In this paper, a simple proof of the Morley's Trisector Theorem is presented which involves basic plane geometry only. The use of backward geometric approach, trigonometry or advanced mathematical techniques is not required. It is suitable for introducing to secondary or undergraduate students, as well as teachers or instructors for learning or…

The purpose of this study was to analyze the activities in the Problem-Based Learning (PBL) methodology among high school students when solving problems related to the field of plane figures, both in extra-mathematical and intra-mathematical environments. The research was qualitative and constituted a case study. The technique used to select the…

The authors take a mathematical journey into polygonal chains to provide an algorithm that will construct a closed polygonal chain where the lines intersect exactly an exactly an odd number of times.

This study aimed to define the concepts and learning objectives related to the polygons sub-learning area of the 7th - grade mathematics course as ontology-based and to develop a measurement tool based on this ontology within the framework of competency ontology. In this study, we determined and included the learning objectives in the ontology…

In this pedagogical action research study, we, as post-secondary mathematics teacher educators, built on an existing effort to improve pre-service teachers' mathematical vocabulary understandings by intentionally addressing their struggles related to polygonal area formulas. Utilizing cognitive load theory and Bruner's levels of developmental…

Aim/Purpose: This paper addresses the effectiveness of flipped learning and teaching as a didactic innovation in math instruction. We are interested in comparing traditional and flipped learning and teaching in terms of acquired knowledge and retention and students' perceptions of flipped learning and teaching. Background: Traditional lessons, in…

Often, straightforward notions from one mathematical domain, when altered even slightly, can become rich and rewarding investigations involving numerous additional domains -- particularly when the investigation includes rigorous proof. This study begins with a familiar high school geometry problem (namely finding the circumcentre of a triangle),…

The paper focuses on students' understanding of the concepts of axial and central symmetries in a plane. Attention is paid to whether students of various ages identify a non-model of an axially symmetrical figure, know that a line segment has two axes of symmetry and a circle has an infinite number of symmetry axes, and are able to construct an…

The paper explores the division of a polygon into equal-area pieces using line segments originating at a common point. The mathematical background of the proposed method is very simple and belongs to secondary school geometry. Simple examples dividing a square into two, four or eight congruent pieces provide a starting point to discovering how to…

The purpose of this article is to present and discuss two recommended sequences of learning the areas of polygons, starting from the area of a rectangle. Exploring the algebraic derivations of the two sequences reveals that both are valid teaching progressions for introducing the area formula for various polygons. Further, it is suggested that…

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…

Business ethics is a highly discussed and debated subject in today's corporate and business world, as well as in educational and academic circles. There are certain parameters, which influence the extensive level and degree to which ethics has been analyzed by scholars and researchers in recent years, such as globalization, technology, intangible…

The present paper describes a dynamic investigation of polygons obtained by reflecting an arbitrary point located inside or outside a given polygon through the midpoints of its sides. The activity was based on hypothesizing on the shape of the reflection polygon that would be obtained, testing the hypotheses using dynamic software, and finding a…

In this design experiment study, we investigated the problem: What conditions might foster students' discernment of a critical aspect--variation in unidirectional change (e.g., discerning a "decreasing" increase)? At a public middle school in a large US city, we led a sequence of three days of whole class lessons, followed by task-based,…

Perceiving a 3-dimensional (3D) diagram on a 2-dimensional (2D) surface or plane can be a challenging endeavor for students at the elementary or primary grade levels. Adding to this challenge are the intricacies present in understanding the processes involved in geometric problems of such a nature. To ease the comprehension of these processes,…