Desarrollo del pensamiento relacional y comprensión del signo por alumnos de tercero de educación primaria

  1. Marta Molina
Supervised by:
  1. Encarnación Castro Martínez Director
  2. Enrique Castro Martínez Director

Defence university: Universidad de Granada

Year of defence: 2007

  1. Luis Rico Romero Chair
  2. Isidoro Segovia Alex Secretary
  3. Bernardo Gómez Committee member
  4. John Mason Committee member
  5. Martín Manuel Socas Robayna Committee member

Type: Thesis


This research study is a teaching experiment, related to the proposal Early-Algebra, within the methodological paradigm called research design. Our research goal is the study of the students¿ use and development of relational thinking and the meanings of the equal sign that students display when solving number sentences based on arithmetic properties. We describe and characterize relational thinking and analyze its connection with other terms of the mathematics education literature: number sense, operational sense, structural sense, symbolic sense, flexible computation strategies, mental computation, conceptual meta-strategies and quasivariable thinking. We deepen on the meaning of the terms equality, equivalence and identity, the origin and historical evolution of the equal sign and the various meanings given to this symbol in arithmetic and algebraic context. We discuss the origin, foundation, main characteristics, potential and limitations of design research and, particularly, of transformative and conjecture driven teaching experiments. From the data collection of the empirical part of this study, (a) we identify the strategies used by the participant students when solving the considered number sentences; (b) we characterize the use of relational thinking evidenced in their productions and interventions and identify the elements at the focus of their attention; (c) we analyze and evaluate the students¿ understanding of the equal sign displayed when solving and constructing number sentences; and (d) we describe the evolution of students¿ understanding of the equal sign and of the use of relational thinking they display.