Number pattern generalisation is often regarded a difficult topic for students to learn. To explore this perception, the present study undertakes an empirical investigation with the main aim of providing a comprehensive description of how 14-year-old secondary school students in Singapore generalise figural patterns and justify their generalisations when varying the formats of pattern display and the types of function. Comprising two interrelated parts, the study first examines 515 students’ strategies and justifications and probes systematically the influence of the formats of pattern display and the types of function on their generalisations through a specially developed paper-and-pencil test. The other part, through a specially designed questionnaire, looks at their beliefs about which strategy would best help them to derive the rule for predicting any term of a figural pattern as well as their ability to construct the rule using their choice of strategy. The first part uses an independent-measures research design to examine whether different formats of pattern display have any effect on students’ rule construction and a repeatedmeasures research design to determine whether their rule construction is influenced by the different types of function. In the second part, a survey study is employed with all students asked to identify their choice of best-help generalising strategy. This is then followed by interviews with 16 of the 515 students to probe whether they are able to derive a correct functional rule using their chosen strategy. This study complements many previous studies mainly undertaken in the west in that its findings indicate that the more academic students are competent in developing a functional rule for linear patterns but falters when working with quadratic patterns. There is a widespread failure of the less academic students in both linear and quadratic patterns, confirming the oft-regarded view that expressing generality is elusive. Successful students perceive the patterns in several ways and generate wide-ranging functional rules, predominantly symbolic, to describe them. They employ a variety of generalising strategies, especially the figural type, and some of which are new in the literature. Both the test and the survey confirm that the figural strategy involving the breaking up of the whole configurations into non-overlapping parts is their clear favourite. For rule justification, verifying it using the numerical cues and drawing diagrams to explain its development are their favourite approaches. Task features such as the format of pattern display and the type of functions do contribute to student difficulties in generalisation. Based on these findings, some useful teaching strategies for teachers and teacher educators are then suggested to help them improve their teaching of pattern generalisation. The findings also point the direction for future research studies on pattern generalisation by suggesting some recommendations for researchers.

This study investigates students’ construction of the English for Specific Purposes (ESP) classroom, that is, ESP teaching and learning, and uses the Participatory Design (PD) approach to the design of educational technology as a means to improve and refine our understanding of their construction of the classroom. The study was carried out with Brazilian university students on a Computer Science course. Following general guidelines of the PD approach, the researcher invited an ESP teacher, a number of students, and a Software Engineer to collaboratively design a Web Portal to support ESP teaching and learning. The research questions were: (i) how do students construct the ESP classroom? and (ii) to what extent does students´ involvement in the process of designing educational technology for ESP bring to light different elements of this construction? Data were collected in two phases. Firstly, an initial interview was carried out and then records of students´ participation in the workshops, their entries in an online diary and a final interview were collected. A bottom up approach was adopted to categorisation of the beliefs constituting the students’ construction of the classroom, and the analytical framework outlined by Benson and Lor (1999) was used to help to interpret and group these classifications. The final model of the students’ construction identified four groups of beliefs, clustered around the ideas of accumulation, communication, autonomy and unease with what the ESP course offered. The use of Participative Design as a method to facilitate the collection of data about the students’ construction of the classroom was found to be effective in enabling the research to move from an description based on students’ de-contextualised descriptions of the classroom in the initial interviews, to a more articulated and detailed level of description that emerged from involvement with the design task.

This study has investigated the search options and features teachers use and prefer to have, when personalising their online search for teaching resources. This study focused on making web searching easier for UK teacher practitioners at primary, secondary and post-compulsory levels. In this study, a triangulated mixed method approach was carried out in a two phase iterative case study involving 75 teacher practitioners working in the UK educational setting. In this case study, a sequential evidence gathering method called ‘System Development Life Cycle’ (SDLC) was adapted linking findings obtained from the structured questionnaires, observations and semi-structured interviews in order to design, develop and test two versions of an experimental search tool called “PoSTech!”. This research has contributed to knowledge by offering a model of teachers’ web information needs and search behaviour. In this model twelve search options and features mostly used by teachers when personalising their search for finding online teaching resources via the revised search tool are listed, in order of popularity. A search options is selected by the teacher and features is the characteristic of an option teachers experiences. For example, search options 'Subject', ‘Age Group’, ‘Resource Type’, ‘Free and/ Paid resources’, ‘Search results language’, and search features that ‘Store search options selected by individual teachers and their returned results’. Teachers’ model of web information needs and search behaviour could be used by the Government, teacher trainers and search engine designers to gain an insight into the information needs and search behaviours of teachers when searching for online teaching resources by means of tackling technical barriers faced by teachers, when using the internet. In conclusion, the research work presented in this thesis has provided the initial and important steps towards understanding the web searching information needs and search behaviours of individual teachers, working in the UK educational setting.