Abstract
Beginning university training programs must focus on different competencies for mathematics teachers, i.e., not only on solving problems, but also on posing them and analyzing the mathematical activity. This paper reports the results of an exploratory study conducted with future secondary school mathematics teachers on the introduction of problem-posing tasks in formal mathematics courses, specifically in abstract algebra and real analysis courses. Evidence was found that training which includes problem-posing tasks has a positive impact on the students’ understanding of definitions, theorems and exercises within formal mathematics, as well as on their competency in reflecting on the mathematical activity.
Highlights
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)
The objectve of this research was: Objectve: To study the efect that introducing problem-posing tasks in abstract algebra and real analysis courses has on the comprehension of mathematcal concepts and the academic achievement of prospectve secondary school mathematcs teachers
This research was based on the MAB500 Introducton to Analysis and MA0371 Abstract Algebra courses in the mathematcs-teaching programs at the Universidad Nacional de Costa Rica and the Universidad de Costa Rica, respectvely
Summary
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). This work intends to show how training including problem-posing tasks is a powerful tool to facilitate the comprehension of mathematcal concepts, and the refecton on the mathematcal actvity. The objectve of this research was: Objectve: To study the efect that introducing problem-posing tasks in abstract algebra and real analysis courses has on the comprehension of mathematcal concepts and the academic achievement of prospectve secondary school mathematcs teachers. Malaspina (2013) states that problem-posing is closely related to problem-solving and contributes to the development of mathematcal thinking, by providing opportunites for students and teachers to discuss generalizatons and take inital steps towards mathematcal research. Beginning university training programs must develop the problem-posing —or at least the problemreformulatng— skills of future mathematcs teachers in order to achieve their educatonal objectve. Problem-posing is a means of achieving formal understanding of mathematcal concepts; it is a means through which future teachers can refect on the mathematcal actvity
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