The article presents some examples of plane geometric variance of an area with the use of computer technology. These tools can offer teachers opportunities for adaptation and preparation of pedagogical presentations which will help students along the process of fruitful conjectures formation and eventually construction of formal deductive proofs.…

An interesting Sangaku problem was chosen and a multidirectional study was performed, which included finding the locus of a circle's center moving while being tangent to two circles. It also included finding the radius of that circle given the datum that it is also tangent to the side of an isosceles triangle. Two different proofs are presented of…

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…

It has been more than two decades since researchers advocated the inquiry-based instruction in their classes. The idea, as appealing as it is in the theory, appeared not to be as fruitful in implementation. There are reports of students' resentments, frustrations, withdrawals, as well as challenges that instructors faced in their choice of…

The article is dedicated to solving extrema problems in teaching mathematics, without using calculus. We present and discuss a wide variety of mathematical extrema tasks where the extrema are obtained and find their solutions without resorting to differential. Particular attention is paid to the role of arithmetic and geometric means inequality in…

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,…

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…

Based on Steiner's fascinating theorem for trapezium, seven geometrical constructions using straight-edge alone are described. These constructions provide an excellent base for teaching theorems and the properties of geometrical shapes, as well as challenging thought and inspiring deeper insight into the world of geometry. In particular, this…