Developing Pre-Service Teachers’ Noticing of Students’ Understanding of the Derivative Concept

Abstract

Abstract. This research study examines the development of the ability of pre-service teachers to notice signs of students' understanding of the derivative concept. It analyses pre-service teachers' interpretations of written solutions to problems involving the derivative concept before and after participating in a teacher training module. The results indicate that the development of this skill is linked to pre-service teachers' progressive understanding of the mathematical elements that students use to solve problems. We have used these results to make some suggestions for teacher training programmes.

Conocimiento de los estudiantes para maestro cuando interpretan respuestas de estudiantes de primaria a problemas de división-medida

“…Although noticing effectively is, both complex and challenging, previous studies have shown that this competence could be developed in teacher training programs. Proof of such development can be found in Fernández, Llinares and Valls (2013) in the proportionality context and in Sánchez-Matamoros, Fernández and Llinares (2014) in the derivative context. However, the difficulties found in the development of this competence make further research necessary in order to know which is the mathematical teaching knowledge required by PSTs in the different mathematical domains.…”

Application of the APOS-ACE Theory to improve Students’ Graphical Understanding of Derivative

“…Students could not explain why the graph of is not differentiable in some points (Question 2). If a function is not presented in equation form, and the values of the function are presented in a Table (Question 3) many students cannot estimate the value of the derivative at a point with the use of the data from that table and with the use of the limit of the sequence of difference quotients, Badillo et al, 2011;Sánchez-Matamoros, Fernández, & Llinares, 2015). Furthermore, this difficulty is seen when the function is only presented graphically (Question 4) and students had to sketch the graph of the derivative function (Borji, Font, Alamolhodaei, & Sánchez, 2018).…”

Learning Pathway of Length and Its Measurement as a Conceptual Instrument Used by Future Teachers

“…En esta línea de investigación el trabajo de Sánchez -Matamoros, Fernández y Llinares (2015), en el que se diseñó un módulo de enseñanza sobre la derivada para el desarrollo de la mirada profesional en estudiantes para profesor de secundaria, se apoyaba en una trayectoria de aprendizaje sobre la derivada basada en una revisión de la literatura sobre dicho concepto. Por su parte Wilson, Mojica y Confrey (2013) estudiaron cómo maestros de primaria que habían seguido un programa de formación donde se les había presentado una trayectoria de aprendizaje sobre la equipartición (EPLT -EquiPartitioning Learning Trajectory; Confrey, Maloney, Wilson y Nguyen, 2010) utilizaban los estadios de esta trayectoria para identificar la comprensión de los estudiantes.…”