One of the most remarkable devices embedded in a Microsoft Excel spreadsheet is known as the spinner. Its staggering simplicity is undoubtedly its strength. As an incrementing device that allows graphs to dance across the screen, it gives the concept of variability a whole new meaning. Spinners and their close cousins scroll bars can be grabbed…

This paper analyses the answers of a group of first-year university Mathematics students to a questionnaire, with the aim of determining the difficulties they have when carrying out non-routine tasks related to improper integrals. The questionnaire consisted of nine questions including not only calculus tasks and determining the convergence of…

Resistance destroys symmetry. In this note, a graphical exploration serves as a guide to a rigorous elementary proof of a specific asymmetry in the trajectory of a point projectile in a medium offering linear resistance.

The five Platonic solids are constructed (as graphs) from their rotational symmetry groups. The constructions are based on an idea of Bertram Kostant and are quite simple; conjugacy classes in the group are the vertices of the graphs and products determine adjacency.

When technologies are used in mathematics education it is important to assess how activities will support the development of mathematical understanding and the technical expertise that students will need. The two issues are discussed in this paper. Literature is reviewed and findings from a recent study in a high-school class are reported. The…

The motion of a magnet through a coil is analysed through a model of magnetic monopoles. The magnetic flux of a monopole passing through a loop is explained and also its rate of change. By a superposition of voltages produced by the monopoles on the coils the shape of the voltage versus time graph is explained. Also examined is the interaction of…

Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

In this article, the learning progress of one fifth-grade student is examined with regard to the development of her graph interpretation skills as she participated in the Junior Science Institute (JSI), a two-week, science intensive summer camp in which participants engaged in microbiology research and application. By showcasing the student's…

In this exercise the US Standard Atmosphere is used as "data" that a student is asked to model by deriving equations to reproduce it with the help of spreadsheet and graphing software. The exercise can be used as a laboratory or an independent study for a student of introductory physics to provide an introduction to scientific research…

This article examines a classroom discussion of multiple interpretations of the scales on two distance versus time graphs. The analysis describes how two students and a teacher used multiple meanings for phrases of the form "I went by" and coordinated these meanings with different views of the scales. Students' ambiguous and shifting meanings did…

This book examines learning science from multiple perspectives--especially a child's. The whimsical character of Mary Froggins guides readers through the steps of igniting students' natural sense of wonder, incorporating brain research, integrating science concepts with other subjects, and applying science to daily life. The authors demonstrate…

This paper discusses a research study that focused on middle grades students' abilities to read and to move between different graphical representations before and after instruction. The data analyzed were collected from a group of 76 sixth grade students who were in 3 different mathematics classes in a middle school located in central North…

The typical path of instruction in high school algebra courses for the study of polynomial functions has been from linear functions, to quadratic functions, to polynomial functions of degree greater than two. This paper reports results of clinical interviews with an Algebra II student. The interviews were used to probe into the student's…