Changes in How Prospective Teachers Anticipate Secondary Students’ Answers

Abstract

This study focuses on how prospective teachers learn about students' mathematical thinking when (i) anticipating secondary students' answers reflecting different characteristics of understanding and (ii) propose new activities in relation to the classification of quadrilaterals. The data were collected from forty-eight prospective secondary school teachers enrolled in an initial training programme. The results indicate three changes in how the prospective teachers anticipate secondary students' answers in relation to the role given to a perceptual or relational perspective of the classification of quadrilaterals. These changes are described considering how prospective teachers grasp the students' understanding of the inclusive relation among quadrilaterals as a conceptual advance. We argue that prospective teachers' learning was promoted after participating in a structured environment where they had the opportunity to discuss how to recognize the features of student's understanding.

Who says Organic Chemistry is Difficult? Exploring Perspectives and Perceptions

“…Evidence from research in Mathematics education has found that teaching and learning can be enhanced in a supported environment where teachers have the opportunity to recognise intricate features of their learners' meta-cognition (Llinares et al, 2016). This is not to suggest that teachers should teach using only strategies and techniques that learners approve of, but that they should try to bridge the gap between their perspectives of effective teaching and those of their learners.…”

Apoyando el desarrollo de la competencia mirar profesionalmente del futuro profesorado de matemáticas: Práctica e investigación

“…Un KDU implica un avance conceptual por parte de los estudiantes, es decir, un cambio en la capacidad para pensar y/o percibir determinadas relaciones matemáticas (Simon, 2006, p. 362). En este sentido, si el futuro profesorado reconoce los KDU de un concepto matemático particular, será capaz de anticipar o interpretar cómo la comprensión de un determinado concepto se desarrolla (Buforn et al, 2020;Llinares, Fernández y Sánchez-Matamoros, 2016;Sánchez-Matamoros et al, 2015).…”

Noticing students’ mathematical thinking

“…High school student answers revealed different characteristics of the understanding of the concept of derivative, in relation to mathematical elements and modes of representation, in accordance with the progression in understanding (Figure 8). We have considered different mathematical domains and teaching levels: preservice preschool teachers, length and length measurement (Sánchez-Matamoros, Moreno, Callejo, Pérez-Tyteca & Valls, 2017); pre-service primary teachers and fractions (Ivars, Fernández & Llinares, 2017), pre-service secondary teachers and classification of quadrilaterals (Llinares, Fernández & Sánchez-Matamoros, 2016), the concept of derivative (Sánchez-Matamoros et al, 2015) and the concept of limit of a function (Fernández, Sánchez-Matamoros, Callejo & Moreno, 2015). Results allowed us to characterize degrees in the development of teaching competence.…”

“…Some studies have attempted to characterize degrees of development based on this aspect. Llinares et al (2016), Sánchez-Matamoros et al (2015) and studied how pre-service secondary teachers considered the understanding of some mathematical elements of the concept as a Key Developmental Understanding (KDU). A KDU implies students advance conceptually, that is, they undergo a change in their ability to think and/or perceive mathematical relationships (Simon, 2006, p. 362).…”