This article investigates the participation enablers and learning affordances identified by teachers through participation within an in-service community of practice (CoP) of primary teachers called the Numeracy Inquiry Community of Leader Educators (NICLE) in the Eastern Cape. The article draws on three qualitative sources of data: the annual teacher questionnaires of 42 participating teachers, interview data from 8 of the 42 sampled teachers and reflective journal entries of these 8 teachers over the first 2 years of NICLE. All three data sets point to teachers foregrounding the affordances and enablers of NICLE participation across the fundamental elements of a CoP, namely domain, community and practice. We illuminate the way in which teachers’ identification of learning affordances relates to these three structural features of a CoP. In concluding, we argue that explicit consideration of these structural elements, and their interrelationship in the design of in-service programmes, could enable clearer articulation of programme aspects and support reflection on the coherence between teacher feedback on these as programmes evolve.
South African primary education, and mathematics education in particular, is struggling to overcome the lingering effects of its apartheid past. Inequality continues along racial lines with the 2003 Trends in International Mathematics and Science Study (TIMSS) indicating that South Africa was the lowest performing of 50 countries with the largest variation in scores (average scores of learners in African schools were almost half of that of historically white schools) (Reddy
Despite two decades of curriculum revision, the basic features of primary mathematics classrooms under apartheid continue. These include the dominance of oral discourse with limited reading and writing opportunities, classroom interaction patterns that privilege the collective (chorusing) and concrete working, and little evaluation and feedback of students’ responses (Hoadley
It is against this background that the first author began the Numeracy Inquiry Community of Leader Educators (NICLE) as a long-term teacher development programme in the Eastern Cape as a key intervention of the South African Numeracy Chair Project (SANCP). It commenced in 2011 and ended in November 2015. The second author began his doctoral research investigating the nature of teacher learning within NICLE from the start of the programme.
This article investigates the mathematical participation enablers and learning affordances identified by 42 teachers (Grade R–6) within their NICLE participation in the first 2 years of the programme. Our article draws on the 42 teachers’ responses to end-year questionnaires and a smaller sample of 8 of these teachers’ interviews and reflective journals. In this article, we illuminate the way in which teachers’ stated take-up of learning affordances, and participation enablers within the community of practice (CoP), relates to the three structural features of a CoP outlined by Wenger, McDermott and Snyder (
The design of NICLE, and the research of teacher learning within it, was informed by Lave and Wenger’s (
to become a full member of a CoP requires access to a wide range of ongoing activity, old-timers, and other members of the community; and to information, resources, and opportunities for participation. (p. 101)
Wenger (
a living context that can give newcomers access to competence and also invite a personal experience of engagement by which to incorporate that competence into an identity of participation …and a good context to explore radically new insights. (p. 214)
He argues that:
a history of mutual engagement around a joint enterprise is an ideal context for this kind of leading-edge learning, which requires a strong bond of communal competence along with a deep respect for the particularity of experience. When these conditions are in place, CoPs are a privileged locus for the creation of knowledge. (p. 214)
The NICLE focused on establishing partnerships with teachers where teaching competence develops through ‘deep respect’ for the teachers’ particularity of experience and drew on this as a critically important resource for engaging with the relevance of ‘new insights’ and research-informed resources for local contexts. The 2011 orientation document states that teachers, project staff and other key partners would:
form a partnership in which we are all co-learners. In this co-learning agreement we will all be participants working together, bringing different experiences and expertise to share in the community. (SANCP
It further states that teacher experiences were ‘the foundational basis’ from which to proceed’ (SANCP
The fundamental structural elements of a CoP (domain, community and practice) and their indicators were used as a structuring device for analysis of teacher data on learning affordances and participation enablers. Here we unpack the ingredients of these three elements and discuss the meaning of resources and their use in the analysis.
The structural element of domain creates ‘common ground [that] brings people together and guides their learning’ (Wenger et al.
The structural element of practice encompasses the body of shared knowledge, resources, ‘latest advances in the field’ and a set of ‘socially defined ways of doing things’ (p. 38) in a specific domain, which enables participants to learn and become practitioners in their craft. Wenger et al. (
Wenger et al. (
In 2011 and 2012 NICLE met every second week across the two-year period. This meant that 3–4 sessions were held per term across each school year. In total, 27 workshop sessions were held. Various local, national and international guest speakers and a number of NICLE teachers provided stimulus input and activities for workshops. On several occasions, NICLE teachers provided live classroom demonstrations of their teaching. All workshops followed a similar structure: presenters provided teachers with a stimulus for discussion in the form of presentation of ideas, followed by group work, discussion and activities. Resources for classroom use, based on the topics of discussion, were provided. In subsequent sessions, teachers provided feedback on their experiences of using these resources in their classrooms. In this section, we outline how NICLE was designed as a CoP and unpack specific aspects of the domain, practice and community elements that constituted the NICLE joint enterprise.
The first author coordinated NICLE and presented about half the NICLE workshops over the two-year period, while the other half were presented by invited speakers who ran workshops on a range of topics in areas of their expertise. ‘Number-sense’ was foregrounded and presenters were chosen for their expertise in key topics supporting the development of number-sense. Examples of topics included using key conceptual resources, connecting concepts, developing efficient calculation strategies and mental fluency, and using language as a resource for learning. These topics constituted the NICLE domain providing ‘common ground’ and ‘best knowledge’.
The NICLE practice included the provision of a range of resources including session handouts (usually summarising key ideas or activities) and resources for use with learners in class. These resources captured in written or physical form some of the key aspects of the NICLE joint enterprise. The ‘defined way’ of engaging with these resources was through active engagement of all participants with them in NICLE sessions and in their own classrooms – then feeding back in NICLE sessions experiences of using these resources along with suggested adaptations. Key resources included physical teaching resources provided, models and concepts shared (i.e. multiple representations for concepts/perspectives of learning, i.e. socio-constructivism) and related pedagogical practices (such as learner-centredness). Socio-constructivist views of learning became the shared and socially defined ways of how NICLE members interpreted effective mathematics teaching and learning.
The NICLE community was constituted by teachers, project members and invited partners who interacted and learnt together regularly. Induction into NICLE foregrounded mutual respect between members and acknowledgement that member contributions were a key resource for engagement. In the partnership of teachers, academics, researchers and teacher educators, the critical resources of classroom experiences, knowledge of learners and knowledge of the key challenges they faced were the basis for NICLE engagement. Active teacher participation was key to the NICLE joint enterprise. While university-based members brought research-informed resources and local, national and international networks of mathematics education experts to engage and share key resources with, NICLE teachers brought the critical experiences of using such resources in local contexts. Active participation was enabled by group discussions in every session and through strong working relationships among members. With time, the sharing of ideas by teachers increased and NICLE teachers themselves presented workshops including lesson demonstrations.
Our research of teacher learning adopted a qualitative, interpretive approach in which our knowledge and understanding emerge from our interpretation of teachers’ lived experiences (Merriam
In reporting the questionnaire data, we have used teacher initials (adapted for anonymity), followed by the grade(s) taught (e.g. AM4) for each teacher. As 8 of these 42 teachers additionally participated in interviews and reflective journal writing, these teachers are referred to by pseudonyms so as to identify them within the larger sample. In this article, we analysed teacher responses to the questionnaire items: (1) Do you feel you are learning through your participation in NICLE? If so, explain the nature of that learning; (2) Has anything changed in your mathematics teaching classroom practice as a result of your participation in NICLE? If so, explain.
For the eight interviewed teachers, we focused on the following questions:
What do you think are some of the advantages of participating in NICLE? Some disadvantages?
Which NICLE activities did you enjoy most? Why did you enjoy these activities?
Which activities or materials did you use most in your mathematics classes? Why?
Did NICLE support your own understanding of mathematics at all? If so, explain.
Did NICLE support your teaching of mathematics at all? If so, explain.
A deductive data analysis approach was used to interpret data obtained from questionnaires, interviews and reflective journals. Recurring themes of learning affordances and participation enablers were identified. These themes covered the features of domain, practice and community.
Borrowing from the work of Greeno (
qualities of systems that can support interactions for an individual to participate in. Affordances can be represented, using situation-theory notation, as if-then relations between types of situations, in which the antecedent involves resources in the environment and enabling characteristics of a person or group and the consequent type of activity that is possible whenever those environmental and personal properties are present. (p. 9)
Attunements to constraints become learning enablers in the sense that they ‘include well-coordinated patterns of participating in social practices, including conversational and other interactional conventions of communities’ (p. 9). Our article illuminates the way in which NICLE learning affordances and participation enablers expressed by teachers related to understanding specific numeracy domain concepts, appropriating numeracy teaching and learning practices into their classrooms, and a mutually supportive and respectful community.
For each structural feature, a summary table is provided that shows the number of teacher utterances in questionnaires and interviews across identified indicators. The first column of figures in each table (
Utterances of Numeracy Inquiry Community of Leader Educators’ domain-related affordances.
Domain |
|||||
---|---|---|---|---|---|
Indicator | |||||
Key emerging themes | Fluency progression | 12 | 13 | 4 | 4 |
Problem-solving | 11 | 15 | 4 | 5 | |
Number sense | 11 | 12 | 2 | 3 | |
Hot topics | Mental mathematics | 22 | 47 | 2 | 3 |
Place value | 16 | 17 | 2 | 3 | |
Zero | 7 | 10 | 5 | 8 | |
Bar model | 7 | 9 | 3 | 3 | |
Fractions | 7 | 9 | 1 | 1 | |
Common experiences | Language | 6 | 8 | 3 | 6 |
Three key themes emerged from teacher responses when explaining their learning: teaching for number-sense and sense-making (11/42 teachers; 2/8 interviewees), developing problem-solving strategies (11/42; 4/8) and developing computational fluency, particularly through the use of games (12/42; 4/8). These cohere well with the NICLE domain design features discussed above. Within each of these themes, most comments related to how engagement in these NICLE sessions enabled teachers to teach these aspects more effectively in classes. In addition, teachers noted the way in which NICLE enabled them to develop their own number-sense and problem-solving skills. A sample of typical teacher comments related to number sense and problem solving is presented below:
Now I tend to think and do things differently than I used to do, and there are a lot of things especially with the number sense, that I have a clear understanding now. (Edna, I, Nov 2012)
[I learnt] new concepts, knowing how to solve problems … and also questions that you may ask when you are dealing with [
Word sums can be classified using [
Pamela’s journal comments reflect her perceived success at using the shared problem-solving approach presented by a guest speaker in her classroom. The problem-solving steps noted by Pamela for ‘word sums’ are one of many heuristics available for mathematics problem solving. Research has shown that explicitly teaching such heuristics supports students’ problem-solving performance (e.g. Schoenfeld
A wide range of topics were noted by teachers in relation to what they had learnt. As expected, these linked closely with topics covered in NICLE.
The most noted topic in the questionnaires was mental mathematics (47 comments by 22 teachers). Developing mental mathematics skills with learners was included as a topic in three non-consecutive NICLE sessions. The second most noted topic was ‘place value’. While this topic had an entire session dedicated to its teaching, it was also included in several other sessions, one of these being a demonstration by one of the NICLE teachers of her work with a group of Grade 3 learners using individual sets of place value cards. The topics ‘zero’ and ‘the bar model for problem solving’ were each topics of a single NICLE session. The topic ‘fractions’ was extensively covered in three consecutive sessions and although not noted by teachers widely, they commented extensively on their use of the laminated fraction chart resource, as enabling student conceptual understanding.
Similar to the utterances relating to themes, ‘topic’ comments related to both the teachers’ own learning and learning about how to teach the topic. In addition, several teachers noted awareness of the importance of focusing attention on key topics or what is also referred to as ‘big ideas’ in mathematics teaching (e.g. Siemon, Bleckly & Neal
I have realised that the learners continuously need exercise building and decomposing numbers. … The learners’ ideas of place value need more attention than I normally anticipate. The Flard (place value) cards were readily available and easy to use in whole class teaching and learning. When the learners saw the parts of the whole number and how it is built from a single number it became clear – more so for slow/low-ability learners. (Robert, Journal, undated 2012)
Siemon et al. (
While language policies in schools allow for learners to receive mother tongue instruction in primary schools, the majority of schools switch to English as the medium of instruction from Grade 4, resulting in 72.2% of Grade 4 children entering English-medium classrooms being non-native speakers of English (Robertson & Graven
Two NICLE sessions dealt explicitly with addressing such language challenges. The importance of reconceptualising language as a resource (Planas & Setati-Phakeng
Teacher utterances included comments on how sessions provided support for using language more effectively in mathematics teaching, as well as how they now understood the importance of paying explicit attention to language in mathematics teaching as is promoted in local and international literature (e.g. Moschkovich
I must compliment [
I want a copy of this [
Language is a problem in my case as learners are isiXhosa speaking and I am Afrikaans speaking. The medium of instruction is however English. I must make sure that I have more resources explaining things in English and Xhosa. (Calvin, Journal, Sep 2012)
The above analysis shows teachers’ identification of their learning in relation to domain-related themes, topics and common issues and how teaching problem-solving heuristics, focusing on ‘big ideas’ and the issue of language (as promoted by the literature referred to above and engaged with in NICLE) supported their mathematics teaching practices.
Next, we interrogate the nature of primary mathematics teaching and the learning practice affordances reported as enabling primary mathematics teacher learning within the NICLE CoP.
Practice-related affordance utterances had high frequencies in both questionnaires and interviews when compared to the frequencies of domain-related affordances. Comments fell into four categories aligned with Wenger et al.’s (
Utterances of Numeracy Inquiry Community of Leader Educators’ practice-related affordances.
Practice |
|||||
---|---|---|---|---|---|
Indicator | |||||
Physical resources | Cards and dice | 33 | 52 | 6 | 8 |
Homework books | 17 | 25 | 2 | 2 | |
Flash cards | 12 | 13 | 2 | 3 | |
Wooden cubes | 9 | 9 | 5 | 6 | |
Alphabet-Mathematics cards | 7 | 8 | 2 | 4 | |
Number Sense workbooks | 5 | 5 | 2 | 3 | |
Edupeg workbooks | 4 | 5 | 2 | 3 | |
Conceptual resources, models and tools | Place value cards | 34 | 53 | 3 | 3 |
Fraction chart | 13 | 16 | 4 | 4 | |
100-chart | 13 | 13 | 0 | 0 | |
Number lines | 5 | 5 | 1 | 1 | |
Bar model | 5 | 5 | 2 | 3 | |
Resources for learning about teaching | Watching demonstration lessons or videos | 12 | 16 | 4 | 8 |
Teaching and learning theories | Socio-constructivism | 32 | 63 | 7 | 11 |
Learning environments need absence of fear and enjoyment of or satisfaction in learning | 24 | 57 | 6 | 8 |
The majority of NICLE sessions provided sets of physical teaching resources for use in class (e.g. dice, flashcards, wooden cubes and learner workbooks). Teacher comments pointed to valuing these resources and, in particular, how these enabled using session ideas in their classrooms. At the end of the first year, analysis of a sample of learner books across schools pointed to low levels of written learner activity (Graven
Thirty-three teachers wrote in questionnaires about how playing NICLE card- and dice-related games enhanced their teaching. Many noted that they developed learner fluency, especially mental fluency, in the four basic operations. For example, Robert explained:
Usually I use the dice and they do multiplication of two digits, and you expand it to three digits, playing around and having a grid where they have to complete by adding those numbers. … So I know the learners really enjoyed it. (Robert, I, Nov 2012)
Like Robert, many teachers (five of the eight interviewed teachers and four in questionnaires) said that dice and card games provided playful learning possibilities, which made numeracy learning interesting and enjoyable. For example:
I used the boxes full of resources very often especially the cards and dices for playing mathematical games and the learners enjoy it very much. (AM4, Q, 2012)
Seven teachers in interviews and 23 in the questionnaires reported using the NICLE physical resources in their mathematics classes. In particular, the homework books were highlighted as being useful and teachers explained that they, and their learners, ‘enjoyed’ using these. For example, Melania emphasised her and her learners’ enjoyment in using these books:
Those [
Lave and Wenger (
Conceptual resources, models and tools are fundamental mathematics teaching resources that are commonly and universally used in practice to represent specific numeracy concepts. The seminal work by Ball, Thames and Phelps (
Thirty-four of the teachers in the questionnaires and three in interviews explained that using the place value cards (also known as arrow or Flard cards) in their teaching was useful in developing learner understanding of place value. Such sets of cards are promoted for use and provided in the South African Department of Basic Education’s ‘Grade 3 teaching resource booklet’ (
Data from both interviews and questionnaires noted that the fraction chart supported conceptual teaching of fractions. A range of literature promotes the use of fraction charts or fraction strips for supporting student understanding of fractions and comparison of fractions (e.g. Van de Walle & Thompson
For children who don’t understand, for example fractions, that is a concept that some of them don’t. I will actually stick these fraction boards on their desks and I will say ‘right if you are comparing fractions’ (Everton, I, Nov 2012)
I have learnt a lot from this session. The way that I am teaching fractions needs a new approach. The learners must do more mental mathematics relating to fractions. I should let them count in fractions. I must always make sure that they have a variety of ways of representing fractions, e.g. fraction circles, fraction charts, strips, etc. (Calvin, Journal, May 2012)
Twelve teachers in the questionnaires and four during interviews noted that the teacher demonstration lessons particularly enabled their teaching practices. Questionnaire responses about lesson demonstrations included terms such as ‘useful’, ‘helpful’ and ‘interesting’. The following excerpts are examples of this:
I become more aware of the learners’ actual and potential learning trajectory through observing simulated teaching at NICLE. (AR 4–7, Q, 2012)
To discern how certain activities aid the learning of concepts in maths by observing demonstration lesson by peers, and unpacking the unfolding of the lesson. … I developed a sense of where it’s coming from and where it’s going. (AA6, 2012)
In addition, two of the teachers noted in questionnaires the value of watching a video of an international lesson. Classroom videos and lesson demonstrations have been reported to be strategic artefacts that convey realities, proofs and complexities of classroom events and practices (e.g. Ball
All eight teachers interviewed, and 40 of the 42 teachers in total, explained that engaging with specialists in NICLE improved their teaching, especially in terms of increasing learner participation. This coheres with the socio-constructivist perspective of learning promoted in the curriculum and NICLE. Increasing engagement with learners’ sense-making, and increasing learner activity (including written activity), was a key goal in NICLE. The excerpts from two questionnaires, and from Melania’s interviews and journal data, illuminate the learning noted in utterances related to adopting learner-centred practices:
I allow learners to explore more and giving them more time to think and allow them to explain their procedure or thinking and how they got to an answer. (GL5–7, Q, 2012)
I have been encouraged to build on learners’ contributions, thus giving them confidence. (SE4–6, Q, 2012)
It [NICLE] just sharpened my awareness … about interacting more with children and having them explain to you how they are thinking how they are working out problems from that perspective, definitely it has saved my teaching because I have communicated more with the children about how they are doing things and why they are doing things. (Melania, I, Oct 2011)
Learners must be able to explain why and how they did things. Think, pair and share – work together. … (Melania, Journal, May 2012)
In addition, teachers noted creating a more relaxed ‘learning can be fun’ ethos and an openness to a variety of learner methods and contributions. Emphasising that mistakes and a variety of different learner contributions are rich opportunities for learning was a consistent message in NICLE. This was emphasised in NICLE generally, as well as specifically in a session in which a local psychologist spoke about the way in which fear can block learning. Mary and Robert explained:
I have become more holistic in my thinking, there isn’t just one method in maths and it is important to allow children to explore and work things out for themselves. I try and make maths fun for my learners and use a variety of approaches because not all children learn in the same way. (Mary, Q, 2012)
I think personal enjoyment is always activated, I would say, by playfulness. … This year we had an activity where we had games. The playful nature of mathematics. It was refreshing, also energising on a personal note. You see to learn maths like not in a routine way. … (Robert, I, Nov 2012)
Within the CoP perspective, teaching and learning tools or artefacts were part of NICLE’s shared resources, which deepened teachers’ knowledge and strengthened their teaching practices. Teacher responses showed that physical and conceptual resources such as the place value cards, fraction charts, empty number lines, the 100 number grids and the bar model (used for problem solving) were used by the teachers to support learner understanding of key mathematical concepts. Teachers noted that exposure to and engaging with NICLE’s conceptual resources, models and tools, paired with an emotionally safe and ‘learning can be fun’ classroom ethos enhanced their teaching. This coheres with Darling-Hammond and Richardson’s (
All 42 teachers commented on at least one of the three community affordance elements (i.e. nature of relationships, forms of participation and interaction with experts) (see
Utterances of Numeracy Inquiry Community of Leader Educators’ community-related affordances.
Community |
|||||
---|---|---|---|---|---|
Indicator | |||||
Nature of relationships | Friendly relationships | 12 | 13 | 4 | 4 |
Mutually respectful | 3 | 3 | 5 | 7 | |
Forms of participation | Sharing classroom experiences and practices | 32 | 63 | 7 | 12 |
Active participation | 7 | 7 | 4 | 7 | |
Interaction with experts | Guest speakers | 13 | 18 | 4 | 6 |
Here we share the way teachers expressed these as enablers of their learning.
The nature of relationships as learning enablers received 27 utterances across questionnaires (16) and interviews (11) (see
The following excerpt from Ruth’s 2012 questionnaire captures teachers’ appreciation of the ‘atmosphere’ of NICLE:
Yes, I have learnt and I am learning. I love the attitude and the atmosphere – unlike departmental workshops that are patronizing and ‘schoolish’! Participation is genuine, questions are challenging – being treated as an equal adult. (Ruth, Q, 2012)
Similarly, excerpts from Melania’s interview and Mary’s journal illuminate how they noted NICLE relationships as enabling learning.
Often you go to these Departmental things and they almost talk down to you. Like you are a teacher and you don’t know what you’re doing, you know. NICLE has really gone, from the onset, they are trying to help, they are trying to uplift, they are trying to improve, they respect you, you know. (Melania, I, Nov 2012)
What a dynamic spirit! Focused on problem solving using fractions. I would have broken out into a cold sweat if asked to explain that concept but she just has a way of helping us who are ‘mathematically challenged’ to understand. (Mary, Journal, May 2012)
Wenger et al. (
Wenger et al. (
Most teachers noted certain forms of participation in NICLE as enablers of their own learning. The majority of these utterances referred to the way in which participation involved sharing classroom experiences (63 in questionnaires and 12 in interviews), while 14 related this to the active teacher participation in sessions (seven in questionnaires and seven in interviews).
Exposure to other teachers. Discovering other ways of solving problems. Interacting with a range of maths teachers. I liked the interaction with the Foundation phase teachers because they are your experienced teachers in this regard. (GL5–7, Q, 2012)
The big thing is seeing other people do it and discussing it with them and finding out what your common problems are and finding solutions to those common problems. (Everton, I, Nov 2012)
Other teachers such as Pamela and Edna expressed the view that NICLE provided a context for sharing ideas on numeracy teaching ‘resources’. Ruth remarked how it exposed her to ‘relevant material’ to use in her mathematics classes. Other teachers said NICLE enabled opportunities for ‘meeting’ (Edna, BN3, GN4), ‘interacting’ (AS1, GL5–7, SE4–6), ‘team working’ (BC4–7) and ‘learning from other teachers’ (GB2, SR3, SE3). Such professional community engagements according to BC4–7 and SE4–6 allowed educators to ‘reflect’ on their work and ‘reinforce’ positive aspects in their practices.
Teacher data thus reveal how sharing classroom experiences and practices provided opportunities which enabled teacher numeracy practices to evolve, and developed a sense of belonging to the community. These findings concur with research that emphasises that sharing classroom experiences is an important source of teacher learning (e.g. Putman & Borko
Yes, the different activities stimulated thinking and reasoning. In their small groups teachers discussed and questioned each other herein developing their mathematical inclination. (AR4–7, Q, 2012)
People come with different ideas with sessions and it demonstrates it is not just a talk show it is active participation, that keeps it lively. … The interaction is not where you have to just be absorbing theoretical knowledge of someone else. (Robert, I, Nov 2011)
Similarly, Edna and Mary, respectively, in their second interviews noted that NICLE sessions were characterised by ‘actively involving and engaging’ forms of participation which involved ‘a lot of practical, concrete … hands-on experiences’, which made it easier to implement such practices in their classrooms. The CoP theory as well as professional teacher development literature resonates with the sampled teachers’ comments that their active participation and practical experiences in the NICLE community created opportunities for the positive evolution of their primary mathematics practices. This coheres with the findings of Darling-Hammond and Richardson’s (
Another aspect noted as an enabler of learning was access to, and interaction with, presenters and guest speakers. Half of the NICLE sessions during the period of the research study were presented by invited numeracy education specialists.
Interaction with session presenters and guest speakers received 24 utterances across questionnaires and interviews. Learning from specialists was noted by 13 of the 42 teachers in the questionnaires and by four of the eight teachers in interviews. Teachers explained that access to the invited ‘specialists’ and ‘experts in mathematics’ provided them with current information on numeracy teaching that enabled their learning. For example, AA6 wrote that NICLE ‘exposed [him] to the accumulated expertise, experience, skill and knowledge of a variety of mathematics education researchers and practitioners’ (AA6, Questionnaire, 2012). Similarly, BC4–7 and IL3 acknowledged the expertise of the invited NICLE presenters in ‘their field of work’ and ‘what they talked about’ which allowed them to ‘understand more’.
Aside from being knowledgeable, several teachers (Edna, Calvin, AN3, AM4, GR3, NL4–6 and SB4) noted that invited experts (which included teachers) addressed many of their classroom challenges. AN3 and SB4 wrote that the guest speakers helped them to ‘solve some mathematical problems’ (AN3) and ‘clarified uncertainties’ (SB4). Calvin, Edna and GR3 said that the invited specialists’ presentations tackled different and new ‘mathematical topics’, while some remarked that presenters provided the teachers with ‘up to date information’ (SB4).
The following excerpts capture teacher views of the effects of engagement with guest presenters:
You are introduced to new concepts all the time. It’s exciting and stimulating, and a lot of things you can relate to as well. You know? Like especially with the guest speakers. (Mary, I, Sep 2012)
Started NICLE today!!! Good to be back and to see the gang – oh the maths experts!!! Really enjoyed the TED clips. Made a lot of sense ‘children do have different abilities and talents’ and I think we are always so quick to label children who are different. (Mary, Journal, Feb 2012)
In CoPs, ‘masters’, ‘experts’ and ‘old-timers’ are critical for ensuring participants’ learning and for identifying and confirming existing knowledge and new developments within a community (Lave & Wenger
The data discussed above show that specific relations, forms of participation and invited experts provided opportunities for interactions, engagement and sharing classroom practices in the CoP. These supported teachers in their learning and appropriation of NICLE domain concepts and practices into their teaching.
An investigation of the NICLE teacher learning affordances and participation enablers across different data sources highlighted the importance of Wenger et al.’s (
Cross-case analysis of empirical data related to these key variables revealed that the NICLE domain and practice resources were highly valued as key learning enablers. Furthermore, this learning was enabled because of the nature and ethos of engagement in the CoP. That is, the respectful participatory relationships in NICLE, which foregrounded teacher experience as critical in judging the value of resources, were seen to enable the adaptation and adoption of resources for teaching. The article has illuminated how domain, practice and community are interrelated aspects central to enabling mathematics teacher learning. This structural transformation of professional development towards a content-, practice- and community-focus transcends the limitations of more traditional forms of teacher ‘workshops’ or in-service training sessions and could usefully inform the design of teacher development programmes.
A key limitation of this research is that it has focused on teachers’ written responses and verbal utterances of their experiences of participating in NICLE and their perceptions of how this has influenced their learning and teaching. Further research into how this perceived learning may be observed in mathematics teaching practice would strengthen and broaden understanding of teacher learning through participation in such CoPs.
This work was supported by the FirstRand Foundation (with the RMB), Anglo American Chairman’s fund, the Department of Science and Technology, and the National Research Foundation.
The authors declare that they have no financial or personal relationships which may have inappropriately influenced them in writing this article.
M.G. gathered the annual questionnaire data on teacher participation while P.P. was a doctoral student under her supervision and gathered interview and journal data on a smaller sample of teachers within the PD program. M.G. conceptualised the article and both authors contributed to the analysis of the data and the writing of the article.