LAUSR

We analyzed the written answers and explanations by 26 Brazilian high-school students who attempted to solve double and multiple proportionality problems using the cross-product algorithm. We focused on students’ awareness of the scalar and functional relations among the quantities described in verbal problems, an aspect that has been part of their school instruction. Our results show that, in their written work, the students included data tables or pairs of values, usually with their referents and connected by arrows indicating the scalar or the functional relations described in the problems. In most cases, during individual interviews, they explained their solutions in terms of these relations. Our findings suggest that students’ understanding of proportion relationships between quantities in verbal problems constitutes a basis for their understanding and correct use of algorithms.