No abstract

In this paper we present a professional development course designed to impact on teachers' mathematical knowledge for teaching fractions. The main features of the course are the use of i) problem solving activities related with mathematical knowledge for teaching fractions ii) peer discussions and iii) monitor's interventions focused on answering with questions. The objective of this paper is to present some insights on how this type of course may contribute to the development of teachers' knowledge for teaching fractions. To do that we analyze in depth the case of one teacher, using the recording of his work during the course (video, audio, and written documents), his answers to two questionnaires and his responses to an interview six months after the course. Results show how the course's features contributed to the development of this teacher's specific fractions knowledge, knowledge of fractions and students, and of fractions and teaching.

This paper presents some results of an investigation on the number sense of a group of pre-service secondary teachers from Spain. The objective of this research was to analyze students' use of strategies associated to number sense and compare them with those obtained in a previous study with pre-service primary teachers in Taiwan, ( Yang, Reys & Reys, International Journal of Science and Mathematics Education, 7, 383-403, 2009). Pre-service secondary teachers showed lower success than pre-service primary teachers in a number sense test. Nevertheless, these last based their reasoning mainly on rules and algorithms, while pre-service secondary teachers used more strategies of number sense. In an attempt to delve into the low success shown by of Spanish pre-service secondary teachers, some students were interviewed. Those interviews showed that a deeper work on number sense in the training of these students is needed.Ministerio de Ciencias e Innovacion. Madrid EDU2011-29324 FONDECYT 3140597 PIA-CONICYT Basal Funds for Centers of Excellence. Chile BF000

Prácticas docentes, autoeficacia y valor en relación con la resolución de problemas de matemáticas: diseño y validación de un cuestionario. Enseñanza de las ciencias, 36(3), 99-120.

No abstract