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…

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…

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…

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,…

Prospective teachers and cryptography students use programming, statistics and guile to enrich both their courses.

Teaching teachers to participate in mathematical inquiry has the potential to both transform belief systems about mathematics and to transform teachers from consumers of mathematics to producers of mathematics. The focus of this paper is to describe the use of a problem, based on a non-traditional binary operation, to encourage and teach…

Preparing students placing into developmental mathematics for success in undergraduate mathematics and preparing future teachers for the increasing demands of K-12 school settings are both persistent, yet seemingly divergent, problems facing higher education. In this paper, we shed light on a model that attempts to address aspects of each problem…

Future teachers often claim that advanced undergraduate courses, even those that attempt to connect to school mathematics, are not useful for their teaching. This paper proposes a new way of designing advanced undergraduate content courses for secondary teachers. The model involves beginning with an analysis of the curriculum and practices of…

We present a first-hand, longer-term account of one student's (Christine's) experiences in and after a mathematics inquiry course. In this course, students actively posed problems, conducted their own mathematical explorations, and wrote journal entries about their experiences. During the course, Christine found that inquiry helped her develop…

In this paper I will share my experience with flipping a math content course for pre-service elementary teachers. The flipped class format involves students receiving instruction outside the classroom through readings and/or video lectures and working on "homework" inside the classroom. I will share strategies for creating lessons for my…

In this article, I will discuss a collective research project that I designed for my History of Mathematics course. My students, who are by and large pre-service teachers, explored online, digital versions of 18th-century British almanacs that contained question-and-answer sections for mathematics. In a multi-stage research process, they explored…

Problem-based learning (PBL) is a pedagogical technique recommended for K-12 mathematics classrooms. However, the mathematics courses in future teachers' degree programs are often lecture based. Students typically learn about problem-based learning in theory, but rarely get to experience it first-hand in their mathematics courses. The premise…

We describe several service-learning initiatives implemented by the mathematics and education departments. College students with majors and minors in math and math education have helped to design and implement math events for elementary and middle school students. Formal and informal reflections on these service-related experiences have…

In this article, the authors describe how prospective secondary mathematics teachers designed their own adaptations of popular board and computer games to learn the history of mathematics. They begin the article by describing some of the games students designed and used, and follow this with a discussion of factors for successful use of games in…