This article describes part of the findings of a teaching experiment whose objective is to investigate the algebraic abilities of elementary students when they solve situations that involve a functional relationship. In particular, we focus on describing the use and meanings attributed to letters by third-year primary school students when faced with verbal problems related to the generalisation of a functional relationship. Drawing from the functional approach to early algebra and set in Spain, the study expands on earlier research conducted on primary school students’ use of letters in algebraic contexts. Their initial reactions to the use of letters to represent indeterminate quantities and how those reactions changed in the course of three sessions are described. Analyses of the students’ written answers together with their participation in group discussions yield qualitative data on how students associate the idea of variability with indeterminate quantities and use letters, numbers or both to represent that notion.

La Investigación de Diseño (Design Research) es un paradigma metodológico relativamente joven que está siendo de gran utilidad en el campo de la Didáctica de las Ciencias. En este trabajo aportamos una descripción general de dicho paradigma centrándonos en más detalle en la metodología concreta de los experimentos de enseñanza. Presentamos y ejemplificamos las principales características de este tipo de estudios, enriqueciendo la descripción aportada por la literatura con las conclusiones extraídas en nuestra experiencia en su puesta en práctica. Nuestro objetivo es contribuir a su divulgación y desarrollo, así como promover la reflexión y discusión sobre esta metodología.

How third-grade students developed an understanding of the equals sign and began to use relational thinking as they discussed true/false and open-number sentences. The sequence of instructional activities and children's responses to them are provided.