Visual representations, such as diagrams, are known to be valuable tools in problem solving and proof construction. However, previous studies have shown that simply having access to a diagram is not sufficient to improve students' performance on mathematical tasks. Rather, students must actively extract information about the problem scenario from…

Decades of research have established that solving geometry proof problems is a challenging endeavor for many students. Consequently, researchers have called for investigations that explore which aspects of proving in geometry are difficult and why this is the case. Here, results from a set of 20 interviews with students who were taught proof in…

In calculus, related rates problems are some of the most difficult for students to master. This is due, in part, to the nature of the problems, which require constructing a nuanced mental model and a solid understanding of the function. Many textbooks present a procedure for their solution that is unlike how experts approach the problem and elide…

Background: Math is a difficult subject with which many upper middle-school students struggle. In addition to knowledge, skills, and motivation, effective learning strategies play an important role in learning math. Aims: This study aimed to examine the effects of comprehension-oriented learning strategies (perceptual and abstract grouping of…

One of the most challenging tasks in the field of Educational Data Mining (EDM) is to cluster students directly based on system-student sequential moment-to-moment interactive trajectories. The objective of this study is to build a general temporal clustering framework that captures the distinct characteristics of students' sequential behaviors…

Framing mathematics ability as innate or intimately connected to someone's intelligence is common. Have you ever heard a parent or colleague say something akin to, "Jonathan can really write, but I don't know what happened in math!"? Unfortunately, this framing not only narrowly describes how mathematics learning occurs but also raises…

Mathematics educators promote student engagement in the Process Standards and create problem-solving tasks and facilitate discussions to help their students develop strengths in explaining their methods, using and interpreting multiple representations, and making connections between topics. They are excited and encouraged when they see students…

This paper examines part of a set of students who were followed during their first-term, first-year studies in formal definition-based real analysis at a British university. It explores the approaches to problems about convergence of sequences and series made by students who have a tendency to include visual imagery in their reasoning. We explore…

Investigates the thinking process underlying students' improper linear reasoning and how this process is affected by their mathematical conceptions, beliefs, and habits. Explores the actual process of problem solving from students falling into the linearity trap and the mechanism behind it. Discusses specific mathematical conceptions, habits, and…

A systematic series of studies by De Bock et al. revealed a strong, deep-rooted tendency among secondary school students to apply the proportional model in non-proportional problems involving lengths, areas and volumes of similar geometrical figures. In these studies, however, items were used involving direct measures for area and volume as well…

This paper describes insights on how to promote mathematical reasoning in problem solving based on the mathematical experiences of participants in a long-term study in which the students engaged in strands of well-defined, open-ended mathematical investigations, as a context for research on the development of particular concepts and ways of…

The first volume of the 29th annual conference of the International Group for the Psychology of Mathematics Education contains plenary lecture and research forum papers as listed below. Short oral communications papers, poster presentations, brief summaries of discussion groups, and working sessions are also included in the volume. The plenary…

These Proceedings document an educational research forum held at Wake Forest University (Winston-Salem, North Carolina) on December 7, 2005. Table of contents and 26 research studies of high school teaching are included. Studies include: (1) Mathematical Reasoning in Multiple Representations: Connections and Confidence (Justin Allman); (2) The…

The IADIS CELDA 2012 Conference intention was to address the main issues concerned with evolving learning processes and supporting pedagogies and applications in the digital age. There had been advances in both cognitive psychology and computing that have affected the educational arena. The convergence of these two disciplines is increasing at a…