The notion that a universally effective problem solver may still exist, and is simply waiting to be found, is slowly being abandoned in the light of a growing body of work reporting on the narrow applicability of individual heuristics. As the formalism of the constraint satisfaction problem remains a popular choice for the representation of problems to be solved algorithmically, there exists an ongoing need for new algorithms to effciently handle the disparate range of problems that have been posed in this representation. Given the costs associated with manually applying human algorithm development and problem solving expertise, methods that can automatically adapt to the particular features of a specific class of problem have begun to attract more attention. Whilst a number of authors have developed adaptive systems, the field, and particularly with respect to their application to constraint satisfaction problems, has seen only limited discussion as to what features are desirable for an adaptive constraint system. This may well have been a limiting factor with previous implementations, which have exhibited only subsets of the five features identified in this work as important to the utility of an adaptive constraint satisfaction system. Whether an adaptive system exhibits these features depends on both the chosen represen-tation and the method of adaptation. In this thesis, a three-part representation for constraint algorithms is introduced, which defines an algorithm in terms of contention, preference and selection functions. An adaptive system based on genetic programming is presented that adapts constraint algorithms described using the mentioned three-part representation. This is believed to be the first use of standard genetic programming for learning constraint algo-rithms. Finally, to further demonstrate the efficacy of this adaptive system, its performance in learning specialised algorithms for hard, real-world problem instances is thoroughly evaluated. These instances include random as well as structured instances from known-hard benchmark distributions, industrial problems (specifically, SAT-translated planning and cryptographic problems) as well as over-constrained problem instances. The outcome of this evaluation is a set of new algorithms - valuable in their own right - specifically tailored to these problem classes. Partial results of this work have appeared in the following publications: [1] Stuart Bain, John Thornton, and Abdul Sattar (2004) Evolving algorithms for constraint satisfaction. In Proc. of the 2004 Congress on Evolutionary Computation, pages 265-272. [2] Stuart Bain, John Thornton, and Abdul Sattar (2004) Methods of automatic algorithm generation. In Proc. of the 9th Pacific Rim Conference on AI, pages 144-153. [3] Stuart Bain, John Thornton, and Abdul Sattar. (2005) A comparison of evolutionary methods for the discovery of local search heuristics. In Australian Conference on Artificial Intelligence: AI'05, pages 1068-1074. [4] Stuart Bain, John Thornton, and Abdul Sattar (2005) Evolving variable-ordering heuristics for constrained optimisation. In Principles and Practice of Constraint Programming: CP'05, pages 732-736.

Magister Educationis - MEd / This study argues that not all children in the Junior Primary phase benefit from the Problem Centred Approach in mathematics that was adapted by the Research, Unit for Mathematics at the University of Stellenbosch (RUMEUS). \One of the reasons could be that not all pupils can construct their own knowledge and methods. There are the highly capable pupils who cope well with this approach. These pupils are able to solve mathematical problems with little or no teacher interaction. Then there are the average and weaker pupils who cannot solve a mathematical problem on their own. These pupils need strategies and skills to solve problems and they need the teacher to mediate these strategies and skills to them, which will help these pupils to become autonomous problem solvers. ,Working in groups can, to some extent, supplement mediation or teacher interaction. Peer group teaching can be effective, whereby pupils are placed in groups so that the more capable pupils can teach concepts or make concepts clearer to the average or weaker pupils). There is, however, the possibility that when pupils of mixed abilities are placed in groups of four there might be one pupil who might refuse to work with the group. This pupil will work on her own and will not share ideas with the other members of the group. If this happens, mediation is necessary for those pupils who cannot solve a mathematical problem on their own. The purpose of this study is to investigate how exposure to mediation can improve pupils' problem solving abilities. As directions for my research I've chosen the first six criteria of Feuerstein's Mediated Learning Experiences (MLE). The first three parameters: intentionality and reciprocity, mediation of transcendence and mediation of meaning _are conditions for an interaction to qualify as MLE. Mediation of competence and regulation of behaviour are functions of specific experiences that combine with the first three to make an adult-child interaction one of mediated learning. Mediation of sharing behaviour . can be added. Here the child and the mediator are engaged in a shared quest for structural change in the child. In addition to this, the five mechanisms of mediational teaching, i.e. process questioning; challenging or asking reasons; bridging; teaching about rules; and emphasising order, predictability, system, sequence and strategy are also used in the implementation of mediation as described by Haywood. Two methods of investigation were chosen. The pupils' problem solving abilities were studied by means of eight word sums, of which the first four word sums were done in the pre-test and the other four word sums in the post-test. After the pre-test and before the post-test there was a period of mediational teaching for the experimental group. During this period and during the post-test the control group was denied mediation. After this research, mediation was also available for the control group. Two pupils from the experimental group were then chosen for further in-depth, think-aloud, person-to-person interviews. The aim of the interviews was to determine why these pupils could not solve the problem in the pre-test, but could successfully solve the post-test question. The results of the word sums in the pre-test and the post-test were compared. The role of strategies and thinking skills is concentrated on in the results. Mediation was not equally successful in all of the four different types of problem sums. Questions one and five contained two or more numbers and here pupils tended to either plus or minus these numbers. Questions two and six also contained numbers, but this is a problem situated in a real life situation. Questions three and seven contained no numbers and questions four and eight compelled pupils to first work out a plan. Mediation was most successful in problem sums situated in a real life situation, followed by problem sums which compelled pupils to first work out a plan, and then by problem sums where there were no numbers. Mediation was least; successful in problem sums that contained two or more numbers. Analysis of these results shows that with mediation there is an improvement in the pupils' problem solving abilities; Mediation can be viewed as S-H-O-H-R, in which the human mediator (H) is interposed between the stimulus (S) and the organism (0), and between the organism and the response (R). We can argue that the Problem Centred Approach without mediation can produce individuals who are little, if at all, affected by their encounter and interaction with new situations. Due to the lack of support in the Problem Centred Approach to Mathematics, it is the aim of this mini-thesis to propose mediation as an essential component in the Problem Centred Approach to Mathematics in the Junior Primary phase.