Un análisis del concepto de pensamiento algebraico basado en evidencia empírica

• Marilena-Barbara Chrysostomou ^[1] ; Constantinos Christou ^[1]
  1. [1] University of Ciprus
• Localización: Journal for the Study of Education and Development, Infancia y Aprendizaje, ISSN-e 1578-4126, ISSN 0210-3702, Vol. 42, Nº 3, 2019 (Ejemplar dedicado a: Pensamiento algebraico temprano : estudios desde diversas perspectivas, enfoques y regiones), págs. 750-781
• Idioma: español
• DOI: 10.1080/02103702.2019.1604022
• Títulos paralelos:
  • Analysing the notion of algebraic thinking based on empirical evidence
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• Dialnet Métricas: 1 Cita
• Resumen
  • español

    El objetivo del presente estudio era analizar la estructura y el Desarrollo del pensamiento algebraico en sus diversas dimensiones. Para ello, 803 estudiantes de entre 10 y 13 años completaron una prueba de pensamiento algebraico. De ellos, 101 estudiantes con distintos resultados en la prueba participaron en entrevistas semiestructuradas para estudiar en mayor detalle las estrategias que utilizaban y las dificultades alas que se enfrentaban. Los resultados confirmaron la naturaleza polifacética del pensamiento algebraico y revelaron que este consta de tres aspectos: razonamiento sobre la covariación, generalización de propiedades aritméticas y capacidades relacionadas directamente con la sintaxis algebraica. Cada uno de estos aspectos se compone de capacidades específicas de pensamiento algebraico como, por ejemplo, formular relaciones utilizando símbolos algebraicos. Se identificaron cuatro grupos de estudiantes con distintos perfiles de pensamiento algebraico: ‘pensamiento pre-algebraico’, ‘pensamiento protoalgebraico-procedimental’, ‘pensamiento algebraico simbólico-relacional’ y ‘pensamiento algebraico global-estructural’. Los resultados también corroboran la presencia de una tendencia constante en el nivel de dificultad en todas las capacidades de pensamiento algebraico que sugiere una tendencia específica en el desarrollo desde una perspectiva más procedimental del pensamiento algebraico hacia unamás estructural.

  • English

    The purpose of the present study was to examine the structure and development of algebraic thinking across multiple dimensions. An algebraic thinking test was administered to 803 students aged 10–13 years old. One hundred and one students of different performance outcomes in the algebraic thinking test participated in semi-structured clinical interviews in order to develop further insights into students’ strategies and difficulties. The results confirmed the multifaceted nature of algebraic thinking and showed that algebraic thinking consists of three aspects: reasoning about covariation, generalization of arithmetic properties and abilities directly related to algebraic syntax. Each one of these aspects is composed of specific algebraic thinking abilities, such as modelling relations using algebraic symbols. Four groups of students of different algebraic thinking profiles were identified: ‘pre-algebraic’, ‘protoalgebraic-procedural’, ‘relational-symbolic algebraic thinking’ and ‘structural-global algebraic thinking’. The results also supported the presence of a consistent trend in the difficulty level across the algebraic thinking abilities, which suggests a specific developmental trend from a more procedural perspective of algebraic thinking to a more structural one.

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