Teaching undergraduate mathematicseditors, Bob Burn, John Appleby, Philip Maher.

Facilitating understanding and concept building.

Includes bibliographies and index.

Foreword; Contents; Introduction; Acknowledgements; Glossary of UK Educational Terms; Chapter 1 The Undergraduate Mathematics Teaching Conferences- the Source of the Material; Chapter 2 The Process of Teaching Mathematics; 2.1 The New Student Comes to University; 2.2 The New Lecturer Starts to Teach Undergraduates; 2.3 Teaching Undergradua; 2.3.1 Some Problems Stemming from the Mathematical Training of the Lecturer; 2.3.2 Modes of Teaching; 2.3.3 Good Practice; 2.4 Communication; 2.4.1 Communicating What?; 2.4.2 Books; 2.4.3 Microcomputers; 2.4.4 Video; 2.5 Appraisal; Quality Assurance.

Teaching Modes and TasksConclusions; 2.6 Suggestions for the Future; Variety; Intentions; Fostering a Questioning Approach in Mathematics; Teaching Strategies; Mastery, a Necessary Aim; Study Materials; Chapter 3 Content of A-level and Undergraduate Mathematics; 3.1 Rigour at A-level; 3.2 First Year Undergraduate Courses; 3.3 Geometry; Geometry at A-level; Undergraduate Geometry; Chapter 4 Detailed Expositions; 4.1 Analysis; 4.2 Number Theory; 4.3 Quadratic Equations; 4.4 Friction; Comments:; Chapter 5 History of Mathematics.

5.1 The Role of the History of Mathematics in theUndergraduate Curriculum5.1.1 Why History of Mathematics?; 5.1.2 Construction of Courses in the History of Mathem; 5.1.3 The Cameo Approach; 5.1.4 Bibliography and Other Materials; 5.2 Education Imitating History; Bibliography; Chapter 6 Needs of Society and the Professions; 6.1 Mathematics for the Needs of Society; 6.1.1 'Adapting the Undergraduate Curriculum to the Needs ofSociety'; 6.1.2 Courses on 'Mathematics in Society'; 6.2 Mathematics for Employment; Attitudes; The Contribution of Project Work to Subsequent Employment.

Initial EmploymentSubsequent employment; Recommendation; 6.3 Mathematics for the Teaching Profession; 6.3.1 University Mathematics and the Teaching of Mathematicsin Secondary Schools; 6.3.2 Routes into the Teaching Profession; 6.4. Service Teaching of Mathematics; 6.4.1 Traditional; 6.4.2 Service Teaching to Biologists; References and Booklist; 6.4.3 Mathematics for Computer Science; 6.4.4 Service Teaching for Liberal Arts; Chapter 7 Applications and Modelling; 7.1 Applications of Mathematics; 1. Introduction; 2. Skills involved in the application of mathematics; 3. Possible topics.

4. An applications course7.2 Why isn't Modelling Taught More Widely?; Strategy for development; 7.3 Classical Applications vs Modelling; Using Mechanics As A Vehicle For Teaching Modelling Skills; Mechanics; Probability and Statistics; Operations research; 7.4 The Experience of Mathematical Modelling; References; Chapter 8 Learning Mathematics; 8.1 Enjoyment; 8.2 Learning (or Not Learning) Mathematical Concepts; Some questions; Rigour versus Understanding; Some examples of areas where misconceptions arise.; Factors hindering concept construction.

Research into the teaching and learning of mathematics in higher education is in its infancy as a recognised academic field, and little has been published to inform and assist those teaching the subject. However, interest is growing in teaching quality, in the training of teaching assistants, and in staff development. This book makes available a wide selection of material on mathematics teaching and learning - purpose, curriculum design, teaching methodology and specific material - produced at a series of working conferences. It will be useful to all teachers and tutors of mathematics in higher education.

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