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…

Doctoral programs in mathematics education were established more than a century ago in the United States. From 2010-2014 over 120 different institutions graduated at least one doctorate in mathematics education. There has been limited research reported on the nature of doctoral programs in mathematics education and/or their doctoral graduates.…

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…

Mathematicians are often inimically portrayed in popular culture, resulting in an abundance of non-mathematical identities in the classroom. Various tropes are propagated by the media that dominate our mental schemas of what makes a mathematician: the eccentric Einstein-like old man; the young, tortured genius; and the "genetically…

Over several hundred different institutions in the USA have graduated people identifying a doctorate in mathematics education. Some institutions graduate people every year, other institutions graduate one person every 3-5 years. Some institutions have one faculty member, others have more than ten. There is no agreed upon common core of knowledge…

Multiplicative reasoning is a key concept in elementary school mathematics. Item statistics reported by the National Assessment of Educational Progress (NAEP) assessment provide the best current indicator for how well elementary students across the U.S. understand this, and other concepts. However, beyond expert reviews and statistical analysis,…

This paper describes an after-school club aimed to engage elementary students in project-based learning by integrating mathematics and literacy connections within a community-based topic. Building on students' backgrounds and interests, researchers created the Community Super Investigators (CSI) Club as part of an after-school program to explore…

Quantitative analysis of the Factors Influencing College Success in Mathematics (FICSMath) Survey data indicates that high school mathematics teachers' abilities to teach for conceptual understanding is a significant and positive predictor of student performance in single- variable college calculus. To explore these findings further, we gathered…

rowth mindset is an important belief for students to be successful in mathematics and in their current and future lives. Solving open-ended problems also has many positive benefits for students. Little research has been conducted though on growth mindset and mathematics at the middle school level and particularly growth mindset with open-ended…

I qualitatively reviewed mathematics education literature to offer explicit classroom-based examples and recommendations on the learning opportunities that can be embedded into mathematics content courses, designed specifically for prospective elementary teachers (ePTs), to help develop their knowledge of students and their mathematical thinking,…

In this article I explore some of the underlying mathematics of Poke´mon battles and describe ways that teachers at the secondary level could explore concepts of mathematical game theory in this context. I discuss various ways of representing and analyzing a Poke´mon battle using game theory and conclude with an example of applying concepts of…

We present a reconceptualized framework for opportunity to learn (OTL) in school mathematics that builds on previous conceptualizations of OTL and includes features related to both quantity (i.e., time) and quality. Our framework draws on existing literature and on our own observational research of mathematics teaching practices. Through the…

The purpose of this research was to compare two definitions and assessments of Mathematics Pedagogical Content Knowledge (PCK). As part of a larger study, nine current and future teachers took an online version of the Measures of Knowledge for Teaching (MKT)--Mathematics assessment and the Cognitively Activating Instruction in Mathematics…

Mathematics teachers frequently provide concrete manipulatives to students during instruction; however, the rationale for using certain manipulatives in conjunction with concepts may not be explored. This article focuses on area models that are currently used in classrooms to provide concrete examples of integer and binomial multiplication. The…

This paper explores the viability and development of the first edition of the researcher's mathematical card game, Groups, as a learning tool for elementary group theory, a topic in abstract algebra. "Groups" was play-tested by six undergraduate students in late 2016 who provided feedback on "Groups" from both utility-centric…