How prospective kindergarten teachers develop their noticing skills: the instrumentation of a learning trajectory

Abstract

The objective of this study was to characterise prospective kindergarten teachers' development of noticing children's thinking about length and its measurement. We used the concepts of instrumental genesis and learning trajectories to identify the ways in which prospective kindergarten teachers used a learning trajectory to learn to notice children's mathematical thinking. Following a teaching experiment, we identified three ways in which prospective kindergarten teachers used the learning trajectory to notice children's mathematical thinking. Two instrumented action schemes supported these ways of using the learning trajectory: a scheme taking into account the mathematics learning progression to interpret children's answers, and a scheme for proposing instructional tasks based on the interpretation of children's mathematical thinking. Approaching the development of noticing as an appropriation process of a learning trajectory helps us to understand prospective teachers' difficulties at endowing meaning to a learning trajectory's conceptual structure. We suggest that these ways of using learning trajectory knowledge to interpret children's mathematical thinking and to make instructional decisions can be understood as an instrumentation process which reveals how noticing skills develop.

Measuring pre-service teachers’ noticing competencies within a mathematical modeling context – an analysis of an instrument

“…For example, with a focus on mathematics education, in TEDS-FU 2 items were used concerning mathematics-related classroom demands and pedagogy-related classroom demands (Kaiser et al, 2017). In terms of a more specific research focus, Moreno et al (2021), for example, examined the development of teachers' noticing competence with regard to the topic length and measurement.…”

Aprendiendo a mirar profesionalmente las situaciones de enseñanza de las matemáticas

“…Por ejemplo, cuando los estudiantes para maestro usan un modelo de progresión de la comprensión del concepto matemático (trayectoria de aprendizaje) para interpretar la comprensión de los estudiantes y poder justificar su propuesta de nuevas tareas para apoyar el aprendizaje de los estudiantes. Por ejemplo, Moreno y colaboradores (Moreno et al, 2021;Sánchez-Matamoros et al, 2018 describen el uso por parte de los estudiantes para maestro de educación infantil de una trayectoria de aprendizaje de la longitud y su medida como instrumento conceptual para interpretar las estrategias usadas por los niños y justificar las nuevas tareas a proponerles. Por su parte, Ivars et al (2016, Claudia Lisete O. Groenwald, Salvador Llinares 2020a, 2020b describen cómo estudiantes para maestro de educación primaria interpretan la comprensión de los niños del concepto de fracción según un modelo de progresión de la comprensión para justificar las nuevas tareas a ser propuestas.…”

“…Cuando el foco de atención es un tópico matemático particular se generan particularidades que han puesto de manifiesto necesidades que deben ser tenidas en cuenta en esta línea de investigación (Dindyal et al, 2021). Así, algunas de las investigaciones se centran en conceptos o tópicos matemáticos concretos, por ejemplo, la magnitud y medida, las fracciones como en los casos indicados anteriormente (Ivars et al, 2016(Ivars et al, , 2020Moreno et al, 2021; o el razonamiento proporcional (Fernández et al, 2011). Estas investigaciones se han centrado en cómo y en qué medida los estudiantes para profesor identifican e interpretan el pensamiento matemático según las evidencias en las resoluciones de los problemas.…”

Supporting Pre-service Mathematics Teachers’ Professional Noticing of Students’ Reasoning About Length

“…Thus, in this study, we investigate how the professional noticing skills of pre-service elementary mathematics teachers in the context of length measurement develop through discussions based on the "Levels of Sophistication in Students' Reasoning about Length" (Battista, 2006) conceptual framework. It is believed that by understanding research-based frameworks of students' mathematical thinking, preservice teachers can recognize significant aspects of contents, associate their knowledge with relevant aspects in students' reasoning and interpret it in order to decide what course of action to take, and thus develop professional noticing skills (Moreno et al, 2021).…”