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Problem posing as a didactic resource in formal mathematics courses to train future secondary school mathematics teachers

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This paper reports the results of an exploratory study conducted with future secondary school mathematcs teachers on the introducton of problem-posing tasks in formal mathematcs courses, specifcally in abstract algebra and real analysis courses. | Journal of Technology and Science Education PROBLEM-POSING AS A DIDACTIC RESOURCE IN FORMAL MATHEMATICS COURSES TO TRAIN FUTURE SECONDARY SCHOOL MATHEMATICS TEACHERS Lorena Salazar Solórzano Universidad de Costa Rica. Universidad Nacional de Costa Rica Costa Rica lorena.salazarsolorzano@ucr.ac.cr Received November 2014 Accepted December 2014 Abstract Beginning university training programs must focus on diferent competencies for mathematcs teachers, i.e., not only on solving problems, but also on posing them and analyzing the mathematcal actvity. This paper reports the results of an exploratory study conducted with future secondary school mathematcs teachers on the introducton of problem-posing tasks in formal mathematcs courses, specifcally in abstract algebra and real analysis courses. Evidence was found that training which includes problem-posing tasks has a positve impact on the students’ understanding of defnitons, theorems and exercises within formal mathematcs, as well as on their competency in refectng on the mathematcal actvity. Keywords – Posing problems, Inital training, Mathematcs educaton, Groups, Contnuity. ---------- 1 INTRODUCTION In the last decade, there has been an increase in the number of research studies on the knowledge and competencies that future mathematcs teachers need to acquire in order to succeed in their profession (Rubio, 2012; Ball, Thames & Phelps, 2008; Hill et al., 2008; Silverman & Thompson, 2008; Font, 2011). For example, Rubio (2012) points out that a mathematcs teacher must not only atain competency in mathematcs, but also competency in the analysis of the mathematcal actvity. This work intends to show how training including problem-posing tasks is a powerful tool to facilitate not only the comprehension of mathematcal concepts, but also the refecton on the mathematcal actvity. Specifcally, the objectve of this research was: Objectve: To study the efect that introducing problem-posing tasks in abstract algebra and real .