Tychonov's 1935 solution of the heat equation, exhibiting nontrivial heat fluxes spontaneously appearing along an isolated conducting rod initially held at zero degrees, has intrigued some specialists for almost a century. No doubt those practicing heat engineers who took mathematics seriously were initially relieved to learn that the construction…

We describe a hands-on project in which students collect data on the impact of distracted driving on driver reaction time. Initially they do this in class via a virtual driving applet, using themselves and fellow students as test subjects. Different applet versions simulate driving with and without distraction and measure the time it takes to…

Rich research evidence supporting the strong, positive connections between spatial ability and mathematical ability has been well documented. Spatial tools, such as computer-aided-design (CAD) software, have been increasingly utilized and researched for promoting mathematics learning in K--12 (kindergarten to 12th grade). Tinkercad, a free online…

Augmented reality (AR) is a valuable tool which is becoming more easily accessible due to the recent developments in mobile device technology and the growing availability of AR content. Augmented reality refers to computer generated 3D objects superimposed onto real life scenes. Unlike virtual reality, AR simply needs a device with a camera, the…

Augmented Reality (AR) and Virtual Reality (VR) platforms now support shared, immersive experiences that enable people to directly physically and perceptually engage with mathematical objects, including shared objects. These new forms of AR/VR technology -- which we call "shared holographic AR/VR" (shAR) -- enable multiple learners to…

The lottery has rich potential for mathematical explorations. It serves as a real-world context to explore concepts of permutations, combinations, sample space, and probability in terms of making sense of the lottery games. The lottery offers additional possibilities in terms of scaling, data analysis, and spatial analysis. Finally, by readily…

There is currently significant interest in 3D fabrication in middle school classrooms. At its best 3D printing can be utilized in authentic design projects that integrate math, science, and technology, which facilitate deep learning by students. In essence, students are able to tinker in a virtual world using 3D design software and then tinker in…

Learning-by-teaching has been identified as one of the more effective approaches to learning. Recently, educational researchers have investigated virtual environments in order to utilize the learning-by-teaching pedagogy. In a face-to-face learning-by-teaching situation, the role of the learners is to teach their peers or instructors. In virtual…

Building physical models is a natural activity for children and provides a context for lessons on two-dimensional (2D) and three-dimensional (3D) shapes. However, children do not think of their models as prisms, cylinders, and pyramids. Their creations are spaceships, tunnels, castles, and nets on the floor. Creating these types of shapes with…

Abstraction is a key concept in CS, one of the most fundamental ideas underlying CS and its practice. However, teaching this soft concept to novices is a very difficult task, as discussed by many CSE experts. This paper discusses this issue, and suggests a general framework for teaching abstraction in CS to novices, a framework that would fit into…

The use of projectiles is a concept familiar to most students, whether it is a classic slingshot, bow and arrow, or even a spit wad through a straw. Perhaps the last thing a teacher wants is more projectiles in the classroom. However, the concept of projectiles is relevant to most students and may provide a means of bringing more authenticity into…

This article discusses the integration of student-generated GeoGebra applets and Jing screencast videos to create a YouTube-like medium for sharing in mathematics. The value of combining dynamic mathematics software and screencast videos for facilitating communication and representations in a digital era is demonstrated herein. We share our…

It has been recognised that the general lack of enjoyment of institutional mathematics learning at the secondary level is one of the basic reasons behind the bad reputation of mathematics in society. Increasing students' motivation to learn mathematics through enjoyment and playing, especially in their free time, might therefore be a relevant…

Students acquire knowledge and skills through different modes of instruction that include classroom lectures with textbooks, computers, and the like. The availability and choice of learning innovation depends on the individual's access to technologies and on the infrastructure environment of the surrounding community. In this rapidly changing…

Objectives of a project-oriented mechanical engineering course, Engineering Design, were achieved through a design project, where students designed, built and demonstrated an extreme version of a basic Theo Jansen device. Through this project, junior students in the University of Louisiana fully developed the capability of applying mathematic and…