GeoGebra

GeoGebra as Dynamic Problem-posing Environment

Author:Magdalena Petkova

Some researchers of the school training in mathematics have developed the possibilities of GeoGebra as a dynamic environment for using and generating strategies for solving and posing mathematical problems:

  • Problem solving and posing, using Dynamic Geometry Software (DGS), involves the direct and indirect effects of the software’s interface on students’ procedures and understandings. In addition, DGS’s interface provides students with the opportunity to use visual reasoning in mathematics and helps them, through the dragging facilities, to generalize problems and relationships (Christou, Mousoulides, Pittalis, & Pitta-Pantazi, 2005, p. 127). 

  • DGS can be used and transformed by students in visually confirming and negating conjectures and in developing a new perspective on solving and posing original problems (Meira, 1998; Sinclair, 2004).

We used some methods of instructions in dynamic GeoGebra environment, which has been created, based on the concept of problem-posing situations (E. N. Stoyanova, 1997). The methods of instruction in mathematics include the following main points:
1. Usage of geometrical problems for:
  • extracurricular or class work in Geometry for acquiring new knowledge related to learning objects such as arbelos and Archimedean circles;
  • forming and developing skills for creating new problems;
  • forming and developing skills for solving problems in the field of work;
  • stimulating and maintaining the interest of students towards the mathematical field studied;
  • stimulating mathematical creativity in the interests of the trainees;
2. Usage of three kinds of problem-posing situations (P-P situations) for forming and developing of problem-posing skills:
  • Free P-P situations;
  • Semi-structured P-P situations; 
  • Structured P-P situations;
3. Usage of  P-P situations for:
  • solving problems with mathematical tools in GeoGebra environment; 
  • solving problems via constructing or proving statements in GeoGebra environment;
  • posing new problems with GeoGebra; 
  • creating interesting problems from the perspective of the learner and in accordance with the scope of work; 
4. Usage of GeoGebra for:
  • individual work;
  • mathematical investigations;
  • experimentation;
  • a logical evidence;
  • analysis of geometric structures;
  • creating new structures and tasks;
  • problem formulating and problem solving;
  • different approaches, such as exploring students' posed problems and confirming their new approaches, analysing, exchanging, and evaluating posed problems (Fukuda & Kakihana, 2009);
  • mastering students’ new knowledge and developing the students’ skills for working with GeoGebra.

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