ICMI Study 22: Task Design in Mathematics Education July 2013 Designing Professional Tasks for Didactical Analysis as a research process Yuly Marsela Vanegas ; Joaquin Giménez ; Vicenç Font; Universitat de Barcelona In the present paper, we show a process of designing, assessing and re- designing (following DBR methodology) professional tasks for preservice mathematics teacher training for Secondary School, based on Ontosemiotic perspective for cognition and mathematical instruction (OSA) and the correspondent reflective analysis about associated professional practices. Such a process has been carried out during three consecutive years in the context of the Master’s degree for training teachers of mathematics in Spain. The study shows how the successive revisions promote growing depth analysis in the teaching school practices of the future mathematics teachers. Keywords: Professional tasks, design based research 1. Presentation. In this paper, we show a part of a wider investigation in which we analyze the design of professional tasks in the teachers' formation of Secondary Mathematics Teachers. We focus on the role of design based research (DBR) and teaching experiment (Gravemeijer, 1998) analyzing the planning cycle and redesign of our training process in successive phases, aiming the growing and building knowledge for teaching (Zavlaswski & Sullivan, 2011) by future teachers. We explicitly focus ourselves in recognizing factors that promote the feedback in the design of professional tasks for development of the of didactic analysis competencies of the future mathematics secondary teachers. Our intention is that they can develop sequences of suitable tasks and to be able to re-plan their own designs of school tasks. This work has been carried in a funded Research Project (Assessing and developing professional competencies in mathematics and didactics during initial Secondary Mathematics Teacher Training courses) being the first two authors of this work members of the team who implemented the course. The professional tasks have been evaluated and re-designed by the whole research team during the period 2009-2012. In our study we call professional task those tasks that we propose to the future teachers in order that they realize didactic analysis and develop their didactic analysis competencies understood as the ability for designing, applying and evaluating sequences of learning by means of didactic analysis techniques and quality criteria. The aim is to establish cycles of planning, implementation, evaluation and proposals for improvement. It is also assumed that one could identify criteria and indicators regarding the development of this competence and how it relates to the other professional competencies required by future secondary school mathematics teachers. This assumption is related to the question: How might professional mathematical tasks being designed in order to make best use of the opportunities for being a teacher as teacher enquirer? (Mason & Johnston-Wilder, 2004).