the power of professional learning communities

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Education As Change, Volume 17, No. 1, July 2013, pp. 5–18

ISSN: Print 1682-3206, Online 1947-9417 © 2013 The University of Johannesburg DOI: 10.1080/16823206.2013.773929

The power of professional learning communities

Karin Brodie

University of Witwatersrand

Abstract

In this paper I share some key principles and examples from the Data Informed Practice Improvement Project. The project develops an innovative model of mathematics teacher development, with three main strands: teachers work with data from their classrooms, they use this data to understand and engage with learner errors in mathematics, and they do this collectively in professional learning communities, with facilitation from members of the project team. I describe each of these strands and present three examples that show how the strands work together to support teacher learning in professional communities. These examples illuminate a key achievement of the project: a focus on learner errors in professional learning communities can develop powerful conceptual knowledge of mathematics among teachers at the same time as developing teachers’ knowledge for teaching and teaching practices.

Keywords: professional learning communities, teacher learning, learner errors

Introduction

The current view of mathematics teacher professional development is that professional development programmes that focus on teacher learning in and from practice are more likely to result in lasting changes in teaching practices (Borko 2004; Kazemi & Hubbard 2008). Six key characteristics of successful professional development programmes have been identified: they are long term and developmental; they focus on artifacts of practice such as student thinking, tasks and instructional practices; they use actual classroom data; they encourage design and reflection on the part of teachers; they are job-embedded (school-based) and therefore blur the boundaries between teaching and learning about teaching; and they promote the development of professional learning communities (Borko 2004; Jaworski 2008; Katz, Earl & Ben Jaafar 2009; Kazemi & Hubbard 2008). The effectiveness of such professional development programmes is believed to lie in supporting teacher collaboration in order to produce shared understanding, a focus on curriculum and instruction, and being of sufficient duration to ensure progressive gains in knowledge (Little 1993).

The Data Informed Practice Improvement Project takes all six of the above criteria into account. The key strands of our project are working with classroom data in the form of learners’ mathematical errors in professional learning communities. These three strands bring the six characteristics above together and create powerful learning for mathematics teachers, both in terms of their own conceptual knowledge of mathematics, and how they might teach mathematics more conceptually in classrooms. In this paper, I use some results from our project to engage with two current issues in the South African teacher-development landscape: how do in-service teachers best develop their conceptual knowledge of mathematics and how to create professional learning communities so that they provide spaces for teacher learning and development. Although our focus is on mathematics teacher development, our

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work does provide lessons for professional learning communities more broadly, and I will conclude the paper with some of these lessons.

Professional Learning Communities

The term ‘professional learning communities’ usually refers to teachers ‘critically interrogating their practice in ongoing, reflective and collaborative ways’ in order to promote and enhance student learning (Stoll & Louis 2008:2). For Katz and Earl (2010:28), professional learning communities are ‘fundamentally about learning – learning for pupils as well as learning for teachers, learning for leaders, and learning for schools’ and for Louis and Marks (1998:535) they support teachers to ‘coalesce around a shared vision of what counts for high-quality teaching and learning and begin to take collective responsibility for the students they teach’. While these definitions capture the essence of the idea – professionals engaged in ongoing learning for the benefits of their ‘clients’ – they are also relatively broad and allow for a range of meanings and consequences, some of which are contradictory (Hargreaves 2008). So, clearer definitions are necessary to indicate exactly how the term is being used.

Stoll and Louis (2008:p.3) review the literature and present a definition that highlights key aspects. The term ‘professional learning community’ suggests that the focus is not only on individual teachers’ learning but on collective professional learning within the context of a cohesive group that works with an ethic of interpersonal care, which permeates the life of teachers, students and school leaders. The collective and caring nature of professional learning communities is important because individual teachers learning from conventional teacher development programmes do not necessarily make for coherent or sustained changes for learners. Also important are the contents of the learning and the methods that members of the professional learning community use to engage in learning. Katz, Earl and Ben Jafaar (2009) identify four key characteristics of successful professional learning communities: (1) they have a challenging focus; (2) they create productive relationships through trust; (3) they collaborate for joint benefit, which requires ‘moderate professional conflict’, although not personal conflict; and (4) they engage in rigorous enquiry. For Katz et al successful learning communities are those that challenge their members to reconsider taken-for-granted assumptions, because this is the only way that genuine learning can happen. This is why professional conflict is to be encouraged, as it promotes rigorous inquiry and growth. In order for professional conflict not to become personal conflict, an ethic of care and trust is necessary. McLaughlin and Talbert (2008) distinguish between teacher communities that maintain traditional practices and the status quo, and those that re-invent and re-invigorate practice.

While collaboration, rigorous inquiry, trust and care are necessary, they are not sufficient for successful professional learning communities. A crucial element is the focus, or content – what the community collaborates to inquire into, or what is being learned. The research suggests that in order to have the greatest effect on student learning, the focus must relate to the instructional core – the relationship between teacher, student and content (City, Elmore, Fiarman, & Teitel 2009) and involve a problem of practice based on learner needs (Boudett, City, & Murnane 2008). For example, students might be able to solve simple, single-step problems in mathematics, but cannot go further to solve multi-step problems (learner need). If teachers choose this as their focus, they need to work out why learners struggle with multi-step problems, what in their current teaching has not helped learners to solve multi-step problems (problem of practice), and how they might shift their teaching to help learners (Boudett, et al. 2008). A key question for professional learning communities is how do they establish a ‘clear, defensible focus’ (Katz, et al. 2009:23), that is ‘right, shared and understood’ (Katz, et al. 2009:47). The clear focus on learners’ learning needs informs teachers’ learning needs.

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The role of data

A clear and defensible focus or a problem of practice needs to be established on the basis of data. Such data can and should come from a wide range of sources – national or international test results, teachers’ own tests, interviews with learners, learners’ work and classroom observations. The use of data provides a means whereby teachers can identify real learner needs, rather than working only with their own intuitions1 as to what learners need. Data might confirm what teachers know to be the problem, or they might suggest a problem that teachers do not know about.

An important distinction needs to be made here between evidence-based practice and data-informed practice. Evidence-based practice is associated with a movement that argues that only research-based evidence is good enough to inform what teachers need to learn. Such an approach ignores the relevance of school and classroom-level data and teachers’ own knowledge of their learners. It also expects that teachers read research, which we know is not always the case. Data-informed professional development suggests that teachers themselves, with some expert guidance, can and should interpret the full range of data that is available to them and that their interpretations will suggest areas of learners’ learning needs and hence teachers’ learning needs (Boudett, et al. 2008; Katz, et al. 2009).

But the data alone is not enough. Local data has to be brought into contact with current knowledge and research in order for teachers to find ways forward with their problems of practice. Jackson and Temperley (2008) argue for a model where practitioner knowledge – in particular knowledge of subject, learners and the local context – meets public knowledge, which is knowledge from research. These come together to form new knowledge, which is both research-based and locally relevant.

There is general agreement that in order to truly shift practice in ways that support learner improvement, teachers must be willing to challenge their own practice and give up long-held beliefs if these are seen to not be working (Jaworski 2008; McLaughlin & Talbert 2008). This is what makes the work difficult. At the same time there is also general agreement that no single practice or set of practices is necessarily the ‘right’ one in any school. Although there is general support for practices that support learners’ conceptual understanding and reasoning, Hargreaves (2008) makes an important point when he says that conventional wisdom about teaching must be considered in relation to current research and what the data shows – intuition and craft knowledge must come into contact with research knowledge so that both can be interrogated.

The Data Informed Practice Improvement Project

The Data-Informed Practice Improvement Project (DIPIP) is a professional development project that works with mathematics teachers to build and sustain professional learning communities in which teachers engage with data from a range of sources and work together to better understand the nature of learners’ errors and how they might respond to them. In the first two phases of the project (2008–2010) we developed a number of activities that help teachers to do this: test analysis, interviewing learners and curriculum mapping (Brodie, Shalem, Sapire, & Manson 2010). Based on these activities teachers identify a key concept that underlies a number of learner errors. They then read and discuss research on learners’ thinking in those concepts (Molefe, Brodie, Sapire, & Shalem 2010), design lessons to engage with learners’ thinking, and then videotape and reflect on those lessons (Brodie, 2011; Brodie & Shalem 2011). In the current phase of the project, DIPIP Phase 3 (2011–2012), we are working in schools with mathematics departments, using the activities to build the departments’ collective engagement with data from their schools, and their design of and reflection on lessons based on their data analysis.

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The communities within schools also meet across schools in their district, in networked learning communities (Katz, et al. 2009), to share findings and build common solutions to common errors across schools2. We conducted a pilot for Phase 3 in one school in 2010 (Chauraya & Brodie 2011, 2012). Teachers meet once a week during school terms. In Phases 1 and 2 they worked across schools at Wits University, led by Wits facilitators and in Phase 3 they work in their schools, also led by Wits facilitators, who travel to each school once a week. The idea in Phase 3 is to hand over leadership of the professional learning communities to teachers in the schools so that they become ongoing spaces of engagement for teachers, with teacher leadership and some support from university facilitators.

The facilitators and project team work hard to set up and sustain the professional learning communities. Initial access is negotiated with teachers, heads of department and principals and most schools and teachers buy in to the project at that point. However, the project makes substantial demands on teachers’ time and energy, and so maintaining enthusiasm over time is key for sustaining the professional learning communities. There are three ways in which we do this. First, we make sure that teachers experience the benefits of what they are learning (Guskey 2002). Every activity as well as every session has a focus, which takes the teachers a step further in understanding learner errors and developing their own knowledge. Second, the facilitators work in ways that show respect for the teachers’ time and knowledge, and the difficult conditions in their schools. They set an example for building trust and care in the communities. The facilitators form their own professional learning community with the project leader, also meeting once a week, where they reflect on their own practice and the teachers’ learning, and in so doing, improve their own facilitation skills (Molefe, Lourens, & Brodie 2011). Third, we make sure that all meetings start and finish on time, to show respect for teachers’ time, and if meetings do need to be missed for various reasons, for example, district meetings or public holidays, these are made up at some point. We develop a timeline of activities for the whole year, which is discussed with teachers at the beginning of the year, and we make sure to keep up to date, or catch up, with this timeline3. The network meetings also function to support the professional learning communities. Teachers know in advance when these meetings will be, and they know that they need to prepare what to present at the meetings. Teachers tell us that they really enjoy the network meetings because they provide a broader range of feedback and learning opportunities, with more teachers and facilitators involved.

Learner errors

In our project we define errors to be systematic, persistent and pervasive mistakes performed by learners across a range of contexts (Nesher 1987). We, together with others, distinguish errors from slips (Olivier 1996), which are mistakes that are easily corrected when pointed out. Since errors are systematic and persistent, they are not necessarily responsive to easy correction or re-explanation of concepts.

Teachers can work with errors in different ways. One way is to avoid errors, which may arise from teacher concerns about judging or shaming learners, or a fear that bringing errors into the public realm will support a ‘spread’ of errors among learners and create more obstacles to learning, or teachers’ own uncertainty about the nature of the errors. This approach does not give learners access to correct mathematical ideas and does not help them to build appropriate knowledge. A second approach is to correct errors. This makes the correct knowledge available to learners but depending on how the errors are corrected, may not illuminate the criteria by which something is judged to be an error, thus still denying access to important mathematical knowledge (Brodie, Slonimsky, & Shalem 2010). A third possibility is to embrace errors (Swan 2001) as a point of contact with learners’ thinking and as points of conversation, which can generate discussions about mathematical ideas. In this way learners’ thinking and mathematical knowledge are brought into contact with each other.

A key theoretical consequence of the third position is that errors are a normal part of the learning

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process, for both old-timers and newcomers (Smith, DiSessa, & Roschelle, 1993). Even experienced mathematicians make errors and in so doing create new knowledge in mathematics, thus recreating and shifting the boundaries of the practice (Borasi 1994). The key point here is that errors are reasonable, make sense to the person who makes the error and are part of gaining access to mathematics and developing it further. So errors make for points of engagement with current knowledge. This notion of errors gives us a way to help teachers to see learners as reasoning and reasonable thinkers and the practice of mathematics as reasoned and reasonable (Ball & Bass 2003). If teachers search for ways to understand why learners may have made errors, they may come to value learners’ thinking and find ways to engage their current knowledge in order to create new knowledge.

The DIPIP project works with this third position, and our aim is for teachers to come to see this approach as useful in working with learners’ errors. However, we acknowledge that most teachers work with either the first or second approach, and that the second can also be useful in some cases. Moving to the third approach is a collective learning task that takes a long time and a lot of support (Brodie 2012). The DIPIP activities are planned to support this learning. In the initial error analysis activity, teachers interview learners to find out the thinking and reasoning behind their errors. The idea here is for them to learn how to probe learner thinking in class. However, in classroom situations there is often not time to delve into each learner error in depth and so teachers need to learn to judge which errors to approach in this way. Discussions in both the professional and networked learning communities focus on how different kinds of errors might be engaged with. Teachers choose examples of where they have successfully engaged with learner errors and where they have not so successfully engaged, and present these for discussion (see Brodie & Shalem 2011 for more details).

Teacher learning in professional learning communities

In the rest of this paper, I provide three examples of teachers’ learning in professional learning communities. The first example comes from DIPIP Phase 2, and I use it to show how a focus on an unexpected learner error in the classroom provides an opportunity for teachers to think about the complexities of engaging with learners’ errors, that they are not easily corrected because they make sense to learners. The second example comes from the pilot of DIPIP Phase 3 and I use it to show how a focus on learner errors helps teachers to reconsider how they teach a key mathematical concept. The third example comes from DIPIP Phase 3 and shows how a focus on learner errors supported stronger conceptual understandings of mathematics, as well as how to teach mathematics.

Example 1: The Number line and the Cartesian plane

The first example comes from a Grade 9 classroom where the teacher was working with the learners on the Cartesian plane. He called up a learner to label the axes of the first quadrant and the learner drew the following:

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The teacher, Tebogo4, presented this to a group of Grade 7–9 teachers5. He acknowledged that he was taken by surprise at this error. The facilitator, Kathy, also acknowledged surprise and said that she had never seen such an error before. At this point, two grade 7 teachers, Nadine and Tarryn made suggestions as to why the learner could have made such an error:

Nadine: I think that the kids are understanding that the number line has no starting and end point and they know that there are positive and negative numbers, so when it goes from nought to twenty or whatever, then they know that after zero comes negative numbers, minus one, minus two and so on, so they going minus one, minus two, minus three but regardless that its supposed to be a straight line like this (Tarryn nods), its just the lines, these are the positive ones, (indicates horizontally) and these are the negative ones, (indicates vertically), so it’s just, it’s a line

Kathy: Ohhh, so that one becomes flipped over that wayNadine: Ja (yes)Tarryn: Ja (yes) …Tarryn: I’m nodding my head because I had a grade 7 who did that last year and when I asked him

about it, he said, ma’am you told me zero must be in the middle between the positive and the negative, and he had positive numbers (indicates horizontally), a zero, and then he had negative numbers (indicates vertically), so the way that I have explained it about zero being in the middle between the positive and the negative, I obviously didn’t make it clear enough that it must be on one straight, horizontal, one line, as far as he’s concerned, it is still a line, it’s just got a bend in it.

A key element of Nadine and Tarryn’s explanations are that they present a case for why the learner’s error made sense to him. This is an important part of our project and for every error we see, we ask the question: how can this error be sensible and reasonable from the learner’s perspective. Nadine explained what the learner did understand about number lines, that there are no end points, that there are positive and negative numbers and that the negative numbers precede the positive numbers and zero. She also explained what he might not understand, that it had to be a straight line, from his perspective a bend in the line seemed acceptable. Tarryn confirmed that a learner had provided a similar explanation to her.

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The assumption, stated by Tarryn and shared among the three participants is that such an explanation is sensible, although incorrect, and they could see the sense in the learner’s thinking. Tarryn took the discussion a step further, arguing that she had not explained clearly enough that axes need to be straight lines, thus suggesting a role for the teacher in dealing with errors.

A few turns later, Jacob again raised issue of the teachers’ role in sustaining errors:

Jacob: Besides that I think again … when we introduced the concept of the Cartesian plane, it was not well explained to them about the quadrants, which quadrant, which axis is positive and which axis is in which quadrant …

Here Jacob supports Tarryn’s comment above that if the teacher had given better explanations previously, the error might not have occurred. As we have worked with teachers in the project and as I have analysed the data, it has become clear that once teachers see learners’ errors as reasonable and stop blaming learners for making them, they often begin to blame themselves for learners’ errors and suggest that if they had taught better originally, learner may not be making the errors (Brodie 2012).

To counteract this view, the facilitator took the teachers’ contributions and developed a stronger explanation for the learner’s error, drawing on her knowledge of the literature (Borasi 1996; Nesher 1987; Smith et al. 1993).

Kathy: Because in grade 7 the teacher could have explained very nicely about the number line, in grade 8 or grade 9 the teacher could have explained very nicely about the Cartesian plane, the Cartesian plane with the four quadrants, now the teacher draws only half of each if you want, one quadrant, so the kid’s now got two competing explanations, the number line, which flips, or a quarter of the Cartesian plane, which one does he choose, maybe the one that he learned first (people nod and smile) so its no-one’s fault, that’s the whole thing with these misconceptions, its no-one’s fault, it just happens in the process of learning, and this is a fantastic example, I haven’t seen it in the literature, you know, it’s a new one that maybe we’ve discovered here.

In the above conversation we see a number of indications that a professional learning community is functioning well. First, we see a ‘challenging focus’, trying to explain an error that is not easy to understand from the learner’s perspective. The focus comes from real classroom data, so teachers are motivated to understand the error and understanding it is likely to help in similar situations in the future. Second, we see both the teacher and the facilitator willing to acknowledge that they do not understand the error and two primary school teachers able to explain it, given their knowledge of learners. A key element for the success of professional learning communities is to be able to admit to one’s own difficulties in understanding learning and to be able to learn from others. All members of the community need to be able to do this, including the facilitator6. Third, we see that the facilitator is able to link the discussion to the broader research literature thus creating possibilities for further learning, in this case the key principle is that errors are a normal part of the learning process and cannot be avoided through ‘better’ teaching, but need to be engaged as they arise in classrooms.

Example 2: Decimal Fractions

This example comes from a professional learning community based in a school just outside Johannesburg. The teachers had set a common test and had analysed the results in their Grade 7–10 classes. In the example I discuss here, the learners had been asked to express 5/8 as a decimal fraction and had given various answers such as 5,8; 0,85 and 0,58, and when asked to express 5/8 as a percentage, had given answers such as 58%, 85% and 5.8%. The facilitator, Sibanda, had asked about the similarities among these errors, which started the following conversation:

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Nozipho: Decimals means he knows or she knows that we have a nu … a number before comma and a number after, so what she said or what she writes just add zero and comma because…

Mandla: No I think …Nozipho: … and gets zero comma five eightSibanda: Yes but it’s now five eight…Mandla: InaudibleNozipho: … how can I doSibanda: But if you look at the digits that appear in their answers thereMandla: They are the same …Tshepo: JaMandla: … they are still thereSibanda: Who … what is still thereMandla: The very same number, but there are problems … as the that one denominator is

numeratorSibanda: Where one of them has zero point eight, that’s right, zero point five eight, the other has

zero point eight fiveMandla: UuhmSibanda: But the bigger observation as Mandla was saying …Mandla: Ehm that one that is numerator in the expression and eight is the denominatorChorus: UuhmMandla: The learner just got rid of this sign, the division sign …Sibanda: UuhmMandla: Then he puts …Sibanda: Play around …Mandla: JaSibanda: … play around with five and eight …Chorus: Ja

In the above transcript, we see the teachers and the facilitator co-produce an explanation for the learners’ errors. First, Nozipho stated what the learners do understand – the form of a decimal number, that it has a comma separating two or more numbers. Sibanda focused the teachers’ attention onto the actual digits that the learners had written, various combinations of 5 and 8. Mandla then built an explanation that the learner merely used the numbers in the original fraction, they got rid of the division sign in the fraction and then they ‘play around’ with the numbers and inserted the commas where they wished, not taking account of the differences between the numerator and denominator in the original fraction. After some discussion on the answers for the percentage, the facilitator asked, ‘what is the bigger misunderstanding here’ and the following conversation took place:

Tshepo: The … I think there is the belief that ah that five over eight has to be represented in its equivalent form because now still we have the ah five comma eight…

Sibanda: So their belief is that …Tshepo: Five over eight has to be equally represented in its equivalent form Sibanda: The digits …Tshepo: JaSibanda: … five and eight must not disappearTshepo: JaMandla: Uuhm (laughter from all) all thisSibanda: That’s the bigger, the big misconception, when you are converting a number whether to

a fraction whether to decimal fraction or to percentages, the original digits simply cannot disappear

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Here the facilitator re-voiced Tshepo’s contribution as a claim that the learners believed that the numbers in the original fraction must somehow remain in the decimal. This explanation is powerful in that it explains all the errors in expressing of the common fraction as both a decimal and a percentage.

After this, the facilitator continued to challenge the teachers as to why learners might make such an error. He suggested to them that it might be because when they first teach conversion from fractions to decimals and percents they use examples with multiples of ten in the denominator, and in those cases the numerator remains in the decimal. He argued that the use of easier examples creates the possibility of learners over-generalising to other cases. The teachers agreed with the facilitator and spoke about how they might use a range of examples when teaching concepts.

This episode again shows the development of a collective explanation for what learners do know and what they do not know when converting decimals. With some prodding by the facilitator, the teachers came to see why learners made the errors and why the errors might seem reasonable to them. In this case, the reasonableness in the error was seen as more directly linked to the ways in which teachers teach, and so the teachers were supported to think in new ways about their teaching practices and how these might produce errors. Again, we see teachers willing to acknowledge weaknesses in their practices, to refrain from blaming learners for their errors, to critique their own teaching and to find ways to improve their practices. We also see a community where various voices and positions come together to build a stronger, collective understanding of errors in mathematics and the reasons for them.

Example 3: Variables and numbers

This example comes from a professional learning community based in a school just outside Johannesburg, relatively close to the school in the example above. Here, the learners had written a test in algebra. One question asked learners to write more simply, where possible, a number of expressions such as 2a + 5a, 2a + 5b, 2a + 5b + a. Four of the classes in the school, two Grade 10 and two Grade 11 classes, wrote the test. The distribution of answers for 2a + 5b was as follows:

Observed answer Percent of learners

2a + 5b = 2a + 5b or leaving answer open (correct answer) 10

2a + 5b = 7ab 70

Other incorrect answers 20

The teachers at the school were shocked and concerned that their Grade 10 and 11 learners were making the basic algebraic error: 2a + 5b = 7ab. At the first network meeting of the three schools in their district, each school-based professional learning community presented a discussion on the five common errors identified in their learners’ tests. All the communities identified the error 2a + 5b = 7ab and there was extensive discussion on this error.

At one point a teacher made a comment about the learners being unsure about the collecting of like terms and suggested using the metaphor of having two apples and five bananas – which stay as two apples and five bananas when you put them together. This is a very common, and problematic, metaphor that mathematics teachers use to help learners to manipulate algebraic expressions appropriately. The project leader commented that the metaphor is actually not a good one because learners can, and often do, say that two apples and five bananas are seven fruit, which may encourage the answer 7ab. She then stressed the more important point that a does not represent an apple and b does not represent a banana, they represent numbers. She then asked the meeting if 2a can be added to 5b. Initially some teachers said that it could not, but after some wait-time on the part of the project leader, other teachers responded

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by saying that it can be added and that the answer is 2a + 5b. The project leader explained further that while it cannot be simplified into one term, the expression shows addition – 2a is being added to 5b.

During the first professional learning community meeting after the network meeting the community discussed the network meeting, including the metaphor of apples and bananas. Towards the end of the discussion, one of the teachers, Elelwani, remarked that while she accepted the view that the metaphor is mathematically incorrect, her experience was that it worked. She further indicated that she was taught the same metaphor when she was at school. Initially the three other teachers agreed with her, but then one teacher, Chimonya challenged Elelwani. He asked her why, in terms of the metaphor, we cannot add apples and bananas, but we can multiply them, since 2a × 5b = 10ab. Immediately after that he followed up his own comment and said, ‘No man, the a is not for apples – it is for a number and it cannot be the number of apples if there are 2 apples.” The community did not continue the discussion at that time and Elelwani seemed to leave the meeting unconvinced. At the next meeting the activity was to design a lesson drawing on the issues that had come up in the error analysis and the network meeting. All four teachers would teach this lesson. When the facilitator asked the community what the critical issue in the lessons should be, Elelwani said that it should be for learners to understand that a variable represents a number and not an object. This comment shows that she had developed her own mathematical thinking since the previous meeting.

This episode shows that Elelwani felt safe enough to have and express an opinion about the metaphor of apples and bananas – even though it meant that she disagreed with the project leader and the facilitator. Elelwani defended the metaphor saying that she knows why it cannot be used, but still thinks that it is a good metaphor. It was only when she was challenged in the professional learning community and the challenge indicated again that the a cannot stand for apples but must stand for a number, that Elelwani and the other teachers in the professional learning community really agreed that it should not be used and understood why. The reflection on the network meeting in the professional learning community meeting supported a critical reflection on the metaphor and helped to develop a consensus in this school that it should not be used. This consensus generated a deeper mathematical understanding among the teachers and a commitment to teach with this new understanding. In their lesson planning, the teachers found a new, more appropriate metaphor to help learners understand the meaning of a variable.

Discussion and conclusions

One of the common arguments against professional learning communities as a teacher-development tool in the South African context is that they cannot develop teachers’ mathematical content knowledge in systematic ways, and that deep, conceptual content knowledge is what our teachers need if they are going to improve their learners’ access to mathematics. I agree with the latter point, that teachers do need to develop their knowledge of the subject in deep and conceptual ways. In this paper, I have argued that such development can and does happen in professional learning communities and I have presented some evidence to suggest that when deep mathematical development does happen it can be of a powerful and sustained nature, first, because it takes teachers beyond what they know already, and second because it can be related to and used in teaching.

In the three examples presented above, and we have many others, all the teachers had a basic understanding of the content and how to teach it. The teachers in the first example knew how number lines and the Cartesian plane work and could explain it to one another and learners. In the second example, the teachers knew how to convert fractions to decimals and percentages, and had explained the conversion process to their learners, using easier examples, as many teachers do. When initially faced with the range of errors that their learners made, they could not bring the errors together into a framework to think about how they might deal with them. In this case it turned out that through the

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discussion and the facilitator’s interventions, they could think about a small way of improving their practice that might produce big gains in learner understanding. In the third example, it is likely that had the teachers been asked about variables and numbers, they would have answered that variables stand for numbers. However, they had never thought more deeply about how this key conceptual understanding in mathematics relates to a metaphor that fundamentally denies this relationship and that they continue to use, because they were taught in that way, and current practice in most schools is to teach with the metaphor.

One of the key principles of the DIPIP project is that in coming to understand learner needs, teachers can come to understand their own learning needs: what mathematics they need to learn and how to use this new knowledge to improve their practice. In professional learning communities, they are supported to challenge their current thinking and to develop new conceptual ideas in mathematics and in relation to teaching mathematics. I suggest that had these teachers been sitting in lectures on the same content, they would not have reached the depth of learning that they did here. I suspect that very few content courses for high school teachers would focus on the number line at all, that those that might focus on decimals and fractions would most likely overlook the common learner error that these teachers unearthed and that those focusing on the concept of variable would most likely not have challenged the key misconception underlying the metaphor. All three cases above show how a deepening of content knowledge in the communities could lead to new teaching practices, where this new content could be used and tested, and the teachers were supported to engage their new understandings in practice. These lessons were videotaped and reflected on, in the professional and network communities and new, deeper understandings were reached.

Arguing that professional learning communities can be sites where deep and powerful learning among teachers takes place is not the same as an argument that all such communities are generative in this way. The Integrated Strategic Planning Framework for Teacher Education and Development in South Africa (April 2011) suggests a medium-term goal (to be achieved by 2020) to have established and functioning professional learning communities in schools across the country. Our project team is both excited by and concerned with this vision. Based on our experiences in and research into professional learning communities, we have seen that they indeed can be a powerful resource for teacher development. However, to create powerful learning communities takes a lot of thought and commitment, both from the teachers involved and those who lead the communities. To create the successes that we have, has taken immense planning on the part of the project team, immense skill and expertise on the part of the facilitators and tremendous commitment from the schools and teachers. How to scale this up, even to double the number of schools that we currently work with, let alone the whole country, is an issue that deeply concerns us. We believe that it needs to be done, but, as is the case with many policy innovations in our country, if it is not done carefully and well, it is destined to fail.

From the literature that we have reviewed and the work that we have done, we argue that the following are key to the success of professional learning communities. First, that the learning is professional, that is, based on data from teachers’ own classrooms that can be connected with data from other schools and most importantly connected with other forms of knowledge of best practice and research. If there is no way in which external knowledge can inform teachers’ thinking, then professional learning communities will continue to maintain the status quo and will not provide opportunities for powerful teacher learning. Second, learning is collaborative, and must be supported by departments, schools and principals. Professional learning is time consuming and demanding, and teachers need support to put in the necessary work and time. If other parts of the education system work against this, the communities will not succeed. Third, absolutely key to the success of the communities are the facilitators. Facilitators need skills and knowledge to design and implement appropriate activities for teachers; to manage the collaborative nature of the process, so that communities are both safe enough to admit weaknesses and

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challenging enough for growth to occur; and to bring in external knowledge appropriately to help the community grow and learn.

Without proper thinking, planning and commitment, professional learning communities will not live up to their promise. With proper thinking, planning and commitment, they can provide safe and challenging spaces for profound and powerful teacher learning and growth.

Notes

1 This is not to say that teachers’ intuitions are not important, but they need to be supported with classroom data to justify a learning focus.

2 We are currently working in eight schools in two districts.3 We note here that although we are currently working successfully in eight schools, we have had

three schools leave the project. Two left relatively early on in the project, citing time and other demands as reasons. The third school left in the third term of the first year and we are still unsure about their reasons for leaving. We are currently conducting interviews to establish what factors influenced schools that chose to stay and those that left the project.

4 All teachers’ and facilitators’ names in this paper are pseudonyms.5 A design feature of DIPIP Phase 2 was that teachers worked in both small grade-level groups and

then presented their thinking to larger cross-grade level groups (Brodie and Shalem 2011).6 It is important to note that this does not detract from the facilitator’s role in providing expertise

in the community, but that is a subject for another paper.

Acknowledgements

I would like to acknowledge the tremendous commitment and dedication of the DIPIP Phase 3 team: Nicholas Molefe, Million Chauraya and Rencia Lourens, whose thoughtful teacher development and research work has contributed significantly to my own thinking and to the work reported in this paper.

I would also like to acknowledge Yael Shalem, Ingrid Sapire and Lynne Manson whose work on DIPIP Phase 1 and 2 contributed to the original conceptions of the project and the activities, and formed a strong foundation for the current work.

A previous version of this paper was presented as a plenary paper at the 17th National Congress of the Association for Mathematics Education of South Africa (AMESA), July, 2011.

References

Ball, D. L. & Bass, H. 2003. Making mathematics reasonable in school. In J. Kilpatrick, W. G. Martin & D. E. Schifter (Eds.), A research companion to principles and standards for school mathematics, 27–44). Reston, VA: National Council of Teachers of Mathematics.

Borasi, R. 1994. Capitalizing on errors as ‘Springboards for Inquiry’: A teaching experiment. Journal for Research in Mathematics Education 25(2):166–208.

Borasi, R. 1996. Reconceiving mathematics instruction: A focus on errors. Norwood, NJ: Ablex.Borko, H. 2004. Professional development and teacher learning: Mapping the terrain. Educational

Resarcher 33(8):3–15.Boudett, K. P., City, E.A. & Murnane, R.J. 2008. Data-wise: A step-by-step guide to using assessment

results to improve teaching and learning. Cambridge, MA: Harvard Education Press.Brodie, K. 2011. Learning to engage with learners’ mathematical errors: An uneven trajectory. In T.

17


Mamiala & F. Kwayisi (Eds.), Proceedings of the Nineteenth Annual Meeting of the Southern African Association for Research in Mathematics, Science and Technology Education (SAARMSTE). Mafikeng: North West University.

Brodie, K. 2012. Learning about learner errors in professional learning communities. Paper presented at the Proceedings of the Twentieth Annual Meeting of the Southern African Association for Research in Science, Mathematics and Technology Education (SAARMSTE), Lilongwe.

Brodie, K. & Shalem, Y. 2011. Accountablity conversations: Mathematics teachers learning through challenge and solidarity. Journal for Mathematics Teacher Education 14:419–439.

Brodie, K., Shalem, Y., Sapire, I. & Manson, L. 2010. Conversations with the mathematics curriculum: Testing and teacher development. In V. Mudaly (Ed.), Proceedings of the eighteenth annual meeting of the Southern African Association for Research in Mathematics, Science and Technology Education (SAARMSTE), 182–191). Durban: University of KwaZulu-Natal.

Brodie, K., Slonimsky, L. & Shalem, Y. 2010. Called to account: Criteria in mathematics teacher education. In U. Gellert, E. Jablonka & C. Morgan (Eds.), Proceedings of Mathematics Education and Society 6 (MES6). Berlin: Freie Universitat Berlin.

Chauraya, M., & Brodie, K. (2011). Mathematics teacher learning in data-informed practice: Preliminary findings from an on-going study. In T. Mamiala & F. Kwayisi (Eds.), Proceedings of the Nineteenth Annual Meeting of the Southern African Association for Research in Mathematics, Science and Technology Education (SAARMSTE). Mafikeng: North West University.

Chauraya, M. & Brodie, K. 2012. Mathematics teachers change through working in a professional learning community. In D. Nampota & M. Kazima (Eds.), Proceedings of the Twentieth Annual Meeting of the Southern African Association for Research in Science, Mathematics and Technology Education (SAARMSTE), Vol. 1:19–31. Lilongwe: University of Malawi.

City, E.A., Elmore, F.R., Fiarman, S.E., & Teitel, L. 2009. Instructional rounds in education: A network approach to improving teaching and learning. Cambridge, MA: Harvard University Press.

Guskey, T.R. 2002. Professional development and teacher change. Teachers and Teaching: Theory and Practice 8(3/4):381–391.

Hargreaves, A. 2008. Sustainable professional learning communities. In L. Stoll & K. S. Louis (Eds.), Professional learning communities: Divergence, depth and dilemmas, 181–195. Maidenhead: Open University Press and McGraw Hill Education.

Jackson, D. & Temperley, J. 2008. From professional learning community to networked learning community. In L. Stoll & K. S. Louis (Eds.), Professional learning communities: divergence, depth and dilemmas, 45–62. Maidenhead: Open University Press and McGraw Hill Education.

Jaworski, B. 2008. Building and sustaining enquiry communities in mathematics teaching development: Teachers and didacticians in collaboration. In K. Krainer & T. Wood (Eds.), Participants in mathematics teacher education: Individuals, teams, communities and networks, 309–330. Rotterdam: Sense Publishers.

Katz, S. & Earl, L. 2010. Learning about networked learning communities. School Effectiveness and School Improvement 21(1):27–51.

Katz, S., Earl, L. & Ben Jaafar, S. 2009. Building and connecting learning communities: The power of networks for school improvement. Thousand Oaks, CA: Corwin.

Kazemi, E. & Hubbard, A. 2008. New directions for the design and study of professional development. Journal of Teacher Education 59(5):428–441.

Little, J.W. 1993. Teachers’ professional development in a climate of educational reform. Educational Evaluation and Policy Analysis 15(2)L:129–151.

Louis, K.S. & Marks, M. 1998. Does professional community affect the classroom? Teachers’ work and student experiences in restructuring schools. American Journal of Education 106(4):532–575.

McLaughlin, M.W., & Talbert, J.E. 2008. Building professional communities in high schools: Challenges and promising practices. In L. Stoll & K. S. Louis (Eds.), Professional learning communities:

18

Karin Brodie

Divergence, depth and dilemmas, 151–165). Maidenhead: Open University Press and McGraw Hill Education.

Molefe, N., Brodie, K., Sapire, I. & Shalem, Y. 2010. Thinking about the equal sign: Results from the DIPIP project. In M.D. de Villiers (Ed.), Proceedings of the 16th Annual National Congress of the Association for Mathematics Education of South Africa (AMESA), Vol. 1:156–165. Durban.

Molefe, N., Lourens, R. & Brodie, K. 2011. Using vignettes as a tool for teacher and facilitator development. Paper presented at the 20th Annual Meeting of the Southern African Association for Research in Mathematics, Science and Technology Education (SAARMSTE), Lilongwe, Malawi.

Nesher, P. 1987. Towards an instructional theory: The role of students’ misconceptions. For the Learning of Mathematics 7(3):33–39.

Olivier, A. 1996. Handling pupils’ misconceptions. Pythagoras 21:10–19.Smith, J.P., DiSessa, A.A. & Roschelle, J. 1993. Misconceptions reconceived: A constructivist analysis of

knowledge in transition. The Journal of the Learning Sciences 3(2):115–163.Stoll, L. & Louis, K.S. 2008. Professional learning communities: Divergence, depth and dilemmas.

Maidenhead: Open University Press and McGraw Hill Education.Swan, M. 2001. Dealing with misconceptions in mathematics. In P. Gates (Ed.), Issues in teaching

mathematics. London: Falmer Press.

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Karin [email protected]

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