It is commonly agreed that learning with understanding is more desirable than learning by rote. Understanding is described in terms of the way information is represented and structured in the memory. A mathematical idea or procedure or fact is understood if it is a part of an internal network, and the degree of understanding is determined by the number and the strength of the connections between ideas. When a student learns a piece of mathematical knowledge without making connections with items in his or her existing networks of internal knowledge, he or she is learning without understanding. Learning with understanding has progressively been elevated to one of the most important goals for all learners in all subjects. However, the realisation of this goal has been problematic, especially in the domain of mathematics where there are marked difficulties in learning and understanding. The experience of working with learners who do not do well in mathematics suggests that much of the problem is that learners are required to spend so much time in mathematics lessons engaged in tasks which seek to give them competence in mathematical procedures. This leaves inadequate time for gaining understanding or seeking how the procedures can be applied in life. Much of the satisfaction inherent in learning is that of understanding: making connections, relating the symbols of mathematics to real situations, seeing how things fit together, and articulating the patterns and relationships which are fundamental to our number system and number operations. Other factors include attitudes towards mathematics, working memory capacity, extent of field dependency, curriculum approaches, the classroom climate and assessment. In this study, attitudes, working memory capacity and extent of field dependency will be considered. The work will be underpinned by an information processing model for learning. A mathematics curriculum framework released by the US National Council of Teachers of Mathematics (NCTM, 2000) offers a research-based description of what is involved for students to learn mathematics with understanding. The approach is based on “how learners learn, not on “how to teach”, and it should enable mathematics teachers to see mathematics from the standpoint of the learner as he progresses through the various stages of cognitive development. The focus in the present study is to try to find out what aspects of the process of teaching and learning seem to be important in enabling students to grow, develop and achieve. The attention here is on the learner and the nature of the learning process. What is known about learning and memory is reviewed while the literature on specific areas of difficulty in learning mathematics is summarised. Some likely explanations for these difficulties are discussed. Attitudes and how they are measured are then discussed and there is a brief section of learner characteristics, with special emphasis on field dependency as this characteristic seems to be of importance in learning mathematics. The study is set in schools in Nigeria and England but the aim is not to make comparisons. Several types of measurement are made with students: working memory capacity and extent of field dependency are measured using well-established tests (digit span backward test and the hidden figure test). Performance in mathematics is obtained from tests and examinations used in the various schools, standardised as appropriate. Surveys and interviews are also used to probe perceptions, attitudes and aspects of difficulties. Throughout, large samples were employed in the data collection with the overall aim of obtaining a clear picture about the nature and the influence of attitudes, working memory capacity and extent of field dependency in relation to learning, and to see how this was related to mathematics achievement as measured by formal examination. The study starts by focussing on gaining an overview of the nature of the problems and relating these to student perception and attitudes as well as working memory capacity. At that stage, the focus moves more towards extent of field dependency, seen as one way by which the fixed and limited working memory capacity can be used more efficiently. Data analysis was in form of comparison and correlation although there are also much descriptive data. Some very clear patterns and trends were observable. Students are consistently positive towards the more cognitive elements of attitude to mathematics (mathematics is important; lessons are essential). However, they are more negative towards the more affective elements like enjoyment, satisfaction and interest. Thus, they are very realistic about the value of mathematics but find their experiences of learning it much more daunting. Attitudes towards the learning of mathematics change with age. As students grow older, the belief that mathematics is interesting and relevant to them is weakened, although many still think positively about the importance of mathematics. Loss of interest in mathematics may well be related to an inability to grasp what is required and the oft-stated problem that it is difficult trying to take in too much information and selecting what is important. These and other features probably relate to working memory overload, with field dependency skills area being important. The study identified clearly the topics which were perceived as most difficult at various ages. These topics involved ideas and concepts where many things had to be handled cognitively at the same time, thus placing high demands on the limited working memory capacity. As expected, working memory capacity and mathematics achievement relate strongly while extent of field dependency also relates strongly to performance. Performance in mathematics is best for those who are more field-independent. It was found that extent of field dependency grew with age. Thus, as students grow older (at least between 12 and about 17), they tend to become more field-independent. It was also found that girls tend to be more field-independent than boys, perhaps reflecting maturity or their greater commitment and attention to details to undertake their work with care during the years of adolescence. The outcomes of the findings are interpreted in terms of an information processing model. It is argued that curriculum design, teaching approaches and assessment which are consistent with the known limitations of the working memory must be considered during the learning process. There is also discussion of the importance of learning for understanding and the problem of seeking to achieve this while gaining mastery in procedural skills in the light of limited working memory capacity. It is also argued that positive attitudes towards the learning in mathematics must not only be related to the problem of limited working memory capacity but also to ways to develop increased field independence as well as seeing mathematics as a subject to be understood and capable of being applied usefully.

Recent public debates over the place of religious education in the curriculum have focused attention on the threshold status of the subject. While the subject makes claims to an academic standing equal to others in the humanities, for many years its status in the curriculum has relied on a multiplicity of claims as to the effectiveness of religious education in preparing young people for life in a multicultural society. Beginning with an appreciation of the factors which have influenced policymakers and key theorists, this thesis traces the conflicts and controversies in the definition of the subject. Approaches to religious truth claims and cultural practices in the curriculum are evaluated with reference to prominent public critiques of the subject. Although these approaches are neither exhaustive nor exclusive, they form the basis of anxieties about the place of religious education in the curriculum. These anxieties are located within a broader crisis of multiculturalism and anxieties about the role of values in an increasingly performative and examination-driven educational environment. Employing an ethnographic paradigm, a series of in-depth case studies were carried out in secondary schools in Scotland, Northern Ireland and England in 2009, with particular emphasis on students between the ages of 14 and 16. In the course of these case studies, two strands of data analysis emerged, with findings clustered around 10 key themes. A linguistic approach at times takes priority within the analytical framework, while other data lends itself to multimodal analysis, providing rich contextualisation for the linguistic encounters. Focusing on four case studies, some key pedagogical approaches relating to the ways in which religious education deals with religious and cultural commitment and diversity are examined in detail. This analysis, drawing on theological and pedagogical theories, provides a richly contextualised series of findings relating to the spiritual, social and affective dimensions of religious education, in critical sites where identities and truth claims are highly valued and highly contested. The depth and authenticity called for in these contexts go beyond performative and examination-driven approaches, requiring a robust sense of teachers’ professional values and identity. Key strengths emerge in observed practice which are not reflected in pedagogical literature. The empirical findings have relevance to public debate about the aims, practices and models of effectiveness in British RE.

In this project, the nature of open-ended problem solving is explored and working descriptions presented. In order to study the ways by which secondary pupils (ages 14-17) seek to solve open-ended problems in chemistry, a set of eighteen problems was devised. These were used with several hundred school pupils and data was gathered to examine the nature of difficulties experienced in facing such problems. The set of problems (described as units) was designed to be difficult and pupils worked in groups of three to seek solutions. They were encouraged to discuss the problem as they tried to solve it and to make notes of their attempts at solution. After each problem, they completed an assessment individually where they were asked to reflect on the process through which they had moved as they tried to solve the problem. Tape recordings of the discussions of many groups of pupils were made and other observations were made to build up a more complete picture. The information obtained was analysed and summarised to seek to gain insights into the process of problem solving where the problems were open-ended, unfamiliar and difficult. The main area of interest was to explore the way long term memory affected problem solving in such situations. Pupils enjoyed the units and liked working in groups. They tended to perceive the problems as difficult because they were unfamiliar and they felt they did not have enough knowledge. In fact, all the units were based specifically on the syllabus content and, therefore, pupils should have had enough knowledge. Nonetheless, they felt a knowledge inadequacy. It is possible that this observation might be linked to the lack of long term memory connections between islands of knowledge: while they should have known the key facts, perhaps the way they were required to link them to solve the problem was itself a major source of difficulty.

This study warns that Scottish education is in danger of losing a valuable and venerable element of the school curriculum: the Classics. In order to demonstrate what Scottish education stands to lose, this study defends one particular element of the Classics, rhetoric, understood as the practice of effective speaking and effective writing for the purpose of persuasion. Scotland’s Curriculum for Excellence (CfE), first conceived in 2002 and implemented in 2010, is still a fledgling curricular initiative and schools are currently in an adjustment phase while existing syllabus content and pedagogical approaches are reviewed in order to better reflect the aims and purposes of the new curriculum. With increased focus on teacher autonomy, flexibility, personalisation and choice (Scottish Government 2008), now is an ideal time, I claim, to reveal and defend the contribution of rhetoric to this curriculum. This study promotes the learning and teaching of rhetoric in Scottish secondary schools, citing its potential to enrich not just the Classics but many areas of the curriculum, and makes particular claims for its contribution to cultivating critical and responsible citizens. Set against a broader backdrop of political and philosophical influences on curriculum reform and educational policy, this research examines the origins, aims and purposes of CfE and suggests that, although clearly influenced by supranational expectations regarding employability, economic growth and adequately equipping the future workforce, the curriculum appears to uphold the value of the Arts and Humanities and places education for citizenship at its core. These moves imply progress, at least in Scotland, towards ameliorating the ‘crisis in the Humanities’ and making room for increased focus on cross-curricular skills and abilities which are considered important for responsible citizenship: literacy, speaking and listening, argumentation and debate. The retention of Classical languages in Scotland’s new curriculum offers renewed hope, at least at the policy level, for the revitalisation of Classics teaching in Scottish schools. Yet despite their inclusion in the curriculum, they have received no promotion and there are no teacher training places available in Classical languages in Scotland so, at a practical level, the future of the subjects remains in crisis. By focussing on the educational merit of just one feature of the Classics, this study aims to highlight the value of rhetoric in CfE and in so doing raise the profile and improve the image of Classical language education. I argue that the Classical rhetorical framework, developed as a method for citizens to represent themselves effectively in public, has much to offer the development of literacy, critical literacy and critical thinking. These skills are shown to be linked to citizenship education and particular attention is paid to what is meant by ‘responsible citizenship’ in CfE. The argument is made that popular interpretations of the policy imply personally responsible or participatory conceptions of citizenship, but I promote a maximal interpretation in the form of ‘justice-oriented’ citizenship (Westheimer and Kahne 2004: 242). I defend that it is this conception of citizenship which is optimal for Scottish democracy both to appeal to the Scottish democratic intellect (Davie 1961) and to advance the values of wisdom, justice, compassion and integrity, the values inscribed on the mace in the Scottish Parliament (Gillies 2006). Despite ambiguity in CfE regarding the form of democracy envisaged for the 21st century, I argue that the study of rhetoric cultivates knowledge and skills which are particularly pertinent and beneficial to deliberative democracy and that in such a conception of democracy, rhetoric complements critical argumentation as a method of deliberation between citizens. I claim that it does so by facilitating narrative imagination, engaging the emotions and by providing a communicative bridge between diversely positioned deliberators. After highlighting and defending the value of rhetoric in CfE, the study concludes with the consideration of how rhetoric might best be positioned in the curriculum and advances a number of possible pedagogical models for its delivery, the most practical of which is offered by a cross-curricular approach but the most desirable of which is conferred by Classical languages.

I show how my previous MA research indicated useful data regarding motivation in secondary school Religious Education (RE) but needed augmented theoretical and empirical substance to inform a general pedagogy (chapter 1): to this end I address issues of adolescent agency and identity (chapter 2) and creativity (chapter 3). Draft recommendations for an active, creative, existential and hermeneutical RE pedagogy result from these augmentations (chapter 2, revised in chapter 3). The heart of this thesis is a classroom-based empirical study designed to apply and assess my recommendations for RE practice. I argue action research and ethnographic strategies fit for my field study purposes (chapter 4). I then present and analyse my field study data, identifying categories of student motivation in RE, namely dialogue with difference, existential or ethical interest and personal significance. These categories are seen to be highly compatible with my earlier draft recommendations for RE practice (chapters 5, 6, 7 and 8). Next, I integrate my data into a critique of Andrew Wright’s religious literacy pedagogy, arguing that Wright’s oppositions of language to experience and intrinsic to pragmatic value are misleading, but conceding that his fundmental principles are sound and that his recent theory overcomes some earlier difficulties. This includes consideration of Ninian Smart’s phenomenological Religious Studies and John Dewey’s educational philosophy. I go on to re-affirm that dialogue with difference, existential or ethical interest and personal significance are basic to what motivates RE pupils. Therefore, effective RE requires hermeneutical learning, including attention to the development of pupils’ own ideas and values over time; action research indicates ways for teachers to handle this requirement (chapter 9).

This multiple ethnographic case studies aims to investigate the critical literacy which emerged and emanated in the Chinese classrooms using drama as pedagogy. Drawing on the perspectives of Critical theories, Bakhtin Mikhail's dialogism, and also the literatures on critical literacy, this study argues that there is disparity of statuses of languages, knowledges, cultures and peoples within the Chinese language classrooms. Considering that indoctrinated teaching, official Chinese language and functional literacy are deeply ingrained within Chinese education, this study explore the efficacy of drama to promote pupils' voices and transform the Chinese language education. Concepts grounded in dialogism such as habitus, anwerability, voice, carnival were applied to constitute a theoretical frame for data analysis. Finally, six Chinese classrooms were selected as cases for in-depth discussion. It was found that there was an absence of dichotomous practice of critical dialogical literacy when drama was used. Instead, shades of grey of criticality and dialogicality were identified within those case study classrooms, showing that the dynamic and intricate power relations between pupils and teachers, as well as the interplay between the official language, culture, knowledge and habitus and those of the unofficial. The results also revealed that the more drama was applied in the classroom, more lively and carnivalesque the classroom was, and hence a higher degree of criticality and dialogicality. It was found that drama allows pupils to participate and create their learning content and environment. In addition to the use of drama, the use of space, the classroom order, the teaching materials, the classroom talk and discussion, the pupils' bodily response all are crucial for giving rise to a dialogic space for drama to take place. All these elements worked as the integral architectonics which affected the emergence and development of pupils' voices.

Malawi is party to a number of international human-rights standards and frameworks that embrace the goals and values of inclusion and education for all. The country has therefore made promising start with inclusive education (IE) in basic education. The challenge now is to extend IE to secondary education and other levels of education. Located within the interpretative paradigm, this study aims to contribute toward knowledge development and transfer through the exploration of the extent to which IE policy initiatives in Malawi's secondary schools have appropriately responded to the context of practice and the experience of pupils with disabilities and their teachers. No study has been conducted at secondary school level to explore meanings given to and interpretations of the policy-to-practice contexts for Malawi. This study employed Ball's (1994; 2009) policy-trajectory model as an analytical framework and tool for interrogating the policy-to-practice context of Malawian inclusive secondary schooling. The research design, methodology and research questions were structured according to this model. A mixed-methods approach, using both quantitative and qualitative data collection methods was adopted to fulfil the aims of the study. Evidence was collected from the contexts of influence through elite semi-structured interviews, text production through documentary analysis, and practice through teachers' questionnaires, classroom observations and semistructured interviews with pupils with disabilities. The findings confirm the mismatch between the policy and practice, although there is much goodwill for inclusion to succeed in Malawi. Two critical issues that challenge inclusion in countries of the South such as Malawi still need to be addressed: how to make IE more effective for both pupils with disability and those without disabilities; and how to redistribute resources to ensure appropriate preservice, in-service and specialist training for secondary teachers and adequate teaching and learning materials. With regard to both issues, responsiveness has to provide space for bottom-up initiatives in all the three broad contexts of influence, text production, and practice. Considering the historical imbalance in the resourcing of primary and secondary education in Malawi and the non-contestation of inclusion in the contexts of influence and practice, the conclusion is that IE policy that adequately responds to contexts of practice and achieves leverage on adequate resources can build on the existing goodwill of elites, teachers, and pupils to have effective IE in Malawi's secondary schools.

This thesis investigates a network of new independent Christian schools in England, with special reference to their teenage pupils. The place of faith-based schools in British society currently constitutes a contentious issue; the nature of this controversy is explored before a description and evaluation of the schools and their educational aims is given. A wide-ranging survey is then described. This survey investigated the views, values and beliefs of 695 teenage pupils who were receiving their education in the schools in 2006. Its purpose was to discover to what extent the aims of the schools were being realised amongst their older pupils. At the same time, the survey was designed to address the criticisms aimed at faith-based schools, particularly the charge that such schools might be inadequately preparing young people for life as citizens of modern Britain. The results reveal an unusual cohort of young people. The majority of the pupils claim to hold religious beliefs and values which differ from the current norms of British society but which would not necessarily jeopardise acceptable British citizenship. The data indicate that the schools are achieving their aims of enabling pupils to develop and retain the belief system and moral position taken by their parent bodies and founding churches. The results show that male pupils hold the same beliefs as female pupils and that the older pupils are as likely to be religious as are the younger. These findings differ from those found by similar surveys conducted in other British contexts. Finally, the data reveal the existence of a small subset of pupils who claim not to hold religious beliefs and whose views and values differ substantially from those of the majority of their fellow pupils. The data also suggest that the anomalous position of these pupils is not necessarily detrimental to their well-being.

This three-phase, sequential mixed methods study explores two aspects of communicative language teaching in Taiwanese senior high schools. Firstly, it examines the extent to which the communicative approach is implemented in the English classroom in Taiwan and secondly it investigates the attitudes of senior high school students towards their learning of English at school. This research study employed the dominant-less dominant mixed method design, with a combination of a dominant qualitative approach and a less-dominant qualitative data aggregation procedure. Results from the focus group interviews are mostly consistent with those of the classroom observations. The findings revealed that the traditional approach, which focuses on the teaching of vocabulary, grammar and the explanation of the textbook contents, still prevailed in the English classroom. Teachers’ classroom practices reflected students’ current learning purpose, which is to achieve good exam results, as revealed in the focus group interviews. The questionnaire survey found that despite their pressing need to “pass exams”, the majority of students had positive attitudes communicative activities in class, believing that the best way of learning English is to be able to use it in real situations outside of the classroom. Nevertheless, students exhibited contradictory attitudes in that they showed inhibitions about speaking or participating actively in class, even though they had the belief that English is best learned through speaking. Finally, the data analysis revealed that some variables, such as “gender” and “major”, played important roles in influencing learner attitudes towards English learning at school. On the other hand, there was little relationship between the variables “programme” and “mother tongue” and learner attitudes in this study.

This thesis describes an investigation of the trigonometry schemas developed by a group of 16-18 year old English students during their study of A-level mathematics. It is concerned with identifying differences in the schemas of students who are successful with solving trigonometric problems to those who are less successful. The study is guided by the theoretical frameworks of mathematical schema development proposed by Sfard (1991) and Dubinsky’s (1991) APOS theory that describe how operational knowledge of one or more procedures develops into an understanding that is conceptual. The benefits of a conceptual understanding are greater flexibility in problem solving and greater cognitive economy. The study of trigonometry prior to starting the A-level course is predominantly concerned with problems relating to triangles either right-angled or scalene and it is during the Alevel course that trigonometry broadens into the study of the properties of function. Experience as a mathematics tutor suggests however that not all students finish the A-level course with a conceptual understanding of trigonometric functions that is a coherent entity. Some students have little more than a collection of arbitrary facts and procedures that they struggle to use cohesively. Traditionally trigonometry is taught by mediating the core ideas through a mixture of spatial-visual images and algebraic identities that together provide the basis for function properties and behaviour. This study examines student perceptions of these mediating representations through a phenomenological investigation based on concept maps, interviews, classroom observations and observed problem-solving by selected students. The results of the study suggest that different students focus upon different aspects of the mediating representations. Students schemas as evidenced by the concept maps varied between those that were predominantly composed of algebraic representations for instance formulae, to those that were composed of a mixture of algebraic and specific spatial visual representations such as graphs, the unit circle and special angles triangles, to those that portrayed trigonometry through a series of overlaid graphs that signified the essence of function behaviour. The students whose schemas included spatial-visual components were more successful in problem solving and assessments than those whose schemas were focused on algebraic aspects. The study also supported documented research by Gray, Pinto, Pinner & Tall (1999) that spatial-visual imagery has a qualitative aspect and by Delice & Monaghan (2005) that teaching style plays a considerable part in the students’ development of schema. A significant aspect to the development of a flexible schema is the teacher’s philosophy of trigonometry and approach to the construction of sub concepts. Finally the study considers the merits of the two main theoretical frameworks of mathematical development proposed by Sfard and Dubinsky’s APOS theory from a teaching perspective and concludes that the empirical findings of this study are better described by Sfard’s explanation of the dual nature of mathematical conceptions whereby a process schema has the potential to develop into a flexible, stable object conception through interiorisation, condensation and reification.