'n Ondersoek na semantiese nette in probleemoplossing vir die skoolvak Wiskunde

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.