Brazilian math teacher’s magnitude representation and strategy use in fraction comparison: a mixed methods study

Resumo

Fractions are fundamental in constructing mathematical knowledge, the basis for algebra, and other advanced mathematical content. However, historically, those representations of rational numbers present obstacles for students and teachers. One conceptual base for fractional thinking is magnitude, yet how teachers process fraction magnitudes remains unknown. We investigated Brazilian math educators’ knowledge of fraction magnitudes through a convergent parallel mixed-method approach. We collected quantitative data based on teachers’ fraction magnitude comparisons, followed by a qualitative task where participants explained their answers on a subset of the comparisons. Participants’ magnitude comparison accuracy suggested holistic fraction magnitude processing as rational but not componential distance modulated performance. However, educators’ reported strategies revealed many used a flawed Gap strategy, whereby they calculated the difference between the numerator and denominator and selected the fraction with the smallest gap as the larger fraction. As this strategy fails to generalize, teachers’ use signals flawed reasoning. Given the relationship between teacher knowledge and student learning, these results have important implications for improving students’ rational number outcomes.