This paper presents research activity in the solution of geometric tasks by mathematics teachers and by mathematics teacher trainees at a College of Education as part of an advanced courses. This activity tested the level of knowledge and ability to apply it in the solution of problems that can be solved in a number of ways: by using various tools…

To improve understanding of identities and inverses, and to provide a stronger foundation for future mathematics, Sandra Miles designed a two-part lesson that makes the relationship between identities and inverses explicit. This article illustrates Miles' teaching of the first part of the lesson, focused on addition and subtraction, and then gives…

The aim of this research is to advance in the teaching-learning process of representing quadratic functions, both with pencil and paper and with a technological tool. For this purpose, a didactic experience is presented. Firstly, it is explained in the traditional way how to graph a quadratic function; secondly, students are introduced to the…

The most influential books on geometry are those of Euclid called "Elements". In our century, in addition to classical learning, various interactive software are used in teaching geometry. Among them, we can mention GeoGebra. GeoGebra is an interactive math measurement program that consists of teaching and learning from elementary to…

In this paper, we investigate how a research mathematician conjectures and proves when conducting her research. To be precise, the aim of this study is to achieve a comprehensive understanding of the way this research mathematician develops these mathematical practices and thus gain insight to improve the teaching and learning of these two…

This paper presents research into closed orbits parallel to quadrilaterals inscribed in various geometric shapes that can be represented by mathematical functions: straight lines, circles, ellipses, parabolas, and hyperbolas. Mathematical proofs have been given for the existence of an infinite number of parallel orbits for each of these shapes.…

When technologies like GeoGebra are implemented in mathematics lessons, the focus should be on learners and their learning processes rather than on technologies. Student-centeredness is a core characteristic of flipped classroom approaches. Recent further developments of flipped classroom approaches aim to foster learning through inquiry in…

This article covers how a computer algebra system (CAS) "wxMaxima" can be explored for teaching single-variable and multivariable calculus to Korean digital natives. We present several examples where "wxMaxima" can handle calculus problems easily, not straightforwardly but still successfully with some human intervention, and…

Over the past 20 years, the authors have designed an interdisciplinary approach that integrates Arts-based methods into STEM education. This integrated STEAM education perspective is particularly useful for enabling students to develop (i) not only their traditional scientific (and mathematical) understanding of the outer world but also (ii) their…

Integrating information and communication technology (ICT) in mathematics education has been increasingly recognized as a powerful tool for increasing students' interest and performance. It is widely discussed that students' understanding of mathematical ideas is not satisfactory, especially in terms of conceptual understanding. Using narrative…

Background: Previous research has shown that students often struggle to understand algebraic expressions and solve equations, and that traditional instructional approaches may not be sufficient to address these challenges. While the use of technology and physical manipulatives independently has been shown to support students' conceptual…

Educational institutions around the world have been integrating AI into their educational practices. Many studies and reports highlight both the advantages and disadvantages of this integration. This paper focuses on the positive aspects of AI in education, specifically through the lens of a high school geometry project at a technology-focused…

The integration of artificial intelligence (AI) tools in educational environments presents creative chances to improve mathematics education in elementary schools. This mixed-method study investigates the use of artificial intelligence tools in elementary mathematics classrooms. Complementing qualitative data from semi-structured interviews, the…

Classroom dialogue is widely used in mathematics teaching and learning, and if managed strategically, it will have productive benefits for mathematics achievement. However, dialogic participants often lack awareness of how dialogue could be constructed, and few studies show the characteristics of dialogic patterns in different stages of education.…

Limited literature addresses how elementary preservice teachers (PSTs) can advance their thinking about hierarchical geometric relationships. Informed by a commognitive perspective, we investigated this phenomenon as a matter of discursive change, focusing on word use, visual mediators, and narratives. We report on a teaching experiment involving…