The Development of Multiplicative Calculation Flexibility by 3rd Grade Students

Abstract This article aims to understand how the students develop the multiplicative calculation flexibility in a context of exploratory teaching, answering three research questions: (i) What are the strategies used by students when solving multiplication tasks?; (ii) How do the strategies used by the students evolve?; and (iii) How do the students use the multiplicative calculation in a flexible manner? The investigation adopts a qualitative methodology within an interpretive paradigm having been held a teaching experience in a 3rd grade classroom. The data collection took place through the following techniques: participant observation and documentary collection. The article focuses only one pair of students. The results show that students used multiple strategies to solve tasks involving multiplication, evolving from additive strategies, associated with sequences of multiples, to multiplicative strategies, establishing numerical relationships, and using known basic multiplication facts and properties. This evolution is associated to the development of multiplicative calculation flexibility by the students, which is initially anchored in organizing the objects in equal parts, evidencing, at the end of the teaching experience, a clear connection between the idea of the same product being symbolized by a high number of multiplicative decompositions, the operation of division and the identification of the proportional relationship. The study shows the lack of parallelism between the development of multiplicative strategies in calculation and proportional situations.