As three-dimensional (3D) printing technology is fast becoming more affordable and accessible, calculus instructors can now consider using 3D printing and 3D printed models to actively engage students in core concepts relating to objects in R[superscript 3]. This article describes three lessons for a multivariable calculus class in which students…

Knowing when students have the prerequisite knowledge to be able to read and understand a mathematical text is a perennial concern for instructors. Using text describing Newton's method and Vinner's notion of concept image, we exemplify how prerequisite knowledge influences understanding. Through clinical interviews with first-semester calculus…

Data collected in psychological studies are mainly characterized by containing a large number of variables (multidimensional data sets). Analyzing multidimensional data can be a difficult task, especially if only classical approaches are used (hypothesis tests, analyses of variance, linear models, etc.). Regarding multidimensional models, visual…

It is essential that chemists develop strong oral communication skills. At the undergraduate level, this requires students to build confidence in their ability to speak without a script and to utilize graphics effectively. We have developed a short activity that helps address common presentation issues such as overuse of text and reading verbatim…

A new laboratory experiment investigating the ternary phase equilibrium of water-propan-2-ol-sodium chloride with one-, two-, and three-phase regions has been developed. Observations of the type and number of phases of a series of mixtures of the three components were made, and the results are then used in a systematic way to more finely choose…

A well-constructed just qualified candidate (JQC) description is needed to arrive at a reasonable passing score for licensure tests. Traditionally, such descriptions consist of a list of knowledge and skill statements without sufficient context to internalize its intended meaning, allowing the standard-setting panelists to make idiosyncratic…

The interpretation of medical images is a primary task for radiologists. Besides two-dimensional (2D) images, current imaging technologies allow for volumetric display of medical images. Whereas current radiology practice increasingly uses volumetric images, the majority of studies on medical image interpretation is conducted on 2D images. The…

We propose that there exists mathematical knowledge for teaching (MKT) specific to visual representations (VRs), abbreviated MKT-VR. We define a VR as a graphic creation, such as a diagram or drawing, which illustrates quantities and shows quantitative relationships or which illustrates geometric properties of figures and shows geometric…

Within the broad area of whole number operations, understanding and solving word problems continues to be an important area of inquiry. In the present study we draw on the framework of representational fluency to examine conceptual and procedural understandings that are exhibited by a group of Malaysian seven-year-olds as they attempted to solve…

Findings are presented from an analysis of how six future middle-grade teachers reasoned with strip diagrams and a variable parts perspective on proportional relationships to develop and explain equations in two variables. One equation was for two quantities varying together and one was for a line through the origin in a coordinate plane. Both…

The importance of plants is not as clearly understood as that of animals. This lack of attention is called "plant blindness" and is considered one of the most important problems in biology education. Textbooks do not put much emphasis on plants and, therefore, they may contribute to plant blindness. In this research, ten textbooks used…

This study was conducted to examine the effects of modality across gender on undergraduate student achievement when learning Algebra concepts. Cognitive Load Theory (CLT) and Cognitive Theory of Multimedia Learning (CTML) provided a framework for this study to describe in depth the concept of the modality principle. Participants were undergraduate…

This qualitative study explores how middle school students in the Western United States participated in a curricular unit that focused on action for socioenvironmental sustainability. Using inductive coding and building on prior research, I examined actions that students took during this sustainability unit and how students talked about action…

Using electronic tablets to present flash cards for teaching skills is becoming common among practitioners. However, no published study compared the effectiveness of the electronic tablet-based flash cards to paper flash cards for teaching receptive labeling skills. The purpose of this study was to compare the efficacy of the iPad-based and paper…

Background: Recent evidence suggests PechaKucha--a presentation style utilizing simplified visuals, narration, and rigid time constraints--may promote various learning outcomes and instructor goals better than traditional PowerPoint presentations. Objective: The purpose of this study was to test the effectiveness of students' PechaKucha compared…