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Amram, Meirav; Mouftakhov, Artour – Australian Mathematics Education Journal, 2019

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.

Descriptors: Geometric Concepts, Plane Geometry, Graphs, Mathematics

Byrd, James L., III; Bossé, Michael J.; Spurr, Michael J. – International Journal of Mathematical Education in Science and Technology, 2021

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),…

Descriptors: High School Students, Secondary School Mathematics, Geometric Concepts, Mathematics Skills

Moravcová, Vlasta; Robová, Jarmila; Hromadová, Jana; Halas, Zdenek – Journal on Efficiency and Responsibility in Education and Science, 2021

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…

Descriptors: Geometric Concepts, Plane Geometry, Foreign Countries, Cognitive Processes

Sinitsky, Ilya; Stupel, Moshe; Sinitsky, Marina – International Journal of Mathematical Education in Science and Technology, 2018

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…

Descriptors: Geometric Concepts, Plane Geometry, Arithmetic, Mathematics Instruction

Panuski, Christopher L.; Mungan, Carl E. – Physics Teacher, 2016

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…

Descriptors: Geometry, Optics, Lasers, Spatial Ability

Grigoropoulos, Jenny E. – International Journal of Progressive Education, 2019

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…

Descriptors: Foreign Countries, Middle School Students, Blindness, Concept Formation

Oxman, Victor; Stupel, Moshe – International Journal of Mathematical Education in Science and Technology, 2021

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…

Descriptors: Mathematics Instruction, Preservice Teachers, Preservice Teacher Education, Geometric Concepts

Trenkler, Götz; Trenkler, Dietrich – International Journal of Mathematical Education in Science and Technology, 2017

Given three planes in space, a complete characterization of their intersection is provided. Special attention is paid to the case when the intersection set does not exist of one point only. Besides the vector cross product, the tool of generalized inverse of a matrix is used extensively.

Descriptors: Algebra, Geometric Concepts, Equations (Mathematics), Matrices

Johnson, Heather Lynn; McClintock, Evan – Educational Studies in Mathematics, 2018

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,…

Descriptors: Statistical Analysis, Middle School Students, Grade 7, Interviews

Kenan, Kok Xiao-Feng – International Electronic Journal of Mathematics Education, 2018

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,…

Descriptors: Visual Perception, Visualization, Geometric Concepts, Mathematics Instruction

Totikova, Guldana A.; Yessaliyev, Aidarbek A.; Madiyarov, Nurlybai K.; Medetbekova, Nurgul – European Journal of Contemporary Education, 2020

The use of planar and volumetric geometric figures in the form of didactic games and exercises, the participants in the experiment showed a significant improvement in the results of the level of spatial representation compared with the control group. The methodology of the use of didactic games and exercises with geometric figures showed the…

Descriptors: Thinking Skills, Skill Development, Spatial Ability, Visualization

Risnawati; Andrian, Dedek; Azmi, Memen Permata; Amir, Zubaidah; Nurdin, Erdawati – International Journal of Instruction, 2019

This research aimed to develop a definition maps-based plane geometry module to improve the student teachers' mathematical reasoning skills based on the level of Van Hiele. This development research was to produce a product in the form of a module at the college level. This research referred to the ADDIE model involving five stages, i.e. analyze,…

Descriptors: Mathematics Instruction, Plane Geometry, Student Teachers, Mathematics Skills

Farris, Frank A. – PRIMUS, 2017

The "domain-coloring algorithm" allows us to visualize complex-valued functions on the plane in a single image--an alternative to before-and-after mapping diagrams. It helps us see when a function is analytic and aids in understanding contour integrals. The culmination of this article is a visual discovery and subsequent proof of the…

Descriptors: Color, Mathematical Concepts, Mathematical Logic, Plane Geometry

Seah, Rebecca – Australian Primary Mathematics Classroom, 2018

Using the correct materials and manipulatives appropriately allows the richness of geometrical concepts to be fully investigated to enable students to explore and reason about shapes. This article explores some of the key ideas involved in learning about two dimensional shapes and discusses how materials can be used to support learning.

Descriptors: Geometric Concepts, Plane Geometry, Media Selection, Resource Materials

Horzum, Tugba; Arikan, Ahmet – International Journal of Progressive Education, 2019

This study investigated the concept images of blind students about the polygon concept. For this purpose, four open-ended questions were asked to five blind middle school students. During the interviews, geometric shapes were presented with raised-line materials and blind students were given opportunities to construct geometric shapes with…

Descriptors: Foreign Countries, Middle School Students, Blindness, Students with Disabilities