Please select a resource from the list below.
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The Transition Module is designed to audit the mathematical skills of incoming students and thereby design and implement appropriate teaching, learning and assessment strategies to ease the transition to university.
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Problem classes are traditionally used in the teaching of mathematics. For a first year Chemical Engineering course in mathematical modelling, a quiz based on the TV programme “Who Wants to Be a Millionaire?” has been introduced, in a problem class supporting lectures. Following group work, with one set problem per group, students present their solutions to the rest of the class. The quiz follows the presentations. Each group is represented by a volunteer, who attempts to win chocolate prizes. The questions are both general, and specific to the particular problem done by the group. Besides reinforcing earlier learning, the quiz is fun. Certainly it appears to have been appreciated by two successive student cohorts. The lecturer and postgraduate demonstrator have also enjoyed the problem classes more than traditional formats.
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A review of MATHWISE Pre-Calculus and CALMAT.
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New support mechanisms have been introduced for Engineering students in their first year at Lancaster University to help maintain standards in all subject areas that are underpinned by Mathematics. Resources that have already been developed by Loughborough University are being used in a slightly modified form to help students to work through and overcome any weakness in Mathematics. Help sheets from Engineering Maths First Aid Kit are used to reinforce student learning. All material is used with the help of tutors to form a good foundation for further studies.
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MATLAB is the chosen simulation environment that is used throughout the Department of Electronic and Electrical Engineering. MATLAB is used by the students at several levels. It is used in earlier years as an 'Engineering' calculator that is useful for scientific calculations and visualisation particularly for complex analysis. As the course develops MATLAB becomes invaluable for investigating the time-frequency characterisation of signals and systems. MATLAB also gives the students an environment that allows them to write programming code in a 'C' like format. Finally MATLAB facilitates greater contextual teaching and problem based learning, which has become increasingly important in current Electronic and Electrical Engineering.
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The Mathematics Department at Keele University has pioneered the use of diagnostic testing linked to Computer-Based Learning (CBL) self study modules for students entering Principal Mathematics. In particular, the department has invested in the use of Mathwise modules to provide support materials. Recent advances in software have produced a new generation of courseware but there is considerable inertia in changing to such new material without some evidence that students will benefit. This case study considers this problem and considers how diagnostic testing can be used to decide when to update the courseware being used.
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The Mathematics Support Centre at Coventry University (originally known as the BP Maths Centre) was established in 1991. The Centre aims to provide early identification of problems and on-going support for individual students. This is achieved through use of diagnostic testing, the provision of a wide range of resources and the availability of one-to-one assistance on drop-in basis. The Centre’s website was launched in September 2000 to:
- extend the support provision to students who did not find it easy to visit the Centre (e.g. part-time students).
- provide access to a range of resources at times when the Centre is closed.
- deliver new support activities such as online practice tests and email questions.
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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.
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Students arriving in many of the UMIST departments are required to take a brief maths test on arrival. Mathematics students who underachieve on this test are assigned some questions relevant to sections where they did poorly and also referred to sections from texts and Internet notes. The student’s attempt at the assigned questions acts as a basis for a feedback session. Certain students in other departments (receiving mathematics as a service course) are asked to complete a computerised assignment on areas where they underachieved. Again, they are provided with references to texts and Internet notes.
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Students on Engineering awards at UWE come from a range of academic backgrounds that include A2/AS-Level, B-TEC, Foundation year, overseas qualifications and mature students who in some cases are returning to education after an absence of over ten years. Ensuring that individuals from such a diverse population can develop the necessary mathematical skills and knowledge to cope with the demands of an Engineering award is clearly difficult. In this case study we describe the development of diagnostic testing at UWE and its role in a strategy for teaching mathematics to a large mixed ability group.
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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.
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All students are assessed using a paper-based, but optically marked, written test of 12 multi-choice questions (MCQs). The test covers algebraic simplification, approximation, logs, trigonometry and calculus. It is based on a test developed at Coventry University. It is used to assess students' strengths upon entry.
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Diagnostic testing at Coventry University encompasses various disciplines. Co-ordinated by the Maths Support Centre, the test is used to assess the students’ ability and target appropriate mathematics support as early as possible. This case study reviews the testing process and how it is linked to appropriate support material, advice and learning resources.
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All students are tested via two computer-based tests each consisting of 10 multi-choice questions (MCQs). These tests are set from a large bank of questions using the ‘TAL’ (Teach And Learn) computer system developed at the University of Bristol. The topics covered include arithmetic, algebra, geometry, functions, calculus, and probability. A ‘leave unanswered’ option is provided and negative marking used to discourage guessing. The tests are accessed through a Web interface, so in principle could be accessed from anywhere. It has been run with large-scale simultaneous access and, although a little slow, is relatively robust.
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School of Mechanical and Systems Engineering DIAGNOSYS has been used by the Department of Engineering Mathematics, now the School of Mechanical and Systems Engineering, since 1993. By 1996 there were five departments involved in using the software. Based on an interview with the administering lecturer and a student questionnaire this case study examines the procedure, results and student responses to the diagnostic testing process.
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Students in Aeronautical Engineering are taught MATLAB in the first year to provide them with programming skills and for use in later courses. In the second year MATLAB is used to enhance the teaching of linear algebra and to apply the mathematical techniques to engineering problems.
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The first summer mathematics course ran during July and August of 1997, financed by South Bank University (SBU). In subsequent years the course became HEFCE funded. The Fast Track mathematics course was a specifically designed free summer course to help equip the students with those skills required to enter a degree of Higher National Diploma in science or technology. SBU established the six week daytime course, which helped students identify gaps in their knowledge and provided a tailor made mathematics learning programme. This course now runs every summer to equip new students with the mathematical skills required for a smooth transition into university.
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The Summer School has operated on the same general principles since 1991. It helps prepare students for entry into programmes for which they have a conditional offer. It features tailored instruction, flexible attendance and delivery and continuous supportive feedback.
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The subject of A-Level mathematics has attracted a great deal of political and academic controversy. Those who represent the academic community in Higher Education have argued for over a decade that the standards of A-Level mathematics have been declining and continue to do so. Elsewhere it has been argued that much of the decline perceived by those who teach in engineering and science departments is more likely to be attributed to the very substantial national decline in entry standards to engineering and science courses rather than any real change in A-Level standards. Using available statistics, a study of the electronics students at York set out to discover whether these questions could be answered and the results
were published in a detailed paper [1] of which the following is a summary.
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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.
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The Mathematics Summer School was run for the first time in September 2001, lasting one week immediately prior to the start of term. Many students admitted to courses in the School of Science and Technology are perceived to have major weaknesses in the type of fundamental algebra that underpins much of their analytical work, both in mathematics units per se and in other units. This development represents one strand of additional support given to such students; the fledgling Mathematics Support Unit can give such support as the course progresses. This initiative is not funded in any direct way and depends on the availability of already heavily committed staff.
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During the early 1990s, mathematics software was written using Visual Basic for students at Bournemouth University. With the advent of the Java programming language, this software was translated and extended into MathinSite, a website containing mathematics applets (small programs that can be run through a web browser). The primary aim of these applets is to help deepen mathematical insight through dynamic, interactive visualisations. Use of the Internet not only ensures that the content can be delivered within a student’s own educational surroundings, but also that any user can access the content any time of day or night from any computer in the world with an Internet connection.
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The problem of declining mathematical skills and appetite amongst university entrants is well known. In order to soften the impact that this makes on student recruitment and retention in the School of Electronics at the University of Glamorgan, it became necessary to explore a 'minimal-math' or 'engineering-first' teaching approach. MATLAB-based graphical user interfaces, simulations and animations are employed to give students an unclouded insight into the engineering concept and the underlying physical considerations, and a clear appreciation of the interplay of the parameters involved. This type of first encounter helps to stimulate the students' interest in the subject, erects crucial knowledge pegs, and lays a solid foundation to support a more mathematically rigorous approach during later encounters with the topic when any deficiencies in math skills will have been remedied.
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Examines the use of diagnostic testing amongst engineering, mathematics and physical science departments.
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The Open Learning Resource Centre (OLRC) at the School of Computing and Mathematics, University of Huddersfield provides a quiet environment with seated study places for up to sixty students. The Centre originally operated from 8.30am to 4.30pm every day but that has now been extended to cater for the needs of part-time students. Every day a tutor provides a surgery on a one-to-one basis to answer questions posed in mathematics, statistics or operational research (MSOR). It was also commended by the QAA Visiting Panel during a recent Teaching Quality Assessment.
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Peer Support (PS) has been running in the Department of Mathematics and Computer Science at the University of Leicester for the past 9 years. In this scheme students from the second and third years (called leaders from now on) help first year students in their efforts to assimilate first year material. The help occurs in small timetabled groups containing up to 8 or 10 first years and 2 to 4 leaders. In its first year the scheme had 6 second year leaders and now we have typically between 15 and 20 second and third year leaders.The number of first year students taking part in the scheme has also grown from about 10% of students in the early years to around 50% of students making some use of the scheme at some stage in the year.
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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.
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EXCEL has been used to provide simulation facilities in support of teaching control to engineers. This dictates a sampled data approach which fits in naturally with digital implementation of control. The technique also allows students to explore the affects of non-linearities in systems such as control signal saturation. It provides a ‘hands-on’ dimension which students find valuable. The approach is capable of use with other dynamic systems and is not restricted to teaching control.
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The date of the formal introduction of student proctors within the Faculty of Engineering and Information Sciences is unclear. However, we have certainly been using student proctors for more than ten years. The purpose is to offer students the opportunity to learn from their peers in a one-to-one situation. Within the Faculty three departments have a student proctor programme each of which runs in much the same way but with differences which reflect the different custom and practice of each department.
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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.
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Mathematical Advice and Co-ordination Service (MACS) was established in 1995 within the Faculty of Mathematics to support students within their studies at the University and to help prepare them to go into the world. Funding was made available for an initial period of 3 years and was then continued on a year-to-year basis. The emphasis has changed over the years and most of the work is now linked to students’ current problems but also includes help for those facing employers’ tests at interview. The University accepted that the concept of student support offered in Mathematics needed to be extended into other areas and, through The Higher Education Funding Council for England (HEFCE), established the Student Advice Service (SAS). The SAS is now a permanent feature of the University serving any member of the student body (and indeed staff) who might benefit from what it offers. The remainder of this case study considers only the mathematical part of the SAS, though many of the comments apply to the other areas of the SAS (Academic English, Study Skills and ICT).
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The approach to teaching Maths to Year 1 students in the Department of Engineering underwent a major reorganisation prior to the start of the 2002/3 session. The aim was to provide an optimum framework within which students studying four different engineering disciplines could be taught Maths within the resource constraints imposed by student numbers, and to cope with the extremely wide range of their Mathematical abilities on entry to these degree programmes. After much discussion, students are now taught their Year 1 Maths topics in two different cohorts, streamed according to initial Maths ability, and using different approaches in terms of the depth of understanding expected. This also involves the use of different assessments. This approach has been much more popular and created far fewer difficulties than the previous system which divided the students into two groups according to degree programme.
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Mathletics Diagnostic Tests
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Mathematics is vital for civil engineers but its role is changing. Arup chairman Duncan Michael [1] has argued for less emphasis on the teaching of mathematics. Here we report on a necessary change of emphasis but also argue the importance of a good mathematical education for all engineers
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The education Drop-in Centre at the University of Glamorgan was established during the academic year 1996/97. Its aim has always been to provide generic study support for students with writing and study skills as well as mathematics and statistics skills. Since its creation the Centre has been through a variety of changes in terms of staffing and layout. It has grown steadily each year and now comprises of two sites and seventeen staff, three full-time administrators and fourteen part-time tutors. The Centre is seen to play a key part in retaining students and has become part of the fabric of the University.
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The Centre was established in 1996 within the Department of Mathematical Sciences in order to underpin the Department's service teaching commitment to engineering undergraduates. In the first instance funding had been made available through an internal university learning and teaching initiative for a period of two years. Because of its early successes the Centre became a permanent feature in 1998 and now serves any student in the university who might benefit from additional resources, over and above those normally provided, to help them in their learning of basic mathematical techniques.
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Computer-based diagnostic testing has been used for new engineering students for some years at University of Newcastle upon Tyne. Follow-up support has been available only in some departments. In summer 2001, new students were issued (in advance or on arrival) with a ‘Maths Revision Booklet’ covering the basic maths topics that we didn’t intend to teach. Following the diagnostic test, lunchtime classes were offered for six weeks, based on the booklet, for those students who wished to attend.We report on the student opinion, analysis of diagnostic and examination performance.
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The Maths Learning Centre (MLC) was first established as a library service in 1994 but initially struggled for funding and recognition at a wider University level. Since 2000 it has been incorporated into the centrally funded Student Learning Advisory Service (SLAS).
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The Study Support Centre (SSC), within the Robert Gordon University (RGU), aims to provide students with assistance in Mathematics, Writing & Communication skills, Information & Communication Technology applications, Statistics, Study Skills and support for dyslexic students. The SSC offers students independent assistance through individual and small group tuition outwith their normal programme of study, as well as Computer Assisted Learning (CAL) packages, specialist software for special needs students and text based self-learning materials. The SSC has created a basic mathematics diagnostic assessment, which we give to first year students in many Schools. Currently, in collaboration with the School of Engineering, an engineering principles diagnostic assessment is being designed and implemented.
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The Mathematics Clinic is provided throughout the ‘teaching year’.
- Offered on a drop-in basis to ALL university students accessing mathematical modules.
- Timetabled to be accessible to all Stage One and Stage Two specialist mathematics students, (main users: Stage One students in first semester).
- Clinic is staffed by friendly, approachable and experienced members of staff.
- Feedback confirms student appreciation of this facility.
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Wider access students i.e. those people who have narrowly missed the entrance requirements, are given a chance to “topup” their mathematical knowledge before entering Napier University. They can study at their own pace over the summer vacation. There is regular communication with a university tutor and extra study sessions are held during August at the University.
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Mathcad is used in all years of the engineering mathematics course to enable students of civil engineering to investigate real engineering problems which have no analytical solution but which illustrate important mathematical concepts. In the second year engineering mathematics course Mathcad is used to assist in the teaching of numerical solutions of second order boundary value differential equations. Comparisons are made between classical analytical solutions and the numerical solutions.
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Computer based assessment has been used at UWE for a number of years on certain modules run by the School of
Mathematical Sciences. In this case study we discuss the operation of the assessment for a first year engineering
mathematics module in which students are permitted multiple attempts and are allowed, within an specified period of time,
to choose when they take the assessment. Feedback from students has been highly positive about the assessment regime and our observation is that operating the tests in this way does encourage students to work steadily throughout the year.
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Even as long ago as the mid-1990s, a survey for the Open Learning Foundation [1] found that most universities were using some form of mathematics diagnostic testing on their first-year undergraduates, usually during Induction Week. With the advent of computer-aided mathematics diagnostic systems such as DIAGNOSYS [2], it has become easier to obtain an off-the-shelf diagnostic system. Even so, many people still use their own in-house tests. This study considers one such example.
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This case study reports on the approach at one institution to helping first year engineering students to acquire the
mathematical skills they need. The approach involves a range of support mechanisms, and the concerted use of technology
as well as paper and pencil methods. Changes in curriculum, pedagogy and indeed assessment style have all proven
necessary.
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For first and second year engineering students at Napier University, the TI-83 graphics calculator plays a major role in an integrated technological approach to mathematics. This case study reviews the process of integration and its current position in the teaching of students.
