Globally education authorities are placing increasing emphasis on the development of literacy and numeracy in primary schools. This paper reports on research designed to assist teachers to improve the numeracy of their students by making the use of mathematics games a more focused aspect of the teaching and learning experience in mathematics. Classroom experience and anecdotal evidence suggest that games are often used without really focussing on the mathematics involved in playing the game,and are justified simply on the basis of children having ‘fun’. In this paper we report on the use of one game, Numero and how teachers made use of the game and the impact on the children’s learning when using the game.

In the teaching of the subject of Mathematics and in particular, in the teaching of the linear function f(x) = ax + b, the use of Microsoft Office Excel programme ( 1st grade of Eniaio Lykeio/ Unified upper-secondary school) equally facilitates both participants of the learning process, as the particular programme is incorporated in the context of the learner-centered educational procedure. Within the framework of this point of view and with the aim of effectively compiling the syllabus, the application of twelve (12) basic principles hinging on the active participation of learners in mutual cooperation, is considered necessary. Selfevaluation and the need to establish specific incentives and set concrete aims and objectives constitute indicative examples of basic principles. Within the frame of the afore-mentioned educational principles, it is suggested that the class is divided in groups of 2-3 students and new technologies are implemented, with the ultimate goal to clarify and comprehend concepts and applications relevant to the subject. Criteria for the design of such an activity are the exploitation of learners’ background knowledge and experience as well as the experimental involvement in new teaching practices. As prerequisites, we pose the formulation of conjectures and conclusions and the ‘depenalization’ of errors in the mind of learners.

The importance of family involvement is highlighted by findings that parents’ behaviours, beliefs and attitudes affect children’s behaviour in a major way. The Family Maths programme, which is the focus of this study, provides support for the transformative education practices targeted by the South African Department of Education by offering an intervention which includes teachers, learners and their families in an affirming learning community. In this study participating parents were interviewed to investigate their perceptions of the Family Maths programme mainly in terms of their engagement, enjoyment and confidence levels. The major themes and ideas that were generated in this study include the development of positive attitudes, parents and children working and talking together, and the skills exhibited by Family Maths facilitators. These findings are analysed within the parameters of complexity science and the pre-requisite conditions for developing a complex learning community, viz. internal diversity, redundancy, decentralized control, organised randomness and neighbour interactions.

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In this presentation I will report on a work-in-progress study that I am presently undertaking with second year General Mathematics undergraduate B.Ed students at a private institution for teacher education in South Africa. I first implemented the idea of reflective writing informally with scholars and then later for assessment purposes with undergraduate students. These tasks provoked very different responses from the scholars and university students, both positive and negative and prompted informal research by myself to ascertain how reflective practices can be incorporated into the mathematics curriculum. My primary objective is to investigate how I, as a lecturer can encourage and motivate students to engage in and make reflective practices an integral part of both their learning and understanding of mathematics and their teaching practice. Thus the focus of my presentation will be on different types of reflective practices and how they can be incorporated into a higher education mathematics programme.

The aim of this investigation was to determine the applicability and weaknesses of the regional distribution model SimpleBox and to make proposals for improvement. The validation was performed using a scheme of which the main aspects are the division into internal and external validation. With its default values, the regional distribution model represents a generic region, and it is connected with a model which estimates indirect emissions from sewage treatment plants. The examination was carried out using a set of sample substances, the characteristics of which cover a wide range of different physico-chemical properties, use patterns and emissions. These substances were employed in order to enable us to make common statements on the model´s applicability. Altogether, the model complies with its designated purpose to calculate regional background concentrations. A scrutiny of theory did not show serious errors or defects. Regarding sensitivity, it could be shown that the model contains only few parameters with a negligible influence on the results. The comparison with measured results showed a good agreement in many cases. The highest deviations occur if the preliminary estimations of emissions, degradation rates and partition coefficients deliver unrealistic values. Altering the regional default parameters has a lower influence on the modelled results than replacing unrealistic substance properties by better ones. Generally, the model employed is a reasonable compromise between complexity and simplification. For the sewage treatment model, it could be shown that its influence on the predicted concentration is very low and a much simpler model fulfils its purpose in a similar way. It is proposed to improve the model in several ways, e.g. by alternative estimations functions for partition coefficients. But the main focus for future improvements should be on the amelioration of release estimations and substance characteristics.

In this thesis, we present two fairly general classes of so called overflow queueing networks. These networks consist of two queues, where the capacity of the first queue is always finite. Customers arriving at the first queue have an overflow capability from the first to the second queue if the first queue operates at a certain fixed capacity, i.e., under certain conditions, demands arriving at the first queue are allowed to join the second queue. The overflow stream will additionally be weighted with a parameter p. This parameter can be used as a control parameter or to model the customers´ impatience. We reduce the number of unknown steady-state probabilities of these system in a considerable amount by a generating functions approach and a separation technique.