Middle School Mathematics Students' Justification Schemes for Dividing Fractions

Three theoretical frameworks were used to guide this intervention case study: dividing fractions; sociomathematical norms, and justification.

Middle school mathematics students were given the opportunity to solve partitive and measurement division of fraction word problems with different contexts.

The teacher purposefully implemented a sociomathematical norm that an explanation consists of a mathematical argument, not simply a procedural description or summary.

In order for students to justify based on reasoning they were expected to use three guiding principles: convince themselves by making personally-meaningful solutions to problems; convince others by communicating their understanding through graphic representations, words (written and oral), and symbols; and make sense of other students' justifications to raise challenges if disagreements occurred.

The case of one student was documented in depth. Three claims emerged from the three guiding principles: Taylor was aware of her own thinking and learning so she used strategies that made sense to her; Taylor was not always explicit about the unit as a whole, and she was not always able to convince others; and Taylor asked clarifying questions when she disagreed with another student's justification.