Descriptores del Desarrollo de la Mirada Profesional en el Contexto de la Generalización de Patrones

Abstract

Resumen El objetivo de esta investigación es generar descriptores del desarrollo de la competencia docente mirar profesionalmente el pensamiento matemático de los alumnos en estudiantes para maestro (EPM), en el contexto de la generalización de patrones. Para ello, se pidió a futuros maestros que describieran las respuestas de tres alumnos de Primaria a un problema de generalización de patrones, que interpretaran la comprensión de los alumnos y que propusieran acciones para mejorar o ampliar el proceso de enseñanza-aprendizaje. A partir de las destrezas que conceptualizan la mirada profesional (identificar, interpretar y decidir) se generaron descriptores de cuatro niveles de desarrollo: (1) EPM que no identifican los elementos matemáticos relevantes en el proceso de generalización de patrones, (2) EPM que identifican los elementos matemáticos, pero no los usan para interpretar la comprensión de los alumnos, (3) EPM que identifican los elementos y los usan para interpretar la comprensión de los alumnos y (4) EPM que identifican los elementos, los usan para interpretar la comprensión de los alumnos y proponer acciones adecuadas para el progreso del aprendizaje de los alumnos de Primaria. Los niveles establecidos y sus descriptores pueden ser el punto de partida para establecer una futura trayectoria de aprendizaje de la mirada profesional y ofrecer información a los formadores para interpretar el progreso de los EPM en el desarrollo de la competencia mirar profesionalmente el pensamiento matemático de los alumnos en el contexto de la generalización de patrones.

Preservice Teachers’ Mathematical Knowledge about Repeating Patterns and their Ability to Notice Preschoolers Algebraic Thinking

“…Although both analyses include elements of interpretation of children's algebraic thinking, in which the pairs try to explain how they have thought, at times, especially in the case of Anabela and Bianca, they eventually focus on retelling the situations. This difficulty in interpreting aspects addressed is in line with several studies (Callejo & Zapatera, 2017;Llinares, 2019;Walkoe et al, 2020), which underscore the added difficulty of the interpretive component.…”

“…Although there are different characterisations of this skill, most authors seem to agree that it refers to aspects that are considered in an educational context and highlight two essential components related to the actions of attending and interpreting (Sherin & van Es, 2009;Walkoe et al, 2020). Several authors (Buforn et al, 2020;Jacobs et al, 2010;Llinares, 2019;Walkoe et al, 2020) have focused their attention on a particular aspect of the teacher's noticing ability regarding children's thinking. In short, the teacher's noticing ability regarding children's thinking is defined as the cognitive ability to identify and interpret the outstanding aspects of the children's activity so that, in this way, they can make conscious decisions (Jacobs et al, 2010).…”

“…Despite its importance for teaching practices, the noticing ability is not innate to teachers (Ivars et al, 2020;Jacobs et al, 2018), so initial teacher education has been seeking to provide PTs with contact with students' work through means such as the analysis of classroom videos (Rodrigues et al, 2019;Walkoe et al, 2020). Several studies seek to investigate how the MK relates to the PTs ability to notice the children's thinking, and the results have shown that, although the MK is important, it is not enough, especially regarding the interpretation of children's thinking (Buforn et al, 2020;Callejo & Zapatera, 2017;Jacobs et al, 2010;Llinares, 2019). About the noticing capacity in the context of algebraic thinking and, in particular, in the context of sequences, some studies have focused on the development of the components of identification and interpretation of the children's thinking.…”

“…About the noticing capacity in the context of algebraic thinking and, in particular, in the context of sequences, some studies have focused on the development of the components of identification and interpretation of the children's thinking. Besides the perception that these two components are related, there seems to be a consensus that interpretation is a more complex process for PTs (Callejo & Zapatera, 2017;Llinares;Rodrigues et al, 2019).…”

“…Although this skill does not have a unique characterisation, it seems to be globally recognised that it refers to attending to important moments, reasoning about them and deciding how to act (van Es et al, 2017). Research has highlighted the importance of this ability for teacher practices (Jacobs et al, 2018;Mason, 2002) and the relevance and need for studies that analyse the noticing of the PTs of the early years in specific mathematical domains, and specifically in algebra context (El Mouhayar, 2019;Llinares, 2019;Walkoe et al, 2020).…”