The cosine theorem is used in solving triangulation problems and in physics when solving problems of addition of unidirectional oscillations. However, this theorem is used only for the analytical calculation of triangles or when solving problems of adding two oscillations. Here we propose a generalization of the cosine theorem for the case of…

The purpose of this note is to describe several challenging problems in Euclidean geometry. The note also contains author's solution sketches to the two problems.

The present study aims to examine mathematical creativity in students' work in geometry. Research conducted was based on two aspects: (a) examining the influence of geometrical figure apprehension on the production of multiple solutions and (b) how the necessity to construct auxiliary lines in the given shape promotes the production of multiple…

Windmill images and shapes have a long history in geometry and can be found in problems in different mathematical contexts. In this paper, we share and discuss various problems involving windmill shapes and solutions from geometry, algebra, to elementary number theory. These problems can be used, separately or together, for students to explore…

This article discusses the role of the three components of executive functions (EF) in geometric understanding. Discussing several examples of geometry problems, this article shows how EF are actively employed to solve geometry problems. Inhibition as the first component of EF helps the individual to suppress contextually irrelevant information.…

As a distinct mode of mathematical representation and communication, geometry diagrams are both signs that represent abstract geometric concepts and visual images that offer graphical-spatial properties. Dynamic geometly environment offers a wide range of tools for its users to create and interact with geometry diagrams. In this paper, I propose a…

The general objective to be achieved in this study is to determine the effect of using Blended Learning in terms of Intrapersonal Intelligence on Problem Solving Ability. This research is a quasi-experimental research with a two × three factorial design. Documentation, questionnaires, and tests were carried out the data collection method. The…

Problem-solving is an essential part of teaching, learning, and assessment of physics and mathematics. The continuing educational reforms have a deep impact on everyday teaching as well as working with talented students. In the Macedonian educational system, the curricula do not explicitly point out the connection between mathematics and physics,…

The mode of assessment is one of the most important factors influencing learning. E-assessment usually includes only checking the final answer, thus limiting teacher's ability to check the complete solution, and it does not allow inclusion of math proofs problems that constitute an important part of math content. The e-assessment module of Halomda…

Research studies are abundant in pointing at how the transition from additive to multiplicative thinking acts as a core challenge for students' understanding of proportionality. This said, we have yet to understand how this transition can be supported, and there remains significant questions to address about how students experience it. Recent work…

This study investigates how learners collaboratively construct embodied geometry knowledge in shared VR environments. Three groups of in-service teachers collaboratively explored six geometric conjectures with various virtual objects (geometric shapes) under the guidance of a facilitator. Although all the teachers were in different physical…

This study investigates how learners collaboratively construct embodied geometry knowledge in shared VR environments. Three groups of in-service teachers collaboratively explored six geometric conjectures with various virtual objects (geometric shapes) under the guidance of a facilitator. Although all the teachers were in different physical…

Coordinate geometry is an important part of mathematics. It helps students develop thinking, logic, and problem-solving skills. This study was conducted to test the effectiveness of the CORE learning model in promoting students' mathematical problem-solving skills when they learn the method of coordinates in a plane. Consequently, this study used…

To encourage students' self-regulated learning at home, developing skills for textbook use to overcome learning-related impasses is crucial. This study examined the effects of providing mathematics class sessions that combined teacher instruction on appropriate textbook use with peer instruction, aimed at promoting students' spontaneity and…

In mathematics, problem-solving can be considered to be one of the most important skills students need to develop, because it allows them to deal with increasingly intricate mathematical and real-life issues. Often, teachers attempt to try to link a problem with a drawn diagram or picture. Despite these diagrams, whether given or constructed, the…