Additive problem posing with integers by students in 6th year of Primary Education and 1st year of Secondary Education

Abstract

This work shows how 266 students in the 6th year of Primary Education and the 1st year of Secondary Education pose additive problems with integers based on two questions raised from the abstract and number line dimensions. Transfers from these two dimensions to the contextual dimension are studied, depending on the propositional structure of the problem, the type of model used, and its semantic structure. The problems posed reproduce the ones worked on in class and are, for the most part, problems of change that use displacement models with little contextual variety. The results in 1st year of Secondary Education do not exceed those obtained in the 6th year of Primary Education, which indicates that the formulation of problems does not develop spontaneously, and that greater knowledge does not imply a better understanding of the connections of contextual situations with operations and with the number line. From the results it is inferred that problem posing is a skill that improves understanding and problem solving, stimulates curiosity, motivation and creativity, and, therefore, it is necessary to design a specific instruction to improve this.