24 SES 02 A, Issues in Mathematics Teacher Education (Part 1)
Paper Session: to be continued in 24 SES 03
In this paper we analyse how the didactical analysis of specific professional tasks in mathematics may led mathematics teachers’ trainers to redesign specific mathematics tasks to better support prospective teachers to develop their mathematical and educative competences. We aim to encourage future teachers of mathematics to improve their professional practice by equipping them with didactical tools based on a rigorous theoretical foundation (Zavlaswski & Sullivan, 2011). For this reason we discuss in this paper the results of a research process framed in the “Mathematics Teacher Training Program” [Master Program] addressed to future teachers for middle and high schools, provided at the University of Barcelona. We expect to discuss tools for a descriptive and explanatory analysis aiming to answer “what happens in the classroom and why?”
Our general intention in such a program is led future teachers to develop the [professional] ability to (re)design sequences of suitable tasks, as well as to make them able to re-design their own designs of school tasks. In our study we call ‘professional task’ those tasks that we propose to future teachers in order to encourage them doing didactic analysis and developing their didactical analysis competencies. We understand ‘competence’ the ability for designing, applying and evaluating sequences of learning by means of didactic analysis techniques and quality criteria. It is also assumed that someone may reflect and improve their competence in terms of the analysis of mathematical classrooms, in order to make best use of the opportunities for being a teacher as teacher enquirer (Mason & Johnston-Wilder, 2004).
We want to focus on some immediate effects over the Program. We found them when analysing prospective teachers’ thoughts emerging from their feedback with the researchers; and also emerging from our analysis of some impacts of the program itself. Such above mentioned development, it is stated when future teachers incorporate and use tools for the description, explanation and process valuation of mathematical school teacher/learning practices.
In this paper we discuss data emerging out from a teaching research project based on an inquiry and reflective practicing framework in which we design and implement diverse teacher training cycles as teaching experiments (Tzur, Sullivan & Zaslavsky, 2008) for developing transversal competencies such as “citizenship”, “digital competency”, “didactical analysis”, among others.
The development of the cycles was based from the very beginning of the research process in six big types of professional tasks: (a) analysis of practices, objects and mathematical processes; (b) analysis of didactic interactions, conflicts and norms; (c) evaluation of tasks and classroom episodes using criteria of didactic suitability or quality; (d) design and implementation of a lesson in their [prospective teachers] period of internship; (e) analysis and valuation of the suitability of the didactic implemented unit; (f) improvement of their lessons designs (for future implementation).
The analysis and description of the mathematical activity is conducted using the theoretical constructs proposed by the ‘Ontosemiotic’ approach (Font, Planas y Godino, 2010). According to this perspective, the mathematical activity plays a central role and it is modelled in terms of systems of operative and discursive practices. From these practices the different types of related mathematical objects emerge building cognitive or epistemic configurations among them. Problem-situations support and contextualize the mathematical activity; languages (symbols, notations, and graphics) may serve as tools for action; arguments justify the procedures and propositions embedded within the concepts. According to this approach, the objects appearing in mathematical practices might be considered from a dual dimension.
Font, V., Planas, N. & Godino, J. D. (2010). Modelo para el análisis didáctico en educación matemática [A model for didactic analysis in mathematics education]. Infancia y Aprendizaje, 33(1), 89-105. Garuti,R & Boero,P (2002) Interiorisation of forms of argumentation: A case study. In A.D. Cockburn & E. Nardi (eds) Proceedings of 26th PME Conference, (Vol. 2, pp. 408-415). Norwich UK University of West Amglia. Laborde, C., Perrin-Glorian, M.J.; Sierpinska, A. (2005). Beyond the Apparent Banality of the Mathematics Classroom (1-12). Netherlands: Springer. Mason, J.; & Johnston-Wilder, S. (2004). Designing and Using Mathematical Tasks. Tarquin: London. Tzur, R., Sullivan, P., & Zaslavsky, O. (2008). Examining teachers' use of (non-routine) mathematical tasks in classrooms from three complementary perspectives: Teacher, teacher educator, researcher. In O. Figueras & A. Sepúlveda (Eds.), Proceedings of the Joint Meeting of the 32nd Conference of the PME, and PME-NA (Vol. 1, pp. 133-137). México: PME. Zaslavsky, O., & Sullivan, P. (Eds.). (2011). Constructing knowledge for teaching: Secondary mathematics tasks to enhance prospective and practicing teacher learning. New-York: Springer.
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