A. C. Bajpai

Mathematical Education of Engineers, Part I. A Critical Appraisal.

This paper takes a critical look at the present state of mathematical education of engineers. It then suggests the improvements needed and proposes ways in which these can be implemented. In this part of the paper, attention is concentrated on identifying the problems and outlining a course developed by the authors in an attempt to meet the criteria for improvement. The paper is concluded by an examination of the refinements needed in this course to fully meet the required objectives. In Part II the problems in implementing such a course are discussed and examples given of the integrated approach it employs. Finally, developments to the course are suggested.

An Approach to the Teaching of Ordinary Differential Equations

A critical appraisal is made of the usual ways of teaching ordinary differential equations. In an attempt to improve students’ understanding of the structure and solution of a differential equation, the authors suggest an approach embodying the three methods of solution— analytical, numerical and analogue. They describe how this could be put into practice and, in particular, what would be done in the introductory lectures. The examples selected for illustration are the simple first‐order differential equation which expresses Newtons law of cooling, and the linear second‐order equations with constant coefficients which arise in problems involving damped and forced oscillations. An outline is given of the demonstrations, either filmed or on closed‐circuit television, using both digital and analogue computers, which are an essential feature of this approach.

The MIME project at Loughborough — a first report†

† Presented at the Conference on ‘Micros in Education’ held at Loughborough University, 4‐6 April 1984. This paper describes the experiences of the first months of the MIME Project (Micros In Mathematics Education) at Loughborough. The early difficulties and setbacks are mentioned as well as the initial successes. The first part of the paper examines the educational philosophy behind the establishment of the project and details its aims, objectives and scope. Consideration is given to how these aims were put into practice and what revisions to them were necessitated by experience. The second part traces the story of the production of a unit from the authors early ideas, through the program development, to the finished product. Emphasis is given to the way the educational objectives are achieved by careful design of the program. The testing and evaluation of a unit is outlined. The third part reviews the practical programming difficulties that have been encountered; the strengths and weaknesses of the BBC...

The role of mathematics in engineering education: a mathematician's view†

† This paper is written in a format which highlights the salient points raised by the author to generate discussion. It is not a verbatim report of the talk but is intended to be a synoptic view of the authors opinions and beliefs expounded over a number of years and briefly mentioned at the Conference. This paper is written in a format which highlights the salient points raised by the author to generate discussion. It is not a verbatim report of the talk but is intended to be a synoptic view of the authors opinions and beliefs expounded over a number of years and briefly mentioned at the Conference.

What Irish pupils say about mathematics

In this paper we discuss a study conducted in Ireland to investigate pupils attitudes to school mathematics. The authors feel this is a neglected area of research which could produce useful insights for practitioners in mathematics education. The study is described in some detail and the outcomes are discussed. We feel that the issues encountered are universal in mathematics education.

Teaching the formulation stage of mathematical modelling to students in the mathematical and physical sciences

This paper reports research attempts at identifying the skills and concepts involved in the formulation stage of mathematical modelling in the physical sciences and engineering, and tries to relate this to the interactive teaching of students on undergraduate and postgraduate courses. Comparisons are made between formulation activities in the physical sciences and engineering, life sciences, and social and organizational sciences. A teaching strategy is developed and illustrated by drawing on classroom experiences of formulation. The illustrations cover student responses to problem and sub‐problem identification, and detailed responses to formulation of the three ‘real‐problems’: use of a U‐tube accelerometer in cars, laser beams in drilling holes, and speed‐wobble in motorcycles. Suggestions for further research and experimentation are made, particularly in linking formulation with problem solving strategies.

Mathematical education for engineers Part II. Towards possible solutions

This paper describes the course developed by the authors for teaching mathematics to engineering undergraduates (Part I was published in Int. J. Math. Educ. Sci. Technol., 6, 361). The simultaneous treatment of the analytical, statistical, numerical and computer techniques which are relevant to a particular topic is discussed via three examples. A qualitative evaluation of its effectiveness is given. The role of ‘ case studies ‘ is considered and an example provided of the way such a study can be used. Three ‘ mini‐projects ‘ of varying degrees of difficulty are described from the point of view of their educational value. Problems of implementing the course are discussed and suggestions are made as to possible future directions in which to move to keep the course up‐to‐date.

An Educational Philosophy for Scientists and Technologists Using Computers.

Summary This paper examines the educational philosophy for a new approach to the teaching of mathematics to science and engineering undergraduates. It is shown that there is a need for a more practically‐orientated course in which the student is more able to get a feel for the various techniques. The case is argued for an increased role to be played by the digital computer, particularly the greater use in interactive terminals. Finally, some ideas on implementation are presented.

A Survey of Mathematics in Engineering Degree Courses in the United Kingdom

Following the publication of the Organization for Economic Co‐operation and Development Report on the Mathematical Education of Engineers, the Council of Engineering Institutions and the Joint Mathematical Council of the United Kingdom set up a Committee on Mathematics in Engineering. This survey, carried out by the authors at the request of the Committee, is an analysis of the replies to a questionnaire sent out under the auspices of the Committee relating to the time spent on mathematics in engineering degree courses. Recommendations of the Committee, based on the analysis, are included at the end of the survey, which makes frequent comparisons between the United Kingdom and the OECD recommendations.

A proposal for the self‐empowered mathematics teacher

The authors present and argue their case for a new conception of the secondary mathematics teacher as a self‐empowered individual. It is noted that self‐empowerment constitutes a worthwhile intervention strategy for the improvement of secondary mathematics education in general. A major section describes practical illustrations of the empowered mathematics teacher in action as experienced first hand by one of the authors (English). Significant benefits for secondary mathematics education are highlighted. A functional model of empowerment is presented, one which encapsulates new insights for improving secondary mathematics education. Finally, a number of strategies aimed at implementing the proposal are explored.