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Sigler, Avi; Stupel, Moshe; Flores, Alfinio – International Journal of Mathematical Education in Science and Technology, 2017

Students use GeoGebra to explore the mathematical relations among different radii of circles in a triangle (circumcircle, incircle, excircles) and the sides and other segments in the triangle. The more formal mathematical development of the relations that follows the explorations is based on known geometrical properties, different formulas…

Descriptors: Mathematics Instruction, Computer Software, Educational Technology, Geometric Concepts

Stupel, Moshe; Ben-Chaim, David – Investigations in Mathematics Learning, 2017

Mathematics educators agree that linking mathematical ideas by using multiple approaches for solving problems (or proving statements) is essential for the development of mathematical reasoning. In this sense, geometry provides a goldmine of multiple-solution tasks, where a myriad of different methods can be employed: either from the geometry topic…

Descriptors: Mathematics Instruction, Problem Solving, Teacher Education Programs, Geometry

Oxman, Victor; Stupel, Moshe – International Journal of Mathematical Education in Science and Technology, 2018

A geometrical task is presented with multiple solutions using different methods, in order to show the connection between various branches of mathematics and to highlight the importance of providing the students with an extensive 'mathematical toolbox'. Investigation of the property that appears in the task was carried out using a computerized tool.

Descriptors: Mathematics Instruction, Problem Solving, Geometry, Algebra

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

Libeskind, Shlomo; Stupel, Moshe; Oxman, Victor – International Journal of Mathematical Education in Science and Technology, 2018

In this paper, we highlight examples from school mathematics in which invariance did not receive the attention it deserves. We describe how problems related to invariance stimulated the interest of both teachers and students. In school mathematics, invariance is of particular relevance in teaching and learning geometry. When permitted change…

Descriptors: Mathematics Instruction, Mathematical Concepts, Geometry, Teaching Methods

Oxman, Victor; Stupel, Moshe; Segal, Ruti – International Journal of Mathematical Education in Science and Technology, 2017

An important and interesting area in the study of triangle geometry is the related issue of extrema problems and inequalities. These problems play a significant role in the mathematics study program in high school. In tasks such as these, the difficulty level is high when one does not know in advance what the expected answer is. When one knows…

Descriptors: Mathematics Instruction, Geometric Concepts, Teaching Methods, Secondary School Mathematics

Stupel, Moshe; Oxman, Victor; Sigler, Avi – International Journal of Mathematical Education in Science and Technology, 2017

We present a geometrical investigation of the process of creating an infinite sequence of triangles inscribed in a circle, whose areas, perimeters and lengths of radii of the inscribed circles tend to a limit in a monotonous manner. First, using geometrical software, we investigate four theorems that represent interesting geometrical properties,…

Descriptors: Geometry, Geometric Concepts, Investigations, Mathematical Concepts

Segal, Ruti; Stupel, Moshe; Sigler, Avi; Jahangiril, Jay – International Journal of Mathematical Education in Science and Technology, 2018

In this paper we present the results of a study which was carried out in an inquiry-based teaching and learning environment with the use of 'what if not' methodology coupled with the integration of dynamic geometry software. The vast majority of the students reported that they perceived themselves as participants rather than spectators. Most of…

Descriptors: Inquiry, Active Learning, Geometry, Computer Software