Since there are insufficient mathematicians to meet economic and educational demands and many well-qualified, successful mathematics students exhibit signs of disaffection, the student experience of undergraduate mathematics is high on the political agenda. Many undergraduates struggle with the school-university transition, which has been associated with students’ prior experiences of mathematics which, at A-level, are regularly criticised for being too easy and too different to undergraduate mathematics. Furthermore, the University of Oxford administers a Mathematics Admissions Test (OxMAT) as a means of identifying those best prepared beyond the limited demands of A-level. Consequently, a study was conducted into the mathematical enculturation of Oxford undergraduates, specifically in terms of examination questions and students’ approaches to learning. Analysis of the Approaches and Study Skills Inventory for Students (ASSIST) (Tait et al., 1998) revealed the majority of students to adopt strategic approaches to learning (ATLs) in all four year-groups, though the descriptions given by students in interviews of the nature of their ATL highlighted some shortcomings of the ASSIST as the motivation for memorisation appeared to be an important factor. The MATH taxonomy (Smith et al., 1996), revealed that most A-level questions require routine use of procedures, whereas the OxMAT tested a variety of skills from applying familiar mathematics in new situations to justifying and interpreting information to form proofs. This is more in-line with the requirements of undergraduate assessment, although the MATH taxonomy and student interviews revealed that these still allowed for rote memorisation and strategic methods. Thus, the changing nature of mathematics and questions posed to students at the secondary-tertiary interface appears to affect students’ ATLs, though this is not reflected by the ASSIST data.

There were two purposes set out in this study, first to identify the principal associations with educational performance of Scottish students as reported in the 2007 wave of the Trends in International Mathematics and Science Study (TIMSS2007), and second to evaluate methods of data analysis where sample surveys use plausible value (PV) methodology. Four sets of data were used for the secondary analysis of TIMSS2007, with student's responses to cognitive items and questionnaire data emanating from two stages (G$ and G*) that each addressed two disciplines (mathematics and science). Explanatory models for each stage and discipline were analysed using hierarchical linear modelling techniques to accommodate the cluster sample design of the survey. Guided by existing literature in STEM education the study examined elements of students' learning experiences that fell within a social constructivist theory of learning to ascertain whether the empirical data supported current claims on effective practice. A number of control variables were included in the analyses, some well-established constructs and others derived from background questionnaires. Overall, the results showed that selected background characteristics were consistently related to mathematics and science achievement. The strength of association with home resources, and although girls were generally associated with lower achievement scores, that gender association was strongest in G4 mathematics achievement. The findings suggest there is limited support for current claims in respect of a reform agenda that privileges discussion and collaborative group work. Other policy initiatives on assessment for learning and using technologies in class are not supported in the data, with either no evidence of association or a significant negative effect in the models of mathematics and science achievement. Aspects of practical work and scientific enquiry are positively associated with G4 science achievement, with particular credence given to 'doing' and 'watching' experiments or investigations, buy there is no association with achievement scores at G8 for any of planning, watching or conducting experiments. This latter finding provides empirical evidence of difference across stages on an aspect of practice that is heavily debated. The primary method of analysis utilised a four-level structure, with PV as the unit of analysis. Substantive findings were compared with alternative methods: first making the dependent variable an average of the five PVs; second using one PV as the response variable; and third computing statistics from all five PVs and merging results using Rubin's Rules for combining multilevel method underestimates standard errors in the model in the same way as witnessed for the average of PVs. This leads to the conclusion that the only valid route to analysing imputed data is through Rubin's method of combining results from all five PVs.

I begin the thesis with an action research account of an intervention with respect to gender on a mathematics Post Graduate Certificate in Education (PGCE) course at a northern university in 1989-90. Two years after the intervention, I visited in their schools three of the students (now teachers) who had been involved and I interviewed each of them there, with a view to finding out what impact, if any, this intervention had had on their beliefs, understandings, commitments and practice. In the light of this experience, I sought out three teachers who had followed the course and who I had heard were working for change. I conducted several interviews with each of them. I constructed a model of the ways of knowing of (new) teachers of mathematics and linked one epistemology, that based on the authority of self and reason, to an emancipatory curriculum and to critical mathematics education. I have considered, briefly, the implications for initial teacher education. The research was conducted and this thesis is written as a praxis-orientated inquiry and both have been influenced by feminism, critical theory and postmodern tendencies. In this sense, the thesis itself is a research experiment.

This study was conducted to look at some cognitive (working memory and field dependency) and attitudinal factors which relate to learning and teaching mathematics. The purpose was to suggest ways that might help to improve students’ performance in mathematics. A multi-step strategy was used to examine the relationship between these variables and learning mathematics. The first and the second steps focussed on the students and the third step looked at the mathematics teachers and inspectors ideas about learning and teaching mathematics. This research has investigated the influence of working memory capacity and field dependency on mathematics achievement. The working memory space and the degree of field dependency were measured for 1346 school students aged between 14-16 years from public schools in Kuwait. The Digit Backward Test was used to determine working memory space, and the Group Embedded Figure Test was used to measure the degree of field-dependency for the students, both these tests have been used widely and their validity is assured. However, absolute measurements were not important in this study, as rank order was all that was required. In order to investigate the correlations between performance in different topics in mathematics and the working memory space and field dependency, mathematics tests were developed where some questions had high working memory demand and others had very low working memory demand. Furthermore, in order to investigate which versions of tasks will lead to improved mathematics performance, some questions were presented as symbolic tasks; others were presented as visual tasks; some of them presented as abstract tasks and others related to life. This study also explored the attitudes of the students towards mathematics in the following areas: the importance of mathematics as a discipline; attitudes towards learning mathematics; confidence in mathematics classes; the relationship between attitudes and achievement; activities in mathematics classes, and opinions about mathematicians. The perceptions of mathematics teachers and inspectors were investigated to see the extent to which their views related to the findings from work with students. A sample of 25 mathematics teachers and 4 mathematics inspectors was selected randomly and they were interviewed to compare their views. This step involved semi-structured interviews which offered an opportunity to focus on some key areas as well as giving freedom for the teachers to expand their views. The results indicated that field dependent students with low working memory capacity perform badly in mathematics. This might be attributed to their inability to distinguish between relevant and irrelevant items, with consequent working memory overload. Evidence shows that the way the questions or the problems are given to the students is very important for the students to understand and to succeed in solving them. Complicated shapes or long involved text are both more likely to produce overloading of the working memory space. Therefore, the study recommends that teachers should organise their material with great care in order that students are not penalised for some personal characteristic over which they have no control. This study also showed a clear evidence of a decline in attitudes with age and the excessively overloaded curriculum was a likely reason along with the perceptions that some topics were irrelevant. Furthermore, this study reflects the crucial role that the mathematics teacher plays in the formation of student attitudes towards mathematics. Thus, aiming to develop positive attitudes towards mathematics including confidence, enjoyment and an appreciation of it as a powerful tool should be parallel with the acquisition and the understanding of mathematics concepts and skills in mathematics education. Finally, the interviews show that there is no agreement about the objectives of mathematics education in Kuwait between those who decide the syllabuses (mathematics inspectors) and those who are going to teach these syllabuses (mathematics teachers). When the issue of the purpose for mathematics education is agreed, then it may be possible to consider what topics might further these aims most fully. In fact, teachers are involved daily in the teaching processes and they know the population of their students very well. Thus, their views about the syllabuses should be taken into consideration and they should be involved in the process of deciding the syllabuses. The study has major implications for the development of mathematics education in Kuwait but many of the findings will be widely applicable in other educational systems.

Τα σημερινά δεδομένα για την ανάγκη ενσωμάτωσης των ψηφιακών τεχνολογιών σχετικά με τα μαθήματα των Μαθηματικών της Δευτεροβάθμιας Ελληνικής Εκπαίδευσης είναι συνδεδεμένη με την ανάπτυξη των αναγκαίων υποδομών στα σχολεία, αλλά και με το επίπεδο δεξιοτήτων που έχουν αναπτύξει οι εκπαιδευτικοί που διδάσκουν Μαθηματικά στην σχολική εκπαίδευση. Η συγκεκριμένη έρευνα θέτει ερωτήματα που αφορούν στην χρήση των ψηφιακών τεχνολογιών και ιδιαίτερα στην παιδαγωγική αξιοποίηση τους, με βάσιμη υπόθεση ότι οι εκπαιδευτικοί που νοιώθουν αρκετά ικανοί ή θεωρούν ότι το εκπαιδευτικό τους έργο είναι διαφορετικό και κυρίως προς όφελος του μαθητή δεν διστάζουν να το δημοσιοποιήσουν μέσω του Διαδικτύου. Κατά τεκμήριο ο πληθυσμός αυτός αποτελεί ένα «ασφαλές» δείγμα από το στρώμα των περισσότερο απασχολούμενων με τις Τεχνολογίες της Πληροφορίας και των Επικοινωνιών (ΤΠΕ) εκπαιδευτικών. Επίσης γίνεται προσπάθεια διερεύνησης των παραγόντων εκείνων που επηρεάζουν την ενσωμάτωση των ΤΠΕ στην εκπαιδευτική διαδικασία. Στο εμπειρικό σκέλος το εκπαιδευτικό υλικό διαχωρίζεται και αξιολογείται σε σχέση με την αξιοποίηση των ΤΠΕ, την πληρότητα και την χρήση του μέσω μιας σειράς παραμέτρων όπως η προστιθέμενη αξία, η ευχρηστία, η πρωτοτυπία και η καταλληλότητα για την τάξη, καθώς και η προτεινόμενη οργάνωση της τάξης ή/και οι οδηγίες προς τους μαθητές. Εξετάζεται αν χρησιμοποιείται εκπαιδευτικό λογισμικό, η κατηγορία στην οποία ανήκει, το είδος του και με ποιο τρόπο εμπλέκει τους μαθητές στην εκπαιδευτική διαδικασία, αν δημοσιεύεται το ψηφιακό υλικό, η ποιότητα του καθώς και η ακολουθούμενη μέθοδος διδασκαλίας. Τα κυριότερα ευρήματα αφορούν στη διαπίστωση της σχέσης που υπάρχει μεταξύ της δημοσιοποίησης του εκπαιδευτικού υλικού με το προσδοκώμενο αποτέλεσμα. Οι παράγοντες που επηρεάζουν αυτή την σχέση είναι καθοριστικοί για την παρεχόμενη ποιότητα στην μαθηματική εκπαίδευση, την ανάπτυξη κριτικής σκέψης εκ μέρους των μαθητών, της αλλαγής του μοντέλου διδασκαλίας στην τάξη και της στάσης του εκπαιδευτικού απέναντι στη χρήση τεχνολογίας. Κυρίαρχο ρόλο κατέχει η ανάδειξη της απαιτούμενης επιμόρφωσης των εκπαιδευτικών στην παιδαγωγική αξιοποίηση των ΤΠΕ, ώστε η ένταξη και χρήση τους στα μαθήματα της τάξης να αποδίδει καλύτερα αποτελέσματα προς όφελος των μαθητών. / --

Η εργασία αναφέρεται στη διδασκαλία των μαθηματικών στο Γυμνάσιο και ιδιαίτερα στη διδασκαλία της μοντελοποίησης καθώς και στις σχέσεις και συναρτήσεις στο επίπεδο R2. Για τη συγγραφή της πραγματοποιήθηκε διδακτικό πείραμα σε ένα τμήμα της Γ΄ τάξης του Πειραματικού Γυμνασίου του Πανεπιστημίου Πατρών. Κατά τη διεξαγωγή του πειράματος δόθηκε στους μαθητές ένα πραγματικό πρόβλημα με δικές μας επιμέρους διδακτικές επιλογές και διαχείριση της τάξης. Μέσω των απαντήσεων που μας έδωσαν οι μαθητές, επιχειρούμε να κάνουμε γενικές παρατηρήσεις και να εξαγάγουμε συμπεράσματα για περαιτέρω διδακτική αξιοποίηση. / --

This thesis examines students’ experiences of learning to teach mathematics as they complete a primary Postgraduate Certificate in Education to gain qualified teacher status. The research data are drawn from students’ accounts of learning to teach mathematics, which include email communications during their studies and interviews with eight students at the end of the course. Analysis is informed by post-structuralist feminist understandings of discourse, power and knowledge. These tools are used to explore the complexities of learning to teach, the ways in which beginning teachers are ‘produced’, what counts as mathematics and the effects of power relations within pedagogical encounters. I use a reflexive approach to methodology, acknowledging the ways in which my own subjectivity permeates the enquiry, and the ways in which power permeates the research process. The study found performances of gender in students’ accounts of their experiences of the course, both on campus and in schools. Dominant discourses of teaching and mathematics create tensions for students and act as a form of control and categorisation as they strive to be recognised as legitimate mathematics teachers. It is argued that students’ subjectivities are shaped by discursive practices and peer and pedagogical relationships in the context of the course and that students are constituted as mathematical subjects often in inequitable ways. They are both powerful and powerless in different instances as they take up competing discourses, positioning themselves and their peers in shifting locations. Some students are silenced, categorised and marginalised within discourses of mathematics. Most report complying with the established practices of the school and class teacher and focused on the struggle to achieve legitimacy as successful student teachers. They 2 demonstrate both compliance with and resistance to dominant discourses as they are caught between the tensions and inconsistencies of competing and conflicting discourses. A key implication of this study is that teachers, teacher educators and student teachers need opportunities to explore their own gendered subjectivities as learners and teachers and to acknowledge that learning to teach mathematics is not solely a cognitive endeavour but one deeply located in social relations and contexts. Within teacher education more spaces need to be opened up to enable student teachers to embody themselves as mathematics subjects and primary teachers differently.

This thesis is an investigation into conceptions of ‘understanding mathematics in depth’, as articulated by two specific groups of novice secondary mathematics teachers in the UK. Most participants in the sample interviewed have completed one of two government funded mathematics subject knowledge enhancement courses, which were devised with an aim of strengthening students’ understanding of fundamental mathematics. Qualitative data was drawn from semi-structured interviews with 21 subjects and more in-depth case studies of two of the sample. The data reveals some key themes common to both groups, and also some clear differences. The data also brings to light some new emergent theory which is particularly relevant in novice teachers’ contexts. To provide background context to this study, quantitative data on pre-service mathematics Postgraduate Certificate in Education (PGCE) students is also presented, and it is shown that, at the university in the study, there is no relationship between degree classification on entry to PGCE, and effectiveness as a teacher as measured on exit from the course. The data also shows that there are no significant differences in subject knowledge and overall performance on exit from PGCE, between students who have previously followed a subject knowledge enhancement course, and those who have followed more traditional degree routes.

Mathematics permeates almost every aspect of human life and it is a skill much needed by the increasingly complex technological world. It is necessary that this essential skill must be properly developed among students to prepare them for future academic and professional careers. An assessment of the research-based instructional strategies blending with old traditional methods with the modern technological development is a must. Due to the complexity of mathematics learning and the varied learning styles of learners, an integration of appropriate multiple instructional strategies into mathematics education will positively impact mathematical achievement of students. The purpose of this research was to examine the effects of the use of Integrated Technologies Instructional Method (ITIM) as a supplement to the traditional lecture method on mathematics achievement of the Integral Calculus students at the College of Engineering, University of Ha'il, Saudi Arabia. The ITIM includes the four instructional strategies such as the use of the Computer-Supported Collaborative Learning, the collaborative learning, the bilingual support and the study support. Different types of academic supports have been used to examine their effects on students achievement in mathematics. Mathematics, the bedrock of science and engineering, is considered a very important indicator of a student's academic success in professional higher education. Undergraduate engineering students' low achievement in the first year mathematics is an issue demands much attention. The study was undertaken to address students' weak background in mathematics and particularly their high failure rates in this particular course. A total of 218 undergraduate engineering students, comprising of both the experimental and the control groups, were involved in this experimental design study. The control group was taught by the traditional lecture method whereas the experimental group was exposed to the ITIM as a supplement to the traditional lecture method. Apart from the effects of the use of ITIM, students' performance in the previous courses (covariates) such as mathematics, computer, and the English language were compared with their final grades of the Integral Calculus course. The final grades of students were taken as the dependent variable and the ITIM and students' scores in the previous courses as the independent variables. It has been noticed from the literature review that the application of only one instructional strategy does not address the needs of the diverse learning styles of students. A mixed mode method, quantitative and qualitative, was used to collect and analyse data. The quantitative data instruments included students' final exam grades and the student questionnaires. Interviews with students were used as qualitative tools of data collection. An independent t-test, ANOVA, univariate analysis and the stepwise multiple regression analysis were performed to determine the overall statistical significance. The study concluded that there was a statistically significant difference in the performance of the experimental group of students' in terms of their end-of-course grades compared to that of the control group. The regression model revealed significance of covariates on the dependent variable. However, no significant relationship was found between the mathematics achievement and attitudes towards the use of ITIM. The study was an attempt to demonstrate the suitability of the instructional strategies on the bilingual Arab undergraduate engineering students; however, they can probably be applicable to other bilingual students.

The concern over undergraduate engineering students’ mathematical skills and the means of addressing this through the provision of mathematics support is the main driver of this research. With the emergence of mathematics support within mathematics education there has been an associated research community interested in measuring the effectiveness of mathematics support provision. Recent studies have measured improvements in mathematics performance for students who have used mathematics support against those who have not by comparing prior mathematical ability against examination results. This does not address the issue of individual differences between students and resulting changes in mathematical ability. However the provision of mathematics support for individual students is resource intensive hence evaluation of the effectiveness of the support is essential to ensure resources are efficiently used. This mathematics education research examines the effectiveness of mathematics support in addressing the mathematics problem. It does this by considering individual differences and the mismatch of mathematical skills for studying at University by analysing the effectiveness of mathematics support in improving mathematical skills. The dataset for the analysis comprises of over 1000 students from a Scottish Post-92 University, over 8% having made use of mathematics support, and nearly 2000 students from an English Russell Group University, with just over 10% having made use of the support. It was discovered that in both sets of data the students who came for mathematics support in comparison to their peers had a statistically significant lower mathematical skills base on entry to their course, and at the end of their first year had improved their mathematical skills base more than their counterparts. Although the analysis is based on data from UK Universities we believe the findings are relevant to the international community who are also engaged in the provision of mathematics support.