I explore some facts about the area, position, etc. of the Steiner ellipse using GeoGebra and numerical analysis. Students can use these for mathematical inquiry.

This paper seeks to answer the question: How does the handling of the contradictions that emerge in activities of initial mathematics teacher education contribute to the learning of geometric knowledge when pre-service teachers and the teacher educator solve geometric construction problems with GeoGebra? A dialectical-materialist approach is used…

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…

With the introduction of artificial intelligence (AI), specifically generative AI and large language models (e.g., ChatGPT, Google Gemini), into education, there is a conversation regarding what knowledge teachers still need and will need moving forward. In this article, we describe how AI can, and should, be aligned to the Technological…

Sequences are an important topic--not only in mathematics but also in the mathematics curriculum. Exploring sequences related to medial triangles offers learners opportunities to solve problems involving sequences within geometric contexts. Sequences related to medial triangles are also a rich source of beautiful and interesting geometric patterns…

University supervisors responsible for the programming and congruency between field experiences and the physical education teacher education (PETE) preparation program play a pivotal role in the opportunity for pre-service physical education teacher success. Due to limitations of time, quality mentors, and the residual effects of the pandemic,…

Mathematical modelling is acknowledged to be one of the major dimensions of mathematical competence, and well-designed modelling activities can provide students with the opportunity to use mathematical concepts and procedures in a meaningful way. Additionally, modelling activities are regarded as suitable contexts for enabling students to use…

Teacher educators use various measures to gauge pre-service teachers' knowledge, skills, and attitudes, including behavioral measures, self-report questionnaires, and interviews. These measures often fail to capture the granularities of the teaching and learning processes. As such, there has been a burgeoning and recent interest in the use of…

An exploratory project on the use of digital notebooks and collaboration is currently underway in four courses over the span of five semesters at two North Carolina universities. The team currently teaches at two different universities. Professor A is at a private institution and Professor B is instructs at a state university. The team has…

This article condenses five years of professional development based on Technological Pedagogical and Content Knowledge (TPACK) integration principles, National Council of Teachers of Mathematics Principles to Actions (2014), and ISTE Student and Teacher standards to give a launch point for teachers and teacher educators to integrate 3D modeling…

Virtual reality (VR) is an emerging technology that is gaining traction in K12 education. Whereas well-designed and engaging VR experiences may be considered educational, teacher educators with content-area expertise are uniquely positioned to analyze the actual content provided by those experiences when determining VR's educational value.…

In the Czech Republic one of the key tasks of an education system is to ensure the financial literacy of citizens. Scarcely any topic of the school curricula is undergoing such rapid and frequent changes as the topic of financial issues. Therefore, its teaching requires new approaches that would dynamically respond to the current situation. This…

Students use GeoGebra to explore the mathematical relations among different radii of circles in a triangle (circumcircle, incircle, excircles) and the sides and other segments in the triangle. The more formal mathematical development of the relations that follows the explorations is based on known geometrical properties, different formulas…

Mobile technologies open up new ways of fostering reflection in teacher education. With the intention of tying reflection closer to the actions in the classroom, facilitating multimedia recordings, providing prompts for reflection and fostering discussions between pre-service teachers, experienced teachers and university mentors, we developed the…

An important and interesting area in the study of triangle geometry is the related issue of extrema problems and inequalities. These problems play a significant role in the mathematics study program in high school. In tasks such as these, the difficulty level is high when one does not know in advance what the expected answer is. When one knows…