Using teaching representations is one of the common means for preparing pre-service mathematics teachers (PSTs) to learn how to teach mathematics meaningfully. However, turning PSTs' attention to the mathematical objects that students engage with during the lesson is a challenging pursuit. This paper suggests using the Realization Tree Mediator…

This study explores how pre-service mathematics teachers' spatial visualisation skills evolved during a Cognitive Load Theory (CLT) based education. The study used the qualitative theory-testing case study method, which guided the identification of participants, the design of technology-supported education, and the data collection and analysis…

The aim of this study is to examine the concept images of mathematics educators and pre-service elementary mathematics teachers regarding the relationships between the concepts of slope, rate of change and derivative. Four mathematics educators working in different state universities and responsible for Analysis courses, three pre-service…

The study aims to define the processes of pre-service mathematics teachers in reaching spatial visualisation generalisations within the context of drawing surface nets of solids. Two theories, Polya's problem-solving steps and novice-to-expert problem-solving schemas, were used as reference frameworks to describe the participants' spatial…

This research investigates significant moments in college students' drawn life stories in mathematics with the aim of examining implications for STEM engagement and potential reasons for gender-related differences in participation in mathematics intensive STEM fields. My research employs drawn life stories in mathematics specifically focused on…

Diagrams are succinct, visual representations of real-world or mathematical objects that serve to communicate properties of the objects and facilitate problem solving. This study explored perceptions of mathematics teachers in Singapore, who are heads of mathematics departments in their respective schools, related to diagrams and their use in the…

This paper describes outcomes from a project conducted at a small US university where 23 secondary school mathematics teachers participated in the study. Based on sketches created in a dynamic geometry software (DGS) and written responses to an assignment related to developing the trapezoid area formula, we explored how teachers used DGS when…

Globally, the use of visuo-semiotic models (VSMs) in the mathematics classroom is called for across levels and topics. Literature confirms that visual cognition/literacy in teachers is limited and that their capabilities in visual representation is low. The aim of this study was therefore to explore pre-service teachers' (PSTs) conception of VSMs…

To leverage pedagogies of approximation to improve teacher education, educational researchers must first tackle the methodological question, "How can we determine the potential of pedagogies of approximation for supporting the growth of prospective teachers' knowledge and practices for teaching?" In this paper, we offer a model called…

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…

Teaching using the principles of mathematical resilience can lead to a broad range of implementations with different emphases, all intended to mitigate the development of mathematical anxiety in learners and its attendant problems. This article considers 12 primary teachers' responses to the challenge of developing mathematical resilience within…

Given the challenge of visualizing the main constructs of two-variable functions and their differential and integral calculus, it is essential to consider instructional resources' use and perceived potential to contribute to students' understanding. This case study considers how four instructors selected and used digital and physical resources in…

This study used a modified mathematical knowledge for teaching (MKT) framework to compare the "common content knowledge" (CCK) of two groups of purposively selected pre-service primary mathematics teachers (n = 86) in relation to spatial visualization. Specifically, thirty-five pre-service teachers (n[subscript 1] = 35) with a pure…

In this paper, I share an activity that reinforces students' understanding of translations, reflections, and rotations via body movement. As a result of this activity, students gain a different perspective compared to previous explorations on paper, communicate mathematics, and visualize transformations as rigid motions on the plane. Furthermore,…

In recent years, philosophical work directly concerned with the practice of mathematics has intensified, giving rise to a movement known as the "philosophy of mathematical practice." In this paper we offer a survey of this movement aimed at mathematics educators. We first describe the core questions philosophers of mathematical practice…