Calls have been made for the creation of a shared knowledge base in mathematics teacher education with the power to inform the design of scholarly inquiry and mathematics teacher educators' (MTEs) scholarly practices. Focusing on mathematics methods courses, we summarize and contribute to literature documenting activities MTEs use in mathematics…

Mathematical conventions -- which account for the choices of mathematics community regarding definitions of concepts, their names and symbols -- are the focus of this paper. We introduce the task of unpacking, that is, offering plausible explanations and arguments for the choice of conventions. Using responses of four prospective teachers to the…

The purpose of the study is to identify the classroom mathematical practices developed within a learning environment designed by Realistic Mathematics Education for teaching cone and pyramid to preservice teachers. A teaching experiment including five-week instructional sequence by a hypothetical learning trajectory about the solids of cone and…

Teacher telling continues to be poorly understood within inquiry. In this paper I extend prior efforts to reimagine telling within contemporary pedagogical thought. Using a case study, I investigated a well-regarded teacher's use of mathematical telling while supporting groups and individuals working on tasks. The teacher used seven unique types…

Math Teachers' Circles (MTCs) bring math teachers and university mathematicians together to engage in collaborative mathematical activity. Currently there are over 110 MTCs across 40 states. A key claim is that MTCs are "communities of practice." However, to date there has been no research to substantiate this claim. In this paper, we…

In this study, we examined 10 integral lessons to understand students' opportunities to learn cognitively challenging tasks and maintain cognitive demand during integral lessons. Our findings reveal issues with implemented tasks as well as the way these tasks were presented to students. We also examined mathematicians' reasons behind their…

This article discusses ways in which improvisational comedy games and exercises can be used in college mathematics classrooms to obtain a democratic and supportive environment for students. Using improv can help students learn to think creatively, take risks, support classmates, and solve problems. Both theoretical and practical applications are…

The ability to address and solve problems in minimally familiar contexts is the core business of research mathematicians. Recent studies have identified key traits and techniques that individuals exhibit while problem solving, and revealed strategies and behaviours that are frequently invoked in the process. We studied advanced calculus students…

This article presents a study done in an elementary mathematics methods course that focused on the transition of novice teachers' epistemological stances: former elementary student, university student, and teacher stances. In order to help them develop the teacher stance, we designed a three-phase activity, where two phases took place inside…

When young children attempt to locate the positions of numerals on a number line, the positions are often logarithmically rather than linearly distributed. This finding has been taken as evidence that the children represent numbers on a mental number line that is logarithmically calibrated. This article reports a statistical simulation showing…

Concepts of Mathematics (21-127 at CMU) is a course designed to introduce students to the world of abstract mathematics, guiding them from more calculation-based math (that one learns in high school) to higher mathematics, which focuses more on abstract thinking, problem solving, and writing "proofs." This transition tends to be a shock:…

The inclusion of statistics and probability in the mathematics curriculum has always generated challenges to mathematics teachers of elementary schools. This article discusses activities that promote the professional development of such teachers. We present part of a doctoral research study of 16 teachers in which we discuss two case studies of…

This article focuses on a secondary mathematics teacher education program where traditional field placements are prevalent in grades 9-12. Traditional, for this article, is defined as and comprised of: (a) straight-rowed desks in classrooms, (b) explicitly direct instruction (teacher-centered classrooms), (c) predominantly repetition of low-level…

Filling the knowledge gap in the limited research on professional development leaders is an urgent issue if teacher learning is to be improved. This research and development project is studying how leaders learn to cultivate mathematically rich professional development environments. The authors adapted two frameworks from classroom-based…

Mentoring is often assumed to be done by experienced teachers with new teachers in one-on-one settings and designed to help the mentee be successful with the tasks of teaching. In the context of preservice teacher education, mentoring usually takes place during field experiences, particularly student teaching when the mentor is the host classroom…