We present an investigation of the infinite sequences of numbers formed by calculating the pairwise averages of three given numbers. The problem has an interesting geometric interpretation related to the sequence of triangles with equal perimeters which tend to an equilateral triangle. Investigative activities of the problem are carried out in…

Geometric habits of mind (GHoM) are the approaches that individuals use to solve geometry problems. This study aimed to determine the effect of dynamic geometry software (DGS) in activating the GHoM of pre-service mathematics teachers. The study was conducted with six teacher candidates who were enrolled in a semester-long course titled…

This study examines technology-enhanced teacher responses and students' written mathematical explanations to understand how to support effective teacher responding and the centering of students' mathematical ideas. Although prior research has focused on teacher noticing and responding to students' mathematical ideas, few studies have explored the…

Conjecture formulation is crucial to mathematics education. Therefore, this study aimed to evaluate challenges prospective mathematics teachers (PMTs) encounter when using GeoGebra to formulate geometrical conjecture. A qualitative case study was conducted with an exploratory strategy to provide a complete comprehension of the occurrence. Six…

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…

This study examined problem posing situations of pre-service elementary mathematics teachers in dynamic geometry environment by using problem posing strategies. The qualitative method of multiple case study was applied and geometric concepts that participants used for each type of problem posing are examined. Eight participants from 3rd grade…

The purpose of this study was to analyze the prompts that preservice secondary mathematics teachers used for the acquisition of mathematics knowledge in dynamic geometry environment tasks. The participants, four preservice secondary mathematics teachers who were enrolled in a computer-supported mathematics education course, designed a dynamic…

There has been a large amount of research about the impact of dynamic geometry software (DGS) on the learning of mathematics mainly related to different representations of mathematical concepts and functional dependences. This paper goes beyond these investigations by suggesting meaningful connection and integration of DGS with physical resources…

Pre-service mathematics teacher (PST) education often addresses within Geometry Classes how to utilize Dynamic Geometric Software (DGS). Other classes may also incorporate teaching pre-service teachers about the history of mathematics. Although research has documented the use of Dynamic Geometric Software (DGS) in teaching the history of…

This article presents a didactic situation focused on geometric reasoning using 3D GeoGebra, using the concepts Theory of Didactical Situations (TDS). The objective of this work is to bring a didactic proposal for the teaching of Spatial Geometry, working with the students' geometric perception, oriented and elaborated based on the dialectic of…

To fulfill the Standards for Mathematical Practice (National Governors Association Center for Best Practices & Council of Chief State School Officers [NGA Center & CCSSO], 2010), it is important for teachers to empower students to critique, revise, and expand their ideas as they solve problems. However, students often face challenges such…

The initial training of mathematics teachers in Spain can start in the final year of the mathematics degree when the students, and future teachers, select courses related to teaching the discipline. At that time, since over the next two years they will probably be certified to enter the profession, it is worth asking oneself what mathematical…

The aim of this study was to improve pre-service teachers' ability to infer cross-sections of geometric solids with Wolfram demonstrations and Mathematica in Analytic Geometry II course. The study was conducted with third year students studying Elementary Mathematics Education. In this study, the pre-test--post-test control group design was used.…

In order to be able to draw accurately and to interpret the drawings properly, the skills of the students' drawing skills and therefore spatial visualization and spatial orientation must be developed. The studies in the literature are mostly concerned with examining the spatial skills of students with various models or investigating the effects of…

This paper reports on an aspect of a larger research study conceptualised within a teacher development project in Mthatha, Eastern Cape Province. The project was initiated with the objective to develop appropriate skills to use dynamic geometry software (DGS) effectively and strategically as a teaching and learning tool for mathematics. The study…