In this article, we examine the ways in which the creation of a third space can bridge the divide between coursework and practice for preservice secondary mathematics teachers (PSTs) taking a technology, pedagogy, and content course. A university-based instructor partnered with two high school teachers to create a space in which PSTs draw upon and…

Usually, all the applications of dynamic geometry systems (DGS) presented to our students are strictly mathematical, meanwhile their interests are normally far away from mathematics. We would like to introduce here a motivating example outside the "standard applications" of DGS, presenting a completely different application of this kind…

Understanding spatial reasoning is important to success in mathematics. This article shows how the proficiency strands in the "Australian Curriculum: Mathematics" provide the tools needed for effective teaching and learning of spatial thinking.

This study aims to develop geometry learning media on curved-solid objects using Ispring Suite 8 with 3D effects supported by Google SketchUp. It also aims to find the effectiveness of the media towards the basic geometry skills and the learning result of 9th -grade students of junior high school. This study is a development study which refers to…

In a study about pre-service secondary mathematics teachers' (PSMTs) understanding about the nature of theorems in geometry, the researcher noticed that it was challenging for the PSMTs to visualize and draw counterexamples to disprove the given mathematical statements. Meanwhile, the use of the dragging feature of dynamic geometry environments…

This paper, which describes a study undertaken with pairs of future primary teachers using GeoGebra software to solve geometry problems, includes a brief literature review, the theoretical framework and methodology used. An analysis of the instrumental genesis process for a pair participating in the case study is also provided. This analysis…

The purpose of the study was to investigate the effects of mathematics instruction supported by dynamic geometry activities on seventh grade students' achievements in the area of quadrilaterals, based on their van Hiele geometric thinking levels. The study followed a nonrandomized control group pretest and posttest research design. Participants of…

A geometrical task is presented with multiple solutions using different methods, in order to show the connection between various branches of mathematics and to highlight the importance of providing the students with an extensive 'mathematical toolbox'. Investigation of the property that appears in the task was carried out using a computerized tool.

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…

Dynamic geometry software can help teachers highlight mathematical relationships in ways not possible with static diagrams. However, these opportunities are mediated by teachers' abilities to construct sketches that focus users' attention on the desired variant or invariant relationships. The study described in this paper looked at two cohorts of…

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…