This study examined the opportunity to learn function transformations afforded by the GeoGebra applets available on the GeoGebra website. Our analysis focused on the functions and their representations through which function transformations are explored in these GeoGebra applets, the effects and components of transformations that the GeoGebra…

The purpose of this study is to investigate how designers of commercial educational mathematics game apps describe various aspects of "integration". My investigation addresses several research questions, including what integration means to designers, why they build it into games, and how they do so. Integration is a concept described in…

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…

Many studies have documented the challenges facing teachers who use digital technologies in their classrooms. This is especially true for digital technologies that offer new models or representations of school mathematics concepts. In this article, we report on a collaboration between teachers and researchers around the use of a novel touchscreen…

This study employed an alternating treatments design to compare the effects of two types of practice conditions on the subtraction fact fluency in a fifth-grade classroom. Eight, fifth-grade students participated in the study over a 5-week intervention period practicing addition and subtraction facts in a "fact families" condition (A +…

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…

Playing board games is known to improve pre-school student numeracy and many board games are used to motivate and explore concepts in probability. This study investigates whether college students in liberal arts mathematics courses assigned to play the board game "Settlers of Catan" develop a stronger grasp of basic probability concepts…

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…

It is increasingly important for mathematics students to engage in active learning along with discussion of material with their peers. "Slopes" is a mobile application designed to visualize solutions to differential equations and support active learning in the classroom. We implemented group activities using "Slopes" into an…

There is concern about mathematics success and its related pedagogy. Society has seen rapid changes in the economy and technology with a call for these changes to be reflected within the classroom. New methods of teaching mathematics are being sought with the purpose to improve teaching and learning while making mathematics relatable to the new…

This mixed qualitative and quantitative methods study addressed the effect of technology on college algebra and survey of calculus students' understanding. This research study was conducted in fall 2016 on eight college algebra classes with a total of 315 students, and in summer 2017, on two survey of calculus classes with a total of 40 students…

Over the last several years, iPads have become increasingly popular in the classroom. The number of available apps that could be used in the mathematics classroom are countless, but some make better mathematical learning tools than others. This research presents a set of sixteen criteria that can be used to evaluate the potential of an iPad app to…

The purpose of this study is to examine the use of a Vending Machine applet as a cognitive root for the development of preservice teachers understanding of function. The applet was designed to purposefully problematize common misconceptions associated with the algebraic nature of typical function machines. Findings indicated affordances and…

The purpose of this study was to explore relationships between app affordances and user abilities in second graders' interactions with mathematics virtual manipulative touchscreen tablet apps. The research questions focused on varying manifestations of affordance-ability relationships during children's interactions with mathematics virtual…