Search

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]

Countries around the world are striving to improve their educational systems with a view to improving their economy and society. In this global competition, national and international test results are of considerable interest. In this paper, we show that national testing in England and the USA have shown little or no improvement over the years. This finding is not isolated; it appears to be a global phenomenon. Data from large-scale international assessments such as PISA, TIMSS and PIRLS are remarkably stable over time. This paper reviews the trends from country-specific and international data and explores some of the reasons which have been offered for such stability. We argue that these explanations are insufficient and ways forward are discussed. [ABSTRACT FROM AUTHOR]

This study investigates how students in England and Shanghai understand linear function. Understanding is defined theoretically in terms of five hierarchical levels: Dependent Relationship; Connecting Representations; Property Noticing; Object Analysis; and Inventising. A pilot study instrument presented a set of problems to both cohorts, showing that the English cohort generally operated at the levels of Property Noticing and Object Analysis, whereas the Shanghai cohort reached the higher level of Inventising. The main study explored understanding levels and students’ errors within each cohort in detail, in order to gain insights into reasons for apparent differences. The instrument used in the main study included two overlapping items, which were the same for both cohorts, while others were pitched at levels of understanding revealed in the pilot. Analysis of students’ solutions revealed that the English students’ errors were manifested in a lack of basic skills including dealing with negative numbers, while the Shanghai students showed weaknesses in their ability to use graphs. The discussion highlights different views of understanding as a possible background reason for the contrasts observed. Errors and apparent difficulties suggest implications for teaching linear function in each context. [ABSTRACT FROM AUTHOR]

Background:It has been shown that mathematical representations can aid children’s understanding of mathematical concepts but that children can sometimes have difficulty in interpreting them correctly. New advances in eye-tracking technology can help in this respect because it allows data to be gathered concerning children’s focus of attention and so indicate on what aspects of the representations they are focussing. However, recent eye-tracking technology has not been used to any great degree in investigating the way children view and interpret mathematical representations. Purpose: This research explored the use of new advances in eye-tracking technology in investigating how young children view and interpret mathematical representations of multiplication. Sample: Nine Year 5 children (four boys, five girls, aged 9–10 years of age) from a local primary (elementary) school in the North-East of England were asked to complete the test during school time. The children represented a range of attainment levels across the mathematical domain (three higher-, three middle- and three lower-attaining children) and were selected accordingly by their class teacher. We recognise that this study was only based on a small sample of children, however, this number still allowed us to make meaningful comparisons in particular between the different types of representations presented. Design and methods: The study consisted of each child looking at 18 static slides, one after the other, with each slide presenting a symbolic and a picture representation of multiplication problems. The data that was captured by the eye tracker and recorded was then analysed quantitatively (e.g. time on each slide, time on each area of interest specified within the software) and qualitatively (video recordings of each child’s gaze trajectory during each representation was carried out, thereby allowing a categorisation of the different approaches adopted). Results: The study showed that (a) the particular form of the number line representation used in this study was less successful than the other picture representations used (equal groups, array) in promoting multiplicative thinking in children, and (b) the success of children to think multiplicatively with the ‘groups’ and the array representation was related to their general mathematics attainment levels. Conclusion: These findings have implications for teacher practice in that teachers need to be clear about the possible drawbacks of particular representations. Even in using more successful representations, for lower-attaining children, the progression in their understanding of the representation needs to be taken into account by the teacher. The study also highlighted that the eye-tracking technology does have some limitations but is useful in investigating young children’s focus of attention whilst undertaking a mathematics assessment task. [ABSTRACT FROM PUBLISHER]

Background: The research on diagrammatic representations highlights their importance for the teaching and learning of mathematics. However, the empirical evidence to support their use in the classroom is mixed and somewhat lacking. Purpose: The aim of this study was to develop the use of diagrammatic representations of mathematical concepts in primary classrooms, through introducing primary teachers to the research literature in this area, and researching the subsequent impact on children and teachers. A professional development programme was designed, involving three one-day training sessions for mathematics co-ordinators. They were asked to implement the ideas from the training back in their schools. Sample: Mathematics co-ordinators from eight primary schools attended the professional development programme. The study focussed on Year 3 pupils (aged seven–eight) and Year 5 pupils (aged nine–10). Design and methods: In this paper, we report the qualitative findings from the larger project looking at the overall impact of the professional development programme. The paper focuses on semi-structured interviews carried out with the mathematics co-ordinators attending the professional development sessions, and the Year 3 and Year 5 class teachers who subsequently worked with the co-ordinators on their use of diagrammatic representations in their teaching of mathematics. Lesson observations involving the class teachers were also carried out in order to explore further the possible impact of the project on classroom practice. Results: The qualitative results identified the impact of the project on mathematics co-ordinators and class teachers’ knowledge and practice. However, the nature of this impact was complex, with a variety of facilitating and hindering factors identified for the transfer of the professional development ideas on the use of diagrammatic representations. In addition, different levels of sophistication of class teachers’ use of diagrammatic representations were identified. Conclusions: Implications for the development of professional development programmes to facilitate the transfer of research into practice were identified. Recommendations for the use of diagrammatic representations are also put forward. [ABSTRACT FROM PUBLISHER]

Background: Successfully selecting students for undergraduate courses and for teaching is notoriously difficult. Traditionally, in England, A level grades and interviews have been used in conjunction with a variety of other approaches. Purpose: This paper examines the predictive validity of students’ A level grades and of scores from a structured interview on their subsequent degree classification as well as the ratings from their final teaching placements. Sample: A cohort of 71 students who started studying for a Bachelor of Arts (BA) degree in Primary Education in 2007 and graduated in 2010. Design and methods:  The A level grades and the ratings from structured interviews, carried out prior to the start of the course, were linked to the final degree classification and to the teaching placement grades. Results: A-level scores correlated significantly with degree classification but not with the placement grade whereas the interview grades correlated significantly with both outcome measures. Conclusions: These results are discussed in the light of the restricted range available for A-level grades. [ABSTRACT FROM PUBLISHER]

This paper examines the use of ‘league tables’, based upon ‘performance data’, by the Government to distinguish between primary schools. Data concerning one Northern Local Education Authority, were analysed. It was found that the position of a school in the League Tables of unadjusted scores tended to reflect the background characteristics, in particular the socio-economic status (SES), of its pupil population. Furthermore, the ‘value-added’ measures whilst enhancing our understanding of the differences between schools does not do so in a way that sufficiently takes into account the background factors influencing pupil performance. Currently the League Tables present a simplistic, even potentially misleading, picture of primary schools. [ABSTRACT FROM PUBLISHER]

Despite efforts by the United Kingdom Government, the Teacher Training Agency and other organisations to address the problem of teacher shortages in geography within English schools, the subject is still failing to attract sufficient students into the profession. Whilst the impact of this has yet to be felt fully in higher education, it is only a matter of time before university geography departments may find it increasingly difficult to recruit quality students onto their undergraduate courses. By sampling three distinct populations, geography teachers, geography undergraduates and sixth formers [1], this research presents evidence of the recruitment problem, seeks to understand its nature and suggests strategies for addressing the underlying issues. [ABSTRACT FROM AUTHOR]