Assessing the Epistemic Analysis Competence of Prospective Primary School Teachers on Proportionality Tasks

Solving problems by different methods, identifying the knowledge put at stake in each case, and stating variants of the problems are fundamental aspects of the competence of analysis of mathematical knowledge for teaching. This paper reports on the design, implementation, and results of a formative intervention with primary education prospective teachers to promote developing this competence using tasks that involve proportional and algebraic reasoning. The experience has been carried out with a sample of 88 students (two class-groups), applying a didactic model that includes work in teams, institutionalization, and assessment of the individual learning achieved. Seventy three percent of students were successful in solving problems; however, only 27% of students managed to solve the four problems proposed by at least two different procedures. More than half of the students adequately identified the knowledge involved in each problem and the algebraization level was correctly assigned in more than half of the proposed solutions. Elaborating meaningful variants to the problems was only achieved in a suitable way by less than 20% of the students. It is concluded that developing the epistemic analysis competence of tasks bringing into play proportional and algebraic reasoning requires a greater attention in the teachers’ formative programs.