This study examined processes at the core of teacher professional development (PD) experiences that might positively impact teacher learning and more specifically teacher change. Four processes were considered in the context of a PD program focused on student mathematical errors: analysis of students' mathematical misconceptions as a lever for…

This study shows how separate and combined contextual and conceptual problem rewording can positively influence student performance in solving mathematical word problems. Participants included 80 seventh-grade Iranian students randomly assigned in groups of 20 to three experimental groups involving three types of rewording and a control group. All…

The aim of this study was to propose a didactical situation for the confrontation of the epistemological obstacle of linearity (routine proportionality) and consequently for the enhancement of meta-analogical awareness. Errors caused by students' spontaneous tendency to apply linear functions in various situations are strong, persistent and do not…

Data analysis methods, both numerical and visual, are used to discover a variety of surprising patterns in the errors associated with successive approximations to the derivatives of sinusoidal and exponential functions based on the Newton difference-quotient. L'Hopital's rule and Taylor polynomial approximations are then used to explain why these…

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…

Learning Disabilities in Mathematics (LDM) or dyscalculia are a frequent and disruptive problem within schools. Nevertheless, this problem has received little attention from researchers and practitioners, if compared with the number of studies published on disabilities in reading. Therefore, teachers do not have enough guidance to help children…

The application to rational numbers of the procedures and intuitions proper of natural numbers is known as Natural Number Bias. Research on the cognitive foundations of this bias suggests that it stems not from a lack of understanding of rational numbers, but from the way the human mind represents them. In this work, we presented a fraction…

In this article, we describe results of a reanalysis of two randomized studies that tested the effects of enhanced anchored instruction (EAI) on the fractions computation performance of students in special education resource rooms and inclusive mathematics classrooms. Latent class analysis and latent transition analysis classified students…

The role geometry plays in real life makes it a core component of mathematics that students must understand and master. Conceptual knowledge of geometric concepts goes beyond the development of skills required to manipulate geometric shapes. This study is focused on errors students made when solving coordinate geometry problems in the final Grade…

We study situations in introductory analysis in which students affirmed false statements as true, despite simple counterexamples that they easily recognized afterwards. The study draws attention to how simple counterexamples can become hidden in plain sight, even in an active learning atmosphere where students proposed simple (as well as more…

Many students enter high school with persistent algebraic misconceptions that limit their success in mathematics and, by extension, limit potential educational attainment and future earnings. The purpose of this study was to assess the effectiveness of a warm conceptual change based intervention on remediating algebraic misconceptions held by…

This article describes how "curriculum-based measurement--computation" (CBM-C) mathematics probes can be used in combination with "error pattern analysis" (EPA) to pinpoint difficulties in basic computation skills for students who struggle with learning mathematics. Both assessment procedures provide ongoing assessment data…

This article describes how the author has developed tasks for students that address the missed "essence of the matter" of algebraic transformations. Specifically, he has found that having students practice "perceiving" algebraic structure--by naming the "glue" in the expressions, drawing expressions using…

Prospective teachers (PTs), enrolled in a mathematics methods course, were asked to analyze children's mathematical thinking by viewing videotaped clinical interviews over the course of an entire semester. They were also asked to conduct two of their own interviews with children as the semester progressed. While the type of analysis varied, all of…

Central in the frameworks proposed to capture the knowledge needed for teaching mathematics is the assumption that teachers need more than pure subject-matter knowledge. Validation studies exploring this assumption by recruiting contrasting populations are relatively scarce. Drawing on a sample of 644 Greek-Cypriots preservice and inservice…