should have the same vision of teaching. A lesson on ‘equations’ provides another example of a teacher learning about the subject and his students’ thinking processes, as well as developing an understanding of the students’ responses. Sahib used stories to increase his students’ participation and to move beyond the text book–for example, he asked his students, ‘Somebody has thought of a number, multiplied it by three, subtracted one, and got five. Tell me the number he has thought of’. Aiming to involve students in the lesson, he invited some of them to use the blackboard to explain the methods that they had used to solve equations. One student had devised his own method to solve the equation x 3–1 ¼ 5 and wrote 2 3 ¼ 6–1 ¼ 5 on the board. Here, the student first multiplied 2 by 3, getting 6, and then subtracted 1 to get 5. However, although the student provided a correct answer, the teacher did not accept it because he wanted an explanation that accorded with the one in the textbook. In the feedback session, Sahib admitted that he was not happy with the lesson because he had not succeeded in improving the students’ level of participation. Here, he revealed the tension that he
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felt between reconciling new approaches with traditional approaches that were based on the textbook. It also suggested that he did not understand how his students might be thinking, the reason being that he did not invite them to explain why they reached certain conclusions. Although, at first, Sahib found it difficult to be to be self-critical and analytical, the evidence suggests that the post-observation discussions helped him to develop reflective thinking. For instance, the discussion that focused on the students’ solutions and his interpretation of them helped him to realise that he had not paid enough attention to their answers. Sahib observed, ‘I think I was not able to understand why the students were confused. It is a fact that when a teacher is not used to getting different answers, he might be confused in dealing with them, and cannot satisfy the students.’
proceeded, as can be seen in the record of the exchange of views below: T ¼ The teacher (Naeem) R ¼ The researcher 1T 2R 3T 4R 5T 6R 7T
5.2. Case study 2: using time effectively and taking responsibility for one’s own actions This study is taken from partnership meetings at the beginning of the new school year. When the researcher arrived at the school, she noticed that classes were not in session and the students were roaming around the premises. Because the head teacher had not yet drawn up the new timetable, the teachers did not have a schedule of classes and were enjoying ‘free’ time. When asked about his duties during this ‘interim period’, the participant-teacher, Naeem, replied, Before you arrived, I was just chatting with the other teachers. There is no work. Teachers have to come to school regularly, because they do record our attendance, but teaching has not begun yet. It is a relief time for us. y We read newspapers, discuss politics, and nothing else. The researcher suggested to Naeem that he could plan lessons to prepare for the weeks to come. By so doing: (a) The time could be used productively; and (b) He might get some ideas about how to use ‘slack’ periods in future. Naeem agreed and identified some topics about which he felt that he could be better informed. One of the topics discussed during the planning meeting was ‘sets’. Naeem’s definition of sets was ‘a collection of similar things’ while the textbook defined sets as ‘a collection of well-defined objects’. Although Naeem did not agree with the definition in the book, he revised his concepts as the discussion
8R
9T 10 R 11 T
12 T 13 R 14 T 15 R 16 T 17 R 18 T
A collection of a bag and a pen is not a set. Why? Would you please give the reasons? There is no connection between them. Would you define the ‘connection’? They are not similar things. They do not have similar characteristics. What about these two things, do you see any connection? These are two different things, they cannot make a set. If I say, this is a collection of things which students often use, then would you consider this as a set? yyyA set of students’ items required in learning. Why did you say that this is a set now? I think now we have made it clearer, that they are two different objects but share one purpose. Let’s work on a set of favourite players. Who are your favourite players? And what would be the element of this set? For example, Waseem Akram If I have a different choice; I might not agree with you. It seems more personal? You need to specify here, such as the set of Naeem’s favourite players. If I ask, the set of players who have got 300 wickets, then it will be more general, everybody has the same answer. I should be careful in using language.
Naeem also found some useful information in the textbook regarding defining and naming a set, which he had not considered before. The discussion recorded above reveals some of the difficulties that Naeem was experiencing in mathematics; however, with support, he clarified
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concepts and also planned a series of lessons that consisted of an introduction to the topic, followed by discussions of ‘kinds’ and ‘operations’ of sets. In fact, he became so enthusiastic about using the time available to the full that on one occasion he asked the researcher to stay longer to complete a discussion. Naeem commented We need the environment to ‘push’ [drive] us. You [the researcher] are here and the work has started again, but what will happen if you leave y I agree with you that an individual can play a role in changing the world but that is not easy. We need favourable conditions. At the school nothing is certain. This is the same school, without electricity and facilities. But the important thing is that you are here with your own willingness and sincerity. If I asked my colleague to do the same thing, he would have changed the topic [connected with teaching and learning] within two min. 5.3. Case study 3: developing a moral perspective One day, when she arrived at the school, the researcher saw that students were filing in to the head teacher’s room one by one. She learned that money had been stolen from a student’s bag— something that had been happening on a regular basis—and to catch the thief, the teachers had decided to use the ‘holy water’ ruse. They mixed an egg in a jug of water and told the students that it was special holy water, which would make the thief sick after he drank it. The researcher was concerned that this ‘trick’ would adversely affect the children’s moral development and expressed the following views to teacher Sahib:
When a teacher’s lies to students, it teaches them that it is acceptable to tell lies. A thief’s contempt for authority could increase when he was not caught by this ruse; this would also encourage students to ridicule the teachers. Fear of ‘holy water’ might psychologically disturb some students.
Sahib did not share the researcher’s concern—a position that seemed to reflect the prevailing culture in Pakistan, where one is not encouraged to question authority. However, the researcher’s experience of this culture led her to believe that actions such as these by teachers contributed to low motivation and low morale amongst the students.
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She also noted that it was difficult for Sahib to analyse his own actions and practices, as they were embedded in the social fabric of the school. For example, although she encouraged Sahib to think about the effects of the ‘holy water’ ruse on the students’ mental, physical and emotional health, he did not think that there could be harmful results, as emerges from the piece of conversation that is recorded below. 1R 2T 3R 4T 5R 6T 7R
There must be some effects of this water on the students’ feelings? I do not think so. The water was not very harmful. How do you think the students would be feeling? I do not think they will take it seriously. What would happen if somebody is innocent and feels sick after drinking it? No it won’t happen, nobody is going to be sick. It was just a trick. What do you think about it? I mean, what will be the attitude of the student who has done something wrong? Do you think that student could get more confidence to steal again?
The researcher’s point of view was that a teacher needs to think holistically, i.e., if he aims to improve his students’ confidence in doing mathematics, he also needs to be sensitive to their self-esteem. She also believed that the role of a teacher educator should not be restricted to ‘academic’ matters alone, because teaching entails moral responsibility. When she realised that simply challenging Sahib’s views was not sufficient to change them, the researcher suggested other ways of improving the students’ values, such as telling stories with moral messages, or giving historical examples. Later in the conversation, Sahib did acknowledge that he had not considered the negative implications of his way of dealing with a moral issue and suggested that, to improve the students’ moral perspectives, he could discuss with them the problems that theft causes for the victim and his family. 6. Discussion 6.1. The process of growth and related issues The case studies demonstrate the positive influences for teacher development of school-based
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professional meetings and dialogues. The professional partnerships, with their interplays between reflection and the teacher’s learning, provided the teachers with practical and moral support to utilise their time effectively, to reflect on significant phenomena in their classrooms, and to discuss various ways to improve their professional practices. The first case study suggests that Sahib tried to translate his new ideas into action by contextually analysing their limitations and possibilities, and then planning to change his practise within the realities of his classroom. Although he had considered using some activities that he had learned during his in-service course at the university, he seemed to have planned no more than a routine lesson. However, the innovations that were in the back of his mind, so to speak, came to the fore when the researcher/teacher educator encouraged him to think beyond the textbook methods. Alone, it appeared that he was unable to conceive of actually using innovative methods because of time constraints, the force of his own habitual thinking, and the restrictive working conditions of the school. However, the on-site influence of the researcher/ teacher educator helped him to see what might be possible. For instance, during his last ‘collaborative’ meeting with the researcher, Sahib made a revealing statement: We always have previous experiences of learning and knowledge; they are all hidden in our minds. Thinking deliberately means bringing them out. It is difficult to think in isolation. When one talks with someone he discloses many ideas to himself. However, that person should have the same vision of teaching. The researcher/teacher educator’s presence implicitly reminded Sahib of what he had learned during his in-service course, and also encouraged him to be innovative, while, at the same time, he was conscious of the expectations of the school, limitations in time and resources, and the students’ needs and difficulties, as well as his own established practices. The second case study provides evidence that although the teacher had a commitment to change and improve, he lacked the initiative to do so in the absence of a learning culture and because of lack of support in his school. Working together with the teacher educator directed him into constructive and positive actions. Improvement was possible, and
was realised, both in his understanding of mathematics and in his teaching. In the third case study, it was difficult for the teacher to analyse his own actions and practices, as they were embedded in the social fabric and were inaccessible to him. Here, while he did not consider that the ‘holy water’ ruse might have problematic consequences, the researcher/teacher educator regarded it as a significant instance of the humiliation of children that is entrenched in Pakistani schools. By sharing their perspectives, the teacher was enabled to view the matter from the perspective of the students’ development. This is an important advance, because a teacher not only has the freedom and power to deal with classroom issues almost autonomously, without consulting parents or students, but also plays an important role in his/her students’ moral and social development (see, for example, Clarke, 1995) and thus needs to be very sensitive to the possible consequences. More broadly, the teacher’s change of perspective can be seen as a significant pointer to the possibility of change in the Pakistani context, where most teachers and their supervisors regard respecting the students’ contributions and perspectives as unthinkable. The above case studies also bring to light the question of most teachers’ conceptual understanding of subject and teaching in the Pakistani context. It is clear that they find it difficult to ‘unpack’ and/ or to apply the conceptual underpinnings of mathematical procedures when they make the effort to plan and teach the lessons in coherent and cognitively engaging ways. Moreover, the teachers’ limitations in analysing and questioning their own practices make it difficult for them to deal with or address related issues, such as their students’ moral development, in a professional manner. Since teachers are not in the habit of asking questions and inquiring into issues related to teaching and learning, it is clear that this ‘dominant culture’ hinders them from reflecting on their own practices and, in turn, from learning from their reflections. Specific obstacles include the fact that, at their schools, there are no resources other than the textbooks available to the teachers. Also, the teachers are not aware that their conceptions about mathematics have severe limitations. In these circumstances, it is very likely that teachers will be locked into repetitive cycles of problems and misconceptions, and will find it very difficult to achieve the new goals that they set for themselves as a result of their in-service training experiences.
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In the light of the above, it is important to realise that teachers need support when they are at the initial stages of implementing changes in their schools. For instance, the researcher’s experience showed that these teachers needed explicit input into improving their understanding of mathematics and pedagogy in order to challenge their misconceptions and to support their development. We believe that the experiences that we have discussed above do show that teachers are able to resolve local problems and develop their teaching when they receive practical and moral support from a teacher educator. It was also evident that when the teachers’ needs were satisfied and their practical realities were addressed, the two parties developed a relationship of trust, as evident from the quotation below: We need the environment to ‘push’ [drive] us. You [the teacher educator] are here and the work has started again but what will happen when you leave? y I agree with you that an individual can play a role in changing the world but that is not easy. We need favorable conditions. At the school, nothing is certain. This is the same school, without electricity and facilities. But the important thing is that you are here with your own willingness and sincerity. If I asked my colleague to do the same thing, he would have switched the topic within two minutes [implying that he would switch to another topic, rather than discussing teaching and learning]. These words reflect one teacher’s positive attitude towards the need for, and outcomes of, a collaborative partnership in the face of the constraints and challenges of the school. This indicates that there is a strong need for a theoretical construct, i.e. a co-learning partnership, borrowed from another context, to be adapted to the cultural and practical needs of the context. In view of the realities of public schools in Pakistan, we suggest that a dialogic partnership, as actuated in the interactions between the teachers and researcher/teacher educator in the case studies that have been presented here, is both more suitable and more attainable. 7. Conclusion 7.1. Why collaboration? Experiences such as those that are discussed in the case studies above revealed an important issue that relates to teacher educators taking on a leading role
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in collaborative work with teachers, namely the extent to which the ‘refreshed’ teachers were nevertheless hobbled by conceptual constraints, and, therefore, just how difficult it was for them to think ‘outside the box’ that was shaped by their routine habits. While the guiding principles of ‘working together’ were borrowed from the culture of developed countries where teachers are regarded as ‘inquirers’/learners, our experiences made us realise that the situation in Pakistani public schools differs enormously from that which informs the literature that we consulted. For instance, many teachers in Pakistan almost completely lack school-based professional support; they largely lack subject knowledge; and they are also not in the habit of asking questions and inquiring into issues related to teaching and learning. This kind of culture hindered the teachers from reflecting on their own practise and, in turn, created barriers for them to learn from that reflection. Therefore it was crucial to revisit the theoretical assumptions related to dialogue and interactive relationships in the light of the practical realities with which the teachers and the researcher/ teacher educator had to deal. The teachers needed explicit input in understanding mathematics and pedagogy in order to challenge their misconceptions and improve practise, because reflection alone, without relevant knowledge and skills, would not help them to move beyond their routinised thinking and practices. The teacher educator, who understood the context, felt a huge responsibility in the sense of being aware of the issues and having the relevant knowledge and expertise to address them, in part if not in full. As a result, while trying to be as sensitive as possible to the requirements of dialogue and partnership, she adopted a leading role wherever and whenever it was necessitated by circumstances. Therefore, we suggest that collaborative learning is not necessarily the result of a contribution of equal levels of knowledge and understanding. Rather, it is the achievement of a growing dialogic relationship where a teacher educator and teachers share their perspectives and experiences, with the teacher educator supporting the teachers while being sensitive to, and respecting, their self-esteem. At the same time, it should be realised that this was truly a collaborative rather that a one-way process, because the teacher educator gained important insights into the realities of public schools as well as into the conceptual and practical challenges of teaching mathematics in this context.
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We consider it to be significant that, as the discussion above shows, the participating teachers definitely changed and grew, particularly in regard to making the transition from routine practices to practices that were based on reflection with understanding. The changes came about mainly because they were encouraged and supported to question long-established routines, to analyse new ways of teaching, and to decide on appropriate ways to make changes in their classrooms and schools. As Cooney and Shealy (1997) suggest, reform is the product of an integration of existing realities with new ways of teaching, in which the reform unfolds through practical actions. The support that was provided by the partnership was vital because teachers found it difficult to advance the process of change on their own and felt constrained by the lack of positive reinforcement in their schools. As we noted, the teachers’ behaviour and experiences during the course at the university were very different from how they and their peers usually behaved in their workplaces. The main reason appears to be that, during their time at the university, classroom realities and the expectations of the system did not press upon them. Instead, they could focus on considering their students’ learning in the light of the new ideas that they were encountering. Thus, the university environment was somewhat ‘unreal’. However, the value of collaborative work between a teacher and a teacher educator in a school setting is that workplace realities are never ignored or forgotten. In this regard, the partnership acted as a bridge between the teachers’ learning during the course and their workplace practices. As noted by Pimm (1993) and Breen (1999), it seems to be unproductive to ‘leave teachers alone’ just when they desire to apply new aims and methods. Moreover, as the research showed, developing teaching practices is not independent of context, and learning is a two-way experience. As we have seen, this study shows how teacher educators might help teachers to improve their confidence and understanding; and if knowledge is power—and power always exists in mentoring relationships—then the possibility of power impeding learning is reduced in a partnership. The fact is that power always exists and should not be denied; instead, ways should be found to negotiate it so as to create a trusting relationship, where the partners feel secure and confident, and are able to act in a consultative manner.
As Sally and Monk (2000) note, in developing countries, trying to improve teaching without addressing wider reform in the school can cause additional pressures on teachers, whose professional lives are already very difficult. While this suggests a large-scale initiative that is beyond the scope of interventions such as we have discussed in this paper, Fullan and Hargreaves (1992) suggest that, for teacher development, much can be achieved by focusing on the teachers’ working environment and on teaching itself. Clearly, these are important considerations when trying to bring about reform when there is a restrictive, authoritarian structure, such as in schools in Pakistan. Teacher educators need to think deeply about how to integrate the phase when ‘teachers develop their profession’ in their workplaces (as suggested by Day, 1999) with the phase when ‘the teacher is developed’ at the university (as discussed in Jackson, 1971). In this paper, we have shown collaboration by means of an on-site dialogic partnership can achieve results which, although relatively modest when set against the full scope of the context, are nevertheless significant for individuals in contextualising their ‘academic’ learning, while at the same time assisting them to move away from routinised practices and to think reflectively. In the context of widespread, ingrained conservatism and traditional practices, these advances are not insignificant. Nor are they insignificant in regard to bridging the gap that frequently exists between ‘academic’ experience and learning, on the one hand, and the unsupportive context of the workplace, on the other hand. References Breen, C., 1999. Circling the square: issues and dilemmas concerning teacher transformation. In: Jaworski, B., Wood, T., Dawson, S. (Eds.), Mathematics Teacher Education: Critical International Perspectives. Falmer Press, London. Clarke, B., 1995. Expecting the unexpected: critical incidents in the mathematics classrooms. Unpublished Doctoral Dissertation, University of Wisconsin-Madison. Cobb, P., Wood, T., Yackel, E., 1991. A constructive approach to second grade mathematics. In: Von Glasersfeld, E. (Ed.), Radical Constructivism in Mathematics Education. Kluwer, Academic Publishers, Dortrecht. Cooney, T.J., Shealy, B., 1997. On understanding of the structure of teachers beliefs and their relationship to change. In: Fennema, E., Nelson, B. (Eds.), Mathematics Teacher in Transition. Lawrence Erlbaum Association, New Jersey. Day, C., 1999. Developing Teachers: The Challenges of Lifelong Learning. The Falmer Press, Norwich. Ernest, P., 1991. The Philosophy of Mathematics Education. The Falmer Press, London.
ARTICLE IN PRESS R.F. Mohammad, B. Harlech-Jones / International Journal of Educational Development 28 (2008) 534–545 Ernest, P., 1994. Social constructivism and the psychology of learning of mathematics. In: Ernest, P. (Ed.), Constructing Mathematical Knowledge: Epistemology and Mathematics Education. The Falmer Press, London. Freire, P., 1971. Pedagogy of the Oppressed. Seaview, New York. Frost, D., Durrant, J., 2002. Teachers as leaders: exploring the impact of teacher-led development. School Leadership and Management (2), 143–161. Fullan, M., Hargreaves, A., 1992. Understanding Teacher Development. Cassell, New York. Jackson, W.P., 1971. Old dogs and new tricks: observation on the continuing education of teachers. In: Rubin, L.J. (Ed.), Improving In-service Education: Proposal and Procedures for Change. Allyn and Bacon, Boston. Jaworski, B., 1994. Investigating Mathematics Teaching: A Constructive Enquiry. The Falmer Press, London. Jaworski, B., 2000. The student-researcher/teacher educatorresearcher in the mathematics classroom: co-learning partnership in the mathematics teaching and teaching development. In: Bergsten, C., Dahland, G., Grevholm, B. (Eds.), Research and Action in the Mathematics Classroom. Proceedings of MADIF 2, The 2nd Swedish Mathematics Education Research Seminar. Linkopings Universitet., Linkoping, Sweden, pp. 24–26. Mohammad, F.R., 2002. From theory to practice: an understanding of the implementation of in-service mathematics
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teachers’ learning from university into classroom practice. Unpublished D.Phil. Thesis, University of Oxford. Mohammad, F.R., 2004. Practical constraints upon teacher development in Pakistani schools. Journal of In-service Education 30 (1), 101–114. Mohammad, F.R., Harlech-Jones, B., 2008. The fault is in ourselves: looking at failures in implementation. Compare 38 (1). Pimm, D., 1993. From should to could: reflections on possibilities of mathematics teacher education. For the Learning of Mathematics 13 (2), 22–27. Rogoff, B., 2001. Learning Together: Children and Adults in a School Community. Oxford, Oxford University Press. Sally, J., Monk, M., 2000. Teacher development in South Africa: a critique of the appropriateness of transfer of northern/ western practice. Compare 3 (2). Skemp, R.P., 1976. Relational understanding and instrumental understanding. Mathematics Teaching 77. Van Glaserfeld, E., 1994. In: Paul, E. (Ed.), Constructing Mathematical Knowledge: Epistemology and Mathematical Education. The Falmer Press, London, pp. 24–25. Wagner, J., 1997. The unavoidable intervention of educational research: a framework for reconsidering researcher– practitioner cooperation. Educational Researcher 26 (7), 13–22.
International Journal of Educational Development 28 (2008) 534–545 www.elsevier.com/locate/ijedudev
Working as partners for classroom reform Razia Fakir Mohammad, Brian Harlech-Jones The Aga Khan University, Institute for Educational Development, PO Box 13688, Karachi 75950, Pakistan
Abstract This paper discusses a partnership involving teachers and a teacher educator working together to develop teaching and learning practices in Pakistan. The partnership was established in response to the teachers’ need for support in developing their professional practices within the actual contexts and realities of their schools, after they had attended an in-service training course at a university. Providing case studies, the paper analyses the processes and outcomes of this co-learning partnership. The findings suggest that the collaborative process advances the understanding of teachers’ problems, resolves them on the spot, and provides teachers with the confidence and courage to transcend the constraints of their workplaces while developing professionally. r 2008 Elsevier Ltd. All rights reserved. Keywords: Collaboration; Teaching and learning; Teacher learning; In-service education; Reform
1. Introduction 1.1. Convential practices of teachers and researcher/ teacher educators In this paper, we show that even in the difficult and often discouraging circumstances of Pakistani schools and in spite of severely asymmetrical relationships, it is possible for teachers to change their practices and also improve the quality and outcomes of students’ learning when teacher educators and teachers work together on-site in partnership. Pakistani society is characterised by hierarchical structures in which respect is unidirectional: for example, from weak to strong, from poor to rich, Corresponding author. Tel.: +92 21 6347611;
fax: +92 21 6347616. E-mail address: [email protected] (R.F. Mohammad). 0738-0593/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijedudev.2008.01.006
from student to teacher, and from teacher to head teacher. Not surprisingly, most schools employ traditional modes of teaching that reflect these wider social practices. Students are expected to follow teachers passively, while teachers are compelled to follow the instructions of their school heads and other professional seniors, usually suppressing their individual potentials and eschewing creative thinking. External bodies impose curricula and set textbooks while, en route to the all-important examinations, teachers are expected to follow prescriptions without any deviations. As can be expected, the teaching of mathematics suffers from the same constraints. Generally, mathematics teachers do not appear to think about their tasks creatively or innovatively; they have taught the same rules in the same ways for many years because this is what they are required to do, and they seem to be prepared to go on doing so for the foreseeable future. The students’ achievements
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are graded according to their ability to define or to apply rules in the prescribed ways, with memorisation looming large in classroom practices. They rote-learn rules such as ‘Invert the divisor and multiply’, or ‘(a+b)2 ¼ a2+2ab+b2’ without understanding why they are doing so or what the rules might mean. Teachers, too, are usually evaluated according to their ability to follow traditional practices. Supervisors make their assessments without consultation with the teachers who are affected. Indeed, questioning authority is considered to be disrespectful and will probably adversely affect a teacher’s annual evaluation report. Similarly, teachers evaluate their own teaching from the external perspectives of their students’ success or behaviour. For example, silence in the classroom and the sight of students busily writing in their notebooks are regarded as evidence of good teaching, without reference to any other indicators of successful outcomes. Self-evidently, traditional teaching practices such as these do not encourage teachers to be active, creative, or innovative. Knowledge is regarded as an entity that emanates from the textbook rather than as something that is constructed by teachers or students themselves in the light of their personal backgrounds, emerging needs, experiences, and interactions with contexts. Many writers (for example, Freire, 1971; Skemp, 1976; Van Glaserfeld, 1994) question the effects of a traditional mode of learning that emphasises performance rather than reasoning. For instance, Van Glasersfeld (1994, p.17) states: Reinforcement fosters the repetition of what gets reinforced, regardless of the acting subject’s understanding of the problem that was posed, and of the inherent logic that distinguishes solutions from inadequate responses. Critiquing the traditional view of teaching, Freire (1971) employed the well-known image of children as empty vessels that are filled up with knowledge by the teacher. Similarly, Skemp posited that a traditional view of teaching promotes the practise of rote learning, in which learning is identified with repetition, which can be done without thinking: Certain actions are reinforced as a result of their outcomes, so learning follows action. And what is learnt is action: the cognitive element is small (1979: p.33).
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Thus, traditional learning practices do not encourage students to explore and extend their mathematical knowledge. In addition, the neverending routines of memorising rules and doing long calculations make mathematics a boring and difficult subject for most children. Finally, perhaps the most serious effect is that many students lose their confidence and self-esteem because, as a result of their inability to solve problems themselves, they depend on the teacher to tell them what to do. Unsurprisingly, most teacher-education institutions employ similar ‘top-down’ methods and approaches. Even when they are advocating more creative and innovative ideas and methods, the teacher educators’ approaches are likely to be formal and transmission based. For the teachersin-training, whether in pre-service or in-service courses, the medium is most of the message. The study on which this paper is based comprised part of the doctoral research of one of the authors of this paper (Mohammad, 2002) and focused on the researcher, who was also a teacher educator, working with teachers to facilitate change. The teachers who were the subjects of the research had attended in-service training courses at a university in Pakistan; before their involvement with the university, the teachers—isolated from practical and moral support in their schools—were rigidly constrained by the authority of their schools, taught for the ‘right answers’, and explained facts and rules rather than developing their students’ intellects and thinking abilities. As will be seen, when they widened their perspectives, these teachers felt that they needed support as they tried to develop their teaching in the face of the constraints of their workplaces. 2. Context of the study Although the majority of teacher-education institutions in Pakistan still employ ‘traditional’ approaches and practices, during recent years some institutions have undertaken conceptual shifts and have implemented more innovative methods. This is particularly true of the university at which this study was undertaken, where the approved perspective is learner centredness, which is based on the concept that teaching should accord with a child’s psychological and social orientations to classroom learning (cf. Ernest, 1991, 1994; Cobb et al., 1991; Jaworski, 1994). The teacher educators thus view teachers as facilitators who support and develop their students’
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thinking. In theory, then, teachers are expected both to set meaningful tasks for the students and to analyse the outcomes of the tasks in order to understand how the students construct meanings. Furthermore, teachers are expected to listen to the students, to understand their levels of thinking, and to help them to achieve common agreement about a concept. When teachers support and develop their students’ thinking capabilities in these ways, it is expected that the students will not only assume responsibility for their own learning but will also develop social responsibility. As discussed in Mohammad (2002) and in Mohammad and Harlech-Jones (2008), research suggests that the teachers’ experiences in the educational programmes at this university generally lead to significant changes in their understanding of what mathematics and/or science teaching could and should be. They also gain insights into the limitations of traditional approaches to teaching. However, in spite of the fact that the teachers who participated in this study developed favourable attitudes towards innovative teaching, to the extent that almost all of them considered it to be highly desirable, most of them were unable to make significant changes to their approaches because of conceptual and contextual constraints. Here, it is necessary to emphasise that the head teachers and colleagues in the schools to which these ‘refreshed’ teachers returned did not expect them to adopt new approaches to their teaching, and were certainly not sympathetic to their desires to implement changes. On the contrary, the heads and colleagues simply anticipated that the ‘refreshed’ teachers would return with the ability to be better implementers of the traditional methods. As a result, the teachers reentered work environments that were indifferent at best and sceptical, even antagonistic, at worst. Not surprisingly, this unhelpful environment resulted in significant discrepancies between their aspirations and practices (as discussed in Mohammad and Harlech-Jones, 2008), to the extent that they almost entirely abandoned their efforts to change their practices; inevitably, however, the clash between their desire for change and their failure to practise it generated further pressures and tensions. It was only when the teacher educator was present to support the ‘refreshed’ teachers, providing the only element of support in otherwise unsupportive workplaces, that they were actually able to translate aspects of their aspirations and new knowledge into improved practices.
It is also necessary to emphasise just how great was the gulf between the environment and experiences that the teachers enjoyed at the university on the one hand, and their work contexts on the other hand. While they were attending the in-service course at the university, they were removed from the problems that they faced in their schools; in addition, they enjoyed new and stimulating learning experiences in a comfortable, well facilitated, encouraging, and supportive environment. However, as discussed above, once they were back in their schools, they faced the same, unchanged conditions, which included an enervating lack of support as well as a rigorous emphasis on set routines. Clearly, teachers such as these cannot be effective change agents if they are set adrift without support in their work environments. Here we would add that reforms are more likely to be successful when they are integrated into a comprehensive plan for improvements across the whole system, with all involved agreeing on what is to be done and how. It is clear that if teacher educators are to help to liberate teachers from the constraints of their schools and to support the teachers as they work to effect the changes that they envisage, they (the teacher educators) need to be sensitive to, and understand, the true nature of the difficulties that face the teachers. Furthermore, teacher educators need to appreciate not only how the constraints affect the teachers’ ability to transfer knowledge and ideas from the university to the schoolroom, but also the effects that these constraints have on learning in the classrooms. However, although important, these matters are beyond the scope of this article, which deals only with onsite interventions by an individual teacher educator.
3. Theoretical framework In the study on which this paper is based, the researcher was also a teacher educator at the university at which the teachers—the participants in the study—had taken an in-service training course. After they had completed the course, the researcher partnered the teachers in their workplaces, supporting, encouraging, and dialoguing with them as they tried to implement what they had learned. The guiding principles behind the partnership between the teachers and the researcher/teacher
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educator were that dialogue and reflection on one’s actions would: Enable the participants to understand the realities and difficulties of practise, and Assist them to make improvements. These principles were adopted from the work of Wagner (1997), who used the term ‘co-learning agreement’ to refer to partnership and a dialogic relationship between the participants in research projects. In this partnership, the research is regarded as embodying a significantly interactive, social approach to the educational reform process. As Wagner states: In a co-learning agreement, researchers and practitioners are both participants in processes of education and systems of schooling. Both are engaged in action and reflection. By working together, each might learn something more about the world of the other. Of equal importance, however, each may learn something more about his or her world and its connection to institutions for schooling. (1997, p.16) From the above, it appears that the essential feature of the co-learning agreement is that all partners are learners. This means that teachers do not work under external control or imposed authority; rather they commit themselves to learn as equals with the researcher, with all parties sharing an agenda and respecting each other’s goals. Jaworski (2000, p.6) extends the perspective to apply specifically to the relationship between teachers and teacher educators, stating that, ‘A colearning partnership implies an explicit arrangement agreed between participants’. Here, it is important to recognise that the quality of the relationship is central to achieving a collaborative culture of learning; also, that a commitment to learning together fosters shared understanding through mutual dialogue, leading the participants to achieve ownership and confidence in creating knowledge. Similarly, in her study of collaborative partnerships between parents and teachers, Rogoff (2001) states that learning through collaboration requires respect for all of the participants’ ideas, views, and opinions. Differences in views are regarded as resources rather than stumbling blocks, and as enhanced opportunities for learning. Conflicts and differences of opinion should be dealt with by discussion and problem solving in trusting, nonjudgmental environments.
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Although teachers are often depicted as uncreative and passive, this literature suggests that teachers are (or can be) self-aware agents of their own learning, with the capacity to reflect. A culture of collaboration, focusing explicitly on nurturing teachers’ thinking and practices, can be promoted by both teachers and researchers or teacher educators committing themselves to learning. This commitment promotes mutual dialogue, the product of self-reflection and/or a trusting relationship. The result is that external control and authority over teachers’ learning are reduced, while responsibility for self-improvement intensifies. Thus the ideal situation, as depicted here, is one in which teacher and teacher educator relate to each other as equal partners in a symmetrical relationship, contributing each learning equally from the other. However, in most public schools in Pakistan, in the short- to medium term it would be difficult if not impossible to achieve this sort of relationship, because most teachers regard teacher educators and/or supervisors as professional superiors. This inclines the teachers to adopt attitudes of deference and dependence, and makes them less inclined to exercise initiative (Mohammad, 2004). Selfevidently, under these conditions teachers feel neither sufficiently autonomous nor adequately motivated to initiate or sustain their own professional development. Describing how, in these situations, teachers experience a lack of professional autonomy and have a sense of being isolated and powerless when it comes to promoting change, Frost and Durrant (2002, p.144) observe that, What really needs to be emphasised is not autonomy, but the capacity of individual teachers to make a real difference, in other words to exercise leadership and to experience the satisfaction of having a significant impact on professional practise and ultimately on the quality and outcomes of students’ learning. This is the thrust of our article—namely, that while ‘autonomy’ is unrealistic in such difficult contexts, it is possible for teachers to change their own practices and also improve ‘the quality and outcomes of students’ learning’. While these might be viewed as modest outcomes under more fortunate circumstances, they are considerable and significant advances in the situations that are depicted here.
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In the case studies that are presented here, we show that significant achievements were possible, given the context, even although the relationships between the teacher educator and the teachers were neither equal nor symmetrical. It is important to emphasise that a journey always begins with a single step—a step that is often made into uneven and ‘asymmetrical’ terrain. Through dialogue and support, and by reducing the distance between the participants, the teachers were able to translate some of their new aspirations and knowledge into practise. We wish to re-emphasise that, small as these achievements might appear to be within the overall constraints of a rigid and tradition-bound system, for the individuals concerned they were nevertheless substantial advances, opening windows into new possibilities. 4. The design of the study As already stated, the study on which this paper is based comprised part of the doctoral research of one of the authors of this paper (Mohammad, 2002) and focused on a researcher, who was also a teacher educator, working with teachers to facilitate change. It also examined processes and issues that are related to collaborative partnerships. The nature of this research was reflective and participatory, with the researcher having two roles. The first was as a teacher educator assisting teachers to convert their learning into practise. The second role, in the over-arching position of researcher, was to analyse processes of teacher development. As a teacher educator, the researcher supported the teachers in trying out new ideas and helped them to gain insights into their teaching. As a researcher, she investigated the processes by which the teachers developed their teaching in collaboration with her. 4.1. Data collection Three teachers collaborated in this study, which lasted for 12 weeks, during which the researcher met with each teacher at least once every week. The researcher adopted interpretive research methods, collecting data by audio-recorded conversations during pre- and post-observation meetings; making field notes during teaching sessions and while the participants discussed their learning with her; collecting the teachers’ written comments; and compiling her own reflective journal entries. During this period, the participants were involved in
planning lessons that embodied their new aims for effective teaching, as well as implementing their plans and reflecting on the outcomes and issues that arose. 4.2. Method of analysis Initial analysis entailed reading the data from visits to the teachers in their schools and, for each meeting, writing an analytical memo that described the collaborative work that had taken place, with particular reference to pre- and post-observations. For example, the data included descriptions of how the collaborators initiated their work, what the teachers said or did, how the researcher reacted, and ongoing observations about the limitations or successes. During the researcher’s scrutiny of these analytical memos, a wide range of examples, which provided evidence of the teacher’s learning were highlighted in tabulated form. Items were clustered together to form categories describing one or other aspect of the learning that was taking place. 5. Working together examples and outcomes In the section, from the wider set of findings we present case studies that are representative of the teachers’ learning. As will be seen, during the collaborative work in the schools, the teachers made concerted efforts to implement new ideas that reflected what they had learned during their course at the university. Analysis showed that, amongst other responses, the teachers were thinking through and modifying or re-modifying their lesson plans, analysing students’ responses, and improving their mathematical knowledge. Note: In these examples, whenever we refer to ‘the researcher’, it should be remembered that in the school contexts, the researcher was also a teacher educator. 5.1. Case study 1: developing a practical understanding of new strategies In this study, the teacher, named Sahib, initially intended to teach the topic ‘circles’ through a practical activity that he had learned during the in-service teacher education programme. However, for a variety of reasons, such as lack of time and the forthcoming examinations, he seemed to have decided to omit the practical activity and teach in
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a routine manner. His main concern was that developing conceptual understanding was unnecessary to pass examinations; as he said: I have to complete the syllabus before the final examination. A teacher does not need to bother about their [students’] learning; it depends on students how much they want to ‘absorb’. We check their memory and skills of drawing in the examination; conceptual clarification is not a basic requirement of the examination. If we ‘check’ [assess] their concepts, none of them will pass the examination. Sahib’s statement seemed to indicate that he adhered to a transmission view of teaching, despite his apparent appreciation of the value of practical activities. The teacher educator encouraged him to imagine himself in a teaching situation at a school with a more favourable environment. Under those conditions, how would he teach the lesson while incorporating a practical activity? Sahib responded, ‘I have not tried out any practical activity in teaching the topic previously, although I have always been thinking about teaching it differently’. It appeared that, although he had talked about it, Sahib had not considered actually integrating his new learning into his teaching practise. When the teacher educator asked him to give an example of a practical activity that could apply to the topic of the lesson, Sahib described an activity related to ‘circles’ that he had experienced during the university course, when the course participants were asked to stand at an equal distance from a fixed point holding a rope. Sahib said that this activity would not only be a practical demonstration of ‘circles’ but would encourage the students to explore the concept for themselves. However, he cautioned that, ‘I need a full period to take the students outside the classroom and to ask them to arrange themselves. Getting a rope is difficult, too. [After all this,] I do not think that any time will be left for written work.’ These words show how difficult Sahib found it to integrate an activity into his lesson; in particular, he thought that it would be difficult to obtain materials, as well as to find the time and space. His statement also shows how much he struggled to accept new ideas while his thinking was still largely rooted in the ‘traditional’ transmission view of teaching and learning. However, his collaboration
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with the researcher motivated him to try out a new method; as he said: As you are also here, I should try this method in the classroom and you can tell me how I can improve in the activity.’ From this point onwards, he thought more creatively, saying that he could ask the students to stretch out their arms to form a circle themselves. Sahib commented, ‘I could do this activity inside the classroom in the available space by calling some students. It could be a small circle, and if there is some space between them, I will tell them to imagine no gap. Later analysis of his teaching showed that his thinking did not stop where the discussion with the researcher ended. Sahib continued to reflect on new ideas and their practicality in the realities of the classroom. In evaluating his teaching, he acknowledged that the partnership had helped him to extend his thinking by accessing new ideas and activities, and by discussing how they might be applied: We always have previous experiences of learning and knowledge; they are all hidden in our minds. Thinking deliberately means bringing them out. It is difficult to think in isolation. When one talks with someone, he discloses many ideas to himself. However, that person should have the same vision of teaching. A lesson on ‘equations’ provides another example of a teacher learning about the subject and his students’ thinking processes, as well as developing an understanding of the students’ responses. Sahib used stories to increase his students’ participation and to move beyond the text book–for example, he asked his students, ‘Somebody has thought of a number, multiplied it by three, subtracted one, and got five. Tell me the number he has thought of’. Aiming to involve students in the lesson, he invited some of them to use the blackboard to explain the methods that they had used to solve equations. One student had devised his own method to solve the equation x 3–1 ¼ 5 and wrote 2 3 ¼ 6–1 ¼ 5 on the board. Here, the student first multiplied 2 by 3, getting 6, and then subtracted 1 to get 5. However, although the student provided a correct answer, the teacher did not accept it because he wanted an explanation that accorded with the one in the textbook. In the feedback session, Sahib admitted that he was not happy with the lesson because he had not succeeded in improving the students’ level of participation. Here, he revealed the tension that he
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felt between reconciling new approaches with traditional approaches that were based on the textbook. It also suggested that he did not understand how his students might be thinking, the reason being that he did not invite them to explain why they reached certain conclusions. Although, at first, Sahib found it difficult to be to be self-critical and analytical, the evidence suggests that the post-observation discussions helped him to develop reflective thinking. For instance, the discussion that focused on the students’ solutions and his interpretation of them helped him to realise that he had not paid enough attention to their answers. Sahib observed, ‘I think I was not able to understand why the students were confused. It is a fact that when a teacher is not used to getting different answers, he might be confused in dealing with them, and cannot satisfy the students.’
proceeded, as can be seen in the record of the exchange of views below: T ¼ The teacher (Naeem) R ¼ The researcher 1T 2R 3T 4R 5T 6R 7T
5.2. Case study 2: using time effectively and taking responsibility for one’s own actions This study is taken from partnership meetings at the beginning of the new school year. When the researcher arrived at the school, she noticed that classes were not in session and the students were roaming around the premises. Because the head teacher had not yet drawn up the new timetable, the teachers did not have a schedule of classes and were enjoying ‘free’ time. When asked about his duties during this ‘interim period’, the participant-teacher, Naeem, replied, Before you arrived, I was just chatting with the other teachers. There is no work. Teachers have to come to school regularly, because they do record our attendance, but teaching has not begun yet. It is a relief time for us. y We read newspapers, discuss politics, and nothing else. The researcher suggested to Naeem that he could plan lessons to prepare for the weeks to come. By so doing: (a) The time could be used productively; and (b) He might get some ideas about how to use ‘slack’ periods in future. Naeem agreed and identified some topics about which he felt that he could be better informed. One of the topics discussed during the planning meeting was ‘sets’. Naeem’s definition of sets was ‘a collection of similar things’ while the textbook defined sets as ‘a collection of well-defined objects’. Although Naeem did not agree with the definition in the book, he revised his concepts as the discussion
8R
9T 10 R 11 T
12 T 13 R 14 T 15 R 16 T 17 R 18 T
A collection of a bag and a pen is not a set. Why? Would you please give the reasons? There is no connection between them. Would you define the ‘connection’? They are not similar things. They do not have similar characteristics. What about these two things, do you see any connection? These are two different things, they cannot make a set. If I say, this is a collection of things which students often use, then would you consider this as a set? yyyA set of students’ items required in learning. Why did you say that this is a set now? I think now we have made it clearer, that they are two different objects but share one purpose. Let’s work on a set of favourite players. Who are your favourite players? And what would be the element of this set? For example, Waseem Akram If I have a different choice; I might not agree with you. It seems more personal? You need to specify here, such as the set of Naeem’s favourite players. If I ask, the set of players who have got 300 wickets, then it will be more general, everybody has the same answer. I should be careful in using language.
Naeem also found some useful information in the textbook regarding defining and naming a set, which he had not considered before. The discussion recorded above reveals some of the difficulties that Naeem was experiencing in mathematics; however, with support, he clarified
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concepts and also planned a series of lessons that consisted of an introduction to the topic, followed by discussions of ‘kinds’ and ‘operations’ of sets. In fact, he became so enthusiastic about using the time available to the full that on one occasion he asked the researcher to stay longer to complete a discussion. Naeem commented We need the environment to ‘push’ [drive] us. You [the researcher] are here and the work has started again, but what will happen if you leave y I agree with you that an individual can play a role in changing the world but that is not easy. We need favourable conditions. At the school nothing is certain. This is the same school, without electricity and facilities. But the important thing is that you are here with your own willingness and sincerity. If I asked my colleague to do the same thing, he would have changed the topic [connected with teaching and learning] within two min. 5.3. Case study 3: developing a moral perspective One day, when she arrived at the school, the researcher saw that students were filing in to the head teacher’s room one by one. She learned that money had been stolen from a student’s bag— something that had been happening on a regular basis—and to catch the thief, the teachers had decided to use the ‘holy water’ ruse. They mixed an egg in a jug of water and told the students that it was special holy water, which would make the thief sick after he drank it. The researcher was concerned that this ‘trick’ would adversely affect the children’s moral development and expressed the following views to teacher Sahib:
When a teacher’s lies to students, it teaches them that it is acceptable to tell lies. A thief’s contempt for authority could increase when he was not caught by this ruse; this would also encourage students to ridicule the teachers. Fear of ‘holy water’ might psychologically disturb some students.
Sahib did not share the researcher’s concern—a position that seemed to reflect the prevailing culture in Pakistan, where one is not encouraged to question authority. However, the researcher’s experience of this culture led her to believe that actions such as these by teachers contributed to low motivation and low morale amongst the students.
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She also noted that it was difficult for Sahib to analyse his own actions and practices, as they were embedded in the social fabric of the school. For example, although she encouraged Sahib to think about the effects of the ‘holy water’ ruse on the students’ mental, physical and emotional health, he did not think that there could be harmful results, as emerges from the piece of conversation that is recorded below. 1R 2T 3R 4T 5R 6T 7R
There must be some effects of this water on the students’ feelings? I do not think so. The water was not very harmful. How do you think the students would be feeling? I do not think they will take it seriously. What would happen if somebody is innocent and feels sick after drinking it? No it won’t happen, nobody is going to be sick. It was just a trick. What do you think about it? I mean, what will be the attitude of the student who has done something wrong? Do you think that student could get more confidence to steal again?
The researcher’s point of view was that a teacher needs to think holistically, i.e., if he aims to improve his students’ confidence in doing mathematics, he also needs to be sensitive to their self-esteem. She also believed that the role of a teacher educator should not be restricted to ‘academic’ matters alone, because teaching entails moral responsibility. When she realised that simply challenging Sahib’s views was not sufficient to change them, the researcher suggested other ways of improving the students’ values, such as telling stories with moral messages, or giving historical examples. Later in the conversation, Sahib did acknowledge that he had not considered the negative implications of his way of dealing with a moral issue and suggested that, to improve the students’ moral perspectives, he could discuss with them the problems that theft causes for the victim and his family. 6. Discussion 6.1. The process of growth and related issues The case studies demonstrate the positive influences for teacher development of school-based
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professional meetings and dialogues. The professional partnerships, with their interplays between reflection and the teacher’s learning, provided the teachers with practical and moral support to utilise their time effectively, to reflect on significant phenomena in their classrooms, and to discuss various ways to improve their professional practices. The first case study suggests that Sahib tried to translate his new ideas into action by contextually analysing their limitations and possibilities, and then planning to change his practise within the realities of his classroom. Although he had considered using some activities that he had learned during his in-service course at the university, he seemed to have planned no more than a routine lesson. However, the innovations that were in the back of his mind, so to speak, came to the fore when the researcher/teacher educator encouraged him to think beyond the textbook methods. Alone, it appeared that he was unable to conceive of actually using innovative methods because of time constraints, the force of his own habitual thinking, and the restrictive working conditions of the school. However, the on-site influence of the researcher/ teacher educator helped him to see what might be possible. For instance, during his last ‘collaborative’ meeting with the researcher, Sahib made a revealing statement: We always have previous experiences of learning and knowledge; they are all hidden in our minds. Thinking deliberately means bringing them out. It is difficult to think in isolation. When one talks with someone he discloses many ideas to himself. However, that person should have the same vision of teaching. The researcher/teacher educator’s presence implicitly reminded Sahib of what he had learned during his in-service course, and also encouraged him to be innovative, while, at the same time, he was conscious of the expectations of the school, limitations in time and resources, and the students’ needs and difficulties, as well as his own established practices. The second case study provides evidence that although the teacher had a commitment to change and improve, he lacked the initiative to do so in the absence of a learning culture and because of lack of support in his school. Working together with the teacher educator directed him into constructive and positive actions. Improvement was possible, and
was realised, both in his understanding of mathematics and in his teaching. In the third case study, it was difficult for the teacher to analyse his own actions and practices, as they were embedded in the social fabric and were inaccessible to him. Here, while he did not consider that the ‘holy water’ ruse might have problematic consequences, the researcher/teacher educator regarded it as a significant instance of the humiliation of children that is entrenched in Pakistani schools. By sharing their perspectives, the teacher was enabled to view the matter from the perspective of the students’ development. This is an important advance, because a teacher not only has the freedom and power to deal with classroom issues almost autonomously, without consulting parents or students, but also plays an important role in his/her students’ moral and social development (see, for example, Clarke, 1995) and thus needs to be very sensitive to the possible consequences. More broadly, the teacher’s change of perspective can be seen as a significant pointer to the possibility of change in the Pakistani context, where most teachers and their supervisors regard respecting the students’ contributions and perspectives as unthinkable. The above case studies also bring to light the question of most teachers’ conceptual understanding of subject and teaching in the Pakistani context. It is clear that they find it difficult to ‘unpack’ and/ or to apply the conceptual underpinnings of mathematical procedures when they make the effort to plan and teach the lessons in coherent and cognitively engaging ways. Moreover, the teachers’ limitations in analysing and questioning their own practices make it difficult for them to deal with or address related issues, such as their students’ moral development, in a professional manner. Since teachers are not in the habit of asking questions and inquiring into issues related to teaching and learning, it is clear that this ‘dominant culture’ hinders them from reflecting on their own practices and, in turn, from learning from their reflections. Specific obstacles include the fact that, at their schools, there are no resources other than the textbooks available to the teachers. Also, the teachers are not aware that their conceptions about mathematics have severe limitations. In these circumstances, it is very likely that teachers will be locked into repetitive cycles of problems and misconceptions, and will find it very difficult to achieve the new goals that they set for themselves as a result of their in-service training experiences.
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In the light of the above, it is important to realise that teachers need support when they are at the initial stages of implementing changes in their schools. For instance, the researcher’s experience showed that these teachers needed explicit input into improving their understanding of mathematics and pedagogy in order to challenge their misconceptions and to support their development. We believe that the experiences that we have discussed above do show that teachers are able to resolve local problems and develop their teaching when they receive practical and moral support from a teacher educator. It was also evident that when the teachers’ needs were satisfied and their practical realities were addressed, the two parties developed a relationship of trust, as evident from the quotation below: We need the environment to ‘push’ [drive] us. You [the teacher educator] are here and the work has started again but what will happen when you leave? y I agree with you that an individual can play a role in changing the world but that is not easy. We need favorable conditions. At the school, nothing is certain. This is the same school, without electricity and facilities. But the important thing is that you are here with your own willingness and sincerity. If I asked my colleague to do the same thing, he would have switched the topic within two minutes [implying that he would switch to another topic, rather than discussing teaching and learning]. These words reflect one teacher’s positive attitude towards the need for, and outcomes of, a collaborative partnership in the face of the constraints and challenges of the school. This indicates that there is a strong need for a theoretical construct, i.e. a co-learning partnership, borrowed from another context, to be adapted to the cultural and practical needs of the context. In view of the realities of public schools in Pakistan, we suggest that a dialogic partnership, as actuated in the interactions between the teachers and researcher/teacher educator in the case studies that have been presented here, is both more suitable and more attainable. 7. Conclusion 7.1. Why collaboration? Experiences such as those that are discussed in the case studies above revealed an important issue that relates to teacher educators taking on a leading role
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in collaborative work with teachers, namely the extent to which the ‘refreshed’ teachers were nevertheless hobbled by conceptual constraints, and, therefore, just how difficult it was for them to think ‘outside the box’ that was shaped by their routine habits. While the guiding principles of ‘working together’ were borrowed from the culture of developed countries where teachers are regarded as ‘inquirers’/learners, our experiences made us realise that the situation in Pakistani public schools differs enormously from that which informs the literature that we consulted. For instance, many teachers in Pakistan almost completely lack school-based professional support; they largely lack subject knowledge; and they are also not in the habit of asking questions and inquiring into issues related to teaching and learning. This kind of culture hindered the teachers from reflecting on their own practise and, in turn, created barriers for them to learn from that reflection. Therefore it was crucial to revisit the theoretical assumptions related to dialogue and interactive relationships in the light of the practical realities with which the teachers and the researcher/ teacher educator had to deal. The teachers needed explicit input in understanding mathematics and pedagogy in order to challenge their misconceptions and improve practise, because reflection alone, without relevant knowledge and skills, would not help them to move beyond their routinised thinking and practices. The teacher educator, who understood the context, felt a huge responsibility in the sense of being aware of the issues and having the relevant knowledge and expertise to address them, in part if not in full. As a result, while trying to be as sensitive as possible to the requirements of dialogue and partnership, she adopted a leading role wherever and whenever it was necessitated by circumstances. Therefore, we suggest that collaborative learning is not necessarily the result of a contribution of equal levels of knowledge and understanding. Rather, it is the achievement of a growing dialogic relationship where a teacher educator and teachers share their perspectives and experiences, with the teacher educator supporting the teachers while being sensitive to, and respecting, their self-esteem. At the same time, it should be realised that this was truly a collaborative rather that a one-way process, because the teacher educator gained important insights into the realities of public schools as well as into the conceptual and practical challenges of teaching mathematics in this context.
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We consider it to be significant that, as the discussion above shows, the participating teachers definitely changed and grew, particularly in regard to making the transition from routine practices to practices that were based on reflection with understanding. The changes came about mainly because they were encouraged and supported to question long-established routines, to analyse new ways of teaching, and to decide on appropriate ways to make changes in their classrooms and schools. As Cooney and Shealy (1997) suggest, reform is the product of an integration of existing realities with new ways of teaching, in which the reform unfolds through practical actions. The support that was provided by the partnership was vital because teachers found it difficult to advance the process of change on their own and felt constrained by the lack of positive reinforcement in their schools. As we noted, the teachers’ behaviour and experiences during the course at the university were very different from how they and their peers usually behaved in their workplaces. The main reason appears to be that, during their time at the university, classroom realities and the expectations of the system did not press upon them. Instead, they could focus on considering their students’ learning in the light of the new ideas that they were encountering. Thus, the university environment was somewhat ‘unreal’. However, the value of collaborative work between a teacher and a teacher educator in a school setting is that workplace realities are never ignored or forgotten. In this regard, the partnership acted as a bridge between the teachers’ learning during the course and their workplace practices. As noted by Pimm (1993) and Breen (1999), it seems to be unproductive to ‘leave teachers alone’ just when they desire to apply new aims and methods. Moreover, as the research showed, developing teaching practices is not independent of context, and learning is a two-way experience. As we have seen, this study shows how teacher educators might help teachers to improve their confidence and understanding; and if knowledge is power—and power always exists in mentoring relationships—then the possibility of power impeding learning is reduced in a partnership. The fact is that power always exists and should not be denied; instead, ways should be found to negotiate it so as to create a trusting relationship, where the partners feel secure and confident, and are able to act in a consultative manner.
As Sally and Monk (2000) note, in developing countries, trying to improve teaching without addressing wider reform in the school can cause additional pressures on teachers, whose professional lives are already very difficult. While this suggests a large-scale initiative that is beyond the scope of interventions such as we have discussed in this paper, Fullan and Hargreaves (1992) suggest that, for teacher development, much can be achieved by focusing on the teachers’ working environment and on teaching itself. Clearly, these are important considerations when trying to bring about reform when there is a restrictive, authoritarian structure, such as in schools in Pakistan. Teacher educators need to think deeply about how to integrate the phase when ‘teachers develop their profession’ in their workplaces (as suggested by Day, 1999) with the phase when ‘the teacher is developed’ at the university (as discussed in Jackson, 1971). In this paper, we have shown collaboration by means of an on-site dialogic partnership can achieve results which, although relatively modest when set against the full scope of the context, are nevertheless significant for individuals in contextualising their ‘academic’ learning, while at the same time assisting them to move away from routinised practices and to think reflectively. In the context of widespread, ingrained conservatism and traditional practices, these advances are not insignificant. Nor are they insignificant in regard to bridging the gap that frequently exists between ‘academic’ experience and learning, on the one hand, and the unsupportive context of the workplace, on the other hand. References Breen, C., 1999. Circling the square: issues and dilemmas concerning teacher transformation. In: Jaworski, B., Wood, T., Dawson, S. (Eds.), Mathematics Teacher Education: Critical International Perspectives. Falmer Press, London. Clarke, B., 1995. Expecting the unexpected: critical incidents in the mathematics classrooms. Unpublished Doctoral Dissertation, University of Wisconsin-Madison. Cobb, P., Wood, T., Yackel, E., 1991. A constructive approach to second grade mathematics. In: Von Glasersfeld, E. (Ed.), Radical Constructivism in Mathematics Education. Kluwer, Academic Publishers, Dortrecht. Cooney, T.J., Shealy, B., 1997. On understanding of the structure of teachers beliefs and their relationship to change. In: Fennema, E., Nelson, B. (Eds.), Mathematics Teacher in Transition. Lawrence Erlbaum Association, New Jersey. Day, C., 1999. Developing Teachers: The Challenges of Lifelong Learning. The Falmer Press, Norwich. Ernest, P., 1991. The Philosophy of Mathematics Education. The Falmer Press, London.
ARTICLE IN PRESS R.F. Mohammad, B. Harlech-Jones / International Journal of Educational Development 28 (2008) 534–545 Ernest, P., 1994. Social constructivism and the psychology of learning of mathematics. In: Ernest, P. (Ed.), Constructing Mathematical Knowledge: Epistemology and Mathematics Education. The Falmer Press, London. Freire, P., 1971. Pedagogy of the Oppressed. Seaview, New York. Frost, D., Durrant, J., 2002. Teachers as leaders: exploring the impact of teacher-led development. School Leadership and Management (2), 143–161. Fullan, M., Hargreaves, A., 1992. Understanding Teacher Development. Cassell, New York. Jackson, W.P., 1971. Old dogs and new tricks: observation on the continuing education of teachers. In: Rubin, L.J. (Ed.), Improving In-service Education: Proposal and Procedures for Change. Allyn and Bacon, Boston. Jaworski, B., 1994. Investigating Mathematics Teaching: A Constructive Enquiry. The Falmer Press, London. Jaworski, B., 2000. The student-researcher/teacher educatorresearcher in the mathematics classroom: co-learning partnership in the mathematics teaching and teaching development. In: Bergsten, C., Dahland, G., Grevholm, B. (Eds.), Research and Action in the Mathematics Classroom. Proceedings of MADIF 2, The 2nd Swedish Mathematics Education Research Seminar. Linkopings Universitet., Linkoping, Sweden, pp. 24–26. Mohammad, F.R., 2002. From theory to practice: an understanding of the implementation of in-service mathematics
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teachers’ learning from university into classroom practice. Unpublished D.Phil. Thesis, University of Oxford. Mohammad, F.R., 2004. Practical constraints upon teacher development in Pakistani schools. Journal of In-service Education 30 (1), 101–114. Mohammad, F.R., Harlech-Jones, B., 2008. The fault is in ourselves: looking at failures in implementation. Compare 38 (1). Pimm, D., 1993. From should to could: reflections on possibilities of mathematics teacher education. For the Learning of Mathematics 13 (2), 22–27. Rogoff, B., 2001. Learning Together: Children and Adults in a School Community. Oxford, Oxford University Press. Sally, J., Monk, M., 2000. Teacher development in South Africa: a critique of the appropriateness of transfer of northern/ western practice. Compare 3 (2). Skemp, R.P., 1976. Relational understanding and instrumental understanding. Mathematics Teaching 77. Van Glaserfeld, E., 1994. In: Paul, E. (Ed.), Constructing Mathematical Knowledge: Epistemology and Mathematical Education. The Falmer Press, London, pp. 24–25. Wagner, J., 1997. The unavoidable intervention of educational research: a framework for reconsidering researcher– practitioner cooperation. Educational Researcher 26 (7), 13–22.