RUME 26
2024
Omaha, Nebraska
Pre-Service Teachers Understanding of Commutativity, Associativity and the Challenge of Order
Page: 343
Commutativity and associativity are recurring properties in school and university mathematics. In design experiments with pairs of secondary pre-service teachers (PSTs) we investigate what they are focusing when discussing commutativity and associativity, and how they deal with the notion of order. A qualitative discourse analysis shows for commutativity that the focus is on the order of two elements for most PSTs. Few focus on the order of several elements. Regarding associativity, bracketing is a main focus for many PSTs. The order in which operations are computed is sometimes discussed explicitly with also emphasizing the order of elements and sometimes more implicitly. The PSTs struggle with the notion of order so that we suggest coping strategies like “demanding precision in language” and “using alternative terms for order”.