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 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…

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…

We introduce a "W*"-metric space, which is a particular approach to non-commutative metric spaces where a "quantum metric" is defined on a von Neumann algebra. We generalize the notion of a quantum code and quantum error correction to the setting of finite dimensional "W*"-metric spaces, which includes codes and error correction for classical…

For many the phrase "teaching math online" evokes a vision of teaching and learning that is not based in physical classrooms. Perhaps teachers and students are even interacting asynchronously. In math classrooms in the United States, the increasing availability of devices (e.g. laptops, Chromebooks™, smartphones, and tablets) and…

This review investigates effective interventions for teaching algebra to students with learning disabilities and evaluates the complexity and alignment of skills with the Common Core State Standards in math. The review includes the results of 10 experimental and 5 single-subject designs (N = 15) producing a moderate overall effect size (g = 0.48).…

This is an experimental study, made used of the non-randomized experimental and control groups, pretest-posttest designs. The experimental and control groups were two separate intact classes in Algebra. For a period of twelve sessions, the experimental group was subjected to the scientific heuristic method, but the control group instead was given…

This study analyzes the responses of 12 secondary pre-service teachers on two tasks focused on reasoning when solving linear equations. By documenting the choices PSTs made while engaging in these tasks, we gain insight into how new teachers work mathematically, reason algebraically, communicate their thinking, and make pedagogical decisions. We…

Little is known about students' emotions in the field of Mathematics Education that go beyond students' emotions in problem solving. To start filling this gap this qualitative research has the aim to identify emotional experiences of undergraduate mathematics students in Linear Algebra courses. In order to obtain data, retrospective focus group…