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Mathematics in early years settings is often restricted to learning to count and identifying simple shapes. This is partly due to the narrow scope of many early years curricula and insufficient teacher training for exploring deeper mathematical concepts. We note that geometry is an area particularly neglected. In an innovative year-long project, a group of university-based mathematicians and early years teachers collaborated on a child-led exploration of 'patterns in nature.' The early years teachers ran the project within the setting, meeting regularly with the mathematicians to discuss potential areas of interest, and to highlight the children's mathematical thinking. We found that, with the appropriate environment and guidance, the children naturally displayed deep levels of geometrical thinking and found enjoyment and satisfaction in the exploration of mathematical ideas. We define what we mean by the term 'deep geometrical thinking' and demonstrate this by looking at three excerpts through the lens of the van Hiele levels of geometric thought, finding that the children are capable of exhibiting thought at level 3 (abstraction), more advanced than previously thought of children of this age. Using a second taxonomy we also assess the range of skills across which they are demonstrating such geometric thought. [ABSTRACT FROM AUTHOR]

Although creativity has long been recognized as an important aspect of mathematical thinking, both for the advancement of the field and in students' developing expertise in mathematics, assessments of student creativity in that domain have been limited in number and focus. This article presents an assessment developed for creativity that provides a score for mathematical creativity (MaC) in addition to a score for general creativity in the numeric domain, or what we might call numerical creativity (NuC). We developed different rating scales for each and then explored how each scoring method accounts for the students' mathematical/numerical and creative skills. The psychometric properties for both scoring approaches were examined. Each method was shown to reflect different relationships with other performance tests. In addition, it is proposed that MaC may provide useful insight into students' levels of adaptive expertise in mathematics, as reflected by their ability to apply mathematical knowledge (i.e., language, operations, concepts) to novel situations, representing an informative supplement to performance indicators of math achievement.

Teachers in the UK and elsewhere are now expected to foster creativity in young children (NACCCE, 1999; Ofsted, 2003; DfES, 2003; DfES/DCMS, 2006). Creativity, however, is more often associated with the arts than with mathematics. The aim of the study was to explore and document pre-service (in the UK, pre-service teachers are referred to as "trainee" teachers) primary teachers' conceptions of creativity in mathematics teaching in the UK. A questionnaire probed their conceptions early in their course, and these were supplemented with data from semi-structured interviews. Analysis of the responses indicated that pre-service teachers' conceptions were narrow, predominantly associated with the use of resources and technology and bound up with the idea of "teaching creatively" rather than "teaching for creativity". Conceptions became less narrow as pre-service teachers were preparing to enter schools as newly qualified, but they still had difficulty in identifying ways of encouraging and assessing creativity in the classroom. This difficulty suggests that conceptions of creativity need to be addressed and developed directly during pre-service education if teachers are to meet the expectations of government as set out in the above documents.

A recent investigation of primary teachers' epistemological beliefs concerning the teaching and learning of mathematics discovered that teachers' beliefs cannot be said to form neat world views. Teachers' hybrid world views often included epistemological beliefs that supported teaching approaches which evidence suggests leads to greater conceptual understanding of mathematics. Classroom observations and semi-structured interviews with primary teachers suggested that although there is a desire to adopt an investigative approach, this is perceived to be largely incompatible with some of the requirements of the UK National Curriculum. Common potential barriers identified by teachers included: the volume of curriculum content they are required to cover, the limited time available to cover it, some working practices perceived to be associated with the current emphasis on teacher accountability and the current method of assessment by Standard Assessment Task tests (SATs). The findings are discussed in relation to challenges facing UK policy-makers if an approach to teaching primary mathematics, which is known to support conceptual understanding, is to flourish. (Contains 2 notes.)

Objective: To assess the effectiveness of 2 interventions in improving the physical activity and well-being of secondary school children. Design: A clustered randomised controlled trial; classes, 1 per school, were assigned to 1 of 3 intervention arms or a control group based on a 2×2 factorial design. The interventions were peer-mentoring and participative learning. Year 7 children (aged 11- 12) in the peer-mentoring intervention were paired with year 9 children for 6 weekly mentoring meetings. Year 7 children in the participative learning arm took part in 6 weekly geography lessons using personalised physical activity and Global Positioning System (GPS) data. Year 7 children in the combined intervention received both interventions, with the year 9 children only participating in the mentoring sessions. Participants: 1494 year 7 students from 60 schools in the North of England took part in the trial. Of these, 43 students opted out of taking part in the evaluation measurements, 2 moved teaching group and 58 changed school. Valid accelerometry outcome data were collected for 892 students from 53 schools; and well-being outcome data were available for 927 students from 52 schools. Main outcome measures: The primary outcomes were mean minutes of accelerometer-measured moderate-to-vigorous intensity physical activity per day, and well-being as evaluated by the KIDSCREEN-27 questionnaire. These data were collected 6 weeks after the intervention; a 12-month follow-up is planned. Results: No significant effects (main or interaction) were observed for the outcomes. However, small positive differences were found for both outcomes for the participative learning intervention. Conclusions: These findings suggest that the 2 school-based interventions did not modify levels of physical activity or well-being within the period monitored. Change in physical activity may require more comprehensive individual behavioural intervention, and/or more system-based efforts to address wider environmental influences such as family, peers, physical environment, transport and educational policy. [ABSTRACT FROM AUTHOR]