Arithmetic was the first mathematical subject to enter the school curriculum in the United States in a formalized manner. Until the first quarter of the nineteenth century, the prevailing pedagogy of this subject revolved around the tenets of mental discipline theory and the rules method of teaching, which valued memorization and repetitive drill…

In this paper I discuss the possibilities for exploring the hundred chart kinesthetically with elementary preservice teachers using a life-size hundred chart--an innovative tool, homemade from a shower curtain--to build quantity sense. Preservice teachers explored creative approaches to teach mathematics using the life-size hundred chart and…

Game-based learning has received more focus as a way to engage students and increase interest in mathematics. Game-based learning should be integrated with effective practices for teaching mathematics, though these is a need for further research on effective implementation models. The purpose of this article is to describe two modes of game-based…

An increasing number of students are "hyper-accelerating" their study of formal Algebra I to Grade 7 or earlier to maintain a competitive edge in the race to calculus. However, there is a lack of evidence that these students construct the conceptual foundations necessary for persistence in advanced mathematics. This paper maps the drive…

Teaching gerrymandering in our high school geometry classrooms provides students with a unique opportunity to use mathematics to describe, analyze and make sense of the world around them. Our purpose is to provide our students the opportunity to apply learned definitions and formulas of area and perimeter to a sociopolitical context. We present a…

Physical models for exploring multiplication are fixtures in elementary classrooms. The most widely used physical models of multiplication are collections of discrete things, such as Cuisenaire rods, Unifix Cubes, or Base-10 Blocks. But discrete physical models are limited in the products they can represent. By contrast, pictorial models, such as…

While a growing body of research examines teachers' facilitation of discourse-rich classrooms, surprisingly little research is devoted to learners' responsibilities in such classrooms. In this paper, we share a theoretical model for explaining students' responsibilities in yielding mathematical learning in discourse-rich classrooms. These…

Postsecondary mathematics classrooms continue to become more diverse, which implores educators to continue to incorporate more diverse modes of assessment to support all learners. However, researchers have found that mathematics assessment at the postsecondary level has remained mostly stagnant, with traditional, closed-book exams dominating the…

In this paper, we discuss the utilization of an innovative learning tool, the Sphero BOLT robot, in a 10-day algebra-based mathematics education course for graduate students. Students created routes for their BOLTs to travel and determined ways to measure the distance, rate, and time of their robots' movements. The student prompt, sample student…

Generating mathematical conjectures is an important mathematical habit of mind for preservice teachers to develop so that they can, in turn, help their students to develop this skill. In this paper we present a classroom episode in which preservice mathematics teachers experience conjecturing in the context of a rich, open-ended task. They also…

We present in this paper a pair of approaches to support mathematics educators and learners in formulating original tasks. In particular, we facilitate the posing of rich mathematical problems by using two novel methods that were created by a mathematics department at a K-12 school in the United States, and further developed alongside our students…

Curriculum change is inevitable in schooling. For content areas such as mathematics that are already under the national spotlight, transitioning to new curriculum materials while concurrently enacting instructional reform creates both a challenge and an opportunity. This paper discusses how partnerships between two state universities and…

Maryam Mirzakhani is the first and the only female winner of the Fields Medal since its establishment in 1936. She is arguably one of the greatest mathematicians of our generation. This biographical paper outlines her life and work. Her mathematical theorems and noteworthy accomplishments are just as impressive as her determination, imagination,…

High school students often ask questions about the nature of infinity. When contemplating what the "largest number" is, or discussing the speed of light, students bring their own ideas about infinity and asymptotes into the conversation. These are popular ideas, but formal ideas about the nature of mathematical sets, or "set…

Mentoring is an important aspect of mathematics teacher education, and in particular, pre-service teacher education. Faculty at a large Midwestern university developed and refined a mentoring program designed to help pre-service secondary mathematics teachers, called Scholars, become future leaders in mathematics education. This paper describes…