Learners' shifting perceptions of randomness.

This is a phenomenographic study of learners’ perceptions of randomness. Underpinning the study is a sense of randomness as a dynamic process, in which events emerge unpredictably from a generating process, into the determined past, through the curtain separating past from future. Previous research into perceptions of randomness has often used tasks in which people are asked to recognise randomness in a given sequence of outcomes. Other research has asked people to make up sequences of random outcomes. Such tasks do not carry the sense of randomness as dynamic. Interview tasks in this study were designed to present the dynamic sense of randomness using outcomes from random generators such as dice, coins and sampling bags in situ. Interviewees were invited to talk about their experiences of making sense of the emerging sequence of outcomes. The analysis of the interview transcripts addressed two related questions: • What do learners believe about randomness? • To what situations and circumstances do learners consider randomness to be an appropriate model? The first question encompasses learners’ expectations of a random generator and the methods, strategies and heuristics by which learners discern what is random from what is not. Drawing on local and global meanings of randomness identified by Pratt (1998), the thesis argues that learners’ perspectives on randomness shift rapidly and frequently between the local and global as the learners seek to interpret the observed outcomes. Learners’ interpretations of and beliefs about randomness are found to have significant impact upon the kinds of situations to which learners are able and willing to apply the model of randomness

Discussing perception, determining provision : teachers' perspectives on the applied options of A-level mathematics

One-third of the current A-level mathematics curriculum is determined by choice, constructed out of ‘applied mathematics’ modules in mechanics, statistics and decision mathematics. Although this choice arguably involves the most sizeable instance of choice in the current English school mathematics curriculum, and it has a significant impact on students’ post-compulsory study of mathematics, it is not well understood how this choice is navigated. This paper explores how mathematics teachers perceive each of these three areas of applied mathematics, how widely each of the modules is offered, and in what ways perception might be connected to provision. Data from an online questionnaire and follow-up interviews demonstrates that teachers are influenced by a wide range of factors, including strategic concerns and views on the relative worth of each strand. The results also highlight the presence of inertia in centres’ provision. In this way this paper offers some insight into current perception and provision of applied mathematics in England, and speaks to contemporary debates about curriculum content and reform. It argues that students’ exposure to the powerful utility of mathematics is often unhelpfully steered or limited at a critical point in their education

Evolution of positions during a lesson: a case study

International audienc

What happens as student teachers who made very good use of ICT during pre‐service training enter their first year of teaching?

This paper looks at new teachers' use of information and communications technology (ICT) at the start of their first year of teaching. A previous study was made of 40 student teachers (May–July 2007) who were identified as very good users of ICT. This is a follow‐up study involving 30 of these 40 participants during their first months of teaching (November–February 2008). Drawing on interview and observation data the study describes the use these new teachers make of ICT and considers the factors which encourage and discourage that use. It finds that they continue to see ICT as supporting both their whole‐class teaching and pupils' independent working. The impact ICT has in the classroom provides the underlying rationale for its use by new teachers. Environmental factors, including access and expectations in school, further influence ICT use. Pre‐service training remains a strong influence, in particular past modelling of ICT use by mentors and tutors. The findings are discussed in the context of the wider literature

Local and Global Thinking in Statistical Inference

In this reflective paper, we explore students’ local and global thinking about informal statistical inference through our observations of 10- to 11-year-olds, challenged to infer the unknown configuration of a virtual die, but able to use the die to generate as much data as they felt necessary. We report how they tended to focus on local changes in the frequency or relative frequency as the sample size grew larger. They generally failed to recognise that larger samples provided stability in the aggregated proportions, not apparent when the data were viewed from a local perspective. We draw on Mason’s theory of the Structure of Attention to illuminate our observations, and attempt to reconcile differing notions of local and global thinking

Why do some student teachers make very good use of ICT? An exploratory case study

This paper reports the findings from a study of student teachers at a university–school initial teacher education partnership in England. Forty student teachers, on primary and secondary teacher education programmes, were identified through tutor and mentor reports as making very good use of information and communication technologies (ICT). These student teachers were interviewed, and in many cases observed, teaching a lesson using ICT. Interviews covered their use of ICT in a particular lesson; their past experience of using ICT; factors encouraging or discouraging their use of ICT in school; and their beliefs about teaching and learning. Observations recorded their uses of hardware and software. Findings indicate that access, support for, and modelling of, ICT use in the classroom were key issues in developing this very good use of ICT. Equally important, however, seemed to be the belief that ICT could make a positive difference to teaching and learning and a willingness to ‘learn by doing’. These findings are reported in the context of the wider literature

Local and global thinking in statistics inference

In this reflective paper, we explore students' local and global thinking about informal statistical inference through our observations of 10- to 11-year-olds, challenged to infer the unknown configuration of a virtual die, but able to use the die to generate as much data as they felt necessary. We report how they tended to focus on local changes in the frequency or relative frequency as the sample size grew larger. They generally failed to recognise that larger samples provided stability in the aggregated proportions, not apparent when the data were viewed from a local perspective. We draw on Mason's theory of the Structure of Attention to illuminate our observations, and attempt to reconcile differing notions of local and global thinking