Analogy in mathematics: beliefs and competences in a seventh-grade class

Abstract

This paper illustrates the didactic itinerary performed in a 7th-grade class with the aim of investigating the development of the students’ beliefs and skills regarding the use of analogy in solving mathematical problems. After collecting the students’ initial beliefs, an itinerary consisting of multiple activities was developed to deepen and strengthen the students’ awareness of the different types of analogy and their use to facilitate problem solving. Results show how students’ awareness of the different types of analogies and their usefulness has improved. They recognize that knowing how to identify two similar problems with respect to the procedure facilitates the resolution of unknown situations. At the end of the itinerary, it is also found that the ability of a part of the students to apply analogical thinking in solving problems has increased, thus favoring the transfer of knowledge.