This new programme offers senior education professionals the opportunity to study at an advanced level for a Doctoral degree in mathematics education. The course involves the in-depth study of issues related to the teaching and learning of mathematics, as well as the opportunity for course members to apply this knowledge in their own professional contexts. It also provides a grounding in educational research methodology, leading to a supervised project at doctoral level in some aspect of mathematics education.

The course is suitable for experienced primary and secondary teachers, and other related professionals who are specialists in mathematics within some sector of education. In recognition of the many competing demands on the time of senior education professionals the taught content of the degree has been specifically designed in distance learning format, thus reducing the minimum necessary attendance time at Exeter.

The EdD will be awarded on successful completion of five taught modules and a research-based thesis of 40,000 words.

COURSE CONTENT

The taught component consists of five modules, each equivalent to 40 hours of taught input, together with an equal period of personal study. Each module is assessed by means of a 6,000 word assignment based upon some aspect of research into ongoing professional practice. Tutorial support is provided for guidance on assignments, as well as with the thesis.

1. The Psychology of Mathematics Education

   This module aims to bring students up to date on recent research in the psychology of learning mathematics. It is intended to help teachers and related professionals make better informed judgements concerning the planning and teaching of mathematics and on the assessment of pupil learning. It also aims to guide course members in undertaking a self-selected small scale investigation related to course for the assignment. Content includes: Facts, skills, errors, conceptual structures, general processes, attitudes and beliefs in mathematics; Learning theories including constructivism and situated cognition; Language and learning difficulties in mathematics; SEN, mathematical ability, and high and low attainers.

2. The Mathematics Curriculum

   This module aims to up-date students on recent research and developments in the mathematics curriculum, and is intended to help teachers and related professionals reflect on and evaluate the mathematics curriculum. Students will be guided in undertaking a self-selected small scale investigation related to the mathematics curriculum for the course assignment. The content includes the Nature of mathematics; Aims; Historical, social and philosophical perspectives; Analysis and critique; Assessment; Equal opportunities, gender and mathematics.

3. Research and Methodology in Mathematics Education

   This module aims to bring students up to date on educational research paradigms and methodologies in mathematics education, and to help course members to clarify the mathematics related dimensions of the topic and methodology to be used in their dissertation work. Content includes: Mathematics education as a field of study; Current debates and controversies; Research paradigms and methodologies in mathematics education; Research on mathematics teachers and teaching.

4. Research Project Design and Data Generation and Collection

   This module provides an introduction to advanced research design and methodology. It offers a grounding in the essential differences between different research paradigms and the implications for practice, particularly with regard to selecting appropriate methods of data collection as a means of investigating different kinds of research questions.

5. Research Analysis and Presentation The main purpose of this module is to provide an introduction to different ways of analysing data of both a quantitative and qualitative nature. Hands-on experience will be provided in the application of such analytic tools as SPSS, NUDIST and ATLAS, and consideration will be given to the strengths and weaknesses of the different approaches. The emphasis will be upon understanding methods as well as their application. Consideration will also be given to the presentation of research outcomes in both oral and written format.

Length and Structure

Candidates will normally register as part-time students for four years. Each of modules one to three can be taken by means of two weekends' study (comprising Friday evening and all day Saturday) at the School of Education, plus private distance study. Modules four and five are offered one evening per week from 5.30 to 8.30pm at the School of Education, but intensive summer schools and distance learning versions of all the modules will also be made available. Each student will be assigned a personal tutor who will also act as supervisor for their final professional research thesis, and this will normally be the course director.

Entrance Requirements

A Masters degree or equivalent plus at least three years' mathematics-related professional experience in education.

Course Director

The course is directed by Professor Paul Ernest

TEACHING PROGRAMME

The teaching programme for part distance taught mathematics education courses at Exeter is as follows.

The Mathematics Curriculum	Spring 1999	Spring 2001		Spring 2003
The Psychology of Mathematics Education	Spring 2000		Spring 2002
Research and Methodology In Mathematics Education	Autumn 2000	Autumn 2001	Autumn 2002	Autumn 2002

The Mathematics Curriculum module will be taught in Spring 1999 and then subsequently on a two year cycle. The Psychology of Mathematics Education module will be taught in Spring 2000 and then also on a two year cycle. The Research and Methodology In Mathematics Education module will be taught in Autumn 2000 and then on an annual cycle. Each module will be taught over two short weekends (Friday evening plus all day Saturday) in one university term. However the teaching of any scheduled module depends on student take-up. The fully distance taught modules may be taken at any time. For groups of students the taught modules can also be taught at other times or locations, by arrangement.

EXETER UNIVERSITY

Exeter University is one of the most popular in the country. It is a modern University with a high international standing, located in an attractive campus setting with well-established gardens and parkland, providing both a safe and friendly environment. It is a short walk from the centre of Exeter, a historic cathedral city in the heart of the beautiful countryside of the South West of England. It is only two hours by train from London and the climate is mild all the year round.

THE SCHOOL OF EDUCATION

The School of Education is one of the largest and most well known in the UK. It is situated on its own campus near the city centre, tastefully combining modern buildings and equipment in a traditional landscaped college setting. A swimming pool and other excellent recreational facilities are available on campus. The School has a strong international reputation for its research. It boasts many leading academics in a number of different fields of education, and can therefore provide supervision in a wide range of areas of educational research. It is served by a first class Research Support Unit providing support for its active community of full-time and part-time research students. The School has its own well-resourced library, ample computing facilities, and up-to-date multimedia equipment. Strong networks have been established with local schools and other educational establishments, which are often willing to participate in joint research projects.

INTERNATIONAL STUDENTS

International students receive particular attention at the school of Education. Further support is provided by the International Office with regard to all aspects of student welfare and accommodation.

Rationale

The University of Exeter has run a successful Masters Degree specialism in Mathematics Education for many years, which has been offered in part-distance education form for a decade. Significant numbers of mathematics teachers and lecturers in senior positions in Great Britain and overseas have graduated from this programme. As in the masters programme, the present course is aimed at experienced mathematics teachers and lecturers working at all levels who wish to update and enhance themselves professionally, and who wish to improve their qualifications. It aims to recruit mathematics teachers and lecturers who are professional leaders in their field, normally with a masters degree, and who wish to undertake further high level study and guided research in mathematics education. The programme will offer a high-level academically rigorous course to serve the needs of leading education professionals of the 21st Century.

Aims of the mathematics education elective area:

1. To bring educational leaders in mathematics teaching up to date on recent research, developments and theories in mathematics education;
2. To provide a an expert basis for education professionals to make well informed judgements concerning the planning, teaching and the assessment of mathematics and the management of pupil learning and the mathematics curriculum and teaching resources;
3. To develop education professionals' critical faculties through engaging critically with recent research in an academically rigorous way and engaging in enquiry, and to thus develop high-level critical thinking, writing, communication, and other transferable skills;
4. To support teachers and lecturers in identifying and investigating practical problems and issues in their own schools or classrooms with a view to researching, and productively applying theory, within their own professional practice.

Course Format

The course format recognises that with the increased demands of their profession, teachers and lecturers need flexibility in co-ordinating their pattern of study with their other professional and personal commitments. The present course accommodates the changing needs of education professionals of the 21st Century, and the structure of the elective area and the overall EdD programme allows for flexible patterns of study. The electives in mathematics education are to be offered in the part-distance education form which has been successfully tried, tested and refined in the masters degree programme. Attendance requirements are two weekends, enabling teachers to fit the sessions into their busy professional schedules, and permitting students based some distance from Exeter to follow the course. This means that teaching the courses away from Exeter is also feasible. The part-distance teaching mode reduces student-lecturer and student-student face-to-face contact to 16 hours, so maximum opportunities for such contact are built into the taught part of the electives. There are student presentations related to their topics of inquiry, structured discussions, multimedia presentations, as well as presentations by the course leader and visiting speakers. Course members are also required to interact with the course leader and with each other through E-Mail, fax, telephone, post or in person, extending personal contact. Students also benefit from extensive specially written course materials which comprise a further 24 hour teaching equivalent, bringing the overall taught course to the standard 40 hours. In addition set texts and other selected readings in the research and professional literature are specified as part of the course.

THE PSYCHOLOGY OF MATHEMATICS EDUCATION

MODULE CODE: EEDR7006

MODULE TITLE: The Psychology of Mathematics Education

CREDIT VALUE AND LEVEL: Doctoral Level. Ed.D. degree programme module
PREREQUISITES: Experience in mathematics teaching or lecturing and a master's degree in education or mathematics or equivalent.
DURATION OF MODULE: One term, equivalent to 40 hrs. contact time
RATIONALE/EDUCATIONAL OBJECTIVES

This aim of this course is to bring students up to date on recent research, developments and theories in the psychology of learning mathematics. It is intended that it will help teachers and allied professionals to make better informed judgements concerning the planning and teaching of mathematics and in the assessment of pupil learning and the evaluation of the curriculum. A further aim is to direct students to a self-selected small scale investigation related to the psychology of mathematics education, either empirical or theoretical, for the course assignment.

TEACHING/LEARNING METHODS It is planned that the module be taught in part distance learning form using:

1. Two intensive weekends of lectures, seminars, workshops, multimedia presentations (especially video), student presentations and tutorials (total contact time at 16 hours)
2. Extensive specially written course materials
3. Set texts and other readings (utilising an extensive electronic bibliography)
4. E-mail/fax/phone/mail exchanges of ideas, drafts and comments pertaining to the course readings and assignments, constituting tutorials and seminars at a distance.

TRANSFERABLE SKILLS
Self management and independent study and research Use of library and electronic databases to locate appropriate information
Communication both written and spoken
Use of IT resources and computers to write assignments

ASSESSMENT METHODS The course is formally assessed by means of an assignment of 6000 words on an approved student chosen topic applying some of the ideas of the course in practice in a mini-research project or undertaking a conceptual analysis or theoretical essay.

CONTACT HOURS The module is equivalent to 40 hrs. contact time. It will taught in part distance learning form using two intensive weekends of lectures, seminars, workshops, multimedia presentations (especially video), student presentations and tutorials (total contact time 16 hours). Associated study time 24 hours reading distance education course materials and a further 40 hours set text and other additional reading and assignment preparation. (80 hrs. in total).

SYLLABUS AND CONTENT Research paradigms and research styles in the psychology of mathematics education. Methodology of research in psychology of mathematics education.
The nature of mathematics learning outcomes: facts, skills, conceptual structures, general processes, attitudes and beliefs
Errors, alternative conceptions and creativity in maths. Diagnosis and remediation of mathematical skills.
Constructivist learning theory. Information Processing theory Radical constructivism. Social constructivism. Theories of understanding and representation. The work of Dienes, Bruner, Piaget, Skemp, Glasersfeld, Vygotsky.
Problem solving heuristics and strategies.
Attitudes, appreciation and beliefs about mathematics. Goals.
Situated cognition and learning in context
Mathematical ability: current conceptions and research. High and low attainers in mathematics including the mathematically gifted
Psychological aspects of language in mathematics, including dyslexia and dyscalculia.

INDICATIVE READING LIST
Ashlock, R. (1976) Error Patterns in Computation, Merrill, Columbus, Ohio
Bell, A. W., Costello, J. and Küchemann, D. (1983) A Review of Research in Mathematical Education: Part A, Teaching and Learning, NFER-Nelson, Windsor.
Biehler, R. Scholz, R. W., Straesser, R. and Winkelmann. Eds (1994) The Didactics of Mathematics as a Scientific Discipline, Dordrecht: Kluwer.
Bishop, A. J. Ed. (1996) Handbook of Research in Mathematics Education, Dordrecht: Reidel.
Daniels, H. and Anghileri, J. (1995) Secondary Mathematics and Special Educational Needs, London: Cassell.
Dickson, L., Brown, M. and Gibson, O. (1984) Children Learning Mathematics: A Teachers Guide to Recent Research, Holt Education, East Sussex (Holt, Rinehart and Winston).
English, L. D. and Halford, G. S. (1995) Mathematics Education: Models and Processes. Mahwah, New Jersey: Lawrence Erlbaum Associates.
Ernest, P. Ed. (1989) Mathematics Teaching: The State of the Art, London: Falmer Press.
Ernest, P. Ed. (1994) Constructing Mathematical Knowledge, London, The Falmer Press.
Ernest, P. (1997) Social Constructivism as a Philosophy of Mathematics, Albany, New York: SUNY Press.
Glasersfeld, E. von (1995) Radical Constructivism: A Way of Knowing and Learning, London, The Falmer Press.
Glennon, V. J. Ed. (1981) The Mathematical Education of Exceptional Children and Youth, Virginia, NCTM
Grouws, D. A. Ed. (1992) Handbook of Research On Mathematics Teaching and Learning, New York: Macmillan.
Hart, K. Ed. (1981) Children's Understanding of Mathematics: 11- 16, London: John Murray.
Janvier, C. (Ed) (1987) The Problems of Representation in Mathematics, Erlbaum, London
Krutetskii, V. A. (1976), The Psychology of Mathematical Abilities In School Children, University of Chicago Press.
Lave, J. and Wenger, E. (1991) Situated Learning: Legitimate Peripheral Participation, Cambridge: Cambridge University Press.
Miles, T. R. and Miles, E. (1992) Dyslexia and Mathematics, London: Routledge.
Orton A (1992) Learning Mathematics (Second Edition), London: Cassell
Resnick, L. and Ford, W. W. (1981) The Psychology of Mathematics for Instruction, Erlbaum, London
Ruthven, K. (1987) Ability Stereotyping In Mathematics, Educational Studies in Math., 18, 243-253
Saxe, G. B. (1991) Culture and Cognitive Development: Studies in Mathematical Understanding, Hillsdale, New Jersey: Erlbaum.
Skemp, R. R. (1987) The Psychology of Learning Mathematics (2nd Ed.), Erlbaum, London.
Steffe, L. P., Nesher, P., Cobb, P., Goldin, G. A. and Greer, B. Eds. (1996) Theories of Mathematical Learning, Mahwah, New Jersey, Erlbaum.
Vygotsky, L. (1978) Mind in Society, Cambridge, Massachusetts: Harvard University Press.

CO-ORDINATING TUTOR: Professor P. Ernest

THE MATHEMATICS CURRICULUM