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…

Transformations are a central organizing idea in geometry. They are included in most geometry curricula and are likely to appear with even greater emphasis in the future, given the central role they play in the "Common Core State Standards" for K-12 mathematics. One of the attractions of geometry is the ability to draw and construct the…

This article discusses two examples of geometric problem solving suitable for middle and high school students. Both problems are related to students' everyday life experience and allow them to discover deep connections between mathematical properties and nature. With the help of dynamic mathematics software, students have the opportunity to…

Assigning difficulty level indicators to the knowledge units helps the learners plan their learning activities more efficiently. This paper focuses on how to use the topology of a knowledge map to compute and rank the difficulty levels of knowledge units. Firstly, the authors present the hierarchical structure and properties of the knowledge map.…

Counting the number of internal intersection points made by the diagonals of irregular convex polygons where no three diagonals are concurrent is an interesting problem in discrete mathematics. This paper uses an iterative approach to develop a summation relation which tallies the total number of intersections, and shows that this total can be…

In this article quadrilaterals with concurrent maltitudes are characterized. A generalization of the maltitudes is given, and a larger family of quadrilaterals for which an analogous property of concurrency holds is determined and studied.

This paper describes aspects of 13 year-olds activity in mathematics as emerged during the implementation of proportional geometric tasks in the classroom. Pupils were working in pairs using a piece of software specially designed for multiple representation (symbolic and graphical) of the variation in parametric procedures with dynamic…