Thesis (M. Ed.)--University of Hong Kong, 1994. / Includes bibliographical references (leaves 50-54).

Thesis (Ph.D.)--University of Delaware, 2009. / Principal faculty advisors: Tonya Bartell and James Hiebert, School of Education. Includes bibliographical references.

Thesis (M.Ed.)--University of Hong Kong, 1994. / Includes bibliographical references (leaves 50-54). Also available in print.

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.

This study examined the different types of mathematical errors exhibited by primary level pupils in Brunei when working with fractions. In addition, the study examined pupils' attitudes towards the learning of fractions and investigated if there were gender differences among Bruneian pupils' performances with fractions and with their attitudes towards fractions. The study was longitudinal in nature and its two phases involved a single cohort of Primary 5 pupils followed through a full year period in four government-funded primary schools in Brunei Darussalam. Pupils' mathematical errors were assessed by means of researcher-developed paper-and-pencil tests, while pupils' attitudes towards the learning of fractions were measured by means of an adapted version of attitude questionnaire that has been used previously with Bruneian pupils. Guided by six research questions, a number of statistical analyses were carried out to ensure the validity and reliability of the instruments used. These included piloting and revising the instruments, the use of Cronbach's alpha with the items in the attitude questionnaire, and the calculation of the Pearson Product Correlation Coefficient between scales of the questionnaire. The data was analysed by calculating the percentages and means of occurrences of each type of error. Paired and independent sample t-tests were carried out in order to investigate gender differences in pupils' errors and the impact of further instruction on fraction at the P6 level, while the GLM test was administered in order to investigate if there were significant change in pupils' attitudes towards fractions from the pre- to the posttests. Qualitative information obtained through pupils' interviews, field notes and lesson observations was used to support the quantitative data. / The study revealed that though pupils' achievement in the post-test improved, their performances on fraction work remained generally unsatisfactory. Many pupils in the study continued to have difficulty with the basic operations on fractions and resorted to the use of keyword strategies in dealing with word problems. Despite the pupils' unsatisfactory performance in the diagnostic tests, they generally held very positive attitudes towards the learning of fractions. No significant gender differences were observed either in pupils' performance in working with fractions tasks nor with their attitudes towards the learning of fractions. The findings of this study also highlight a number of issues for mathematics teachers to consider when dealing with fractions, and the findings also have implications for the quality of the instructional activities provided by the teachers, for the impact of language transfer in the medium of instruction - that is, from Bahasa Melayu to English at the pupils' Primary 4 level- and for the quality of the teacher training program in Brunei.

This is a study of extreme emotional reactions to the learning of mathematics. It is conducted among mature adults, mostly well-qualified in some academic area, but with relative failure in mathematics, and showing a marked distaste for the subject. It first explores, through interviews with twenty-four people, their memories and feelings about their experiences in the mathematics classroom. Two modes of investigation follow. One is with a group of seven who, with the experimenter, seek both to learn some mathematics and examine their negative reactions to it. The group met for two-hour sessions through thirty-six weeks of an academic year. Side by side with this ran individual studies of three people, who also worked on mathematics, re-experiencing and discussing their fears. These studies lasted respectively through twelve, twenty-four, and twenty-six hourly sessions. Starting with Skemp's model of intelligence, and in particular its view of the emotions, six situations are defined which inhibit learning. A model of the most extreme reaction, panic, leads to the speculation that it is caused by authority and time pressures. This is tested, both in large groups and in individual cases. The belief that the explicit avoidance of them can lead to rewarding mathematical experiences is also examined.

This thesis is an account of experiments into the teaching of mathematics to engineering undergraduates which have been conducted over twenty years against a background of changing intake ability, varying output requirements and increasing restrictions on the formal contact time available. The aim has been to improve the efficiency of the teaching-learning process. The main areas of experimentation have been the integration in the syllabus of numerical and analytical methods, the incorporation of case studies into the curriculum and the use of micro-based software to enhance the teaching process. Special attention is paid to courses in Mathematical Engineering and their position in the spectrum of engineering disciplines. A core curriculum in mathematics for undergraduate engineers is proposed and details are provided of its implementation. The roles of case studies and micro-based software are highlighted. The provision of a mathematics learning resource centre is considered a necessary feature of the implementation of the proposed course. Finally, suggestions for further research are made.

Thesis (Ph. D.)--University of Chicago, Department of Education, December 1999. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

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