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…

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…

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…

In the post-pandemic world, metaverse technology has become a popular approach to facilitating students' online learning experiences. Drawing on Kolb's experiential learning theory, we created immersive scenes using CoSpaces Edu, a 'mirror-world' metaverse platform that enables students to observe mathematical properties virtually. We applied a…

We introduce, motivate, and exemplify a proposed theoretical construct guiding the design and facilitation of collaborative geometry activities, conceptually generative perspectival complementarity (CGPC). Participants in CGPC activities learn content by negotiating their respective perceptions of situated features they manipulate to accomplish…

Once teaching-learning events are conceptualized as inter-discursive encounters, it becomes clear that mathematics classroom talk is rife with invisible pitfalls. There are many types of unacknowledged discursive gaps, some of them necessary for learning and some potentially harmful. Such gaps may exist also between the teacher's intentions and…

To develop an equity-centered orientation in teacher education programs, it is essential teacher educators recognize what prospective teachers attend to in classroom events and how they relate these events to mathematics instruction. In this study, we conceptualize the Equity Noticing Framework and use it as an analytic tool to examine what…

The increase in online education has implications for mathematics teacher educators who are tasked with teaching mathematics content and pedagogy to pre-service teachers (PSTs) who do not attend on-campus. Concerns about PSTs' content knowledge continues to be an ongoing issue, and ways to address this, especially in an online environment, require…

Although raised in the early days of research on teacher noticing, the question of context specificity has remained largely unanswered to this day. In this study, we build on our prior research on a specific aspect of noticing, namely teachers' analysis of how representations are dealt with in mathematics classroom situations. For the purpose of…

Introduction: In the reflective writing process, teachers make identification, information, explanation and evaluation activities (Spanneberg, 2009). It is thought that the scenarios written by the teacher candidates in order to teach a certain subject can give them an opportunity to think deeply. However, these teaching scenarios can be a…

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…