This Round Table presents in a brief way four different studies carried out in Portugal in recent years and that address issues related to mathematics teacher education. The first three studies concern inservice teachers, the first is drawn from a very large scale national teacher education project, the second concerns a format that is been used in many countries but that is applied in Portugal in a rather specific way, the third describes a collaborative study, a common teacher education setting used in our country, and, finally, the last study concerns prospective teacher education regarding creativity, a dimension that is receiving increasing interest in current research. Given the nature of the theme (research in Portugal, the host country of the congress), the presenters are all Portuguese, and there is discussant from another country.

1. In-service teacher education: the importance of classroom supervision. The goal of this communication is to stress the importance of classroom supervision for teacher development, based on data from an in-service teacher education programme that included supervision of classroom practices, which means an action of systematic monitoring of teaching practice, especially through procedures of reflection and experimentation (Vieira, 1993).

2. Lesson study as a professional development framework. Lesson study is a professional development process focused on professional practice that had its origins in Japan, but which in recent years has been widely recognized in several countries. An important feature of lesson studies is their reflexive and collaborative nature (Fernandez, Cannon, & Chokshi, 2003; Perry & Lewis, 2009). Teachers work together, identifying the students’ difficulties, documenting the curriculum alternatives, and preparing what they expect may be an “exemplary” lesson. Afterwards, they verify to what extent this class achieves the desired objectives and what difficulties arise. Therefore, it is a process very close to a small investigation of the teachers on their own professional practice. Such studies are usually informed by the curricular guidelines and by the results of investigations relating to a given topic of school programs. In this research, our aim is to know that professional learning teachers make within the framework of a lesson study regarding the nature of the tasks, students’ reasoning processes, and communication in the classroom. We also seek to know which features of lesson studies make them effective professional development settings.

3. A collaborative project as an opportunity for mathematics teacher development. This talk discusses a long-term collaborative project aiming at understanding teaching practices and developing classroom communication processes. It addresses the following question: What are the influences, if any, of a collaborative project on teacher’s conceptions and practices regarding classroom communication?

4. Creativity as a component of mathematics learning and teaching in pre-service education. Research shows that tasks greatly influence the way students learn. Mainly, challenging tasks related with problem solving and posing that can lead to the understanding of fundamental mathematical concepts, while encouraging fluency, flexibility and originality - the dimensions of creative thinking (e.g. Leikin, 2009; Silver, 1997). Our aims are to: 1) identify traits of creativity in future teachers when they solve challenging tasks; 2) see they identify themselves traits of creativity, when analyzing productions realized by elementary students, of the same type of tasks they have done.

Bogdan, R., & Biklen, S. K. (1982). Qualitative research for education: An introduction to theory and methods. Boston: Allyn & Bacon. Brown, S., & McIntyre, D. (1993). Making sense of teaching. Buckingham: Open University. Denzin, N. K., & Lincoln, Y. S. (1989). Handbook of qualitative research. Sage: Newbury Park. Erickson, F. (1986). Qualitative methods in research on teaching. In M. C. Wittrock (Ed.), Handbook of Research on Teaching (pp. 119-161). New York: Macmillan. Fernandez, C., Connon, J., & Chokshi, S. (2003). A US-Japan lesson study collaboration reveals critical lenses for examining practice. Teaching and Teacher Education, 19, 171-185. Goetz, J. P., & LeCompte, M. D. (1984). Ethnography and qualitative design in educational research. San Diego: Academic Press. Jorgensen, D. L. (1989). Participant observation: A methodology for human studies. Newbury Park: Sage. Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. In R. Leikin, A. Berman and B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 129-145). Rotterdam, Netherlands: Sense Publishers. Miles, M., & Huberman, A. M. (1994). Qualitative data analysis (2nd ed.). Newbury Park: Sage. Perry, R., & Lewis, C. (2009). What is successful adaptation of lesson study in the US? Journal Educational Change, 10, 365-391. Ravid, R., & Handler, M. G. (2001). The many faces of school-university collaboration: Characteristics of successful partnerships. Colorado, CO: Teacher Ideas Press. Schon, D. (1983). The reflective practioner: how profissionals think in action. New York: Basic Books, . Serrazina, l. (1999). Reflexão, conhecimento e práticas lectivas em Matemáica num contexto de reforma curricular no 1.º ciclo. Quadrante, 8, 139-167. Silver, E. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. International Reviews on Mathematical Education, Essence of Mathematics, 29(3), 75–80. Retrieved March 10, 2003, fromhttp://www.fizkarlsruhe.de/fix/publications/zdm/adm97 Smith, M. S. (2001). Practice-based professional development for teachers of mathematics. Reston, Va: NCTM. Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10, 313-340. van der Berg, R. (2002). Teachers’ meanings regarding educational practice. Review of Educational Research, 72(4), 577-625 Vieira, F. (1993). Supervisão. Uma Prática Reflexiva de Formação de Professores. Rio Tinto: Edições ASA.