The development of teachers’ expertise through their analysis of good practice in the mathematics classroom

Abstract

This paper describes a study into the development of teachers' expertise, conceptualised as enhanced understanding of practice. This enhancement is detected through various indicators of the teachers' awareness of the complexity of the learning-teaching process, including purposes, beliefs, subject content, and connections between theory and practice. The study is guided by the search for evidence that discussion of what constitutes good teaching leads to a more complex understanding of practice. It starts with a description of the collaborative analysis of a mathematics lesson by a group of teachers, guided by exploring notions of good practice. From this analysis, the researchers extract evidence of improvements in understanding practice on the part of the teachers, in terms of the above indicators. We conclude that the process of characterising good practice in relation to actual samples of teaching can promote the development of teaching expertise. We also note that, in order to analyse practice, teachers require accessible theoretical tools, which allow reflection to go beyond the specifics of a particular lesson.

Una trayectoria de investigación sobre el conocimiento del profesor de matemáticas: del grupo SIDM a la Red Iberoamericana MTSK

“…Nuestro estudio (Carrillo & Climent, 2011) evidenció este desarrollo, en relación con una conciencia metacognitiva del fundamento que hay detrás de las acciones y decisiones de los profesores.…”

Train as a Math Teacher: Creative and Proactive Process of Professional Development

“…Some investigations that have as object of study the teacher as those that are based on a professional look (Sánchez-Matamoros et al, 2015); in professional knowledge (Montes et al, 2013;Carrillo et al, 2018), professional identity (Sanhueza et al, 2013) and teacher empowerment (Reyes-Gasperini & Cantoral, 2013), among others, provide a framework for thinking about a certain parallelism between this possibility of professional development and initial training. Other research (Carrillo & Climent, 2011;Rhoads et al, 2011;Carrillo et al, 2020), allow to think of the initial and continuous training, as a coherent and consistent training continuum, where reflection has a central role. It is in this complementary dialogue of options, in which the idea of the existence of models of professional knowledge, allows us to consider them as structuring the organization of this Diploma (Carrillo et al, 2013;.…”

Buenas prácticas en la Universidad de Huelva: El conocimiento profesional en la acción del profesor de “Matemáticas y su Didáctica”

“…Por otro lado, la resolución de problemas, como perspectiva y metodología de enseñanza, posee un papel importante en el desarrollo de la pericia de los profesores (Carrillo y Climent, 2011). El uso de problemas no es sólo adecuado para promover que los alumnos construyan sus aprendizajes de una manera sólida y consistente, sino que puede considerarse como un indicador de buena práctica universitaria o, al menos, de profesores comprometidos con desarrollar buenas prácticas universitarias.…”