Difficulties in Codifying, Relating, and Sorting Algebraic Verbal Problems: two studies with secondary students and pre-service teachers

Solving verbal problems by transfer implies the activation of other, previously solved problems by means of the analogies perceived between these and the ‘target problems’. Two related studies are conducted to analyse what features students focus on to codify problems and to build analogies among them when sorting tasks are proposed. Quantitative and qualitative techniques were used in the analysis. First, we analysed how different science problem characteristics influence secondary students’ task performance. A high proportion of participants were not able to perceive suitable analogies and differences among problems. The second study tried to look for explanations. The Academic level and the Familiarity with the problems topic were significant factors. However, our grade participants, in a pre-service post-grade course to be mathematics teachers, found more difficulties than expected, indicating that some usual instructional assumptions should be reconsidered.

Algebraic Verbal Problem Solving; Problem Surface and Structure; Familiarity with the subjetc; Analogies among Problems; Problem sorting