External visualization (i.e., physically embodied visualization) is central to the teaching and learning of mathematics. As external visualization is an important part of mathematics at all levels of education, it is diverse, and research on external visualization has become a wide and complex field. The aim of this scoping review is to…

The current study attempts to investigate whether using multiple diagrams attached to a geometry task could reduce difficulties in the proving process regarding concepts in three-dimensional geometry. Ninety 12th-grade students participated in the study. The research included the use of a questionnaire whose items invited open-ended responses…

Although we move and live in three-dimensional space, many prefer "two-dimensional" thinking in mathematics lessons. As a result, the transition between physical objects and their graphical representations can be considered one of the most common difficulties in learning and teaching solid geometry. This paper describes results of our…

Reasoning is handled as a basic process skill in mathematics teaching. When the literature was examined, it was seen that many types of reasoning related to mathematics education were mentioned. In the present study, it was focused on visual reasoning, which is one of the types of reasoning and also used in different research areas. The purpose of…

Virtual images are often introduced through a "geometric" perspective, with little conceptual or qualitative illustrations, hindering a deeper understanding of this physical concept. In this paper, we present two rather simple observations that force a critical reflection on the optical nature of a virtual image. This approach is…

There is increasing evidence for the impact of spatial training on mathematics performance in early years of education, however little research has focused on secondary school environments, which are traditionally more discipline driven. In the present study, a large-scale classroom-based intervention saw the introduction of twelve hours of…

Visual thinking plays an essential role in solving problems and in learning mathematics. Many students do not understand how to graphically or geometrically represent problems and solve algebra problems. Visual thinking is the ability, process, and results of creating, interpreting, using, and imagining images and diagrams on paper or with…

Building from the evidence-based learning progression in geometric reasoning from the RMFII project, this paper presents data from students' solutions to three problems in geometry and measurement situations to identify key components needed to nurture reasoning. To show emerging analytical reasoning students must coordinate multiple pieces of…

Empirical evidence indicates that students are not learning geometry with relational understanding of the concepts. Studies have shown that digital technologies can support students in mathematics. The purpose of this study was to find which technologies and technological affordances are specific to learners of geometry. This paper presents the…

The paper investigates geometric errors students made as they tried to use their basic geometric knowledge in the solution of the Applied Calculus Optimization Problem (ACOP). Inaccuracies related to the drawing of geometric diagrams (visualization skills) and those associated with the application of basic differentiation concepts into ACOP…

"Proceedings of International Conference on Education in Mathematics, Science and Technology" includes full papers presented at the International Conference on Education in Mathematics, Science and Technology (ICEMST) which took place on May 18-21, 2023 in Cappadocia, Turkey. The aim of the conference is to offer opportunities to share…

This article presents the authors' personal accounts and their experiences in working on mathematics using "arms." "Arms" is an idea that first appeared as a program written by John Warwick and David Wooldridge in an ATM publication "Some Lessons in Mathematics with a Microcomputer," 1983. The introduction to…

The purpose of this study was to assess algebra and geometric prerequisites skills as incorporated into the Applied Calculus Optimization Problem (ACOP) solution. The difficulties that students encounter in applying algebraic and geometric prerequisites at the early stages of the ACOP solution were identified. The study analyzes errors related to…

With both "Cabri" and "Autograph" now venturing into 3D, the dimension that previously was only demonstrated in the classroom with a lot of arm waving and crude wire cages can now be explored dynamically on screen. "Cabri 3D" concentrates on constructions, using the principles of Euclidian geometry, whereas "Autograph" creates objects using a…

Presents activities focusing on the use of visual perspectivity. Includes reproducible student worksheets. (MKR)