Teaching methods courses are a crucial factor in the preparation of secondary mathematics teachers. Throughout the United States, secondary methods courses have diverse curricula, including variation in the topics covered in these courses. To assess this variation, the authors identified 41 topics potentially valued by secondary methods…

The purpose of the mathematics methods course where this study took place was to support pre-service teachers (PSTs) as their thinking about instruction transitioned from a traditional, teacher-centered approach to a more problem-based, student-centered approach, and to guide them as they developed strategies for teaching through problem solving.…

This study examined the effect of a teaching mathematics with technology course on preservice elementary teachers' (PSETs) and preservice secondary mathematics teachers' (PSTs) beliefs about teaching with technology and beliefs about the nature of learning and teaching mathematics. All preservice teachers enrolled in the methods course engaged in…

It is important to support pre-service teachers in terms of mathematical task design so as to increase the success of their future teaching. The purpose of this study was to evaluate mathematical tasks designed by pre-service primary and elementary mathematics teachers within the framework of task design principles. For this purpose, a total of 43…

This multi-case study examines how three elementary mathematics methods instructors, in the same teacher education program, provide their prospective teachers with learning opportunities. Qualitative data were collected through interviews, classroom observations, and artifacts. The findings suggest that the instructors' beliefs associated with…

Reform-based approaches to teaching mathematics are proven to be most effective for students' learning, yet many novice secondary mathematics teachers still use traditional approaches. One reason for this is that novice teachers tend to teach the way that they experienced mathematics as students themselves. There is thus an onus on teacher…

When teaching through problem solving, effective mathematics teachers need to lead discussions that assist students in making connections between different solution strategies. However, while teaching a methods course for preservice teachers (PSTs), we noticed that after solving a problem and presenting various solution strategies, many PSTs…

Approximations of practice provide opportunities for teacher candidates (TCs) to engage in the work of teaching in situations of reduced complexity. A problem of practice for teacher educators relates to how to represent student voice in approximations to engage TCs with interactive practices in meaningful ways. In this article, we share an…

Increased accountability demands are being placed on teacher preparation programs across the USA to demonstrate competencies of their teacher candidates. As a means of evaluating teacher candidates' instructional effectiveness and readiness for their own classrooms, some programs are using standardized teacher performance assessments, with faculty…

Gestures have been shown to play a key role in mathematical reasoning and be an indicator that mathematical reasoning is "embodied" -- inexorably linked to action, perception, and the physical body. Theories of extended cognition accentuate looking beyond the body and mind of an individual, thus here we examine how gestural embodied…

This study examined how 16 female teacher candidates in two sections of a math methods course, which implemented high leverage professional development school practices, described the aspects of richness of mathematics (i.e., linking between representations, explanations, mathematical sense-making, multiple procedures or solution methods, patterns…

Background. This article describes the redesign, implementation, and students' experiences with an elementary mathematics teaching methods course in the Pacific Northwest of the United States that was forced online due to COVID-19 restrictions. We share course design principles, changes to reflect online teaching, and students' experiences of…

This study investigates prospective secondary school mathematics teachers' developing conceptions about the meaning of derivative (as rate of change) while working on a series of tasks involving different non-motion real-life contexts. The study was conducted by employing a case study method. The participants of the study were 25 prospective…

In this article, we share design guidelines for the development and use of online, video-based "teaching playgrounds," which provide opportunities for prospective teachers to engage in professional noticing of teaching practices. Through teaching playgrounds, we provide an instantiation of the Presence+Experience framework, which…

In this study, we investigated how elementary pre-service teachers (PSTs) perceive using representations in teaching mathematics and what fractional representations (e.g., manipulatives or models) they suggest to guide students' incorrect use of representations in learning fractions. A written questionnaire was administrated to 151 PSTs at a large…