This study examined college calculus instructors' preferences in solving two calculus tasks to examine college calculus instructors' use of important cognitive roots in understanding derivatives of function. Our results showed that only one instructor consistently uses cognitive roots while other instructors either focus on algebraic methods or…

Over the last several centuries, mathematicians have developed sophisticated symbol systems to represent ideas often imperceptible to their five senses. Although conventional definitions exist for these notations, individuals attribute their personalized meanings to these symbols during their mathematical activities. In some instances, students…

Precalculus and calculus are considered gatekeeper courses because of their academic challenge and status as requirements for STEM (science, technology, engineering, and mathematics) and non-STEM majors alike. Despite college mathematics often being seen as a neutral space, the field has identified ways that expectations, interactions, and…

Generalization is a critical component of mathematical reasoning, with researchers recommending that it be central to education at all grade levels. However, research on students' generalizing reveals pervasive difficulties in creating and expressing general statements, which underscores the need to better understand the processes that can support…

Conceptual understanding of calculus is crucial in the fields of applied sciences, business, and engineering and technology subjects. However, the current status indicates that students possess only procedural knowledge developed from rote learning of procedures in calculus without insight of core ideas. Hence, this paper aims to assess students'…

When establishing connections among representations of associated mathematical concepts, students encounter different difficulties and successes along the way. The purpose of this study was to uncover information about and gain greater insight into how student processes connections. Pre-calculus students were observed and interviewed while…

A critical component of scientific reasoning is the consideration of alternative explanations. Recognizing that decades of cognitive psychology research have demonstrated that relative cognitive accessibility, or "what comes to mind," strongly affects how people reason in a given context, we articulate a simple "cognitive…

In this study, we examine introductory physics students' ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. 382 students from a calculus-based and an algebra-based introductory physics course were administered a quiz in the recitation…

This article describes the development of the Precalculus Concept Assessment (PCA) instrument, a 25-item multiple-choice exam. The reasoning abilities and understandings central to precalculus and foundational for beginning calculus were identified and characterized in a series of research studies and are articulated in the PCA Taxonomy. These…

This volume, a comprehensive survey and critical analysis of today's issues in mathematics education, distills research to build knowledge and capacity in the field. The compendium is a valuable new resource that provides the most comprehensive evidence about what is known about research in mathematics education. The 38 chapters present five…

Developing the Trends in International Mathematics and Science Study (TIMSS) Advanced 2008 Assessment Frameworks was a collaborative venture involving mathematics and physics experts from around the world. The document contains two frameworks for implementing TIMSS Advanced 2008--one for advanced mathematics and one for physics. It also contains…

The paper considers a teaching experiment carried out with secondary school students (9th grade), who face modelling tasks to approach some basic concepts of algebra and early calculus. The focus is on an embodied analysis of students' cognitive processes. The analysis highlights the use of metaphors as a means of sharing knowledge. (Contains 2…

This issue of "Investigations in Mathematics Education" contains: (1) a review of E. Fischbein's book "The Intuitive Sources of Probabilistic Thinking in Children;" (2) nine abstracts of research studies in mathematics education; (3) a list (by EJ number) of mathematics education research studies reported in the January to…

This volume of the 27th International Group for the Psychology of Mathematics Education Conference presents papers from: plenary panels; research forums; working sessions; discussion groups; short oral communications; and poster sessions from the meeting. Plenary lectures included: (1) Studying and Capturing the Complexity of Practice: The Case of…

This document contains the fourth volume of the proceedings of the 28th annual conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Inclusion and Diversity". This volume features 64 research report papers: (1) Situated or Abstract: The Effect of…