There is an ongoing discussion within the research field of mathematics education regarding the utilization of the history of mathematics within mathematics education. In this paper we consider problems that may emerge when the historical epistemology of mathematics is paralleled to students' conceptual developments in mathematics. We problematize…

We examine different definitions presented in textbooks and other mathematical sources for "continuity of a function at a point" and "continuous function" in the context of introductory level Calculus. We then identify problematic issues related to definitions of continuity and discontinuity: inconsistency and absence of…

In this article, an activity designed and implemented to improve both procedural knowledge and conceptual knowledge of multiplication is introduced. The students were physically and mentally active while exploring a multiplication method developed by the Russian peasants. They not only explained why and how the method works, but also extended the…

In this study, it was tried to determine teaching activities that elementary preservice mathematics teachers exhibited in a micro teaching session. Preservice teachers are required to prepare and later present a sample micro teaching session. First of all, they were advised to freely select a topic (or an attainment) of their own intention within…

The purpose of this study is to investigate whether or not students' understanding of mathematical content typically covered in calculus courses is enhanced by using the TINspire CAS instead of the TI-89. The study was conducted over two phases at a mid-size university in the northeastern United States in Calculus I and Accelerated Calculus I. In…

Understanding mathematical concepts is important for all students, although often challenging for many students with disabilities. Historically, educators have used concrete manipulatives to support and build conceptual understanding. Mobile devices provide a valuable option to support students with disabilities in mathematics through app-based…

Mastering the ability for learning to learn is the most ambitious goal of modern educators. A distinction is made between two relatively independent components of this expertise: (a) the reflective component of the learning to learn ability that allows a person comprehend what knowledge and skills he or she lacks to act in the new situation; (b)…

The importance of ratio and proportional reasoning is regularly emphasised, however, the teaching and learning of these concepts continues to present challenges. In this article the authors explore a hands-on task, designed to encourage student visualisation of the concept of ratio. Teacher perceptions of this task were positive, indicating the…

This article provides an in-depth analysis of the mathematical ways of thinking present in a 15-minute interaction between an African American mother and her preschool son as they worked together on a craft project as part of a family involvement activity. This analysis, which was conducted as part of a broader ethnographic research project,…

Top-down implementation of technology is one of the most pervasive phenomena of the last couple of decades in educational history. It is the subject of many books, articles, and blog posts on how to fix schools or why educational technology is not working in the classroom. The idea of providing teachers with technology so they can make students…

Mathematical modeling is an important and accessible process for elementary school students because it allows them to use mathematics to engage with the world and consider if and when to use it to help them reason about a situation. It fosters productive struggle and twenty-first-century skills that will aid them throughout their lifetime.

This theoretical article describes a framework to conceptualize computational thinking (CT) dispositions--"tolerance for ambiguity," "persistence," and "collaboration"--and facilitate integration of CT in mathematics learning. CT offers a powerful epistemic frame that, by foregrounding core dispositions and practices…

The occurrence of time processing problems in individuals with Development Dyscalculia (DD) has favored the view of a general magnitude system devoted to both numerical and temporal information. Yet, this scenario has been partially challenged by studies indicating that time difficulties can be attributed to poor calculation or counting skills,…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) propose a new vision for the mathematics classroom with updated content standards and Standards for Mathematical Practice (SMP). These practices are founded on NCTM processes (Problem Solving, Reasoning and Proof, Communication, Representation, and Connections) and abilities…

In this mixed methods study, we used a convergent parallel design to create and analyze a task that was implemented across four US institutions with 99 preservice teachers (PSTs) using one of two multi-media platforms: LessonSketch or GoAnimate. We analyzed PSTs' comic-based depictions or animations to examine the level of sophistication for…