This paper shares a flexible activity for engaging people in mathematical inquiry that does not depend on fixed prior knowledge built on a famous property of Möbius strips. The discussion includes the implementation of the activity and its extensions, facilitator moves and common participant thinking, suggestions for adaptation and integration…

This study examines a Technology, Pedagogy, Content Knowledge (TPACK) training framework for pre- and in-service mathematics teachers that enables them to experience inquiry-based learning as learners in a dynamic geometry environment that serves as a mathematics laboratory. We investigate the effect of this experience on the teachers' TPACK,…

Habermas' construct of rationality is a tool adapted from social sciences into mathematics education to identify the difficulties in the proving process and to plan the teaching of proof for reducing these difficulties. According to Habermas, people engaged in an activity/action are considered to "act rationally" if they choose and use…

This paper describes the conceptions about complex numbers that a group of university students has, these were built from the application of an activity sequence centered on these numbers. This sequence is based on the APOS theory, some aspects of semiotic representation theory, and the use of digital technology. Particularly, both the general…

Dynamic Geometry Environments (DGEs) are popular tools in the exploration of geometry. This research is designed to explore the confidence of undergraduate mathematics students as they make mathematical statements when completing geometric tasks using DGEs. Students completed two series of tasks in both Euclidean and hyperbolic geometry. The first…

Our study aims to determine how Habermas' construct of rationality can serve to identify and interpret the difficulties experienced by university students in the mathematical problem-solving process. To this end, a problem which required modelling and solving a differential equation was used. The problem-solving processes of university students…

In this report, we present how one prospective elementary teacher (PT) engaged in the Ant Farm Task, which we designed to investigate PTs' reasoning about coordinate systems. We highlight the cognitive resources the PT drew upon in solving the task via the establishment of a Cartesian coordination and consider educational implications. [For the…

We present an investigative activity that was set as part of a course of pre-service teachers of mathematics. The emphasis in the course was set on the importance of using the computerized technological tool for teaching the subject. The activity focused on investigating interesting geometrical conservation properties which are not known to the…

We discuss how mathematics and secondary mathematics education majors developed an understanding of Fermat points for the triangle as well as Steiner points for the square and regular pentagon, and also of soap film configurations between parallel plates where forces are in equilibrium. The activities included the use of soap films and the…

In this work, we study the mathematical practice of defining by mathematics researchers. Since research is an important part of many professional mathematicians, understanding how they do research is a necessary step before thinking about future researchers' undergraduate and postgraduate education. We focus on the defining process associated with…

This study examined pre-service teachers' views and experiences of building geometric constructions on paper and with the interactive whiteboard. The study group consisted of 26 pre-service elementary teachers in a state university in the Black Sea region of Turkey who took the Geometry Teaching course. The data were obtained from an opinion form…

The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through…

We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…

In this article, we report how a geometric task based on the ACODESA methodology (collaborative learning, scientific debate and self-reflection) promotes the reformulation of the students' validations and allows revealing the students' aims in each of the stages of the methodology. To do so, we present the case of a team and, particularly, one of…

In this article, the authors present two activities in which students explore angles and related geometric properties in the context of dance, namely ballet. The activities have been successfully implemented in pre-service numeracy classes at Monash University's two-year, post-degree teacher education program (MTeach). Specifically, the activities…