Children’s beliefs about mathematics involve epistemological beliefs about the subject, its nature and how it works, as well as beliefs about who can and cannot do mathematics. While children’s beliefs about mathematics have been linked to their achievement in mathematics, there is little research that explores beliefs about mathematics in the New Zealand context. A general concern is that students do less well than they could at mathematics; hence many people give up on and disengage from mathematics. This study explores children’s and their teachers’ beliefs about mathematics and is set against a backdrop of prevailing achievement discourses, both in New Zealand and abroad, that define people’s perceived abilities as usually based on ethnicity and gender. It also considers the multiple worlds of the child, the worlds of mathematics beliefs and of doing school mathematics, the child’s relationships with these worlds and with others who inhabit them. The study combines complementary theories and methods to examine espoused and enacted mathematics beliefs by adopting a predominantly sociocultural perspective and including a combination of constructivist and pragmatic theories as well as multiple methods of accessing and analysing beliefs. In order to develop a picture of mathematics beliefs, I collected data from a number of sources: mathematics beliefs questionnaires from 823 children at 17 schools, drawings from 180 children at two focus schools, video recordings of multiple mathematics lessons in two focus classrooms and observations. The following year, I revisited, observed and interviewed nine focus children and their teachers. I applied multiple analysis ‘frames’ to the data: factor analysis, adapted visual frameworks, metaphors and themes. By combining a variety of methods and applying a number of different analysis perspectives, this study exposed a rich and complex landscape of beliefs about mathematics. In particular, the children’s drawings communicated mathematics beliefs by using metaphors such as ‘maths as problem solving’, ‘maths as useful’, ‘maths as life’, and ‘maths as brain burn inducing’. The children and teachers exhibited a range of beliefs about the world of mathematics and who belongs to this world by positioning certain people as good at mathematics, not good at mathematics, or in certain cases, both positions depending on the context. In terms of assigned mathematics identities, both children and teachers refer to the ‘Asian as good at maths’ discourse but do not position Māori and Pasifika as weak; gender was not viewed as important. On the other hand, the children’s responses were influenced by their ethnicities, gender, socioeconomic status and mathematics achievement levels. The implications for primary school mathematics relate to the powerful influence of how mathematics is done, taught and learnt within the dominant context of the Numeracy Projects which governs ability groupings, the dance of the mathematics class, the ascendency of strategy over algorithm, and the notion that there are multiple ways to solve problems. In particular, the implications of inequality inherent in mathematics ability grouping warrants addressing.

Background and Purpose. This PhD thesis is a qualitative research project using interpretive and socio-cultural theories in a case study design. It explores medical students’ beliefs about scientific knowledge and the nature of evidence as applied to medicine, at key transition points in their education. This thesis situates current theories and conceptual models of epistemological development from the fields of psychology and education within the emergent field of medical education. Its aim is to provide insights into personal epistemological development, any curriculum barriers to such and provide insights into how students can be better supported, notably in transition periods. It addresses both a gap in the literature and the calls for more research into the development of student epistemologies in professional education. The thesis key research questions are: • What are medical students’ beliefs and understandings about the nature of scientific knowledge as applied to medicine? • What curriculum factors appear to facilitate or inhibit medical students’ epistemological development, at key transitions? Methodology. The case study design involved a four phase approach; • Phase 1: This was a critical discourse analysis of key policy and curricula texts to explore assumptions, inconsistencies or disputes relating to science and scientific content in the field of medical education. • Phase 2: This was the observation of learning episodes in preparation for Phase 3 involving participants. The purpose of Phase 2 was to situate and ground conversations with participants in real experiences. • Phase 3: This phase involved task groups and semi-structured interviews with medical students and faculty participants based at the University of Exeter Medical School (UEMS). Task groups and semi-structured interviews explored individual beliefs about the nature of science and scientific evidence as applied to medicine generally and the Bachelor of Medicine, Bachelor of Surgery (BMBS) curriculum content specifically. This included its contested scientific content and the nature of complexity and uncertainty in evidence based medicine. • Phase 4: This final phase involved presenting the case study findings to two other UK medical schools to explore the tentative applicability or transferability. The purpose of Phase 4 was to consider how case-specific and context bound the case study findings are. Findings. Findings suggest there is substantial variation in how medical students and faculty talk about science and evidence in medicine. This is influenced by their experiences of courses studied prior to entering medical school and their maturity in age. Medical students described how faculty informally spoke about the ambiguity within medical practice as clinical decision making, but there were very few reports of faculty explicitly speaking about the uncertain and tentative nature of scientific knowledge underpinning applied medicine. The bio-sciences were still dominant in terms of curriculum and assessment content. Where science in medicine is defined and approaches to scientific research are stated, formal curriculum documents espouse a narrow and positivistic methodological approach, which serves to perpetuate misconceptions regarding scientific research within medicine and may influence epistemological beliefs about the nature of science within medicine. Discussion and Conclusions. It is anticipated this case study will afford medical educators and curriculum designers insights upon which to address imbalances, include appropriate content, and reinforce good practice, so that medical graduates are effectively prepared for the challenges of a career in medicine.