The algebraic group Spin[subscript 3 × 3] arises from spinning collections of the numbers 1-9 on a 3×3 game board. The authors have been using this group, as well as a corresponding online application, to introduce undergraduate students to core concepts in group theory. We discuss the benefits of using this deceptively simple, toy-like puzzle in…

Most any students can explain the meaning of "a[superscript b]", for "a" [element-of] [set of real numbers] and for "b" [element-of] [set of integers]. And some students may be able to explain the meaning of "(a + bi)[superscript c]," for "a, b" [element-of] [set of real numbers] and for…

After a discussion about the possibilities and status of augmented reality in education, a good practice example of an augmented reality application is presented. This case study examines the use of an augmented reality app in higher education to support abstract STEM content, such as vectors. Based on this example, the implementation of such apps…

Following a line of inquiry regarding the exact number of real roots of a real polynomial, this investigation considers: Descartes' Rule of Signs, the Budan-Fourier Theorem, and versions of Sturm's Method in contrast with the approximate root count gleaned from graphing utilities. Online applets are provided to allow the reader to freely…

Understanding mathematical concepts is important for all students, although often challenging for many students with disabilities. Historically, educators have used concrete manipulatives to support and build conceptual understanding. Mobile devices provide a valuable option to support students with disabilities in mathematics through app-based…

This article draws on extensive experience working with secondary and tertiary teachers and educators using an applet to display rational polynomials (up to degree 7 in numerator and denominator), as support for the challenge to deduce as much as possible about the graph from the graphs of the numerator and the denominator. Pedagogical and design…

Color addition and subtraction apps in HTML5 have been developed for students as an online hands-on experience so that they can more easily master principles introduced through traditional classroom demonstrations. The evolution of the additive RGB color model is traced through the early IBM color adapters so that students can proceed step by step…

Teachers increasingly use virtual manipulatives and other apps on touch-screen devices (e.g., "iPads") in an effort to help students understand mathematics concepts. However, students experience these apps and their affordances in different ways. The purpose of this article is to inform teachers' decisions about app implementation in the…

Trying to find quality apps for use in mathematics classes can be time consuming and bewildering. This article outlines a process for evaluating apps and provides teachers with access to comprehensive qualitative evaluations of 53 geometrical apps based on pedagogical, mathematical and cognitive fidelities.

More than 2,200 years ago, Eratosthenes, who was a Greek astronomer, geographer, and mathematician, used a simple proportion involving the distance between two ancient cities and measures of shadows cast in those cities during a summer solstice to estimate the circumference of Earth (Nicastro 2008, 25-28). Today, middle school students can use…

Increased attention to reasoning and justification in mathematics classrooms requires the use of more authentic assessment methods. Particularly important are tools that allow teachers and students opportunities to engage in formative assessment practices such as gathering data, interpreting understanding, and revising thinking or instruction.…

In this paper, an example is offered of a problem-solving task for senior secondary school students which was given in the context of a story. As the story unfolds, the task requires progressively more complex forms of linear programming to be applied. Coding in MATLAB is used throughout the task in such a way that it supports the increasing…

This article proposes a framework for classroom teachers to use in making pedagogical decisions regarding which mathematical materials (concrete and digital) to use, when they might be most appropriately used, and why. Two iPad apps ("Area of Shapes (Parallelogram)" and "Area of Parallelogram") are also evaluated to demonstrate…

The best Science, Technology, Engineering, and Mathematics (STEM) design challenges are student centered, with students themselves making the key decisions. But with young children who are still learning basic academic and social skills, implementing projects where they truly take the lead can be quite challenging. To give students at one…

Having an answer to "When are we ever going to use this in real life?" is important to middle school mathematics teachers. The activity described in this article awakened sixth graders' understanding of how artists use mathematics. By exploring ratio and proportionality in different paintings, students realized the use of proportional…