Author: Ivan De Winne

Origin: AUSTRIA

Implemented in: Portugal, Czech Republic and France

The objective is to build up the students’ mathematical knowledge through problem solving, and to teach students to make geometric constructions by using GeoGebra, the tool for dynamic geometry. The lessons start with a short presentation of the problem, namely Dudeney’s dissection of an equilateral triangle into a square. After that the students have to cut a square into four pieces and create equilateral triangles. Furthermore, they have to do some online research on keywords such as Dudeney, Canterbury puzzles, hinged dissections, etc. Once this preparatory work is done, the students have to construct Dudeney’s puzzle with GeoGebra. They have to make calculations on the area of the triangle and the exact length of the sides of the square. After that the students are encouraged to compare their solutions with the actual solutions proposed by Dudeney in 1908 and to reconstruct Dudeney’s puzzle step by step with GeoGebra.

Success stories

An Irish teacher gave as feedback before implementing this GP that he had “what is called a gentleman’s knowledge of GeoGebra but did not really understand its full potential” and therefore he wanted to learn something more himself, which he would then happily pass on to his students who are “very interested in hand to eye exercises worked on graph paper.” He quickly realized that “through this medium the students acquired massive knowledge and accuracy on grids, axes, co-ordinates, quadrants, lines, angles, bisections and various types of triangles and other 2D shapes. This was the obvious progression and the fact that implementation on the IWB magnified and illustrated their activities made the work on the A4 graph sheet very Neanderthal indeed.” Another Irish teacher said that thanks to this GP and its success with the students, now there are two GeoGebra groups in his school actively engaged in this subject. Also, according to a Czech teacher, this GP was a success as the students, who did not previously know how to work with GeoGebra, quickly learned how to use it and enjoyed working with it. They seemed to enjoy the combination of group work and using computers.