Ponte, J. P., & Henriques, A. (2013). Problem posing based on investigation activities by university students. Educational Studies in Mathematics, 83(1), 145-156.

 Abstract This paper reports a classroom-based study involving investigation activities in a university numerical analysis course. The study aims to analyze students’ mathematical processes and to understand how these activities provide opportunities for problem posing. The investigations were intended to stimulate students in asking questions, to trigger their thinking processes, to promote their ability to investigate and to support them learning numerical analysis concepts and procedures. The results show that the investigations provided opportunities for students to experience mathematical processes, including posing questions, formulating and testing conjectures and, to some extent, proving results. They also provide some understanding about the role of problem posing in these processes. Posing questions occurred mainly in an implicit way, in the interpretation of tasks and in identifying regularities, analyzing graphs and testing cases. The conjectures were often based on pattern identification or data manipulation and the students tended to accept them without testing or proving. The students also proposed alternative formulations for the initial questions and posed new problems from their explorations and attempts to refine previous conjectures.

Ponte, J. P. (2012). A practice-oriented professional development programme to support the introduction of a new mathematics curriculum in Portugal. Journal of Mathematics Teacher Education, 15(4), 317-327. (DOI: 10.1007/s10857-012-9219-y)

Abstract. This paper presents the extended workshop, a national professional development program that was used in the preparatory stages of the introduction of a new mathematics curriculum for basic education (grades 1-9) in Portugal. These workshops are based on five major ideas – orientation towards practice, focus on students’ learning, collaboration, practitioner research, and change of professional culture. The evaluation shows that these workshops constituted a stimulating professional development setting that encouraged teachers to reflect about classroom practice and students’ learning and was quite successful in supporting an overall movement favourable to the orientations of the new curriculum.