Abstract
Background: Many teacher education programmes aim for prospective teachers to learn to notice mathematics teaching-learning situations based on learning trajectories of specific concepts. However, there has not been a deeper study on how they use that knowledge to notice children’s mathematical thinking. Objective: To identify characteristics of the instrumental genesis process in an early childhood prospective teacher as he notices a classroom situation using a learning trajectory of length and its measurement as an artefact. Design: We have adapted Rabardel’s instrumental approach. Settings and Participants: An early childhood prospective teacher solving a professional task (case study). Data collection and analysis: We analyse the student’s activity while solving the task, considering the processes of instrumental genesis. Results: The outcomes reveal characteristics of professional noticing skills: (a) providing mathematical meaning to the elements allows constructing utilisation schemes to identify ; (b) considering the inclusiveness of levels of understanding and the continuity of progression in learning allows constructing utilisation schemes to interpret , and (c) considering the sequentiality of levels of understanding allows constructing utilisation schemes to make decisions . Conclusions: Instrumental genesis allows identifying which schemes a kindergarten prospective teacher constructs and how he/she acquires his/her professional noticing, and provides information for the teacher educator to make instructional decisions. For example, in our case, the teacher educator provides the prospective teacher of this case study with tasks to give meaning to the transitivity element and variety of contexts related to conservation.
Highlights
Many current teacher education programmes design their teaching modules aiming to help prospective teachers learn how to notice at mathematics teaching-learning situations (Bartell et al, 2013; Llinares, 2012; Stokero, 2014; Wilson et al, 2013)
The module consisted of a theoretical document that included a learning trajectory of length and its measurement, three professional tasks composed of classroom situations with three questions for a structured analysis of each situation; and a teaching planning task in which they were asked to select tasks, establish consistent objectives, anticipate possible children’s answers, and make decisions to favour the learning progression (Llinares, 2014, p. 37)
Pedro manifests instrumentalisation processes in the usage schemes to solve question 1, selecting from the learning trajectory the mathematical elements of magnitude and measurement that he thinks the teacher considers necessary for the young children solve the task, as evidenced in his answers
Summary
Many current teacher education programmes design their teaching modules aiming to help prospective teachers learn how to notice at mathematics teaching-learning situations (Bartell et al, 2013; Llinares, 2012; Stokero, 2014; Wilson et al, 2013). Recent rstudies consider that early childhood teachers must develop skills to recognise everyday situations and turn them into teaching-learning situations (Gasteiger & Benz, 2018; Gasteiger et al, 2020). These types of situations of exploring and recognising the concept should allow children to transform informal mathematical knowledge into formal mathematical knowledge (Empson & Junk 2004). Objective: To identify characteristics of the instrumental genesis process in an early childhood prospective teacher as he notices a classroom situation using a learning trajectory of length and its measurement as an artefact. In our case, the teacher educator provides the prospective teacher of this case study with tasks to give meaning to the transitivity element and variety of contexts related to conservation
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