Preservice teachers' pictorial strategies for a multistep multiplicative fraction problem

- We examined 85 Pre-Service Teachers (PSTs) pictorial strategies drawn for a multistep fraction word problem in a multiplicative context.
- Seven types of valid strategies were identified based on the representation of the whole, a set vs. area model, and the order of the strategy.
- Invalid strategies were related to difficulties with multiple wholes, different sized fractional parts, and connecting fractions to integers.
- The results suggest PSTs' potential success if they generate pictorial representations for a contextualized multiplicative problem.

Previous research has documented that preservice teachers (PSTs) struggle with understanding fraction concepts and operations, and misconceptions often stem from their understanding of the referent whole. This study expands research on PSTs' understanding of wholes by investigating pictorial strategies that 85 PSTs constructed for a multistep fraction task in a multiplicative context. The results show that many PSTs were able to construct valid pictorial strategies, and the strategies were widely diverse with respect to how they made sense of an unknown referent whole of a fraction in multiple steps, how they represented the wholes in their drawings, in which order they did multiple steps, and which type of model they used (area or set). Based on their wide range of pictorial strategies, we discuss potential benefits of PSTs' construction of their own representations for a word problem in developing problem solving skills.