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Yiu-Kwong Man – International Journal of Mathematical Education in Science and Technology, 2025
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…
Descriptors: Plane Geometry, Mathematical Logic, Validity, Secondary School Mathematics
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
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
West, John – Australian Primary Mathematics Classroom, 2018
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…
Descriptors: Mathematics Instruction, Mathematical Logic, Problem Solving, Fractions
Pei, Christina; Weintrop, David; Wilensky, Uri – Mathematical Thinking and Learning: An International Journal, 2018
There is a great deal of overlap between the set of practices collected under the term "computational thinking" and the mathematical habits of mind that are the focus of much mathematics instruction. Despite this overlap, the links between these two desirable educational outcomes are rarely made explicit, either in classrooms or in the…
Descriptors: Problem Solving, Thinking Skills, Mathematics Instruction, Mathematical Logic
Perry, Patricia; Camargo, Leonor; Samper, Carmen; Sáenz-Ludlow, Adalira; Molina, Óscar – North American Chapter of the International Group for the Psychology of Mathematics Education, 2014
To interpret in detail the meaning-making in the classroom and the corresponding teacher semiotic mediation, we have resorted to Peirce's triadic ign theory, interpreted by Sáenz-Ludlow and Zellweger. We present an example of the use of a few elements of that theory in the analysis of a classroom episode in which meaning is constructed with the…
Descriptors: Mathematics Instruction, Plane Geometry, Preservice Teachers, Preservice Teacher Education
Srinivasan, V. K. – International Journal of Mathematical Education in Science and Technology, 2012
Three unheralded results, two in Coordinate Geometry and the other in Plane Geometry, provide three proofs of a theorem dubbed by this author as "The Fundamental Theorem". The above theorem offers a uniform proof establishing the positive integral nature of the radii of the incircle and the three escribed circles associated with the right triangle…
Descriptors: Geometric Concepts, Plane Geometry, Mathematics Instruction, Validity

Hurd, Spencer P. – Mathematics Teacher, 1988
Establishes that the congruence criteria for polygons with more than three sides (such as ASASA for Quadrilaterals) are easily proved within the scope of the standard high school geometry course. Also argues that elegant applications of these criteria are more easily found once these new criteria are known. (PK)
Descriptors: Geometric Concepts, Geometry, Mathematical Concepts, Mathematical Logic

Thomaidis, Yannis – For the Learning of Mathematics, 1991
Presents an attempt to combine the history of mathematics of ancient Greece with the course on theoretical geometry taught in Greek secondary schools. Three sections present the history of ancient Greek geometry, geometrical constructions using straightedges and compasses, and an application of Ptolemy's theorem in solving ancient astronomy…
Descriptors: Foreign Countries, Geometric Concepts, Geometric Constructions, Integrated Activities