The aim of this paper is to discuss preservice mathematics teachers' in-the-moment noticing of mathematical opportunities and how they reflected on those opportunities both orally and in writing. A faculty-school collaboration program was set up to enable preservice teachers to work with students in a school setting throughout a year. Ten…

We outline the structure of a term-long graduate course on teaching undergraduate mathematics. We analyze reflections written by the graduate students participating in the course to understand how they experienced the course and how the course impacted their beliefs about teaching. We find that students enjoy the course and find it to be useful.…

Online learning platforms take over a new role in education, especially in times of the COVID-19 pandemic. This paper will discuss pre-service teachers' reflections on attitudes towards online learning platforms and the respective changes due to an online training of using this digital tool in mathematics classes. The special training took place…

This article reports on a framework for collective professional learning and its influence on the development of four early-career mathematics teacher educators as they work to transform their practice. The Collective Reflection for Change (CRC) framework centers on a shared referent to orient collaborative noticing and wondering. Findings from an…

Research in mathematics education highlights the importance of including modelling for the teaching of this subject. In 2020, this trend coexisted with a grave contingency situation caused by the COVID-19 pandemic but which, despite its negative aspects, provided a realistic and authentic context for modelling. Given this situation, it is relevant…

This study aims to show to what extent the variables of reflective thinking, inquiry skill and mathematics teaching self-efficacy belief affect each other, to show their rates of explaining each other, and to show whether inquiry skill is a mediating variable in the relationship between reflective thinking and mathematics teaching self-efficacy…

Noticing the strengths in students' mathematical thinking is a critical skill that teachers need to develop, but it can be challenging due to the prevalence of deficit-based thinking in mathematics education. To address this challenge, a teacher education course was designed to encourage prospective teachers to engage in critical reflection on…

This study examines how collective argumentation in the integration of the ACODESA method (collaborative learning, scientific debate and self-reflection) and GeoGebra can help students understand parametric equations. The participants of the study consist of 24 university students enrolled in a mathematics education programme at a state university…

Affective and cognitive processes may be jointly researched to better understand mathematics learning, paying special interest to emotions related to knowledge acquisition. However, it remains necessary to explore these processes in studies linked to the education of pre-service mathematics teachers. This study aims to characterize epistemic…

Reflections are presented on the first time flipping of an introductory Ordinary Differential Equations course. Assessment results, student motivation, and student attitudes are compared between flipped and traditional learning pedagogies in this course over two terms at a small technical university in the northeast United States. Assessments and…

The performance of pre-service teachers (PSTs) is generally assessed during practicum by supervising teachers or observers who may provide subjectively different evaluations known to lack reliability and validity. This article examines a way to shift the evaluative emphasis to use of affective-reflective skills through use of a protocol that also…

Starting from the elementary school years, geometric reflection has potential for students to improve their understanding of plane geometry. Although it gives them opportunities to investigate the motion view of the transformed figures and mapping of all points in the plane onto itself, the instructional tasks and teaching practices generally…

This study investigates the beliefs and practices of preservice teachers (PSTs) concerning equitable mathematics instruction for diverse learners. Through a comprehensive analysis of lesson plans and reflective essays, we identify key themes that emerge in PSTs' approaches to teaching mathematics. The findings indicate that PSTs employ various…

Generating mathematical conjectures is an important mathematical habit of mind for preservice teachers to develop so that they can, in turn, help their students to develop this skill. In this paper we present a classroom episode in which preservice mathematics teachers experience conjecturing in the context of a rich, open-ended task. They also…

Prospective teachers bring countless stories of success and failure from different mathematics classrooms to their post-field teacher education courses. These reflective stories often glorify school mathematics classrooms and dominant traditions within, instead of confronting the marginalization of diverse groups in school environments.…