David Bolden

Primary teachers’ epistemological beliefs: some perceived barriers to investigative teaching in primary mathematics

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.

Clustered randomised controlled trial of two education interventions designed to increase physical activity and well-being of secondary school students: the MOVE Project

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. Trial registration number ISRCTN82956355.

Location, location, location : what do league tables really tell us about primary schools ?

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.

Have Geographers Lost Their Way? Issues relating to the recruitment of geographers into school teaching

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.

How young children view mathematical representations: a study using eye-tracking technology

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.

A representational approach to developing primary ITT students' confidence in their mathematics

Representations of mathematical concepts play an important role in understanding: both in helping learners understand the to-be-learned material and in facilitating teachers’ understanding of pedagogical processes which, in turn, are involved in developing learners’ understanding. In this paper, we report on work with a cohort of pre-service primary teachers, with the aim of developing their understanding of mathematics, their confidence in their subject knowledge and their confidence in teaching mathematics. This was attempted through the introduction and use of a ‘representational approach’ to the teaching of the mathematical concepts required of teachers training to teach in primary schools in the UK. We present the results of attitude measures and a follow-up qualitative questionnaire in identifying whether and how the use of this representational approach supported pre-service teachers’ understanding and their confidence in teaching mathematics. The results suggest that the representational approach used had a positively significant impact on the attitudes towards studying and teaching mathematics.

Developing the use of diagrammatic representations in primary mathematics through professional development

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.

Predicting success on a Bachelor of Arts Primary Education degree course

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.

Exploring Teachers’ Resilience in Relation to Job Satisfaction, Burnout, Organizational Commitment and Perception of Organizational Climate

This study is a descriptive research study investigating the relationship of teachers’ resilience levels with job satisfaction, burnout, organizational commitment and perception of organizational climate. Within the scope of the study, teachers’ resilience level was also investigated with regard to its relationship with gender, age, experience and the school level they teach. The study group consisted of 581 teachers. The data were collected through “Personal Information Form”, “The Resilience Scale for Adults”, “Job Satisfaction Scale”, “The Burnout Measure Short Version”, “Organizational Commitment Scale for Teachers” and “The Organizational Climate Description Questionnaire.” The results revealed a significant negative relationship between teachers’ resilience levels and burnout; and significant positive relationships between teachers’ resilience levels and organizational commitment, job satisfaction and perception of organizational climate. As a result of the one way ANOVA analysis regarding the differences between resilience levels of the teachers working at different school levels, it was found out that the resilience level of the teachers working at high schools differ significantly from the ones working at secondary schools in the family cohesion subscale, one of the sub dimensions of resilience. Additionally, resilience levels of the teachers who work at secondary schools were found to be significantly lower compared to the teachers who work at elementary schools and high schools. When the level of resilience was examined in relation to gender, it was concluded that there was no significant difference between the mean scores of the male and female teachers. The only significant difference was found in the perception of self subscale, where the mean scores of the male teachers were higher than the female teachers. There was no significant difference in teachers’ resilience or sub-scales of it in terms of age and experience of the participants.

In which ways and to what extent do English and Shanghai students understand linear function

ABSTRACT 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.