This dissertation investigates how early career teachers' orientations of students and their mathematical activity, as surfaced their experience in a simulation, can reveal when their well-intentioned decisions might negatively impact traditionally underserved students. Three early career teachers engaged in two online simulations where they could…

Descriptions of expertise have focused on knowledge and characteristics of mathematics teacher educator (MTE) practice. To contribute to discussion of MTE expertise we share findings from a study of MTE discussion practice with prospective teachers (PTs) concerning pedagogy of teaching mathematics. Research on MTE discussion practices have shown…

In this article, we describe the theoretical and pragmatic considerations behind our development of a set of nine protocols and training materials for engaging prospective secondary mathematics teachers in live, interactive clinical simulations. Our designs are grounded in theoretical principles from situated cognition and variation theory and…

The teacher's use of representations is a crucial aspect of instructional quality in mathematics education, given their pivotal role in facilitating mathematics learning. However, in our international research community, perspectives on what constitutes high-quality use of representations may vary. This cross-cultural study aims to explore whether…

This paper reports on a key representation, a triple number line, designed as part of the first author's doctoral study. The study sought ways to represent multiple constructs of fractions in the context of merging music and mathematics to support learners' understanding of fractions. A problem scenario was designed guided by Realistic Mathematics…

Personas, initially originated in user experience research, are short and simplified representations of particular user groups, and this methodological approach has recently gained ground in educational research. This study aims to explore aspects of personas that may be beneficial for prospective mathematics teachers when they develop digital…

In this article, the authors provide some insight into how teachers can potentially facilitate among students' representations and activities on mathematical tasks: between or among -- (1) student representations and the context; (2) multiple forms of student representations; and (3) processes in student representations. The authors use the…

Among the most urgent matters in contemporary education discourses are those that delve into the justice issues related to diversity, equity, and inclusion. Colleges of Education are critical sites for such discourse. In particular, the teaching methods course is where candidates are to acquire tools to take up such issues. Success of justice…

Psychoanalysis is largely overlooked in mathematics education, yet is relevant to many aspects of the field, such as the institution of the school, curriculum and instruction, and content. Specifically, one content area where psychoanalysis is both exceedingly relevant and absent is that of probability education. In this critical literature…

Using data from teaching experiments and theories from quantitative reasoning, we built second-order accounts of students' mathematics with regards to how they conceived rate of change through operating on existing quantities. In this report, we explain three different ways STEM undergraduates structurally conceive rate of change as they…

In this paper, we propose a teaching approach centered on community and care, aimed at fostering a democratic classroom environment. We highlight the communal co-creation of the Rights of the Learner (RoTL) as the foundation for establishing a shared responsibility atmosphere. Our interpretation of the RoTL challenges traditional power dynamics,…

Technology can play a pivotal role in mathematics education. Qualitative methods were used to report on how a Year 1-2 teacher incorporated "Conveyance technology" (iPads), to support the teaching and learning of mathematics through student reasoning and problem-solving. The study was conducted in Australia. A single case was chosen,…

This report delineates the outcomes of an intervention conducted with in-service high school educators, focusing on elucidating three distinct scenarios within geometric and arithmetic domains: the infinitely large, infinitely numerous, and infinitesimally close. Grounded in the theoretical framework of conceptual change, it is posited that when…

Logarithms, pivotal in advanced mathematics and real-world applications, often present challenges to students who resort to rote memorization without grasping their essence. While the emotional dimensions of learning mathematics are increasingly recognized, research in this area remains limited. This dissertation addresses this gap by examining a…

In this study, we explored enacted task characteristics (ETCs) that supported students' quantitative reasoning (QR). We employed a design-based methodology; we conducted a teaching experiment with eight secondary school students. Through ongoing and retrospective analyses, we identified ETCs which supported students' quantitative reasoning. The…