: This paper is part of broader research being conducted in the area of algebraic thinking in primary education. Our general research objective was to identify and describe generalization of a 2nd grade student (aged 7–8). Specifically, we focused on the transition from arithmetic to algebraic generalization. The notion of structure and its continuity in the generalization process are important for this transition. We are presenting a case study with a semi-structured interview where we proposed a task of contextualized generalization involving the function y = x + 3. Special attention was given to the structures evidenced and the type of generalization expressed by the student in the process. We noted that the student identified the correct structure for the task during the interview and that he evidenced a factual type of algebraic generalization. Due to the student’s identification of the appropriate structure and the application of it to other different particular cases, we have observed a transition from arithmetic thinking to algebraic thinking.

This study is part of a broader study on algebraic reasoning in elementary education. The research objective of the present survey, namely to describe generalization among second grade (7- to 8-year-old) students, was pursued through semi-structured interviews with six children in connection with a contextualized generalization task involving the function y = x + 3. Particular attention was paid to the structures recognized and the type of generalization expressed by these students as they reasoned. In all six, we observed three phases of inductive reasoning: (a) abductive, (b) inductive and (c) generalization. The students correctly recognized the structure at least once during the interview and expressed generalization in three ways.

In this study, we adopted a functional perspective on algebra. Our focus was on tables and how they were first used by second-grade elementary school students (7- and 8-year-olds) when working with functions. This qualitative, exploratory, and descriptive study consisted of five classroom sessions and two semi-structured interviews, one group and one individual, two weeks apart, focused on tasks involving different functions and uses of tables, with and without labels for headings. In this study, we ask the following research questions: How do children organise values in tables with or without (a priori) labels for headings? What are the regularities (structures) identified by students? Our data revealed that students were able to organise the values of variables by listing them in columns and labelling the headings (i.e., identifying the variables involved). The ways in which children organised the data in tables enabled us to identify the structures they identified as regularities between the variables involved in the functions. More structures were correctly identified in the second interview compared to the first.

Este trabajo es parte de una investigación más amplia que se desarrolla en el ámbito del pensamiento algebraico de estudiantes de educación primaria en España. Nos centramos aquí en identificar las estructuras (regularidades identificadas) y las representaciones que aparecen cuando los estudiantes trabajan con tareas de generalización. Involucramos funciones lineales en un estudio de caso dentro del experimento de enseñanza con tres estudiantes de 2º de educación primaria (7-8 años). Destacamos que el número de estructuras y la forma de generalizar la estructura dependen de las tareas planteadas en cada caso, según la función implicada. Las generalizaciones de todos los estudiantes se han representado mediante representaciones verbales y/o numéricas.