### Preservice Teachers’ Understanding of Fraction Multiplication, Representational Knowledge, and Computational Skills

#### Abstract

Despite the importance of teacher fractional knowledge, there are several questions unanswered. The purpose of this study was to characterize profiles of preservice teachers’ (PSTs) mathematical competence on the topic of fraction multiplication by examining PSTs’ understanding of multiplication of fractions in three different contexts. Analyses of 60 PSTs’ written responses revealed that there are distinct gradations of competency, ranging from the PSTs who were unable to solve a given problem in any context to those capable of flexibly portraying understanding of fraction multiplication in three contexts. Most PSTs who recognized the word problem as a multiplication of fractions were able to explain their thinking using graphical representations. However, we also observed various types of errors PSTs made in representing the word problem in graphical representations and translating it to a correct multiplication expression. These findings offer descriptors of how the PSTs understand fraction multiplication in different contexts and provide information for the design of intervention in teacher education. One objective would be to support recognition of the connectivity of fraction multiplication in different contexts.

#### Keywords

#### References

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