Undergraduate Students’ Perceptions of Features of Active Learning Models for Teaching and Learning to Teach Mathematics

Abstract

The recent push toward active learning – engaging students in the learning process – is meant to benefit students. Yet there is still much to learn about students’ perceptions of this phenomenon. We share results from an interview study of students’ perceptions of features of two active learning models institutionalized at a large doctoral-granting university – a model for teaching foundational mathematics courses and an early field experience model for teaching preservice secondary students to teach mathematics. These models were implemented simultaneously in a single precalculus course. Interviews were conducted with both student populations (i.e., precalculus students and preservice teachers) to understand which in-class features of the models students noticed and identified as beneficial to their learning. Precalculus students identified specific opportunities related to active learning in the undergraduate mathematics teaching model – working in groups on mathematics tasks that engaged students in sensemaking and interacting with their instructor around mathematics. Preservice teachers identified specific opportunities related to three features of the university field experience model – observing a mathematics instructor enacting ambitious instructional practices, planning and teaching a “real” lesson, and observing student thinking and practicing teaching moves during groupwork. We conclude with pedagogical recommendations about particular features of the models that may help mitigate student resistance to active learning.

Secondary teachers’ geometrical figure apprehension: their ability to construct geometrical proof and to predict students’ difficulties

“…Nel caso della dimostrazione geometrica, Fuglestad e Goodchild (2009) hanno esaminato le conoscenze degli insegnanti sulla dimostrazione, concludendo che alcuni insegnanti non sembrano sicuri circa la natura e la necessità della dimostrazione. Cirillo (2011) ha indicato che anche un insegnante principiante con un forte background matematico può non essere ben preparato per insegnare le dimostrazioni. DdM 2.2 La teoria della comprensione delle figure geometriche di Raymond Duval Oltre alla teoria riguardante un approccio semiotico all'apprendimento della matematica, le cui nozioni chiave sono i registri delle rappresentazioni semiotiche, le trasformazioni tra le rappresentazioni e il funzionamento cognitivo del pensiero (Duval, 1993), Duval ha sviluppato un'importante teoria relativa all'insegnamento e all'apprendimento della geometria e, più specificatamente, alla comprensione delle figure geometriche (Duval, 1995(Duval, , 1998(Duval, , 2005.…”