Imagining the mathematician: young people talking about popular representations of maths

This paper makes both a critical analysis of some popular cultural texts about mathematics and mathematicians, and explores the ways in which young people deploy the discourses produced in these texts. We argue that there are particular (and sometimes contradictory) meanings and discourses about mathematics that circulate in popular culture, that young people use these as resources in identity making as (non-)mathematicians, negotiating their meaning in ways that are not always predictable, and that their influence on young people is diffuse and nevertheless important. The paper discusses the discourses that prevail in some of the popular cultural images of mathematics and mathematicians that came up in our research. We show how mathematics is represented as a secret language, while mathematicians are often mad, mostly male and almost invariably white. We then explore how young people negotiate these discourses, positioning themselves in relation to mathematics. Here we draw attention to the fact that both those who continue with mathematics after it ceases to be compulsory and those who do not, deploy similar images of mathematics and mathematicians. What is different is how they respond to and negotiate these images.     

Trends in Environmental Education Images of Textbooks from Western and Eastern European Countries and Non-European Countries

Textbook analysis is seen as a major element for studying environmental education addressing pupils, image analysis being rather relevant when studying textbooks written in 11 languages. We analysed 25 textbooks from 14 countries addressed to 14–16-year-old pupils, focusing on: (1) local and foreign/global images; (2) urban/rural and nature images; (3) negative impact, human management, and the beauty of nature; and (4) men and women in images with negative and positive impact. We distinguished some trends between Western (WEc) and Eastern (EEc) European countries and non-European countries (NEc). In contrast to textbooks from EEc and NEc, which tend to show the beauty of nature with little human influence, WEc textbooks tend to exhibit more images of urban/rural landscape, of human negative impact and of human management, expressing an anthropocentric view of the environment. Men are usually more present in textbook images than women. However, some images exhibiting more women than men could be found in textbooks from WEc and EEc, but never in NEc. In negative impact pictures, men are more often present than women but NEc women are never present in such images. Women are more frequent than men in positive impact images. Results suggest that textbooks from EEc and NEc should give more emphasis to human management and urban/rural images, whereas those from WEc should give more attention to the beauty of nature. A balance in the presence of men and women in images should be a matter of greater concern by all textbooks’ authors and publishers.     

Constructions of mathematicians in popular culture and learners’ narratives: a study of mathematical and non‐mathematical subjectivities

In this paper, based on a project funded by the UK Economic and Social Research Council considering how people position themselves in relation to popular representations of mathematics and mathematicians, we explore constructions of mathematicians in popular culture and the ways learners make meanings from these. Drawing on an analysis of popular cultural texts, we argue that popular discourses overwhelmingly construct mathematicians as white, heterosexual, middle‐class men, yet also construct them as ‘other’ through systems of binary oppositions between those doing and those not doing mathematics. Turning to the analysis of a corpus of 27 focus groups with school and university students in England and Wales, we explore how such images are deployed by learners. We argue that while learners’ views of mathematicians parallel in key ways popular discourses, they are not passively absorbing these as they are simultaneously aware of the clichéd nature of popular cultural images.     

Developing mathematical ability in primary school through a ‘pull-out’ programme: a case study

This article reports the findings of a case study which examined a pull-out strategy for provision for mathematically able children in a primary school in London. The research investigated how the needs of a group of pupils, identified as able mathematicians, were being met through a special small group that works outside the regular mathematics lessons. Based on the observations of the lessons and the semi-structured interviews with both the pupils and their teacher, this article presents some interesting and useful ways for teaching mathematics to able children through small, pulled-out classes.     

Do inclusion practices for pupils with special educational needs in the English as a foreign language class in Israel reflect inclusion laws and language policy requirements?

The study of additional languages is mandatory for all pupils in most European countries. Usually, the first foreign language is English. This is due to the status of English as a global language. According to inclusion laws, pupils with special educational needs (SEN) should be taught in regular classes with support services by teachers with special education training. Often, however, foreign language teachers lack training and do not know how to adapt teaching methods for pupils with SEN in the regular language learning class. In this study, 109 elementary school teachers filled out questionnaires examining practices and attitudes about inclusion of pupils with SEN in the English as a foreign language (EFL) class in Israel. Findings indicated that pupils with SEN are included in regular EFL classes, taught with the same materials as the class, usually by teachers with no specialised training and no teaching assistants. Teachers are not always encouraged to take in-service courses on how to teach these pupils. No significant difference were found between teachers with and without special education training regarding inclusion practices, but slight differences were found with regards to attitudes towards inclusion of pupils with SEN. The majority of teachers felt that pupils with SEN should be taught in special education settings with specialised materials, and not in the regular education class. These findings raise questions regarding the efficacy of inclusion laws and language learning policies.     

How do teachers in Ireland and England conceptualise dyslexia?

This paper presents the findings of a comparative study using data from questionnaire surveys carried out in England (n=57) and Ireland (n=72). The researchers examine how teachers and teaching assistants who are currently teaching pupils with dyslexia in primary schools describe dyslexia and what may have influenced their conceptualisation. The paper examines teachers' responses both in terms of how they view their pupils presenting difficulties in the classroom, and how far they link these to underlying differences in cognitive processing. The researchers suggest ways in which this might influence their teaching in terms of methodology. Findings have been mapped to the Morton and Frith causal modelling framework. The implications of these findings for the training and support of teachers are discussed in the light of recent national initiatives to improve the teaching of dyslexic pupils in both countries.     

Do migrant girls perform better than migrant boys? Deviant gender differences between the reading scores of 15-year-old children of migrants compared to native pupils

In this paper, we analyse the gender differences between the educational performance of 15-year-old children of migrants from specific regions of origin countries living in different destination countries with the Programme for International Student Assessment (PISA) 2009 wave. We study whether this gender difference of migrant pupils deviates from the gender difference between the native pupils in their destination country. We analyse the educational performance of 16,612 daughters and 16,804 sons of migrants in destination countries across Asia, Europe, Latin America, and Oceania. We distinguish 62 origin countries and 12 origin areas in 30 destination countries. Female migrant pupils have both higher reading and math scores than comparable male migrant pupils, and these gender differences among migrant pupils are larger than among comparable native pupils. Parental socioeconomic background has an equal effect on the educational performance of daughters of migrants and on that of sons of migrants. The variation in educational performance by region of origin is, however, not clearly related to the poverty or traditionalism of regions.     

Why and how mathematicians read proofs: further evidence from a survey study

In a recent paper (Weber & Mejia-Ramos, Educational Studies in Mathematics, 76, 329–344, 2011), we reported findings from two small-scale interview studies on the reasons why and the ways in which mathematicians read proofs. Based on these findings, we designed an Internet-based survey that we distributed to practicing mathematicians working in top mathematics departments in the USA. Surveyed mathematicians (N?=?118) agreed to a great extent with the interviewed mathematicians in the exploratory studies. First, the mathematicians reported that they commonly read published proofs to gain different types of insight, not to check the correctness of the proofs. Second, they stated that when reading these proofs, they commonly: (a) appeal to the reputation of the author and the journal, (b) study how certain steps in the proof apply to specific examples, and (c) focus on the overarching ideas and methods in the proofs. In this paper, we also report findings from another section of the survey that focused on how participants reviewed proofs submitted for publication. The comparison of participant responses to questions in these two sections of the survey suggests that reading a published proof of a colleague and refereeing a proof for publication are substantially different activities for mathematicians.     

Les désorganisations de la répresentation de soi à l'entrée au collège

The self-representation of children from 4 grades were studied: 5th grade (10–11 years), 6th grade (11–12 years), 7th grade (12–13 years) and 8th grade (13–14 years). In each class, good pupils (E +) were differentiated from poor pupils (E ?). Each child was asked to assess himself on 12 attitude scales from his point of view (own image, IP), from his teacher's point of view, and from his parents' and friends' (social images assigned to others: ISM, ISP, ISC). The teachers were also asked to assess the children on the 12 scales (real image of the teacher, IRM). The coherence of self-representation is estimated by the mean variation and by the correlations between images. The results show less coherence in the self-representation of the 6th grade. This decrease is greater for the pupils E ?when it is sustained into the 7th grade. The correlations between IRM and the images produced by the pupils are positive and significant in the 6th grade only with the pupils E +. All the results are interpreted as a transcient desorganization of the child's self-representation as he enters junior high school. This desorganization is due to the pupils' difficulty, mainly pupils E ?, in understanding how they are judged and assessed.     

The high performance of Dutch and Flemish 15-year-old native pupils: explaining country differences in math scores between highly stratified educational systems

This paper aims to explain the high scores of 15-year-old native pupils in The Netherlands and Flanders by comparing them with the scores of pupils in countries with the same highly stratified educational system: Wallonia, the German Länder, the Swiss German cantons, and Austria. We use the data from the Programme for International Pupil Assessment (PISA) 2006 together with the specific PISA data of Germany and Switzerland. We apply a multilevel model that takes into account the individual-, curriculum-, and system-level features in these highly stratified educational systems. The high scores of the Dutch pupils can be explained by the size of The Netherlands' vocational sector. The high Flemish scores can be partly explained by the high curriculum mobility. Central exit exams are not a good explanation of the high Dutch scores. Despite being limited to highly stratified systems, we still find educational policies and arrangements to have significant effects on the educational performance of pupils.     

Achievement of Black Caribbean pupils: good practice in Lambeth schools

The aim of this research article is to investigate how pupils from Black Caribbean backgrounds are helped to achieve high standards in British schools and to identify a number of significant common themes for success in raising the achievement. It draws evidence of good practice from 13 case study schools in the local education authority (LEA). The main findings of the research carried out show that Key Stage 2 (KS2) and General Certificate of Secondary Education (GCSE) results have improved significantly in the case study schools in the last seven years and all schools are performing above national average with Black Caribbean pupils. The study has also identified a number of good practices in successful schools. Among the key features that contribute to the success in the case study schools for raising the achievement of Black Caribbean are: strong leadership with emphasis on raising expectations for all pupils and teachers; the use of performance data for school self‐evaluation and tracking pupils' performance; a commitment to creating a mesmerising curriculum where teachers use their creative intuition to deepen the quality of pupils' learning; a highly inclusive curriculum that meets the needs of Black Caribbean pupils; a strong link with the community and a clear commitment to parents' involvement; good and well coordinated support to Black Caribbean pupils through extensive use of learning mentors and role models; an inclusive curriculum and a strong commitment to equal opportunities with a clear stand on racism. This article discusses in detail these good practices and pattern of KS2 and GCSE performance by ethnicity to illustrate difference in attainment. Overall, the finding of this case study LEA confirms that in good schools Black Caribbean pupils do well and buck the national trend against all odds. The reasons for this success story are all to do with education provided in the LEA and schools. The implications of the research for all concerned with school improvement receive much attention.     

Reading about the Enemy: school textbook representation of Germany's role in the war with Britain during the period from April 1940 to May 1941

Much analysis of National Curriculum emphasis upon ‘British history’ has centred upon ‘national identity’. This article argues that coverage of ‘British history’ will inevitably present images of other nations. In developing a sense of ‘Britishness’ pupils will attach identities to other nations. The focus is school textbook coverage of Germany's wartime role from April 1940 to May 1941. In covering Britain's ‘finest hour’ texts present images of the German enemy. These images are explored using quantitative and qualitative research techniques. Images of mindless instinctive aggression by automatons are in the foreground of what I term the ‘German condition’. The means employed by school textbooks to construct these images are also analysed. School text coverage is compared with a small number of established academic histories. These are shown to be both richer and more diverse in character. This article concludes by considering the political and educational questions raised. There are concerns about how pupils will view Britain's powerful European partner. There are implications for curriculum control content ana     

Experiences of bullying-related behaviours by English and Zambian pupils: a comparative study

Experiences of behaviours associated with bullying were compared between English and Zambian primary and secondary school pupils. Findings showed different patterns in the incidence of various types of behaviour for English and Zambian pupils overall and across age, school level and gender. English pupils generally reported experiencing proportionally more incidents of bullying-related behaviour than Zambian pupils. Proportionally more boys than girls reported such behaviours in both countries but these differences were only significant among English pupils. These findings are discussed as indicating possible differences in the salience of various types of behaviour, which are a function of age and gender in the two countries studied. Cultural and/or national differences in educational structures that may account for the differences are explored.     

Factors mathematicians profess to consider when presenting pedagogical proofs

This paper concerns proof presentation at the university level. We report on a study in which we observed ten mathematicians constructing or revising proofs for pedagogical purposes. We highlight the factors that they claimed to consider when completing these tasks. We found that intended audience and medium (lecture or textbook) influenced proof presentation. We also found that, although mathematicians generally valued pedagogical proofs featuring diagrams and emphasizing main ideas, these mathematicians did not always incorporate these aspects in the proofs they constructed or revised.     

Roma pupils’ identification with school in Slovenia and Serbia: case studies

The research presented in this paper aims to challenge the belief held by some education professionals that Roma pupils do not value education. The research sample included groups of Roma pupils from two countries (Slovenia and Serbia) and from different socio-economic backgrounds. The results suggest that the majority of the pupils are aware of the importance of education. However, there are significant differences in their sense of identification with school. Roma pupils from families whose socio-economic background is comparable to that of the majority population are more appreciative of educational success, feel more accepted by teachers and classmates and are better able to connect education with their own lives. Roma pupils from families of lower socio-economic background associate school with failure, discrimination and rejection by teachers and classmates. Barriers to these pupils’ learning and social participation may be related to their tendency to drop out of the compulsory education.     

The Effects of International Economic Trends on Gender Equity in Schooling

Educational conditions and opportunities for female pupils, in comparison with male pupils, vary considerably between countries. In the past researchers have tended to explain these conditions in terms of national and local factors. Recently, however, some researchers have begun to focus on the influence of global economic trends in this area. This article describes a survey of 120 countries, examining the influence of economic globalization on gender equity in secondary schools. The article concludes that this influence is significant and should be taken into account by policy- makers.     

Ideological Dilemmas in Special Needs Education: practitioners’ views

Abstract

This study explored what sense groups of educators from Pennsylvania, USA and Northamptonshire, England made of policy issues in the special needs education field. The aim was to find out first, to what extent individual educators recognised the presence or not of dilemmas associated with the identification of pupils with special educational needs, a common curriculum for all, parent‐professional relationships and integration in mainstream classes; and second, whether they believed that these dilemmas could be resolved and how they would resolve them. It was found that educators in both countries saw dilemmas associated with the identification, common curriculum and integration, but not with parent—professional relationships. Resolutions of the dilemmas showed a similar set of contrasting perspectives in both countries. These findings are interpreted as illustrating the ideological nature of the dilemmas which underlie policy issues in special needs education.     

School effects and ethnic,gender and socio-economic gaps in educational achievement at age 11

There are long-standing achievement gaps in England associated with socio-economic status (SES), ethnicity and gender, but relatively little research has evaluated interactions between these variables or explored school effects on such gaps. This paper analyses the national test results at age 7 and age 11 of 2,836 pupils attending 68 mainstream primary schools in an ethnically diverse inner London borough. The groups with the lowest educational achievement and poorest progress were both Black Caribbean and White British low SES pupils. White British middle and high SES pupils made substantially more progress than White British low SES pupils, significantly increasing the SES gap over time. However low and high SES Black pupils made equally poor progress age 7–11. School effects on pupil progress were large, but there was no evidence of differential school effectiveness in relation to SES, ethnicity or gender. Low SES pupils in the more effective schools performed significantly better than high SES pupils in the less effective schools, but all pupils (both low and high SES) benefit from attending the more effective schools and so these schools do not eliminate the SES gap. The limits to change that may be achieved by schools alone are discussed.     

Female Preservice Teachers and Mathematics: Anxiety,Beliefs, and Stereotypes

The purpose of the current study was to examine if preservice teachers’ (PSTs) mathematics anxiety decreased and if their beliefs and stereotypes changed after they completed their early childhood mathematics methods course. It was hypothesized that by using and modeling concrete materials or manipulatives (Thompson, 1992; Vinson, 2001) and placing a greater emphasis on conceptual understanding (Bursal & Paznokas, 2006), two strategies identified as reducing PSTs’ mathematics anxiety, negative beliefs, and stereotypes that are associated with math anxiety, would diminish. Thirty preservice teachers, all female, participated in this study. Using a qualitative research approach, measures included midcourse evaluations, a draw-a-mathematician task (Mewborn & Cross 2007), the Abbreviated Math Anxiety Scale (Hopko, Mahadevan, Bare, & Hunt, 2003), and anecdotal notes. Although we were encouraged that the math anxiety experienced by our preservice teachers slightly decreased by the end of the semester, it was discouraging to find minimal change of beliefs and stereotypes of mathematicians. This confirms that many preservice teachers enter teacher education programs with well-established images of how to do school, along with entrenched beliefs about mathematics and their ability to do math (Vacc & Bright 1999) and these beliefs are very difficult to change.     

Population density and special needs education

This paper contains an analysis of the relation between the percentages of segregated pupils in 15 countries and the population density in those countries. It shows that there is a substantial correlation between these two variables, pointing to the influence of factors such as population density on the integrationsegregation continuum. Findings suggest that the availability of services, travel distances and associated factors are of utmost importance for inclusive education.