Abstract This article reports an empirical study investigating how first-grade students in multilingual classes in Sweden experience number lines in an algebraic teaching aligned with the El'konin-Davydov curriculum. A phenomenographic analysis revealed that the students ( n = 150) experienced number lines in terms of three qualitatively distinct categories: (a) Mathematical properties, (b) Relationships between the properties, and (c) Operations on a number line. These categories involved different types of algebraic thinking, identified in the students’ joint analytical work. The higher categories encompass the lower ones, and a greater variety of algebraic thinking was identified in the higher categories. The first, qualitatively lowest, category includes students’ experiences with points on a number line and the distances between them. The second category includes experiences about relationships between the properties in category one (the iterated unit). The third and highest category includes aspects of value (that the value is from the starting position to a specific position, distinguishing between positions and values), the direction of the number line (relationships between unknown quantities depending on their locations on the number line), and the relationships between operations (e.g., addition and multiplication). Suppose the number lines had been introduced in a ready-made form consisting of numerical positions ; the first and second categories identified in this algebraic teaching might not have been possible. The results indicate that these students might use properties and relationships on a number line to enable their mathematical reasoning.
Helena Eriksson (Sun,) studied this question.