An experiment was conducted over three recent semesters of an introductory calculus course to test whether it was possible to quantify the effect that difficulty with basic algebraic and arithmetic computation had on individual performance. Points lost during the term were classified as being due to either algebraic and arithmetic mistakes…

Literature suggests that the mathematical language of teachers impacts a student's understanding of math concepts. When teachers unintentionally use ambiguous language, students' understanding of a subject can be negatively affected. We share background on specific instances in which teachers can create confusion with the language they use, and we…

This book represents a crop of wide-ranging research conducted by renown scholars in sub-Sahara Africa revolving around mathematics teaching and professional development programs for mathematics teachers. The research-based proposals and actual how-to-conduct professional development initiatives that enhance effective mathematics instruction are…

Algebra is critical to high school graduation and college success, but student achievement in algebra frequently falls significantly below expected proficiency levels. While existing research emphasizes the importance of quality algebra instruction, there is little research about how to conduct problem analysis for struggling secondary students.…

Studies on blended education pay little attention to implementation, thus limiting the understanding of how such programs contribute to student math learning. This article examines the implementation of a widely used blended algebra curriculum and the relationship between implementation and student outcomes. The study was conducted in 74 middle…

In recent years, student surveys have played an increasingly large role in educational research, policy making, and, particularly, accountability efforts. However, research on the accuracy of students' self-reports about themselves and their education is limited to analyses of overall grade point average and ACT/SAT standardized test scores. Using…

We present results of the analysis of knowledge used by a secondary school mathematics teacher in her classroom practice. This knowledge takes shape and is displayed as specific teaching strategies in the management of her class when she incorporates Computer Algebra Systems. Based on observations of regular classes, we find that her knowledge…

Engaging students in self-reflection about their learning performance is a potentially promising pedagogical approach for supporting math learning. However, it is unclear how models for math learning in regular classrooms translate in a virtual environment. The purpose of this paper is to (a) analyze rich assessment data from virtual schools to…

In this article I sketch three key concepts of a cultural-historical theory of mathematics teaching and learning--the theory of objectification. The concepts are: knowledge, knowing and learning. The philosophical underpinning of the theory revolves around the work of Georg W. F. Hegel and its further development in the philosophical works of K.…

Our study concerns the conceptual mathematical knowledge that emerges during the resolution of tasks on the equivalence of polynomial and rational algebraic expressions, by using CAS and paper-and-pencil techniques. The theoretical framework we adopt is the Anthropological Theory of Didactics ("Chevallard" 19:221-266, 1999), in…

By introducing the mathematical concept of orientation, the significance of the minus sign in Faraday's law may be made clear to students with some knowledge of vector calculus. For many students, however, the traditional approach of treating the law as a relationship between positive scalars and of relying on Lenz's law to provide the information…

This paper describes the learning trajectory for Early Equations and Expressions (EELT), one of the 18 learning trajectories presented at www.TurnOnCCMath.net, developed to interpret the Common Core Standards for Mathematics based on research on student learning. The EELT is foundational for introducing concepts of early algebra and setting the…

In recent years, I have cultivated an almost pathological resistance to grading. Here I explore the reasons why and describe how I eventually recovered. In particular, I propose that although grading, or more explicitly, effective assessment of student learning, is a challenging component of a mathematics instructor's job description, reflective…

This study examines the impact of providing parents with an informational brochure about the role of algebra II in college access on students' grade 11 algebra II completion rates in Texas. One hundred nine schools, covering all 20 Educational Service Center regions in Texas, participated in the study. Parents in the 54 treatment schools were…

The goal of the Rural Math Excel Partnership (RMEP) project, a development project funded by the U.S. Department of Education Investing in Innovation (i3) grant program, was to develop a model of shared responsibility among families, teachers, and communities in rural areas as collective support for student success in and preparation for advanced…