Search

In Zambia, as well as many other African and non-Western cultures, the extent and kind of children's chores may contribute to their learning, yet often also conflict with their schooling. In the moderation analysis we present in this manuscript, we aimed to explore the interactive effects of schooling and chores on children's mathematics performance at different levels of math knowledge and computational skill, taking into account how the assessment questions were presented. The sample consisted of 1,535 children (719 girls) living in rural and peri-urban communities in Zambia who were administered the Zambia Achievement Test (ZAT). We categorized the 60 items of the ZAT by their targeted content knowledge, sizes of the numbers involved, and forms of representation. Our results showed that chores supported the development of very basic mathematics skills and knowledge in children who had less schooling, but also significantly lowered the performance of students who were in school once their school attendance rose above certain levels. Moreover, this interaction between chores and school attendance was observed predominantly in girls, with a lesser effect of chores on boys., Author(s): Mei Tan [sup.1] , Nan Li [sup.1] , Joseph W. Pirozzolo [sup.1] [sup.2] , David Bolden [sup.3] , Florence Chamvu, Jacqueline Jere-Folotiya, Bestern Kaani, Kalima Kalima, Sophie Kasonde N'gandu, [...]

Understanding how early reading and mathematics co-develop is important from both theoretical and pedagogical standpoints. Previous research has provided mixed results. This paper investigates the development of reading and mathematics in a longitudinal sample of N = 355,883 students from the United Kingdom (2005-2019) aged 5 to 12 (49% girls). Results indicate a positive relation between the development of the two domains. In addition, a substantial statistically significant positive association between prior reading scores and subsequent changes in achievement in mathematics was found, whereas changes in reading were smaller for students with a higher prior performance in mathematics. The findings suggest that acquiring good reading skills is highly relevant for developing mathematics skills. Implications for theory and practice are discussed.

Peer tutoring is a form of structured peer learning technique. This study develops and tests a new form of peer tutoring technique, 'Interdependent Cross-Age Peer Tutoring' (ICAT). The method is informed by the 'what works literature' within peer tutoring and brings together crucial elements which have been shown to provide high effect sizes. Specifically, ICAT consists of an autonomous/informative structure, with students setting their goals in a cross age peer tutoring mathematics context. ICAT was implemented for six weeks in three different schools across England, with teachers concentrating on teaching their planed topics. School A (n=95) Year 8 students tutored Year 6, school B (n=65) Year 9 tutored Year 7, and school C (n=44) Year 10 students tutored year 8. Schools A and B adopt a pre/post-test quasi-experimental design and school C adopts a single group pre/post-test design. Research made instrument were applied to measure tutees performance gains. Classroom and paired observation were conducted for each school and the ICAT lesson materials for the six weeks were analysed to establish intervention fidelity. School A showed the highest ICAT implementation and effect size, 0.92, significant at (p<0.001). However the findings should be interpreted with caution due to a weak research design.

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]

This paper adds to the limited body of literature and concentrates on investigating the impact of a new peer tutoring framework, 'Interdependent Cross Age-Peer Tutoring' (ICAT), on the socioacademic process of learning of self-concepts. ICAT is informed by Social Interdependence Theory, a socio-psychological perspective which aims to make cross-age peer tutoring more cooperative. The intervention took place in 2013 with three schools in England: Two of the schools adopted a pre-post test quasi experimental design and one school (school C) adopted a single group design. In school A Year 8 students tutored Year 6 (n=201), in school B Year 9 students tutored Year 7 (n=115), and in school C Year 10 students tutored Year 8 (n=102). ICAT was applied once a week for a period of 35-40 minutes across six weeks, covering school-planned mathematic topics. For school A, which implemented ICAT according to programme specifications, some positive and significant effect sizes were observed.

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.

This study describes a comparison of how worked examples in selected textbooks from England and Shanghai presented possible learning trajectories towards understanding linear function. Six selected English textbooks and one Shanghai compulsory textbook were analysed with regards to the understanding required for pure mathematics knowledge in linear function. Understanding was defined as being at five levels: Dependent Relationship, Connecting Representations, Local Properties Noticing, Object Analysis and Inventising. These levels were developed by examining the most prominent theories from the existing literature on understanding function. Findings suggested that the English textbooks constrained the structural aspect of understanding linear function due to a point-to-point view of function, while the Shanghai textbook which focussed on a variable view of function overemphasised the algebraic approach. The discussion explored the drawbacks to each approach and what teachers or textbook writers could do to balance these two approaches in order to facilitate students' understanding towards a structural view of linear function.

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.

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.

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.

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.

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. (Contains 8 tables and 2 notes.)

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.)

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. (Contains 5 figures.)

Background: Palliative care interventions in the ED capture high-risk patients at a time of crisis and can dramatically improve patient-centered outcomes.Objective: To understand the facilitators that contributed to the success of the Primary Palliative Care for Emergency Medicine (PRIM-ER) quality improvement pilot intervention.Design: Effectiveness was evaluated through semi-structured interviews. Reach outcomes were measured by percent of all full-time emergency providers (physicians, physician assistants, nurses) who completed the intervention education components and baseline survey assessing attitudes and knowledge on end-of-life care.Participants: Emergency medicine providers affiliated with two medical centers (N = 197). Interviews conducted with six key informants at both institutions.Approach: Interviews were recorded, transcribed, and analyzed using deductive and inductive approaches. Descriptive statistics include reach outcomes and baseline survey results.Key Results: Both sites successfully implemented all components of the intervention and achieved a high level (> 75%) of intervention reach. Two themes emerged as facilitators to successful effectiveness facilitators of PRIM-ER: (1) institutional leadership support and (2) leveraging established quality improvement (QI) processes. Institutional support included leveraging leadership with authority to (a) mandate trainings; (b) substitute PRIM-ER education for normally scheduled education; and (c) provide protected time to implement intervention components. Effectiveness was also enhanced by capitalizing on existing QI processes which included (a) leveraging interdisciplinary partnerships and communication plans and (b) monitoring performance improvement data.Conclusions: Capitalizing on strong institutional leadership support and established QI processes enhanced the reach and effectiveness of the PRIM-ER pilot. These findings will guide the PRIM-ER researchers in scaling up the intervention in the remaining 33 sites, as well as enhance the planning of other complex quality improvement interventions in clinical settings.Registration Details: ClinicalTrials.gov Identifier: NCT03424109; Grant Number: AT009844-01. [ABSTRACT FROM AUTHOR]

This article reports the main findings from a Review commissioned by the Wellcome Trust into science in primary schools. On the basis of those findings, it is argued that the current approach to primary science and the drive to raise standards in literacy and numeracy are turning pupils off science in primary schools, the fallout of which can be seen in secondary, further and higher education. The authors' interpretations of the findings of the Review lead them to argue that the current approach to primary science in schools is not fostering scientific thought and curiosity to the extent that may be possible. The major problem lies in the way in which the results of the current assessment procedures in schools in England are used. The authors think that there is an argument for a careful reconsideration of the current approach to the teaching and assessment of science in English primary schools. They recommend a four-stage strategy: (1) the need of a national debate about the purpose of science in primary schools; (2) establish the evidence base; (3) develop new approaches and trial them; and (4) the efficacy of new and existing programmes should undergo scientific evaluation involving randomised controlled trials. (Contains 2 figures.)

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]

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. [ABSTRACT FROM AUTHOR]

This article reports the main findings from a Review commissioned by the Wellcome Trust into science in primary schools. On the basis of those findings, it is argued that the current approach to primary science and the drive to raise standards in literacy and numeracy are turning pupils off science in primary schools, the fallout of which can be seen in secondary, further and higher education.