A graph theory model for the computer solution of university time-tables and related problems

The work described in this thesis is concerned with four main fields of investigation, three concerned with the problems of a university administration in producing time-tables, and one concerned with the theory of graphs which provides a convenient mathematical model of a university course-student structure. A university administration's time-table problems may be classified under these headings: 1. the production of examination time-tables, 2. the assignment of students to classes, and 3. the production of class-teacher-room time-tables. These three problems are a class of the general combinatorial problem and thus simple enumeration will, in theory, provide a solution. This thesis describes and evaluates several algorithmic methods of solution and several heuristic approaches to reduce the combinatorial difficulties of the problems. Although heuristic methods do not guarantee the finding of an optimal solution, or, in some cases, any solution at all, the success of particular heuristics is demonstrated an actual course-student data. A new algorithmic method is proposed for the construction of class-teacher-room time-tables. The feasibility of this method is demonstrated with a non-trivial example based on a game. The thesis concludes with an investigation of the theory of graphs, the mathematical model used in previous work. Upper and lower bounds for the chromatic number of a graph are developed and procedures for reducing the size of the problem are constructed and discussed. An algorithm for finding all the complete subgraphs of a graph is developed as an aid in determining the solution to parts of the time-table problem. This is then related to several theorems concerning the eigenvalues and eigenvectors of the matrices associated with graphs and their meaning in the terms of the structure of these graphs. This leads readily to a bound, involving eigenvalues, for the size of the largest complete subgraph in any given graph. The graph theory section ends with a short note on the four colour problem

Design of teacher assistance tools in an exploratory learning environment for algebraic generalisation

The MiGen project is designing and developing an intelligent exploratory environment to support 11-14 year-old students in their learning of algebraic generalisation. Deployed within the classroom, the system also provides tools to assist teachers in monitoring students' activities and progress. This paper describes the architectural design of these Teacher Assistance tools and gives a detailed description of one such tool, focussing in particular on the research challenges faced, and the technologies and approaches chosen to implement the necessary functionalities given the context of the project

Assessing teachers’ beliefs to facilitate the transition to a new chemistry curriculum: what do the teachers want?

In this article, we describe the results of a study of chemistry high school teachers’ beliefs (N = 7) of the chemistry curriculum and their roles, their beliefs on the teacher as developer of materials, and their beliefs about professional development. Teachers’ beliefs influence the implementation of a curriculum. We view the use of a new curriculum as a learning process, which should start at teachers’ prior knowledge and beliefs. The results reveal that it is possible to develop a new curriculum in which teachers’ beliefs are taken as a starting point. Promising approaches to prepare teachers for a new curriculum is to let them (co)develop and use curriculum materials: It creates ownership, and strengthens and develops teachers’ pedagogical content knowledge (PCK)

A teaching experiment to foster the conceptual understanding of multiplication based on children's literature to facilitate dialogic learning

The importance of conceptual understanding as opposed to low-level procedural knowledge in mathematics has been well documented (Hiebert & Carpenter, 1992). Development of conceptual understanding of multiplication is fostered when students recognise the equal group structure that is common in all multiplicative problems (Mulligan & Mitchelmore, 1996). This paper reports on the theoretical development of a transformative teaching experiment based on conjecture-driven research design (Confrey & Lachance, 1999) that aims to enhance Year 3 students’ conceptual understanding of multiplication. The teaching experiment employs children’s literature as a motivational catalyst and mediational tool for students to explore and engage in multiplication activities and dialogue. The SOLO taxonomy (Biggs & Collis, 1989) is used to both frame the novel teaching and learning activities, as well as assess the level of students’ conceptual understanding of multiplication as displayed in the products derived from the experiment. Further, student’s group interactions will be analysed in order to investigate the social processes that may contribute positively to learning

Children's preferences in types of assignments

Thesis (Ed.M.)--Boston Universit