An investigation of post-primary students' images of mathematics

This research study investigates the image of mathematics held by 5th-year post-primary students in Ireland. For this study, “image of mathematics” is conceptualized as a mental representation or view of mathematics, presumably constructed as a result of past experiences, mediated through school, parents, peers or society. It is also understood to include attitudes, beliefs, emotions, self-concept and motivation in relation to mathematics. This study explores the image of mathematics held by a sample of 356 5th-year students studying ordinary level mathematics. Students were aged between 15 and 18 years. In addition, this study examines the factors influencing students‟ images of mathematics and the possible reasons for students choosing not to study higher level mathematics for the Leaving Certificate. The design for this study is chiefly explorative. A questionnaire survey was created containing both quantitative and qualitative methods to investigate the research interest. The quantitative aspect incorporated eight pre-established scales to examine students‟ attitudes, beliefs, emotions, self-concept and motivation regarding mathematics. The qualitative element explored students‟ past experiences of mathematics, their causal attributions for success or failure in mathematics and their influences in mathematics. The quantitative and qualitative data was analysed for all students and also for students grouped by gender, prior achievement, type of post-primary school attending, co-educational status of the post-primary school and the attendance of a Project Maths pilot school. Students‟ images of mathematics were seen to be strongly indicated by their attitudes (enjoyment and value), beliefs, motivation, self-concept and anxiety, with each of these elements strongly correlated with each other, particularly self-concept and anxiety. Students‟ current images of mathematics were found to be influenced by their past experiences of mathematics, by their mathematics teachers, parents and peers, and by their prior mathematical achievement. Gender differences occur for students in their images of mathematics, with males having more positive images of mathematics than females and this is most noticeable with regards to anxiety about mathematics. Mathematics anxiety was identified as a possible reason for the low number of students continuing with higher level mathematics for the Leaving Certificate. Some students also expressed low mathematical self-concept with regards to higher level mathematics specifically. Students with low prior achievement in mathematics tended to believe that mathematics requires a natural ability which they do not possess. Rote-learning was found to be common among many students in the sample. The most positive image of mathematics held by students was the “problem-solving image”, with resulting implications for the new Project Maths syllabus in post-primary education. Findings from this research study provide important insights into the image of mathematics held by the sample of Irish post-primary students and make an innovative contribution to mathematics education research. In particular, findings contribute to the current national interest in Ireland in post-primary mathematics education, highlighting issues regarding the low uptake of higher level mathematics for the Leaving Certificate and also making a preliminary comparison between students who took part in the piloting of Project Maths and students who were more recently introduced to the new syllabus. This research study also holds implications for mathematics teachers, parents and the mathematics education community in Ireland, with some suggestions made on improving students‟ images of mathematics.

The student bullying of teachers in Irish second level schools: exploring the influence of historical low state intervention in education on the development of contemporary policy responses in Ireland

The student bullying of teachers (SBT) is a distinct and complex form of bullying with a multiplicity of diverse, changeable and intersecting causes which is experienced by and affects teachers in a variety of ways. SBT is both a national and an international phenomenon which is under-recognised in academic, societal and political spheres, resulting in limited conceptual understanding and awareness of the issue. This study explores teachers’ experiences of SBT behaviours in Irish second level schools as well as teachers’ perceptions regarding training, policies and supports in Ireland to address the issue. Specifically, the study seeks to explore the influence of historical low State intervention in education on contemporary policies and supports to deal with SBT in Ireland. A mixed methods approach involving a survey of 531 second level school teachers and 17 semi-structured interviews with teachers, Year Heads and representatives from teacher trade unions and school management bodies was employed to collect and analyse data. Findings indicate that SBT behaviours are prevalent in many forms in Irish second level schools. The hidden nature of the phenomenon has simultaneously contributed to and is reinforced by limited understanding of the issue as well as teachers’ reluctance to disclose their experiences. Findings reveal that teachers perceive the contemporary policies, training and support structures in Ireland to be inadequate in equipping them to effectively deal with SBT. State intervention in addressing SBT behaviours to date, has been limited, therefore many teachers are forced to respond to the issue based on their own initiatives and assumptions rather than from an informed critically reflective approach, supported by national guidelines and sufficient State investment. This has resulted in a piecemeal, un-coordinated and ad-hoc approach to SBT in Irish schools both in terms of teachers’ management of SBT behaviours and with respect to the supports extended to staff. The potential negative consequences of SBT behaviours on teachers’ wellbeing and professional performance and thus, on the education system itself, underlines the need for a strategic, evidence-based, resourced and integrated approach which includes, as a pivotal component, consultation with teachers, whose contribution to the process is crucial.

Analyzing and selecting tasks for mathematics teaching: a heuristic

In planning units and lessons every day, teachers face the problem of designing a sequence of activities to promote learning. In particular, they are expected to foster the development of learning goals in their students. Based on the idea of learning path of a task, we describe a heuristic procedure to enable teachers to characterize a learning goal in terms of its cognitive requirements and to analyze and select tasks based on this characterization. We then present an example of how a group of future teachers used this heuristic in a preservice teachers training course and discuss its contributions and constraints.

Two steps forward, one step back: developing the curriculum for training teachers for technical and further education England 1945-1956

This paper discusses the development of provision for the training of teachers in English further and technical education from 1945 to 1956. While these years saw little growth in this provision, they were formative in that the institutional and curricular patterns of teacher training for the diverse fields of technical and further education were developed at this time. The work of the three national centres in Bolton, London and Huddersfield, during the period of the Emergency Training Scheme (ETS) is summarised with particular reference to the influence of the Ministry of Education‟s conditions for ETS colleges and courses. With the ending of the ETS in 1951 the three centres were given permanent status as teacher training colleges which in turn brought them into association with their local universities as constituent colleges of their Area Training Organisations. The consequences of this transfer to the universities for the curriculum and assessment of technical teacher training and the 'policy dichotomy' of teacher training for secondary and technical education are examined.

An exploratory study of specialist and generalist teachers: predicting self efficacy in delivering primary physical education.

We aimed to determine whether primary school teachers’ motivational regulations to exercise and self efficacy in delivering a physical education (PE) lesson are different based on prior PE training. Two groups of qualified primary school teachers were recruited; PE specialists and a group of generalist primary school teachers who also teach PE. All teachers completed the Behavioural Regulation in Exercise Questionnaire-2, International Physical Activity Questionnaire and the Teachers’ Sense of Efficacy Scale. PE specialists demonstrated significantly higher levels of intrinsic motivation towards exercise participation and took part in more physical activity in comparison to the generalist teachers. Regression analysis showed that being a PE specialist predicted higher scores in instructional strategies and classroom management in PE. Our findings support the useof Self Determination Theory concepts in understanding teacher’s exercise participation motivations. These findings have implications for the modelling role of teachers in encouraging children to be physically active.

Accessing prospective early years’ teachers’ knowledge on fractions in order to design tasks for developing teachers’ MKT

Fractions is perhaps one of the most complex and difficult topics pupils explore in the early years of schooling. Difficulties in learning this topic may have its genesis in the fact that fractions comprise a multifaceted construct (Kieren, 1995) or can be conceived as being grounded in the instructional approaches employed to teach fractions (Behr, Harel, Post & Lesh, 1993). Thus, students’ limited understanding might be related to how their teachers understand and interpret fractions — it’s thus related with teachers’ knowledge and practice. Although there is a generalized agreement on teachers’ role on/for students learning, most research on fractions focus on students, leaving aside teachers’ role (and their knowledge on the topic). Thus, teachers’ training has in certain respects been left behind. We still know little about how teachers’ knowledge on fractions influences students’ broader view of mathematics, and its connection and evolution within and along schooling. Aimed at conceptualize ways of improving teachers’ knowledge, training and practices, it’s of fundamental importance to access the areas of knowledge (here conceived as mathematical knowledge for teaching (MKT) (Ball, Thames & Phelps, 2008) in which (prospective) teachers are more deficitaries.

Econometrics as an Academic Discipline in Higher Education: An Exploratory Study of the Need, Relevance and Significance

Econometrics is a young science. It developed during the twentieth century in the mid-1930’s, primarily after the World War II. Econometrics is the unification of statistical analysis, economic theory and mathematics. The history of econometrics can be traced to the use of statistical and mathematics analysis in economics. The most prominent contributions during the initial period can be seen in the works of Tinbergen and Frisch, and also that of Haavelmo in the 1940's through the mid 1950's. Right from the rudimentary application of statistics to economic data, like the use of laws of error through the development of least squares by Legendre, Laplace, and Gauss, the discipline of econometrics has later on witnessed the applied works done by Edge worth and Mitchell. A very significant mile stone in its evolution has been the work of Tinbergen, Frisch, and Haavelmo in their development of multiple regression and correlation analysis. They used these techniques to test different economic theories using time series data. In spite of the fact that some predictions based on econometric methodology might have gone wrong, the sound scientific nature of the discipline cannot be ignored by anyone. This is reflected in the economic rationale underlying any econometric model, statistical and mathematical reasoning for the various inferences drawn etc. The relevance of econometrics as an academic discipline assumes high significance in the above context. Because of the inter-disciplinary nature of econometrics (which is a unification of Economics, Statistics and Mathematics), the subject can be taught at all these broad areas, not-withstanding the fact that most often Economics students alone are offered this subject as those of other disciplines might not have adequate Economics background to understand the subject. In fact, even for technical courses (like Engineering), business management courses (like MBA), professional accountancy courses etc. econometrics is quite relevant. More relevant is the case of research students of various social sciences, commerce and management. In the ongoing scenario of globalization and economic deregulation, there is the need to give added thrust to the academic discipline of econometrics in higher education, across various social science streams, commerce, management, professional accountancy etc. Accordingly, the analytical ability of the students can be sharpened and their ability to look into the socio-economic problems with a mathematical approach can be improved, and enabling them to derive scientific inferences and solutions to such problems. The utmost significance of hands-own practical training on the use of computer-based econometric packages, especially at the post-graduate and research levels need to be pointed out here. Mere learning of the econometric methodology or the underlying theories alone would not have much practical utility for the students in their future career, whether in academics, industry, or in practice This paper seeks to trace the historical development of econometrics and study the current status of econometrics as an academic discipline in higher education. Besides, the paper looks into the problems faced by the teachers in teaching econometrics, and those of students in learning the subject including effective application of the methodology in real life situations. Accordingly, the paper offers some meaningful suggestions for effective teaching of econometrics in higher education

Teachers' views on the nature of models

A semi-structured interview was used in Brazil to enquire into the 'notion of model' held by a total sample of 39 science teachers who were: employed in 'fundamental' (6-14 years) and 'medium' (15-17 years) schools; student science teachers currently doing their practicum; and university science teachers. Seven 'aspects' of their notions of a model were identified: the nature of a model, the use to which it can be put, the entities of which it consists, its relative uniqueness, the time span over which it is used, its status in the making of predictions, and the basis for the accreditation of its existence and use. Categories of meaning were identified for each of these aspects. The profiles of teachers' notions of 'model' in terms of the aspects and categories were complex, providing no support for the notion of 'Levels' in understanding. Teachers with degrees in chemistry or physics had different views about the notion of 'model' to those with degrees in biology or with teacher training certificates.

Transition of pupils from Key Stage 2 to 3 deemed gifted and talented in mathematics: an initial study

In this article Geoff Tennant and Dave Harries report on the early stages of a research project looking to examine the transition from Key Stage (KS) 2 to 3 of children deemed Gifted and Talented (G&T) in mathematics. An examination of relevant literature points towards variation in definition of key terms and underlying rationale for activities. Preliminary fieldwork points towards a lack of meaningful communication between schools, with primary school teachers in particular left to themselves to decide how to work with children deemed G&T. Some pointers for action are given, along with ideas for future research and a request for colleagues interested in working with us to get in touch.

Innovation and change in English teaching in the western provinces of China: the impact of overseas training

In this article we explore issues around the impact of continuing professional development (CPD) for secondary teachers of English offered by an overseas provider through the lens of participants from the Western provinces of China who completed courses at a UK university between 2003 and 2012. We start by offering an overview of English teaching in China. We then report two complementary studies of the same programme. The first aimed for breadth of understanding and involved the collection and analysis of interviews and focus groups discussions with former participants, their teaching colleagues and senior management, as well as classroom observation. The second aimed for depth and drew on data collected from a cohort of 38 teachers on one of the courses, using pre- and post-course surveys; focus group discussions at the end of the course with the whole cohort; and interviews with five of the participants both before they left the UK and again six months later. Evidence is presented for changes in teachers’ philosophies of education directly attributable to participation in the courses; for improved teacher competencies (linguistic, cultural and pedagogical) in the classroom; and for the ways in which returnees are undertaking new roles and responsibilities that exploit their new understandings. Finally, we discuss the implications of these findings for both providers and sponsors of CPD for English language teachers.

The initial formation of teachers in scholastic cartography: a report on a research experience

This paper is derived from the PhD research entitled "The initial training of Geography teacher in school cartography: a reflective analysis", developed by the program of Post-graduation in Geography of UNESP, campus of Rio Claro. The research is in the final phase, focused on data analysis and final writing of thesis. In this context, it may be stated that the research orientates in the problematic focused at the understanding of how the recent knowledge produced by the school cartography unfolds in the practices of Geography licentiate students. However, at this time, we will discuss about issues related to the research by the theoretical and practical point of view.

Windows into Elementary Mathematics:Alternate public images of mathematics and mathematicians

Research on students’ (and teachers’) images of mathematics and mathematicians reveals a number of stereotypical images, most of which are negative. In this paper we present an overview of some these images and stereotypes and consider the questions: (1) how might the image of mathematics and mathematicians be a problem in mathematics education, and (2) what can be done to remedy the situation? Also, we consider an outreach project called Windows into Elementary Mathematics. In this project mathematicians are interviewed about their perspectives on elementary mathematics topics and their interviews are videotaped and are posted online, along with supporting images and interactive content. In this context we consider the questions: (3) what is the Windows project about, and (4) how might it offer an alternate (and perhaps better) image of mathematics and mathematicians? Lastly, we share an example where activities from the project were used in a math-for-teachers course.

Understanding technology integration in secondary mathematics: Theorising the role of the teacher

Previous research on computers and graphics calculators in mathematics education has examined effects on curriculum content and students’ mathematical achievement and attitudes while less attention has been given to the relationship between technology use and issues of pedagogy, in particular the impact on teachers’ professional learning in specific classroom and school environments. This observation is critical in the current context of educational policy making, where it is assumed – often incorrectly – that supplying schools with hardware and software will increase teachers’ use of technology and encourage more innovative teaching approaches. This paper reports on a research program that aimed to develop better understanding of how and under what conditions Australian secondary school mathematics teachers learn to effectively integrate technology into their practice. The research adapted Valsiner’s concepts of the Zone of Proximal Development, Zone of Free Movement and Zone of Promoted Action to devise a theoretical framework for analysing relationships between factors influencing teachers’ use of technology in mathematics classrooms. This paper illustrates how the framework may be used by analysing case studies of a novice teacher and an experienced teacher in different school settings.