The case of disappearing and reappearing zeros: a disconnection between procedural knowledge and conceptual understanding

We report on 25 Year 5-6 students’ written responses to two items taken from an assessment of mental computation fluency with multiplication, alongside their reasoning of the strategy they had employed, which may or may not have made use of the associative property. Coding of this interview data revealed four distinct levels of conceptual understanding of the associative property, which teachers could use to inform their planning. The findings reveal the complexity associated with assessing multiplicative mental computational fluency and students’ reliance on procedures often considered by them to be more magical than logical.