Collaborative Computing Environments in Teaching / Learning Geometry: Efficiency and Difficulties

Collaborative Computing Environments in Teaching / Learning Geometry: Efficacy and Difficulties


IT is now everywhere and micro-computers are one of its most important parts. Of course, it is also in the area which gathers institutions, people and resources to teach and to learn. The financial costs involved in the acquisition, equipage, protection, maintenance and training of users of computer equipment, among others, are tremendous. Pondering is necessary: if applied in other teaching tools / learning, would these features produce better results? If the answer is negative: do they achieve the maximum benefits? What essential interests the addition of this equipment in the teaching / learning process advocates? The education’s? Is it the school’s role to invest their limited resources in teaching of skills to put in place specific softwares of this or that organization? Is the inclusion of computer games, like SimCity or Carmen Sandiego for example, as a pedagogical strategy, justified by the results it produces? Do educational softwares play the role for which they were designed? Must we use educational programs as a support to overcome structural deficiencies in teaching situations?

Collaborative Computing Environments in Teaching / Learning Geometry: Efficacy and Difficulties

As mentioned in the previous paragraph, computers are already present in spaces for teaching and learning. The scope of this research is then centered on daily questions whose responses will maximize the results obtained with the student’s interaction with these systems, justifying their costs. How to plan strategies and adopt teaching methods that will emphasize the use of computer systems as a support to correct structural deficiencies in teaching situations?

The strategy to obtain the search results proposed here can be summarized in four items:

1) Selection of individuals with difficulty to learn the skills of any curricular unit whose prerequisite demand is minimal and whose education is characterized by the adoption of admittedly flawed strategies.

2) Implementation of an instrument that identifies learning difficulties and creates (or selects) materials in various media that address these issues.

3) Planning teaching/learning activities that, when making use of these media, will allow the indiviuals to overcome their difficulties.

4) Creation of several groups of individuals  in order to control external factors which may influence the results, when implementing one (a few) of these instruments.

The leading researcher is an engineer and teacher at CEFET-SP (Federal Center of Technological Education of São Paulo) for thirteen years. He acts as a consultant associated with the PNA – Pfromm Netto and Associates and TTS-Global – Technology Training Systems Development Ltda. (Alexander Romiszowski). He is the author, director, multimedia director, instructional designer, producer and writer of several educational programs produced for distance learning / mediated by technology (examples of some of them can be found on the website: He also served as a member of testing commissions in SETEC / MEC of Higher Degree courses in Technology in the professional field of IT.

Research Problem

Geometry is a body of knowledge that is part of the curriculum of the mathematics course and (or) project and is given in all levels of formal education in Brazil. Its goal is to study the properties, relations and shape of plane geometric figures, ie those contained in the two-dimensional space and that can be drawn with the aid of a ruler and compass, and solids, contained in three dimensional space, whose faces are formed by these figures, aiming to apply them to solve real problems. It is a logical deductive science, based on non-defined concepts, called primitives, and unproven propositions, the postulates.

One of the strategies for their teaching / learning is, usually, practice classic procedures for solving certain problems. It requires no prerequisites. The data it works with are clear and evident propositions, taken as true within a logical system. Its legacy is the reasoning and spatial representation-visualization. Still, this is one of the contents that raise more difficulties when it comes to the acquisition of knowledge and skills that characterize it as a curricular area.

The proposed research has, among other goals, the main objective of identifying the difficulties and specific problems that students from high school and university face when learning geometry. Based on this knowledge, you can draw, or select on the market and use computerized equipment to collaborate more effectively with the student in the field of the corresponding content, and compare the results with those obtained by students who made use of printed materials elaborated with the same rigor. Thus, it would be possibe to confront the effectiveness of the use of computer equipment with the forms taken as tradicional of teaching/learning these skills.

Machado (2001: 139-146) argues that the learning of geometry skills interrelate as in a tetrahedron whose faces are linked to each other. The author assigns to each face of the tetrahedron a different competence: perceiving, building, representing and designing and, like the example of this solid which exists only in the presence of its faces, infers that the meaning of Geometry can only be learned by practising these four skills. The author reveals that non-vocational education relegates the acquisition of skills by representing and building and focuses on the skills by realizing and designing (conceptual). In another metaphor, it establishes correspondence between the four alluded skills and the atoms that, when combined, form the molecule of a new substance. He warns that the atoms can not be separated because the substance would lose its fundamental properties.

The catalyst is an agent which increases the rate of a chemical reaction without, however, altering the process. This project has, as one of its objectives, investigate if the computer educational programs can act as catalysts in the process of acquisition of the above-mentioned skills related to geometry, increasing the speed and quality of the geometric knowledge acquired.


The financial, material, human and technological costs, involved with the planning and production of computer educational programs, especially multimediatic, and its didactic use are much higher than the cost of the forms taken as traditional. One of the goals of this research is to investigate whether the presumed increase in learning effectiveness is compatible with the increase in the involved costs.

The researcher and professor in charge of this project is the author of several hypermedia interactive programs for the acquisition of knowledge, skills and attitudes that, as a rule, in an informal manner, are shown to be effective. Amongst them, there is the “Geometric Design in Media” program which is divided into three applications: “Encyclopedia”, “Virtual Clipboard” and “Game”. The quality of this program has been recognized by the MEC – Ministry of Education and Sport, which gave him first place in the National Software for Higher Education Institution Competition in 1996. In the following paragraphs these three applications will be described briefly.

The “Encyclopedia”

The “Encyclopedia” contains the theory of geometry, divided into topics such as: Point, Line, Plane, Parallel Lines, Competitors, Reverse, Circumference, Polygons, among other examples of this context. The theory is presented in the form of two-dimensional and three-dimensional animations, hypertext, drawings and narratives. This app’s navigation is made in a nonlinear way, stimulating student’s curiosity and (or) allowing the guidance of a teacher.

Interface do Menu principal - Pirâmide de pedras

Home screen “Encyclopedia”

In this module, the contents are explained, the classical procedures are demonstrated and practiced by the student, you have access to hypertext and hypermedia, the glossary, the examples, exercises and comparisons, among other teaching/learning tools. The instruments for assessing the acquisition of knowledge are also available, but they are, however, optional.

Main screen

The “Virtual Clipboard”

The “virtual clipboard” is the graphical environment that simulates the use of a real board, that is, the same procedures used to perform a drawing with the aid of instruments – a ruler and compass – should be repeated in this environment. This is where the student solves the procedural exercises of Geometric Design.
This environment can be used in three distinct modules. In the first module, the environment acts as a real clipboard allowing the student to practice the knowledge and skills and test their hypotheses. In the second, the module “procedure” acts as a tutorial that shows the classic procedures for solving geometric problems step by stpe. In the third, the module “exercise”, the student solves a proposed exercise and the “Virtual Clipboard” system assesses whether the solution is apparently correct. This happens thanks to an algorithm that isolates the objects created by the student and compares their attributes – angle and position, for example – with the expected attributes.

Virtual clipboard

“The game”

In the “game”, the student follows a directed and linear “navigation”, whose sequence is given depending on the grasp of prerequisites. The student earns the right to advance to the next topic by answering a riddle presented by a Sphinx, which is the evaluation of the skills developed in the current topic. The use of a game is justified by its playful and motivating way.

The Sphinx and one of his puzzles
interact with the pyramid edges


The objective of this research is to evaluate the quality of the knowledge, investigating the extent to which computer programs are effective in their collaboration with the individual, to overcome the difficulties that he/she experiences in learning and to investigate their ability to fix structural deficiencies that are possibly present in the teaching of some skills.

This research also aims to confront the quality of learning by using computer systems with the quality of learning that uses planned printed materials, preferably by the same expert and similar regarding strategies, didactic and content.


  • selection of classes of high school students,  post-secondary or higher, not professional, whose main characteristic is having finished the course;
  • structuring of the course program;
  • application of a survey instrument that identifies the difficulties and specific problems that students encounter in the acquisition of this knowledge;
  • study of how each individual is located and identifying those who have problems;
  • selection of a topic that is of great difficulty for many students;
  • creation and selection in the market, of an educational computer program that addresses this topic;
  • creation or selection in the market, of educational material considered traditional, preferably developed by the same author or group that addresses this topic;
  • planning teaching / learning activities that invoke these materials;
  • creation of various groups of subjects in order to control external factors that may influence the result as, for example, the willingness to learn, motivation for being in contact with the computer, mastery of the prerequisites, the time invested in the acquisition of those skills, among others;
  • implementation of the learning/teaching educational activities developed in comparison with the ones established on the teaching plan;
  • analyzing and evaluating the effectiveness with which the computer acts as an attenuator of the structural drawbacks in geometry teaching situations;
  • evaluation of the effectiveness of some computer educational materials available for teaching geometry.

Final considerations

Because it is a research project there are no conclusions to be presented, however, the researcher experience as a teacher, author, instructional designer and producer of hypermedia educational materials anticipates that this is an instrument that probably contributes to the teaching / learning process. However, as was mentioned earlier in this document, such materials consume hundreds of hours of work in planning and production. This research aims also to investigate whether this supposed increase in quality is due solely to the media used or derives more from the planning used in its preparation.
Prof .: Eduardo J. Stefanelli
Prof. Ms. IFSP – Federal Institute of Education, Science and Technology São Paulo.
Research Center Researcher of New Communication Technologies Applied to Education – The School of the Future at the University of São Paulo.
[email protected]

Eduardo Stefanelli

Engenheiro por profissão, professor por vocação