This article explores how the concepts of discourse and its methodological extension discourse analysis can help mathematics educators re-conceptualize their practices using a sociocultural view of learning. It provides conceptual and methodological tools as well as activities that can be helpful in mathematics methods courses and professional…

Within this study, we investigated the association between 10th-grade students' mathematics performance and their feelings of instructional misalignment between their current mathematics knowledge and educator support. Data from the 2002 Education Longitudinal Study, which included a national sample of 750 public and private high schools in the…

In wake of federal legislation such as the No Child Left Behind Act of 2001 that have called for "scientifically based research in education," this study examined the possible trends in mixed methods research articles published in 2 peer-reviewed mathematics education journals (n = 87) from 2002 to 2006. The study also illustrates how the…

In this article, I describe a classroom investigation in which a group of prospective secondary mathematics teachers discovered theorems related to the power of a point using "The Geometer's Sketchpad" (GSP). The power of a point is defines as follows: Let "P" be a fixed point coplanar with a circle. If line "PA" is a secant line that intersects…

The purpose of this study was to compare the perspectives of faculty members who had experience teaching undergraduate calculus and preservice teachers who had recently completed student teaching in regards to a first semester undergraduate calculus course. An online survey was created and sent to recent student teachers and college mathematics…

This paper describes a development and evaluation process used to create teacher education materials that help prepare middle and secondary mathematics teachers to teach data analysis and probability concepts with technology tools. One aspect of statistical reasoning needed for teaching is the ability to coordinate understandings of center and…

Undergraduate preservice teachers face many challenges implementing inquiry pedagogy in mathematics lessons. This study provides a step-by-step case analysis of an undergraduate preservice teacher's actions and responses while teaching an inquiry lesson during a summer math camp for grade 3-6 students conducted at a university. Stumbling blocks…

Providing students in urban settings with quality teachers is important for student achievement. This study examined the differences in content knowledge, attitudes toward mathematics, and teacher efficacy among several different types of alternatively certified teachers in a sample from the New York City Teaching Fellows program in order to…

In this article, we present episodes from two qualitative research studies. The studies focus on students of different ages and populations and their work on different mathematical tasks. We examine the commonalities in environment, tools, and teacher-student interactions that are key influences on the positive dispositions engendered in the…

When solving systems of equations by using matrices, many teachers present a Gauss-Jordan elimination approach to row reducing matrices that can involve painfully tedious operations with fractions (which I will call the traditional method). In this essay, I present an alternative method to row reduce matrices that does not introduce additional…

This paper posits the position that if higher education and secondary schools wish to increase students' college readiness, specifically in mathematics and critical thinking skills, continuous enrollment in secondary mathematics is one avenue worth exploring as opposed to increasing mathematics graduation requirements only in terms of Carnegie…

Increased reading difficulty of mathematics assessment items has been shown to negatively affect student performance. The advent of high-stakes testing, which has serious ramifications for students' futures and teachers' careers, necessitates analysis of reading difficulty on state assessment items and student performance on those items. Using…

Parallels between martial arts and mathematics are explored. Misguided public perception of both disciplines, students' misconceptions, and the similarities between proofs and katas are among the striking commonalities between martial arts and mathematics. The author also reflects on what he has learned in his martial arts training, and how this…

In this article I report on a study of the cognitive tools that research mathematicians employ when developing deep understandings of abstract mathematical definitions. I arrived at several conclusions about this process: Examples play a predominant role in understanding definitions. Equivalent reformulations of definitions enrich understanding.…

Mathematics is motivating; at least, it should be. I argue that mathematical activity is an inherently attractive enterprise for human beings because as intellectual organisms, we are naturally enticed by the intellectual stimulation of mathematizing, and, as social beings, we are drawn to the socializing aspects of mathematical activity. These…