This mixed-methods study examined prospective elementary teachers' (N = 32) mathematical knowledge and mathematics self-efficacy while learning about the Singapore Modeling Method in a university mathematics course. Pre- and post- quantitative data were collected via two content knowledge assessments and one belief survey, and qualitative data…

This paper introduces lessons designed to incorporate applications to teaching high school mathematics in an undergraduate Discrete Mathematics course. Because many prospective high school teachers do not take courses that are specifically designed for teachers, providing materials aimed at teacher preparation that can be easily integrated into…

Preservice elementary teachers tend to have higher mathematics anxiety than other undergraduate majors, which can be mitigated through building self-efficacy. Teacher education programs can address this deficit through methods courses that provide opportunities for preservice teachers to construct mathematical concepts and practice instruction.…

Preservice teachers commonly struggle with topics related to fractions, ratio, and proportion. The use of double number lines can facilitate the teaching in these areas and provide autonomy and flexibility in mathematical thinking. Moreover, double number lines support many topics in the curriculum, including unit rate, convenience scaling, and…

Exploring non-Euclidean geometries is a common way for College Geometry instructors to highlight subtleties in Euclidean geometry. The concept of congruence, going undefined or informally defined in multiple axiomatic systems, is particularly susceptible to conflation with the idea of "same measure." Taxicab geometry provides a context…

As students learn to problem solve in authentic situations, they must also develop metacognitive tools to manage and regulate their problem-solving process. To foster process-focused metacognition utilized by mathematical thinkers and problem solvers, inquiry-based learning classroom practices and an adapted version of portfolio problems were…

This article presents a mathematical modeling activity for students related to the process of memorization in which students collect their own data to drive their model development, parameterization, and validation. Engaging in the data collection gives them insight to critique and evaluate various models. This task is a low-floor high ceiling…

This paper describes a project that sought to simultaneously facilitate the mathematical learning of both preservice teachers (PSTs) and schoolchildren. The project involved the organization of community Math Stations related to research-based number sense activities and was integrated within two university-level courses. This article describes…

We present a mathematical activity called graph talks as a new pedagogical routine to intertwine social justice issues and mathematics. Adapted from "number talks," graph talks involve students analyzing, interpreting, and discussing real-life data represented in graphs. Graphs may be strategically selected to both highlight a relevant…

Undergraduate mathematics instructors are called by many current standards to promote prospective teachers' learning of geometry from a transformation perspective, marking a change from previous standards. The novelty of this situation means it is unclear what is involved in undergraduate learning and teaching of geometry from a transformation…

This paper discusses the ways in which teacher educators can effectively engage prospective teachers (PTs) in lesson study during mathematics methods courses. Evidence from this work suggests that engagement in lesson study provides PTs with opportunities to strengthen their knowledge about mathematics, students, and pedagogy. More specifically,…

Teachers and students had an unusual experience in 2020. Due to the outbreak of the COVID-19 pandemic, regular teaching and learning in schools were suspended in many countries. The prolonged school closure presented unprecedented challenges because all teaching and learning activities had to be converted to a fully online format. This article…

Lesson study, a popular method of professional development in which instructors collaborate to critique and improve a lesson, can be used for curriculum development. This paper describes an implementation of lesson study that went through two iterations across different, related, contexts: an undergraduate mathematics content course for secondary…

In this paper, I share an activity that reinforces students' understanding of translations, reflections, and rotations via body movement. As a result of this activity, students gain a different perspective compared to previous explorations on paper, communicate mathematics, and visualize transformations as rigid motions on the plane. Furthermore,…

In this paper, the authors discuss their experiences with ungrading at a small public university in the U.S. and a large public university in Germany. The courses described are Calculus 1 and a content course for pre-service secondary teachers of mathematics. The professors teach differently: one with lecture, the other with inquiry-based…