Twenty years ago when the author was student teaching, he quickly learned what geometry teachers and researchers (e.g., Senk 1985) have long known: High school geometry students struggle with proof. Throughout his career, he has tried to create instructional materials to make proof more accessible to his students. From field-testing materials with…

A virtual world was created using the popular sandbox game Minecraft to support the development of preservice teachers' knowledge for teaching mathematics. Preservice teachers explored the virtual world for a geometry activity involving area and volume problems. They then discussed how this integration of technology could support students'…

When the author first started teaching twenty years ago, he thought that as long as he was using dynamic geometry software (DGS) for students to "discover" conjectures instead of them learning the conjectures from a lecture or the textbook, he was maximizing their learning potential because they were using technology. Over the years, he…

In the context of rapid technological changes and modernization of society, the issue of ensuring adequacy of content in secondary education based on the use of advanced information technologies (ICT) is being updated. The necessity of an appropriate level of primary intellectual activity development in a person in terms of the current trends in…

Multimodal literacies have been incorporated as social learning practices in content areas, but research regarding multimodality within secondary mathematics instruction has often lacked the sociocultural lens. The author describes practitioner action research in the form of a case study (with one focal participant) from a public high school. The…

While within a geometric repeating pattern, there is an identifiable core which is made up of objects that repeat in a predictable manner, a geometric growing pattern (also called visual or pictorial growing patterns in other curricula) "is a pattern that is made from a sequence of figures [or objects] that change from one term to the next in…

If an object is conveniently located in front of two plane mirrors placed at an angle, an observer can see a superposition of images that results in a face with three eyes, called in this text a "triclops." The conditions of occurrence of such an image may seem trivial, but this is incorrect: rather, the correct interpretation of this…

Many icebergs are vulnerable to capsizing. In doing so the gravitational potential energy of the ice is increased, while that of the displaced sea water is decreased. Applying the principle of the conservation of energy shows that by capsizing, there is also a net transfer of energy to the surrounding sea water. This will be a maximum for a…

Background: This paper compares the effects of two classroom-based technology-enhanced teaching interventions, conducted in two schools in sixth (age 11-12) grade. In one school, the intervention involves the use of a class set of 3D Printing Pens, and in another school the use of dynamic geometry environments, for inquiry-based learning of the…

In this paper we show how we can utilize human-guided machine learning techniques coupled with a learning science practitioner interface (DataShop) to identify potential improvements to existing educational technology. Specifically, we provide an interface for the classification of underlying Knowledge Components (KCs) to better model student…

In this paper, a teaching path on non-Euclidean geometry focused on the Poincare-disk model, and its connection with art is shown. We consider as artistic contents the Escher's hyperbolic art and some paradoxes on Magriue's work. The mathematical aspects are illustrated thanks to a Dynamic Geometry System (GeoGebra) implemented with a laboratory…

This study focuses on how the combined use of graphic calculators with connectivity software promotes the social construction of mathematical knowledge. Particular emphasis is placed on the aspects related to design, development, implementation, and evaluation of didactic activities that integrate these technologies. We use Didactical Engineering…

This paper reflects on the design of tasks that could take profit from the new features for Automated Reasoning, recently available in the dynamic geometry program GeoGebra. We report on some ongoing experiment, involving initial mathematics teacher students, aiming to develop and evaluate the characteristics of tasks that, with the concurrence of…

This qualitative study aimed at describing student verbal interaction verbally through cognitive activities consisting of procedural, disputational, and exploration in solving geometry problems. This research was in the form of students' verbal interaction activities in group discussion which decribe students' thinking process in detail, both the…

National Council of Teachers of Mathematics' (NCTM's) "Principles to Actions: Ensuring Mathematical Success for All" outlines eight teaching practices for effective teaching and learning of mathematics (NCTM 2014). One of the teaching practices, "elicit and use evidence of student thinking," states, "Effective teaching of…