Mental computation with rational numbers: Students’ mental representations - Carvalho, Renata (2018)
We construct mental representations of the world that surround us, which we use to understand reality and make inferences. These mental representations reflect our mathematical and real world knowledge, and both are essential to perform mental computation and to relate numbers and operations. The aim of this study is to analyze students’ mental representations underlying their mental computation strategies with rational numbers. Using a design research approach, we undertook two cycles of experimentation involving two teachers and 39 grade 6 students. The results suggest that students’ mental computation strategies are mostly based on numerical relationships where descriptive representations play an important role. School contexts and daily life experience, where students’ are involved when learning about numbers and operations, seem to be key promoters of mental representations.