We implemented GeoGebra software in Rwandan secondary schools to check its effectiveness during teaching and learning geometry concepts. The quasi-experimental design was used, and four schools were purposefully selected. Two schools were from Northern Province, while the other two were selected from Kigali city. A geometry-based test composed of…

While patterning was commonly seen as evidence of mathematical thinking, interdisciplinary interest has recently increased due to pattern-recognition applications in artificial intelligence. Within two empirical studies, we analyze the analogical-transfer capability of primary school students when completing three types of bi-dimensional patterns,…

This paper describes the conceptions about complex numbers that a group of university students has, these were built from the application of an activity sequence centered on these numbers. This sequence is based on the APOS theory, some aspects of semiotic representation theory, and the use of digital technology. Particularly, both the general…

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…

Reasoning and justification are among the core skills that mathematics education aims for students to acquire. Studies indicate that students having these skills are able to formulate meaningful geometric ideas. It is also important that students know the significance underlying the operations and mathematical ideas employed or, in other words,…

In the disciplines of dance and mathematics, binary identities commonly split individuals into either (non)dance and/or (non)math people. However, these shorthand assessments become dangerous because they constrain disciplinary knowledge, and limiting one's identity and capabilities remains antithetical to broad education goals. Capitalizing on…

Undergraduate mathematics instructors are called by many current standards to promote prospective teachers' learning of geometry from a transformation perspective, marking a change from previous standards. The novelty of this situation means it is unclear what is involved in undergraduate learning and teaching of geometry from a transformation…

The basic design lesson is an introductory course that teaches students the fundamental principles of design, including elements such as form, space, scale, proportion, and composition. It is also an introduction to both concrete thinking and abstract one, which is rather about ideas and general thought. Abstraction is one of the steps ap- plied…

Dynamic Geometry Environments (DGEs) are popular tools in the exploration of geometry. This research is designed to explore the confidence of undergraduate mathematics students as they make mathematical statements when completing geometric tasks using DGEs. Students completed two series of tasks in both Euclidean and hyperbolic geometry. The first…

Findings synthesized across five empirical, laboratory-and classroom-based studies of high school and college students engaged in geometric reasoning and proof production during single and multi-session investigations (346 participants overall) are presented. The findings converge on several design principles for embodied mathematical thinking and…

Suppose a red laser beam (of wavelength ? equal to 0.660 µm) is expanded using an optical telescope into a collimated, approximately plane wave that is 5.68 mm in diameter. Pass that beam through a tall rectangular slit whose width "a" is gradually reduced from 3.30 to 0.100 mm. Look at its image on a screen located at a distance…

The importance of mathematical reasoning is unquestioned and providing opportunities for students to become involved in mathematical reasoning is paramount. The open-ended tasks presented incorporate mathematical content explored through the contexts of problem solving and reasoning. This article presents a number of simple tasks that may be…

The necessity for establishing links between school mathematics and students' personal lives and cultures, as enshrined in the ethnomathematics program, is being recognized and investigated in different regions across the globe. However, a comprehensive understanding of the antecedents that drive the integration of ethnomathematical perspectives…

This article discusses the advanced characteristics of a mathematical and geometrical system explained and published in the course of several preceding journal articles (Teia, 2015, 2016, 2018a and 2018b). The reading of the preceding articles is encouraged for a clearer understanding of the discussion that follows.

Knowing what kinds of patterns are easy for children to recognize early in their kindergarten year, and what kinds are difficult, can be a useful guide for patterning instruction. Hence, the ability of children to recognize complex patterns early in their kindergarten year was assessed in two experiments. One experiment showed that the children…