Students´ reasoning on multiplication in primary school classroom context

Abstract

This article investigates how students in third grade discuss and reason on multiplication when they first encounter that concept in the classroom context. By analysing the data from 24 classrooms focused on teaching and learning multiplication, the article aims at contributing to the research and conceptualisations about students´ reasoning and strategy use in multiplication. The analysis shows that some of the features within previous research are helpful in characterizing the students´ reasoning about multiplication. However, the data material also reveals new aspects of students´ reasoning multiplication in classroom settings. One aspect is how students reason about different characteristics of multiplication, and reason about the concept of multiplication in a more general way. They put it in a broader context by going beyond the actual example in which the activity takes place. The students have moved away from the actual example, shifting their attention towards a focus on mathematical relationships. Another aspect is how a strong emphasis on using addition when they work with multiplication, by for instance that some students may begin to use different sub-totals, can cause tensions in the discussions between the teacher and students. Results are discussed in relation to previous studies of students´ multiplicative reasoning and implications for practice are elaborated upon.