LITERATURE REVIEW AND THEORETICAL FRAMEWORK
2.2 THEORETICAL FRAMEWORK
Reflecting on the data collected during my research led me to view professional development as a form of teacher learning. To better understand professional development in terms of teacher learning I draw on the work of Lave & Wenger (1991) and Wenger (1998), which helped focus my attention to a situative cognition perspective. The situative cognition perspective provides a bridge between the cognitivist perspective and a sociological perspective.
According to Lave & Wenger (1991)
“ … the notion of situative learning now appears to be a transitory concept, a bridge between a view according to which cognitive processes are primary and a view to
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which social practice is the primary, generative phenomenon, and learning is one of its characteristics.” (Lave & Wenger, 1991, p.34).
Adler (2000) stated that Lave’s model does not necessarily relate to student learning but in fact strongly relates to teacher learning in a mathematics class, hence I find it applicable to understanding teacher development in my study of the ACEML teachers.
It is clearly visible within this situative learning perspective the focus is on the broader community rather than individual learners. Hence there is no guarantee in the situative learning perspective that success in a particular situation means success in another. Lave and Wenger (1991) prioritises the importance of participation in the practices of a community and identity as primary features of learning by stating:
“Learning involves the whole person: it implies not only a relation to specific activities but a relation to social communities … learning thus implies becoming a different person with respect to the possibilities enabled by these systems of relations
… learning is not merely a condition for membership, but is itself an evolving form of membership.” (Lave and Wenger, 1991, p.53).
We can conclude that learning and identifying with the learning is therefore synonymous.
Since the development of the identity is dependent on the participation in a community of practice, Lave and Wenger state that:
“…a community of practice is a set of relations among persons, activity and world over time and in relation with other tangential and overlapping communities of practice. A community of practice is an intrinsic condition for the existence of knowledge, not least because it provides the interpretive support necessary for making sense of its heritage.” (Lave and Wenger, 1991, p.98)
Lave & Wenger (1991) stated that professional development of teachers involved teachers learning through a process of co-participation, in an interactive manner and not as individuals. They prioritise the importance of participation in practices of a community and identity as a primary feature of learning. They also went on to say that “school teaching is a special kind of learning practice that must become part of the identity changing communities of children’s practice if it is to have a relationship with their learning.” (Lave & Wenger, 1996, p.161). ML was introduced for this reason. To enable the learners to:
“…recognise that the world is a set of related systems, understand cause and effect, that small numbers sometimes have a big impact and large numbers can sometimes have no impact at all and understanding one’s role in the cycle and/or how the cycle impacts on one.” (Brombacher, 2012, p.3).
Wenger’s later work in 1998 focuses on the concept of community of practice and identity and this has implications for this study that is based on teacher learning. His focus is to relate these communities of practice to the four learning components of meaning, practice, community and identity. Furthermore he based his work on the following four premises which is closely aligned to the assumptions underpinning the subject ML:
• that people are social beings in a central aspect of learning.
• knowledge is about competence with respect to valued enterprises.
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• knowing is about active engagement in the world.
• meaning is ultimately what learning is about. (Wenger, 1998, p. 4) These four premises resonate strongly with the purposes of ML.
Firstly, the idea that learners are social beings who are part of a broader society is a theme that underpins the introduction of ML which seeks to prepare learners to participate in society. It emphasises that ML teachers should provide learners with opportunities to develop and practise communication skills which will help them interact with others and share their understandings.
Secondly, ML is very clear about its purpose being different from that of mathematics, because “the purpose of this subject is to equip learners with the necessary knowledge and skills to be able to solve problems in any context that they may encounter in daily life and in the workplace.” (DoBE, 2011, p.9). Thus its purpose is not to learn more mathematics but to be able to apply basic mathematics to better understand the contexts they encounter which is aligned to Wenger’s second premise about competence being related to valued enterprises.
Here the valued enterprises are the actual contexts that the learners may encounter.
Thirdly, the DoE (2011, p.8) writes that:
“The competencies developed through Mathematical Literacy allow individuals to make sense of, participate in and contribute to the twenty-first century world — a world characterised by numbers, numerically based arguments and data represented and misrepresented in a number of different ways.”
This description of the purposes of ML is reflected in Wenger’s third premise above of knowing is about active engagement in the world.
Furthermore, in order to engage in real life contexts in ML, it is essential to make meaning of the contexts they encounter, and they cannot apply the mathematics without understanding the contextual significance, and this aspect of learning is reflected in Wenger’s fourth premise above. This discussion on Wenger further reinforces the situative perspective where there has to be understanding of “how practice learnt at the universities and colleges courses can be re-contextualised in elementary and secondary schools.” (Peressini et al, 2004, p.70) ML was a new subject taught by teachers who had been previously trained to teach other subjects, such as history, mathematics, life science, Afrikaans etc. One therefore is unable to imagine that the new subject would involve replacing “old” practices with “new” practices. In the teachers previous situation success would have been defined in terms of facilitating knowledge of the previous subject. With the advent of their new specialization of ML, success will be defined differently.
According to (Graven, 2002)
“… implementing the new curriculum would involve a process of fashioning the curriculum in such a way that it becomes part of the teachers’ ‘way of being’. This would be enabled through providing teachers access to a range of resources including opportunities to participate in a community engaged with new information, mathematics content, methodological ideas, new discourses, materials, curriculum documents etc.” (Graven, 2002, p.142)
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According to the study by Graven (2002), there is connection between Lave & Wenger’s perspective of “learning as becoming” to the context of teacher learning in South Africa. ML a subject, unlike mathematics, requires “the need to work collaboratively in teams and groups to enhance mathematical understanding.” (DoE, 2002, p.10). Graven’s (2004) work encompasses Wenger’s (1998) four learning components namely meaning, community, practice and identity and found that confidence was actually the fifth resultant component of her community of practice, PLESME (INSET project researching mathematics).
She stated that:
“…confidence was clearly foregrounded by teachers in terms of their descriptions and explanations of learning ……. It is therefore analysed separately but considered in relation to the components: meaning, identity, practice and community.” (Graven, 2002, p.129)
The following figure shows Wenger’s theory of learning including his four components as explained by Graven (2002, p.153), namely meaning (our ability to experience the world as being meaningful), practice (our ability to share historical and social resources, frameworks and perspectives that sustain mutual engagement in action), community (ability to talk about the social configurations in which our enterprise is defined and our participation is recognisable as competence) and identity (a way of talking about how learning has changed who we are) and fuses his four premises on which his work is based on;
Figure 2.2.1 (Wenger, 1998, p.5)
Hechter’s study (2011) focussed on Wenger’s (1998) four learning components. On researching the ACEML teachers she found that “teachers shared a general understanding of the nature and purpose of ML and how it should be taught” (Hechter, 2011, p.143). She goes on to say that