We describe some classic experiments on the Möbius strip, the projective plane band, and the Klein bottle band. We present our experience with freshmen college students, college teachers, high school students, and Mathematics Education graduate students. These experiments are designed to encourage readers to learn more about the properties of the…

Despite its vital importance in our lives, chemistry is inadequately represented in most museums. Issues such as safety, replenishing and disposal of chemicals, supervision required, and cost are constraints that have limited the number and size of chemistry exhibits. Taking into account the constraints, a 21-station interactive and inexpensive…

Statistics is enjoying some well-deserved limelight across mathematics curricula of late. Some statistical concepts, however, are not especially intuitive, and students struggle to comprehend and apply them. As an AP Statistics teacher, the author appreciates the central limit theorem as a foundational concept that plays a crucial role in…

This technology report outlines a robust and easy to assemble magnetic stirrer that is programmable. All of the parts are recycled from obsolete computer hardware except the Arduino microcontroller and motor driver, at a total cost of around $40. This multidisciplinary approach introduces microcontrollers to students and grants the opportunity to…

The papers in this special issue focus on instructional strategies with manipulatives. Often described as "hands-on learning", these strategies emphasize the use of physical and, more recently, virtual objects to represent target information and concepts. These strategies are frequently suggested as effective techniques for teaching…

This paper provides historical insights and educational background of Froebel's Gifts, hands-on materials developed in the early 19th century. Based on an explorative study with 54 German children (aged 5 to 10) in 2016, we first took steps to explore how these materials meet the demands for early mathematics learning of primary children. Starting…

"Mathematical modeling of the physical world should be the central theme of physics instruction" (Hestenes 1987). Science teachers know this, but because of standardized state testing, many math teachers and some science teachers feel the need to focus on memorizing facts that will be on a multiple-choice test (Volante 2004). As a…

Spatial reasoning, which involves "building and manipulating mental representations of two-and three-dimensional objects and perceiving an object from different perspectives" is a critical aspect of geometric thinking and reasoning. Through building, drawing, and analyzing two-and three-dimensional shapes, students develop a foundation…

Reasoning is central to what Cuoco, Goldenberg, and Mark refer to as mathematical "habits of mind" (1996). "Reasoning is an integral part of doing mathematics. Students should enter the middle grades with the view that mathematics involves examining patterns and noting regularities, making conjectures about possible generalizations,…

Students with high incidence disabilities (i.e., specific learning disabilities, emotional disturbance, intellectual disability, etc.) exhibit impairments in the areas of attention, memory, perception, processing linguistic information, and reasoning that affects their ability to learn. Hence, the ability to design and deliver explicit, enhanced…

The purpose of this classroom note is to provide an example of how a simple origami box can be used to explore important concepts of geometry and calculus. This article describes how an origami box can be folded, then it goes on to describe how its volume and surface area can be calculated. Finally, it describes how the box could be folded to…

Promoting independence in all students is one important part of education. It can be difficult for educators to identify meaningful tasks that students with severe disabilities can complete with full independence. By incorporating visual supports into a student's independent work, the teacher is providing the student with an opportunity to…

Doug Williams presented the opening address at Conference 2012 on the theme of "Enigmas". Here he continues storytelling about the learning and teaching of mathematics at its best. The descriptions are of real classrooms with real teachers, and real learners. As with many good stories this is the narrative of a journey. A journey that…

Teaching computer concepts to individuals with visual impairments (that is, those who are blind or visually impaired) presents some unique challenges. Students often have difficulty remembering to perform certain steps or have difficulty remembering specific keystrokes when using computers. Many cannot visualize the way in which complex computing…

This is an account of events in a real classroom when the notion that there is a distinction between calculation by counting, and calculation by structuring is a focus for learning. Pupils have "hands-on" experiences that support their understanding of "number". The teaching "aid" might be unfashionable in…