Problem solving and proofs have always played a major role in mathematics. They are, in fact, the heart and soul of the discipline. The using of a number of different proof techniques for one specific problem can display the beauty, and elegance of mathematics. In this paper, we present one specific, interesting geometry problem, and present four…

Inverse and injective functions are topics in most college algebra courses. Yet, current materials and course structures may not afford students' conceptual understanding of these important ideas. We describe how students' work with digital activities, "techtivities," linking two different looking graphs that represent relationships…

Building activities can be used any time in the school year in mathematics classes to promote problem solving, perseverance, and to develop students' spatial thinking. Spatial visualization skills are the "ability to mentally manipulate, rotate, twist, or invert a pictorially presented stimulus object." The authors were guided by the…

The 1989 good old days' quote from the "Field of Dreams" by Kevin Costner that "If you build it, he or they will come" is no longer going to be attractive, especially in the field of mathematics education. One such challenging subject in the field of mathematics education is the teaching and learning of geometry. It is the aim…

Undergraduate statistics teaching has always faced the challenge of improving the learning quality on a continuous basis. Interactive statistical applets can enhance statistical knowledge by providing multiple representations of basic concepts and facilitating experimentation. The use of these applets will simplify the efforts for teaching…

Begun in the mid-90s, computers have long been a staple in teaching mathematics to engineering students. In recent years, with the effects of the COVID-19 pandemic and the arrival of Generation Z in tertiary education, the role of blended learning has increased. This paper highlights some of the greater challenges and successes of the transition…

Mathematical writing (MW) can support students' mathematical learning and is common in mathematics assessment. However, MW is known to be particularly challenging for students with learning disabilities. While the use of model compositions of both high- and low-quality writing and the act of revision are evidence-based practices in writing…

Constructing mathematical proofs is a fundamental yet challenging skill in secondary school geometry. While technology has been used to scaffold different aspects of the proving process, existing approaches often separate inquiry and conjecturing from formal proof or focus on structural and technical assistance without addressing students' initial…

The paper describes an implementation of research done over several years, by me and in some cases others, at Stanford University and elsewhere. The implementation comprised the design, building, testing, and marketing of a digital educational technology platform to provide a supplementary tool for explorative mathematics learning and assessment.

Many of today's teachers have successfully incorporated technology into their classrooms through digitally based approaches to student learning. However, the flipped classroom pedagogy can provide for rich experiences in the classroom as the students learn lessons at their own pace, leaving the teachers free to create fun, hands-on lessons in the…

Learn how to engage students in geometry concepts through a real-world task that leverages GeoGebra to provide students with generalization and authorship opportunities. This article shares the story of a geometry task that asked students to choose a city that would best work for their new trucking company. Throughout the task, students noticed…

The duo of artefacts is a simplified model of the complex systems of various manipulatives (either tangible or virtual) that mathematics teachers and their students use in classrooms. It offers a means to study the complexity of the interweaving of the tangible and of the digital worlds in the teaching and learning processes. A duo of artefacts is…

We present a free student-facing tool for creating 3D plots and smartphone-based virtual reality (VR) visualizations for STEM courses. Visualizations are created through an in-browser interface using simple plotting commands. Then QR codes are generated, which can be interpreted with a free smartphone app, requiring only an inexpensive Google…

Many teachers reported improved skills in using technology as a direct result of teaching virtually during the pandemic (Bushweller, 2020). The authors wondered which uses of technology would continue as teachers transitioned back into face-to-face classrooms. Recognizing that mere incorporation of technology into instruction does not guarantee…

In this paper, I discuss the potential transformations to teach K-12 geometry topics with the technology of 3D Pens, which enabled 3D models to be created instantly via one's moving hands. I draw on an example of using constructionist learning activities with 3D Pens to teach young children, 'how tall is the triangle?'