Guides & Case Studies resources
A Learning Framework for Basic Mathematics and Statistics in Science
The teaching of mathematics and statistics forms part of a first year module, Scientific Inquiry, which is taken by students on undergraduate science courses. The range of mathematical backgrounds amongst the students is accommodated through a Virtual Learning Environment (VLE), supporting student-centred learning. The Case Study describes the philosophy of the module and how this is reflected in its structure, delivery, available materials and use of self-assessment.
Developing the Interface between Engineering and Mathematics at Edinburgh University
A few years ago the department of mathematics at Edinburgh looked at the problem of interfacing between mathematics and engineering courses and came up with a system to enable greater student understanding. The implementation of this system and how it is helping students is reviewed in this case study.
Diagnostic Testing within Institutions - Anglia Polytechnic University
The Department of Mathematics, Physics and Electronics (School of Applied Sciences Anglia Polytechnic University, Cambridge) uses DIAGNOSYS to administer a computer-based diagnostic test, testing the mathematical knowledge of primarily foundation year students.
Mathematical Methods for Third Year Materials Scientists at Cambridge University
Mathematical Methods is a revision course for third year materials scientists. Started in 1997, there is no formal examination. It consists of six lectures, an examples class and a questions sheet, and provides revision of past topics, with examples relating to third year materials courses and a background for the fourth year. This case study reviews the course and its role in providing the student with a mathematical foundation in the context of materials science.
National Perspective on Diagnostic Testing
Examines the use of diagnostic testing amongst engineering, mathematics and physical science departments.
Process Systems Engineering - A Course in Computing and Numerical Methods for Second Year Chemical Engineers
We describe a course aimed at providing chemical engineering students with an understanding of the fundamental classes of equations which occur in chemical engineering, the mathematical basis of their numerical solution methods and the basic methods of implementing these in a high level computing language. The course thus integrates elements of both conceptual and practical mathematics and computing.
Streaming Undergraduate Physicists for Mathematics Teaching in Year One
Many departments of mathematics, physics and engineering now use some form of diagnostic test to assess the basic mathematical skills of new undergraduates . Results reveal that a typical cohort consists of students with a diverse range of mathematical backgrounds and capabilities. Tests also help to identify those students who lack both confidence and competence and are deemed to be at risk of failing or dropping out in Year One. It is now commonplace for those teaching first year mathematics to be faced by an inhomogeneous student cohort and all are in accord that it has become almost impossible to teach them effectively together. It is against this background that streaming of first year undergraduate physicists into two more homogeneous groups has been introduced at the University of Leeds. The aim is to provide more effective teaching and mathematics support that will get students up to speed and mathematically prepared for their second year.
Student Support Based on the Three Stream System at UMIST
UMIST introduced a three level course structure to help students entering civil engineering, chemical engineering, electrical engineering, chemistry, mechanical engineering, computing and optometry to cope with the maths content of each of the courses. Based on previous qualifications and a diagnostic test, students are allocated places within the P, Q and R stream.
Support Offered to Natural Science Students at Cambridge University
Nine years ago members of staff within Physical Sciences at Cambridge University began recognizing that some students were having problems not only with the Mathematics Courses but also with applying material from A level in the context of their scientific subjects. The mathematics workbook was introduced to assist students with revision prior to starting university. On completion the student is asked to fill in a questionnaire that helps to define the problem areas. This is presented to their supervisor. The supervision system is a fundamental feature of Cambridge teaching and one of its main strengths. The student sees a supervisor Ã¢?? most commonly in a group of two undergraduates, sometimes in a group of three and only exceptionally one-on-one Ã¢?? to discuss his or her work for at least an hour once a week. Such support is ongoing and essentially provides individual attention to those students who lack fundamental mathematical skills.
Teaching Mathematics to 'Science with Management' Students Using A Graphic Calculator
The introduction of the graphics calculator has provided the fourth year students taking Science with Management Studies with an interactive learning tool. This case study reviews its introduction into the course Discrete and Continuous Models at Napier University.
Teaching Mathematics to Chemistry Students at the University of Sheffield
The department of chemistry offers over two semesters, Mathematics for Chemists 1 and 2, which provide students with the understanding and use of mathematical techniques for various chemistry degrees. This case study reviews these courses and illustrates their value in terms of providing the students with a positive foundation for future study.
Teaching Mathematics to First Year Undergraduate Chemists in the Context of their Discipline
New entrants to chemistry degree programmes are given a 24 hour course in mathematics if they do not have an A level qualification in the subject. This concentrates only on the skills necessary to successfully complete the first year physical chemistry course; these include simple statistics, functions, partial differentiation and integration. The course is taught using chemically relevant examples, in an order related to the chemistry course rather than traditional mathematics courses.
Teaching of Chemical Thermodynamics using Available Data and an Innovative Approach
Analysis is made showing how Helmholtz and Gibbs energies conveniently interrelate enabling typical 2-D and 3-D curves to be drawn across a range of temperature for selected chemical equilibria. Opposing influences leading to a free energy minimum or an entropy maximum are given a physical explanation with the attainment of equilibrium and the choice of conditions made evident. Simplifying assumptions are emphasised and the examples show how the data are manipulated, limits evaluated and trends in equilibrium summarised by EXCEL charts.
Using Spreadsheets to Teach Quantum Theory to Students with Weak Calculus Backgrounds
Quantum theory is a key part of the chemical and physical sciences. Traditionally, the teaching of quantum theory has relied heavily on the use of calculus to solve the SchrÃ?Â¶dinger equation for a limited number of special cases. This approach is not suitable for students who are weak in mathematics, for example, many students who are majoring in biochemistry, biological sciences, etc. This case study describes an approach based on approximate numerical solutions and graphical descriptions of the SchrÃ?Â¶dinger equation to develop a qualitative appreciation of quantum mechanics in an Australian University.