Teaching of the associative property: A natural classroom investigation

In this study we investigate the teaching of the associative property in a natural classroom setting through observation of classroom video of several elementary math classes in a large urban school district. Findings indicate that the associative property was often conflated with the commutative property during teaching. The role of the associative property in many computational tasks remained fully implicit, even after the property had been formally introduced. Most classrooms did not present the associative property with substantial justification in terms of concrete representations, especially those in which the abstract property was formally introduced - while a few classrooms did situate the property in rich concrete contexts, the property remained implicit in these classes, indicating a lack of linking between the concrete and the abstract when teaching the property. Instruction also did little to develop the notion of the associative property as a property of an operation conceptualized as a mental object, rather than as a rule governing the outcome of a procedure. Much of the instruction displayed a significant focus on computational strategies, which aggravated the challenge of providing a clear explanation of the nature and meaning of the associative property.

Barnett, E. & Ding, M. (2018). Teaching of the associative property: A natural classroom investigation. Investigations in Mathematics Learning. DOI: 10.1080/19477503.2018.1425592