| dc.description.abstract | The problem-centred approach in the instruction of Mathematics has gained much ground
in the last few years. Different points of view exist on how this approach ought to be
implemented in schools. Many researchers place great emphasis on the understanding of
the problem by the child, but the role of accompaniment in solving the problem is often left
in abeyance.
It is important that the problem is correctly represented in the solving of geometry
problems. The expert problem-solver does this by memory. This is, however, very
abstract and often difficult for pupils to do.
Expert systems is a field of study within Artificial Intelligence which is aimed at
developing computer programmes that can simulate the problem-solving abilities of human
experts. The two main components of problem-solving that must be simulated are the
expert's knowledge and his reasoning ability. The expert system simulates man's
reasoning process by making use of inference techniques. Inference can be described as
the process used by the expert system to acquire new information from existing
information. Semantic nets are a method of representation used in Artificial Intelligence to
represent knowledge and solve problems. It is a graphic representation that consists of
nodes and links, where a node represents an object, a concept or a fact, and a link
represents the relationship or association between the objects. Any type of knowledge can
be represented by a semantic net.
A geometry problem can also be represented and solved according to a semantic net and
certain inference techniques. The links of the semantic net are the geometry theorems and
the nodes are the new facts.
If a semantic net is used for the solving of geometry problems it is unnecessary for the
child to represent the solution of the problem in his mind. A semantic net provides the
pupil with a clear image of where he finds himself in the solution process. Conclusions
flow logically and this provides the students with a structure to direct their thoughts. The
use of semantic nets in the solution of geometry problems combined with inference and
search techniques can be of great value. It ought to be emphasized in teacher training. | en_US |
