Abstract
We propose a new model for framing teacher education projects that takes both the research and the institutional dimensions into account. The model, which we call Meta-didactical Transposition, is based on Chevallard’s anthropological theory and is complemented by relevant elements that focus on the specificity of both researchers’ and teachers’ roles, while enabling a description of the evolution of their praxeologies over time. The model is illustrated with examples from different Italian projects, and it is discussed in light of current major research studies in mathematics teacher education.
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- 1.
One of the European projects in which we have been involved is the EU funded project EdUmatics (50324-UK-2009-COMENIUS-CMP; European Development for the Use of Mathematics Technology in Classrooms), http://www.edumatics.eu.
- 2.
We refer to this term in tune with the following characterisation of communities of inquiry proposed by Jaworski (2008): “In terms of Wenger’s (1998) theory, that belonging to a community of practice involves engagement, imagination and alignment, we might see the normal desirable state as engaging students and teachers in forms of practice and ways of being in practice with which they align their actions and conform to expectations…In an inquiry community, we are not satisfied with the normal (desirable) state, but we approach our practice with a questioning attitude, not to change everything overnight, but to start to explore what else is possible; to wonder, to ask questions, and to seek to understand by collaborating with others in the attempt to provide answers to them. In this activity, if our questioning is systematic and we set out purposefully to inquire into our practices, we become researchers.”
- 3.
It derives from the Chevallard’s notion of didactical transposition (Chevallard 1985), which roughly speaking, consists in the relationships between the production, the use and the teaching of the scientific knowledge and in the ways, according to which it adapts itself in order to ‘work’ in different types of institutions (compare for example a theorem as expressed in the Journal where it is proved by a mathematician, what Chevallard calls “le savoir savant”, with the same theorem as it is written in a textbook, “le savoir enseigné”).
- 4.
The ‘knowledge level’ can be further decomposed in two components, i.e. Technologies and Theories. The provided description is enough for our purposes.
- 5.
This is true for activities with in-service teachers; in the case of prospective teachers, the second component may be missing but their beliefs are active and still constitute a powerful part of the component.
- 6.
Of course there may be more than one praxeology referring to researchers, as well as referring to teachers: in the text we will use either singular or plural (researchers praxeologies; teachers praxeologies). In particular the researchers have their own praxeologies as researchers, which concern the praxis and the logos of their researches; but they have also their praxeologies as teachers’ educators, where the praxis and the logos concern the concrete way they coach these activities, because of their theories about teachers’ educational processes.
- 7.
The choice of this term to refer to teachers’ education programmes is in tune with Simon definition of Learning Trajectory: “The Hypothetical learning trajectory consists of the goal for the students’ learning, the mathematical tasks that will be used to promote students’ learning and hypothesis about the process of the students’ learning” (Simon 1995).
- 8.
This process has a common feature with the processes of instrumental genesis, as described by Trouche (2005). Space does not allow us to develop this issue.
- 9.
- 10.
According to the Italian paradigm of ‘research for innovation’, in this second step the tutors praxeologies may be assimilated to the researchers ones: as said above, in many cases the tutors are teachers-researchers, i.e. are experienced with research studies and methodologies, having been part of research teams in mathematics education for many years. Of course this is not always the case. For the purpose of the paper, we privilege clarity, taking the risk of over-simplification.
- 11.
Contrasted with their products. e.g. students’ reasoning, arguments, difficulties, and so on.
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Arzarello, F. et al. (2014). Meta-Didactical Transposition: A Theoretical Model for Teacher Education Programmes. In: Clark-Wilson, A., Robutti, O., Sinclair, N. (eds) The Mathematics Teacher in the Digital Era. Mathematics Education in the Digital Era, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4638-1_15
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