In this Section:
Helping Everyone Learn Mathematics
Held on 14 -15 September 2005 at Loughborough University
A conference organised by the Subject Network of the Higher Education Academy and two FDTL4 projects.
Conference Programme
The Helping Everyone Learn Mathematics Conference Programme can be found below.
Full descriptions of the presentations given during each session can be found by clicking on the session title.
Wednesday 14 September 2005
Session 1: Opening Session |
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Welcome Professor Morag Bell, PVC(T), Loughborough University |
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Keynote Speech Excellence in Teaching and Learning Mathematics: What do we know and what do we need to know? Professor Celia Hoyles, Chief Adviser for Mathematics, Department for Education and Skills |
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Session 2: Choice of two sessions |
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| Helping Engineers Learn Mathematics: featuring the launch of resources from the FDTL4 project |
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Session 3: Subject Specific Sessions - Maths for .. |
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| After dinner at Trent Bridge Cricket Ground a talk was given by Dr David Acheson, National Teaching Fellow of the Oxford University | |||||||||||||
Thursday 15 September 2005
Session 4: Choice of two sessions |
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Session 5: Choice of two sessions |
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Session 6: Choice of two sessions |
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Session 7: Choice of two sessions |
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Session 8:Plenary Session |
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A look to the Future of Maths and Stats Support, followed by closing remarks Dr Joe Kyle, Higher Education Academy - Maths, Stats & OR Network |
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Keynote Speech:
Excellence in Teaching and Learning Mathematics:
What do we know and what do we need to know?
Professor Celia Hoyles(www.ioe.ac.uk/people/CeliaHoyles)
BSc Hons in Mathematics cl.1 (Manchester); PGCE (London); MEd (London); PhD (London).
Celia studied honours mathematics at the University of Manchester, following which she was a teacher in London schools, then a lecturer in the Polytechnic of North London, during which time she earned a masters in mathematics education and doctorate. Celia has been a Professor of Mathematics Education at the Institute of Education, University of London since 1984. Her early research involved the study of students’ affective responses to learning mathematics. Her current major research interests are: students’ developing mathematical reasoning and conceptions of proof in secondary school mathematics, the mathematical skills used and needed in various sectors in the workplace, the use of computers in teaching and learning mathematics.
In recent years Celia has become increasing involved in policy-oriented work, most notably in the area of CPD for teachers of mathematics. Celia was elected Chair of the Joint Mathematical Council of the U.K. in 1999 and was a founder member of the Advisory Committee on Mathematics Education in 2002. Celia was awarded an OBE in the New Year’s Honours list (January 2004) for services to mathematics education. Also in 2004, she was chosen as the first recipient of a new International medal, the Hans Freudenthal medal, as recognition of a cumulative programme of research. In December 2004 Celia took up the position of the Government’s Chief Adviser for Mathematics.
The HELM Project
Dr Martin Harrison, HELM Director
HELM (Helping Engineers Learn Mathematics) is a major three-year curriculum development project undertaken by a consortium of five UK universities under FDTL4 funding from October 2002-September 2005.
This presentation described the HELM learning resources, which have been developed to enhance the teaching and learning of mathematics to UK engineering undergraduates. These learning resources consist of Workbooks, Computer-Aided Learning (CAL) courseware and Computer-Aided Assessments (CAA). As well covering the mathematics essential for engineering undergraduates in the first two years of their degrees, the 50 Workbooks include engineering examples and case studies, a students' guide and a tutors' guide.
Download the presentation (Powerpoint file, 723 KB)
mathtutor and mathcentre
Professor Duncan Lawson and Jim Stevenson, mathtutor
Dr Tony Croft and Dr Sarah Carpenter, mathcentre
mathcentre is a virtual mathematics learning support centre which provides help and resources to students making the transition from school mathematics to university mathematics. mathtutor, a sister project, produces complementary on-line and on-disc resources.
Materials are suitable for students in a wide range of disciplines including mathematics, physical sciences, engineering, economics and business. Both websites and discs will enable all universities and colleges to freely establish or enhance their local support provision and empower students themselves to 'bridge the gap'. Resources include free-standing help leaflets, in-depth teach yourself booklets, streamed video tutorials and more. A special area on the mathcentre site contains resources designed specifically for staff. In mathtutor, video tutorials, e-text, interactive diagnostics and exercises are supplemented by motivational materials including mathematical extensions and computer graphics.
This plenary described the outcomes of the three year project, gave details of who is using the resources and how, and suggested ways in which delegates might use them to create a superb local support environment for their own students.
Download the presentation (PowerPoint file, 1.90 MB)
Watch a video about mathcentre (Movie Clip, 18.0 MB)
Download the full paper (Microsoft Word document, 263 KB)
Helping Engineers Learn Mathematics
The Importance of Mathematics to Engineering
Professor Fred Maillardet, Engineering Professors' Council
A sound mathematics education for all has been recognised as important in all the major education reviews in the latter part of the 20th century, including Dainton (1968) and Cockcroft (1982). However, notwithstanding this, concerns started to be expressed in the early 1990s regarding falling mathematics standards in general among entrants to universities, and the Engineering Council Report on the Changing Mathematical Background of Undergraduate Engineers (1995) articulated the growing concerns within the engineering community. Curriculum 2000 failed spectacularly to even begin to address the decline so that UCAS was forced to admit in 2002 that the situation was 'fast approaching a crisis', and published its Mathematics Post-16 Guide for HE Admissions Tutors later that year.
The Engineering Professors' Council has tracked this decline with alarm and worked with colleagues in the Mathematics Community to try to identify the underlying causes and thus propose remedies. The starting point for engineers is an understanding of why mathematics is such an important tool in the engineer's kitbag, and exactly what sort of mathematics is needed. Both these issues were explored, and some of the many contextual factors which appear resistant to change were identified. These include the attitude of parents, the myths surrounding the use of computers and the counter-incentives of school performance tables
Helping Engineers Learn Mathematics: The launch of the HELM Materials
HELM Project Team,Mathematics Education Centre, Loughborough University
HELM (Helping Engineers Learn Mathematics) is a major three-year curriculum development project undertaken by a consortium of five UK universities under FDTL4 funding from October 2002-September 2005.
This presentation described the HELM learning resources, which have been developed to enhance the teaching and learning of mathematics to UK engineering undergraduates. These learning resources consist of Workbooks, Computer-Aided Learning (CAL) courseware and Computer-Aided Assessments (CAA). As well covering the mathematics essential for engineering undergraduates in the first two years of their degrees, the 50 Workbooks include engineering examples and case studies, a students’ guide and a tutors’ guide. The CAL courseware, consisting of on-line interactive lessons to aid understanding, is web-delivered and based on many of the first 20 Workbooks.
An extensive CAA regime, which facilitates the regular testing of large numbers of students, is used to drive student learning. It takes two forms, either an integrated web-delivered version or an alternative stand-alone CD-based version. Its implementation and its use for both formative and summative assessment of engineering students learning mathematics are outlined. The CAA regime powerfully encourages students to engage more in their own learning and has been essential to the success of the project.
Finally the viability of adopting the HELM learning resources and implementing the CAA regime at other institutions was examined.
Download the presentation (Adobe Acrobat file, 53.8 KB)
StatistiCAL Resources
Creating StatistiCAL Resources from Real Datasets
Penelope Bidgood, School of Mathematics, Kingston University
Statistical Resources from Real Datasets (STARS) is an FDTL4-funded project. Its aims are to make available real datasets, with scenarios, applicable to a range of disciplines and to develop associated learning and assessment materials in various packages. The project was partly motivated by the needs stated by lecturers in several workshops run by the Learning and Teaching Subject Network in MSOR.
Currently, worksheets are available to be used in introductory statistics courses in Psychology, Health and Business, using Excel, MINITAB and SPSS. The worksheets cater for a range of student abilities, backgrounds and needs. All worksheets are available with suggested answers and they are designed to be able to be used by students individually at home, or in a class or tutorial setting.
Members of the team have developed resources for individualised datasets and assignments with solutions to be generated from the datasets. Currently two versions are being developed - one based in Excel, which allows lecturers to use their own data as well as that supplied in the project; the other is not tied to any package but is geared to be used with the STARS datasets.
This project was initiated by the needs of staff in the UK and funded as a result of the quality assurance exercise in 1998-2000; the project team feel that the materials developed and the concepts behind them have great potential for use throughout the statistics teaching community.
Participants were able to “try out” worksheets and the assessment tools developed in this project.
Download the full paper (Microsoft Word document, 50.5 KB)
Maths for... STEM
The Racemath Project: Motorsport Mathematics
Sonya Thorley, School of Industrial and Manufacturing Science, Cranfield
University
Cranfield University is presently undertaking the development of a motorsports science and mathematics e-learning website to be launched in early summer 2005.
The world of motorsports has a huge following with a varied and diverse audience. The Racemath project intends to take advantage of this enthusiasm for motorsports to demonstrate the relevance of maths and of physics to a real activity and hence encourage people towards a greater appreciation of mathematics and physics.
The site's content has also been designed to follow and fit in with the key stages from the National Curriculum and site access is free. A section for teachers and parents is also available on the site and again is free, no subscriptions or log in / passwords are necessary
Download the presentation (PowerPoint file, 3.01 MB)
Responding to the Changes in the Teaching and Learning of Mechanics in Schools
Stephen Lee, Maths Learning Support Centre, Loughborough University
National changes that have taken place in A-level mathematics have had major consequences for UK universities. In this paper we focus on engineering students' prior knowledge of mechanics upon entry to university, which has been the subject of a recently completed Higher Education Academy - Engineering Subject Centre Mini-Project.
First we reported on feedback from a questionnaire that was sent to 500 schools, which looked at the availability and uptake of mechanics. Secondly the mechanics background of over 700 first year engineering students at Loughborough University was described. Finally we described how universities are coping with the changing mechanics knowledge, which their students have on arrival. Findings from a questionnaire sent to University academics and details of subsequent follow-up interviews were given. These findings include information on good practice.
Download the presentation (PowerPoint file, 607 KB)
Maths Support for Students with Non-Traditional Mathematics Backgrounds
Dr Sarah Bamforth, Mathematics Education Centre, Loughborough University
Through the Mathematics Learning Support Centre a wide variety of mathematics support is made available to Loughborough University students. This presentation discussed the support initiatives targeted at engineering students, particularly those with non-traditional mathematics backgrounds. The presentation briefly described the rationale for targeting this group of students and the effectiveness of this support. The presentation also discussed the pre-sessional course run for engineering students with non-traditional mathematics backgrounds and the effect that changes to the design of the course have had on student engagement and performance.
Download the presentation (PowerPoint file, 1.74 MB)
Special Technology Programme
Nicole Metje, Department of Civil Engineering, The University of Birmingham
Three years ago, The University of Birmingham introduced a new degree programme: 'Special Technology Programme (STP)', developed for students without a mathematical or scientific background. Traditionally, students studying an engineering degree in the UK need Maths A-level. STP broke with this tradition, and removed the requirement for Maths A-level as an entry qualification. This means students with Maths GCSE are admitted and then taught the necessary skills for the other modules on this course.
With no previous experience of teaching students without Maths A-level, it became apparent in the first year that the course content was pitched at too high a level and the pace was too fast. Having registered for the PGCert at Birmingham, it was possible to share this teaching experience with lecturers from other, non-science/engineering, departments. The question was how, as experts in our subject, we can best teach a group of novices. Designing lectures at an appropriate level was therefore discussed as a key topic during a PGCert peer learning group meeting. It was decided to explore this topic by teaching a Maths session to peers from non-science/engineering backgrounds.
This workshop demonstrated an example of a lecture on straight lines, including questions and examples. It was followed by a short discussion incorporating examples of the difficulties found, and how they might be resolved, when teaching this session. It concluded with reflections from both the expert teacher and novice students. The emphasis was on exploring how students with an apparent fear of Maths can best be supported and enjoy success.
Download the presentation (PowerPoint file, 153 KB)
Maths for distance learning science students
Sally Jordan, Staff Tutor in Science, The Open University in the East of England
The presentation briefly explored three themes:
- Open University undergraduate courses are completely open entry and so, within the Science Faculty, we have considerable experience of teaching students from a wide range of mathematical backgrounds including those with no previous mathematical qualifications at all. Nevertheless, lack of mathematical confidence remains a problem for many of our students. The 10 point level 1 course Maths for Science was designed to increase the mathematical abilities and confidence of students prior to embarking on level 2 OU science courses (in physics, astronomy, chemistry, Earth Science and biology). The maths is taught in the context of science, and includes worked examples and questions. The course is offered four times a year and lasts 10 weeks to 4 months. More than 4000 OU students have studied the course since in started in September 2002 and it is popular and successful. The main course book is available to the HE Sector as a hyper-linked eBook as part of the FDTL4 PPLATO (Promoting Physics Learning and Teaching Opportunities) Project.
- The OU Maths for Science course is assessed, both summatively and formatively, by an innovative web-based assignment. This provides students with instantaneous, targeted and detailed feedback on their answers and gives them the opportunity to amend their answers in the light of the feedback received. The assessment thus underpins and enhances the teaching of the course.
- The Maths for Science Assessment has been fully evaluated and is included in the FDTL4 FAST (Formative Assessment in Science Teaching) Project. Analysis of student responses to the individual questions has led to increased understanding of science students' mathematical misconceptions. This analysis is ongoing.
Download the presentation (PowerPoint file, 415 KB)
Download the full paper (Microsoft Word document, 47.5 KB)
Maths for... Life Sciences
Helping Student Nurses Learn Mathematics - Responding to National Change
in Nursing
HALL CA. Senior Health Lecturer, School of Nursing, The University of Nottingham
DEVITT P. Senior Lecturer, School of Nursing, The University of Salford.
Within nursing there has been continuing international concern about the effect of poor standards of mathematical competency upon the quality of patient care provided by nurses. In the UK, this has led to the Nursing and Midwifery Council to stipulate as an entry requirement that students should be able to demonstrate evidence of their mathematical ability at key skill level 2 or above and an exit proficiency that includes recognition of effective key skills development and application in nursing practice.
How these standards of proficiency are achieved and monitored within Schools of Nursing is an important consideration. It is recognised that the role of the nurse does include a need for numerical skill and that helping nurses to learn mathematics is thus a vital component of ensuring quality of patient care. Whilst other UK countries have tackled these issues through the imposition of nationally agreed study programmes or tests, in England the responsibility for effective numeracy standards in nursing practice have remained with individual universities. Indeed, whilst imposing national testing in England may be an option as there is an issue about patient safety if nurses are unable to practice using maths safely in practice; there is concern that educational testing for maths skills may not validly indicate practice ability.
This short paper aimed to raise the key challenges facing nurse educators in England who are working to ensure that nurses are fit for practice, fit for purpose, and fit for award. The presentation was led by lecturers from the University of Nottingham and The University of Salford and further aimed to include discussion of future directions for the development of numeracy education in nurse education, and explore these principles in relation to other vocational HE programmes.
Download the presentation (PowerPoint file, 713 KB)
Delivering Numerical Methods to Sports Science Students
Barbara Cogdell, Faculty of Biological and Life Sciences, University of
Glasgow
Calculations and the management of numerical data are important skills in the area of sport science. Traditionally our third year students were given a lecture course on numerical methods but this was not liked by the students and was very frustrating for the staff involved. Recently we have changed to a less formal method of teaching these skills. The course lasts for 5 weeks and involves no time tabled teaching sessions. At the beginning of each week the students are emailed a problem. They are required to work on the problem during the week and hand it in by midday on the Friday. The tutor marks the problems and returns them to the students by the following Monday or Tuesday. If the students have any queries they can attend a drop in session on the Wednesday morning. This process is repeated each week.
The key factors that make this scheme work are:
- quick feedback to the students
- problems specific to sports science with some biological interpretation
- students who find the problems easy do not have to attend any teaching sessions, while those who want more help can get it.
This presentation described the process in more detail and gave examples of the problems used.
Download the presentation (PowerPoint file, 44 KB)
Download the full paper (Microsoft Word Document, 44.5 KB)
Adapting mathtutor for the life sciences
Vicki Tariq, Faculty of Health, University of Central Lancashire
The growing concern amongst life science disciplines and professions about undergraduates' mathematical competencies has been well documented over recent years. This presentation will provide the background to and summarise a pilot project which aims to adopt technologies used in the production of mathtutor in the development of a multimedia, e-learning resource to deliver mathematics support for students of the life sciences.
mathtutor is a new mathematics e-learning resource for mathematics and science education, which delivers diagnostic tests, video tutorials, interactive exercises, animations and printable text via DVD and the Internet. A team of academics is currently working in collaboration with the EBS Trust to adapt aspects of mathtutor for life science undergraduates. We plan to adopt a contextual learning model in our creation of a problem-solving e-learning environment. Our aim is to develop a selection of case studies and scenarios, presenting each in a highly visual manner and enabling students to explore and practise the mathematics within each. The principle of this approach is that the context (i.e. the case study) triggers students to want (as opposed to need) to learn the maths. Each case study will have associated with it a series of questions, tasks and calculations for students to complete. Students will also be provided with video-based tutorial support (similar to that adopted in mathtutor) for those maths topics and concepts with which they lack confidence or with which they are unfamiliar. There will also be the opportunity for students to practise and apply their skills to new case studies, thus linking theory to practice.
Download the presentation (PowerPoint file, 94 KB)
Download the full paper (Microsoft Word Document, 68 KB)
Maths for... Psychology
This workshop comprised the following:
- An account of the study entitled 'Assessing numeracy and other mathematical skills in psychology students as a basis for learning statistics' by Gerry Mulhern and Judith Wylie, School of Psychology, Queen's University Belfast, with the newly published report and materials available to participants.
- A presentation of an example of a potential solution to part of the problem: 'Using mathematical puzzles to support the teaching of statistics' by John Maltby, University of Leicester.
- A facilitated discussion to identify potential solutions to the problems experienced by lecturers.
In undergraduate psychology courses, the ability to undertake empirical work and to evaluate empirical evidence in published material had been seen as central to psychological training. Gerry Mulhern and Judith Wylie conducted this study in response to the need to obtain definitive empirical evidence about the standards of numeracy and mathematical reasoning among UK psychology undergraduates, particularly in respect of those mathematical concepts that might be considered a necessary basis for learning about statistics and research methods. Psychology undergraduates (173 males, 676 females) drawn from eight universities participated in the study. These students completed a 32-item test which probed their competencies on eight component scales. Common errors were identified and they found evidence of poor levels of skill among students entering psychology. There appear to be marked deficiencies in mathematical reasoning, as well as gender differences. The report published by the Higher Education Academy Psychology Network, and the associated Instructors'pack (including the test, results and outlines of implications for the teaching of statistics), was available for participants.
In mathematics, puzzles or mathematical problems are used to aid the teaching of mathematical concepts, thus stimulating student interest in the topic. An evaluation study was done to assess the usefulness of using mathematical puzzles and mathematical energisers to aid the learning of statistical concepts in psychology. The findings of this project were described, and examples of the activities were presented. Mathematical puzzles and statistical energisers may present opportunities for exploring mathematical thinking and may form a useful part of a problem-based curriculum which aids students' understanding of statistics.
Supporting Students at the Transition
Using mathtutor
This workshop followed on from the mathcentre/mathtutor plenary and enabled delegates to experience the on-line and on-disc resources at first hand. It provided the opportunity for delegates to meet both members of the team involved in producing the resources and also other staff from universities, schools, and colleges around the UK who have used them in their own teaching or support.
Computer-Assisted Assessment (Part 1)
Computer Assisted Assessment: How many questions are enough?
Carol Robinson, Maths Learning Support Centre, Loughborough University
Charles M. Goldie, Professor of Statistics, University of Sussex
Rosie Shier, University Teacher of Statistics, Loughborough University
Currently many universities make use of computer assisted assessments as part of student assessment. Often these assessments take the form of a test where each question is randomly selected from a bank of alternatives. In this situation, the number of possible tests can be very large. (For example, a test may have five questions and for each question there may be a bank of ten alternatives. The number of possible tests would be 10^5.)
This presentation addressed the issue of how many tests, on average, need to be generated before all available questions will have appeared in a test. By means of probability theory and the use of a computer algebra package, results are generated for a number of typical situations. Some rather surprising results are reported. For the example quoted it is found that, on average, only forty-four tests need to be generated before all available questions will have appeared in a test.
The implications of these results, with reference to plagiarism, were discussed. Recommendations, for practitioners in this area, on how to reduce the possibility of plagiarism were provided.
Download the presentation (PowerPoint file, 311 KB)
Test & Learn - a way forward
Jon Sims Williams & Mike Barry, Department of Engineering Mathematics, University
of Bristol
There is enormous variety in the needs for mathematical skills and the level of understanding from which our students start, so we need to allow staff and students to start where they are and find a way to their goals.
successful learning = motivation* Ease_of_Learning
So to get successful learning we need to motivate students well and then try to make learning as easy as possible.
In this talk we showed how motivation can be improved by:
- Students taking tests to show that they have understood.
- Showing the path through different subjects from simple maths to the maths that students need for their own objectives: surveying, cooking, designing etc.
The student's Ease_of_Learning can be increased by:
- Starting at the level where the student's knowledge is.
- Providing on-line links from the test questions to teaching web-pages.
We have approached this idea by building a database of questions with web-links to relevant teaching pages. The lecturer, or even the student, can then select topics and build a test. When the test is taken the feedback provides links to the web resources.
In this talk we showed how linked sets of tests with supporting teaching web-pages can be used to map out a route [non-unique] from where a student starts to his or her goal. We also demonstrated how easily the tests can be formed from the classified database of maths questions.
This project is supported by the Maths Subject Centre under the title: Diagnostic Tests with Support.
Download the presentation (PowerPoint file, 552 KB)
Encouraging Effort
Jean Cook and Sue Milne, Glasgow Caledonian University
The problems of teaching mathematics to service classes are well known. Often the students lack the basic skills necessary and usually they would rather be doing something else. These two facts contribute to the amount of effort they are willing to apply and consequently to pass rates.
What is needed is a mode of delivery and a system which will
- Cause the student to do the work and not the teacher;
- Provide readily accessible material to make good the deficiencies which have been identified by a diagnostic test
- Contain learning material and tutorial questions sufficient for most service classes;
- Deliver non-objective computer-based assessments to drive the learning;
- Monitor all this activity.
The most important is the latter. If this does not happen, then only the motivated student will do the necessary work.
CALMAT is a tried and tested system, extended in the last couple of years to fulfil all these requirements. Furthermore, it is poised to improve even more with a new web-delivered version which will also provide facilities for
- Authoring QTI2/MathQTI compliant questions
- Adding to the existing monitored material
- Exporting results to a VLE database
Download the full paper (Microsoft Word Document, 167 KB)
Dyslexia and Dyscalculia
Mathematical and Statistical Support for Dyslexic Undergraduates
Clare Trott and Glynis Perkin, Mathematics Education Centre, Loughborough
University
At the present time there is a widening participation agenda in the UK, the government target is that 50% of young people between the ages of 18 and 30 will be entering Higher Education by 2010. Statistics from the Higher Education Statistics Agency show a 52% increase in the number of dyslexic students entering Higher education in the academic year 2003/2004 when compared to the figures for 2000/2001. Additionally, current legislation in the UK makes it unlawful for a university to discriminate against a disabled person and universities must make reasonable adjustments to ensure that disabled students are not placed at a substantial disadvantage when compared to non-disabled students. In order to comply with this legislation and to avoid high failure rates it is imperative that students with specific learning disabilities are given support that is tailored to their individual needs.
It has been found that dyslexic students may experience difficulties in mathematics and statistics, which can be directly attributed to their dyslexia. These problems are often related to, for example, poor short-term memory, sequencing of work, reading the words that specify a mathematical problem, subject specific vocabulary and visual-perceptual difficulties. It is also important to note that dyslexic students are often extremely anxious about the mathematical and statistical elements of their courses. This paper discusses some of the areas of difficulty in mathematics and statistics that were witnessed by the authors during one-to-one support given to dyslexic undergraduate students at Loughborough University.
Three studies, taken from the disciplines of Economics, Engineering and Psychology, will be presented to illustrate some of the difficulties that might be encountered. Suitable support strategies are highlighted and attention is also given to appropriate teaching methods along with the development of support materials. This support enables dyslexic students to attain their optimum performance in the mathematical and statistical elements of their courses.
Download the presentation (PowerPoint file, 117 KB)
Download the full paper (Word Document, 84KB)
The Difficulties Dyslexic Students Experience Using Calculators
Nigel Beacham and Clare Trott, Mathematics Education Centre, Loughborough
University
University recommendations on the use of calculators in examinations are becoming an increasingly widespread practice. Often, these recommendations are produced without reference to the implications for students with specific learning difficulties and there is currently little empirical evidence on this issue. At Loughborough University a small study was carried out to investigate the difficulties dyslexic students experience when using calculators. The study involved carrying out a set of trials. The trials focused on the length of time dyslexic students took when using a familiar and an unfamiliar calculator, and whether the extra time allocated for such students (usually 25%) was reasonable. The trials also focused on the accuracy of both groups students using a familiar and an unfamiliar calculator. The implications of this research for examinations involving mathematical and statistical calculations were also considered. The presentation outlines the rationale for the study and the results obtained as well as theses implications.
Download the presentation (PowerPoint file, 169 KB)
Download the full paper (Microsoft Word Document, 119 KB)
Computer-Assisted Assessment 2
Development of online mathematics and statistics tests in QM Perception
Martin Greenhow, Edward Ellis, Mundeep Gill, Nabamallika Baruah and Justin Hatt, Dept of Mathematical Sciences, Brunel University
This talk gave an overview of the development of online mathematics and statistics tests written in an enhanced version of QM Perception as part of HEFCE's FDTL4 & 5 PPLATO and METAL projects. By using random parameters within questions, including within MathML for dynamic equations and SVG for dynamic diagrams, many millions of (algebraically and pedagogically equivalent) question realisations can be generated, at runtime, from a single question style. Moreover, control of font size/colour and background colour is given to the individual user, which may help with certain types of disability such as partial sight and dyslexia. Recent developments of MathML will be shown, including graphing expressions, naturalistic input of mathematical expressions and the possible use of <maction> tags. All of this technology is exportable to other web-based systems and, indeed, ordinary web pages.
This talk also addressed the pedagogic issues in setting effective objective questions for more advanced mathematics, in particular where are the boundaries for objective testing? Our experiences under the Formative Assessment and Feedback (FAST) project for level 1 mechanics questions have been very positive, with students spending much time on the formative feedback screens. At level 2, we show how some of the content of typical methods courses (e.g. Laplace transforms) can be tested and speculate as to how far these methods can be pushed and what the authoring costs might be.
HELM CAA Question Bank
Dave Pidcock and Aruna Palipana, HELM Project Team
The HELM projects philosophy is that regular short tests of both a formative and summative nature are a motivational factor to students which drives their learning and understanding.
The presentation briefly covered the historical development of the HELM projects CAA materials, the methodology of its implementation at Loughborough, and the influence of the feedback obtained from a variety of evaluation exercises, which has informed the development of different types of question.
Following the presentation there was a “hands-on” opportunity to access a wide variety of the projects questions in the form of sample tests based on the content of several workbooks.
These CAA questions were prepared using Question Mark Perception (3.4) and the entire database of questions in this format were freely provided to conference members who wished to make use of it for formative or summative testing.
For those who do not have access to QMP, a PC based, stand-alone sampler CD was provided which contained several tests for use by individuals in a formative manner.
Download the presentation (PowerPoint file, 1.68 MB)
Student Confidence and Background
Are we adequately preparing our children to survive in a quantitative world?
Ave McIntosh, Head of the Mathematics and Statistics Division, University of Technology, Jamaica
Jamaica, like most other developing countries, has a large percentage of the population who are innumerate. A numerate society is very important for nation building. According to Steern (1999) a numerate society will be better informed and support democratic governments.
Recent studies from the 2004 sitting of the Caribbean Examination Council (CXC) Mathematics examination showed where only 26% of the students passing in Jamaica. This is quite worrying for us at the University of Technology, Jamaica as we inherit some of these students who are mathematically challenged and who enter the university with mathematics blockages even before they start their mathematics courses.
We are a program driven university offering diverse programs such as BSc. in Engineering, BSc in Pharmacy, BSc. in Food Service Management, BSc in Computing and Information Technology etc. All students with a few exceptions are required to do Pre Calculus in their first year. In some disciplines, Pre Calculus is terminal while for others they go on to do up to three more years of Mathematics. Many of these students struggle with mathematics and sometimes get as far as their third year without passing first year Mathematics.
We believe that this systemic problem has its roots cause in the early years of the students. Enough was not done to foster a love for the subject in the early and informative years. The problem must be attacked from this stage and with time will evolve a larger population of numerate citizens. We identified a few ways in which the solution may be approached:
- Parents needed to become more involved in their children's education as they are their children's first teacher.
- Parents should involve their children in real life activities where mathematics is a part.
- Babies should be stimulated from early to count items.
- Children should be left to explore instead of forcing large volumes of information down their throats.
- Trained Teachers (Specialized teachers) should be employed at the Basic school level to teach Mathematics. Too often non qualified teachers at the Basic school level pass on to these young children their own fear of mathematics.
- Reduce drilling and rote learning.
- Pass on confidence to these children by showing them mathematics is not magic but logical.
Download the presentation (PowerPoint file, 961 KB)
What is self-confidence in mathematics?
Sarah Parsons, Engineering, Harper Adams University College
Students from wide-ranging disciplines encounter mathematics and statistics during their university courses. Students' deficit in mathematical skills and knowledge on arrival at university is well documented, particularly for disciplines such as engineering, but is also a recognised problem for students of less numerate disciplines.
A number of students also arrive at university lacking self-confidence in their mathematical skills. Does this have an additional effect on their motivation, effort and success at university? What do we mean by self-confidence in mathematics? A model of three levels of confidence is suggested as follows:
- Overall confidence - a person's overall belief in their general mathematical ability.
- Task level confidence - a confidence which varies according to the nature and level of difficulty of a mathematical task, and the person's past learning experiences.
- Confidence to apply mathematics - the confidence to apply mathematics to new, typically practical, situations.
At Harper Adams University College student surveys have been conducted to assess student confidence, to understand students' views and to explore the three confidence levels.
All Harper Adams students are required to study statistics, and engineering students also study engineering mathematics. The college specialises in subjects related to the rural economy, and many students could be described as reluctant to study mathematics and statistics. All the mathematics and statistics modules have been designed to accommodate students' wide range of abilities and mathematics support is provided.
This presentation presented the background concepts and samples of student survey responses, to encourage discussion and contributions from attendees on the ideas and issues raised.
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Using MATLAB
MATLAB as a Teaching and Learning Tool in The Mathematics Curriculum
Stephen Kane and A.J. Davies, Department of Physics, Astronomy & Mathematics, University of Hertfordshire
In the University of Hertfordshire we use MATLAB in the mathematics curriculum for teaching mathematics, engineering and science students. Two University-funded teaching and learning initiatives has allowed us to develop a set of web-based workshops. These materials have been written for first year mathematics, science and engineering students. In particular we have developed workshops for supporting traditional mathematics lectures and a set of workshops for teaching generic programming skills. We described the resources and showed how the workshops are embedded in our teaching.
Experiences of supporting mathematics learning through MATLAB and a VLE
John Rossiter, Department of Automatic Control and Systems Engineering, The University of Sheffield
This presentation gives an overview of the experiences of staff in teaching mathematics (and engineering) through MATLAB. Specific focus is given to the efficacy of various software tools used to facilitate this within a laboratory environment. Some time was also spent considering, briefly, the efficacy of the overall project.
Background: Within engineering there is a common presumption that mathematics is taught to support engineering learning and not as an end in itself. Students need to have a clear understanding of mathematical basics, such as algebra, but there is no need for example, for them to solve, by hand, large sets of simultaneous equations or to understand the numerical intricacies of various algorithms for doing this. Instead, students are taught the basics and then expected to use a computer to do long and involved algebra and computation.
MATLAB: At Sheffield, it was decided to give the students formal teaching in software packages which support mathematics in the hope that students would use this package both to reinforce their learning and to become more efficient in solving problems with lengthy algebra/computation. This would cover many topics such as curve sketching, matrix algebra, calculus, Bode and Nyquist plots, simulation of ODEs, modelling and simulation of time series, etc. As MATLAB is a well used and readily available package with large functionality, especially within control, this was chosen as the software tool.
The laboratory and VLE setup: For the first year, the module was delivered in a traditional fashion with a lecture theatre, where the lecturer gave many illustrations of how to use the package. This was supported by a weekly 3 hour laboratory session. However, both student feedback and the lecturer felt this did not work well and for the last two years he has moved the lecture into a PC laboratory with the intent that students can interact directly with the package during the lecture and hence learn by being active. However, this has two significant obstacles: (i) the laboratory ceiling is so low that one cannot use a data projector or OHP; (ii) the lecturer cannot illustrate code and its outcome as effectively. Hence there was a need for a tool which allowed the lecturer to pass exact chunks of code to the students dynamically during the lecturer so that they could replicate exactly his screen.
This talk discussed experiences of using:
- The chat facility on WebCT.
- The whiteboard facility on WebCT.
- A dynamic webpage, linked to a word file, on WebCT.
- Ready prepared files on a common access server.
There was also some brief discussion on the students response to this module and whether it is meeting the principal aim of empowering them.
Download the presentation (PowerPoint file, 58.5 KB)
Math Support
Helping Students to Make the Transition from School to University: The NUI-Maynooth Experience.
Ann O'Shea, Department of Mathematics, NUI-Maynooth, Ireland.
All students entering university in Ireland must have taken Mathematics at Leaving Certificate level. This means that they have spent thirteen or fourteen years studying Mathematics at school and have covered quite advanced topics. For instance, all would have seen some Calculus. One would expect therefore, that when these students meet Mathematics in their university courses, that they would be very well prepared and the transition from school to university level Mathematics would be smooth. Unfortunately, however, for many students the transition is difficult. In this talk, we considered some of the problems that these students face and report on efforts made at the National University of Ireland-Maynooth to tackle these problems. These include: bridging courses, tutorial reform, and problem-based learning.
Download the full paper (Microsoft Word document, 45KB)
Transition course for students prior to university entry
Kevin Golden and Alison Hooper, Mathematical Sciences School, UWE
Students are recruited to university engineering departments from a wide variety of backgrounds ranging from vocational secondary education and experiential learning offered by mature students through to the more traditional A-level route. At UWE, we find a significant number of part-time students, who are generally part of the mature student group, need time to become confident with basic mathematical skills, covered in previous courses. Due to the constraints of the part-time award, it is difficult for part-time students to take advantage of the support on offer. However, the part-time cohort are usually well-motivated and would be willing to undertake additional work prior to the start of their University degree to address any weaknesses they may have in mathematics.
The strategy that we have adopted is a pre-university summer courses which is a structured approach with some personal involvement. The course includes material which is broken down into a number of topics supported by an audio recording as if in a class-room environment. Students are prompted to stop the CD at appropriate points so that they can fill in certain gaps in the accompanying booklet. If they don't quite follow something the first time, they can easily play that section again. Each topic is supported by an answer booklet and a set of relevant computer-based questions for formative self-assessment. In addition, a website acts as a front-end to the course, giving an overview of the course and providing links to on-line computer-based testing and to website addresses of relevant on-line resources such as appropriate the mathcentre resources.
The presentation displayed some of the material available. The material can also be repackaged and used to support students throughout their first year.
Download the presentation (PowerPoint file, 7.76 MB)
Download the full paper (Microsoft Word document, 135 KB)
Mathematics Support for Students on Vocational Courses
Susan Starkings, Learning and Development Centre, London South Bank University
The Learning and Development Centre at London South Bank University (LSBU) was set up in 1998 and with this came the first formal, term time, support for mathematics and statistics across the university. Prior to this support of this nature was contained, if at all, within each school/faculty at the university. A number of factors need to be taken into account when running a support service. For example, one of the important considerations is that pools of well-qualified and experienced staff are available, and are essential for the smooth running of the service. The type of mathematics required for nurses, trainee teachers and social workers is very different to those studying engineering and science based subjects and experienced staff in this area is required. This and other salient points with relevant examples will be explained in the presentation. The emphasis, in this presentation, was to give examples of the type of problems students have and their requirements with the emphasis being on students from the vocational areas of study such as nursing, teaching and social work. The LSBU Mathematics Support Service runs throughout the whole year, not just the academic year, and this also raises many poignant issues.
The aim of this presentation focused on the following aspects:
- to briefly describe the LSBU Mathematics Support Service;
- to give practical examples of queries from students on vocational courses and
- to elucidate the constraints and problems of providing this support for students on vocational courses.
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Reviewing and updating a long-standing Maths Support structure.
Dr Neil Challis, Mathematics Subject Group, Sheffield Hallam University
Sheffield Hallam is in the middle of completely reviewing its Maths Support - they were one of the earliest Maths drop-in centres, but feel the need to update and spruce up now. SHU are therefore collecting a variety of evidence and have to make decisions about revamped structures in the next year, so it is an exciting time, and also one where they are looking for discussion and opinions.
This will affect not only engineers (it certainly affects them) but also other groups across the university and outside. The process of reviewing and updating this long-standing Maths Support structure was discussed in this session
e-learning and e-resources
LaTeX/PDF Packages for Supporting Student Learning of Mathematics
Robin Horan, School of Mathematics and Statistics, University of Plymouth
For some years at Plymouth, we have been creating a library of interactive PDF packages to help students learn mathematics. The packages are easy to use, visually pleasing, beautifully typeset and free to all. They require no specialist software and are small enough to fit several on a floppy disc. The packages are constructed using LaTeX and in this Presentation I displayed some of their interesting features. The work has attracted two LTSN grants and is also funded as part of the HEFCE PPLATO consortium.
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MELEES- Reflective overview on use of a VLE in supporting student learning
Stephen Hibberd, School of Mathematical Sciences, University of Nottingham
and Cliff Litton and Claire Chambers
MELEES is a web-based Environment, developed since 2002, to support students who take mathematics modules as a part of their course. In 2004-5 over 2000 students across Engineering and Science used the MELEES to support their learning.
The principal challenge within the service teaching of mathematics is to address the needs of students who are often not provided per se with as extensive a support structure as that associated with their main subject area(s). The scale and diversity of the service teaching provision at Nottingham invited a development focussing on:
- establishing a unified supportive environment;
- providing feedback to students, their lecturers and their home Schools;
- identifying and supporting e-learning strategies;
- specialist support for students with special learning needs.
A variety of resources have been established using local expertise but also importantly from other sources such as those funded by National initiatives (including HELM, mathcentre).
The benefits of using a VLE has been embraced by students and teaching staff as a means of providing an integrated and versatile support mechanism. The culture is developing that students are using the environment extensively which in turn encourages teaching staff to develop more 'e-learning' activities. The monitoring and tracking facilities provide the opportunity to develop the site according to the particular cohort groups in tandem with the teaching preferences of the lecturer and the requirements of the subject matter.
This presentation provided a reflective overview of the MELEES provision and its impact on the enhancement of the student learning experience.
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Download the full paper (Microsoft Word document, 362 KB)
Hands up for Hands on Applied Mathematics
Mark McCartney & Ken Houston, School of Computing & Mathematics, University of Ulster
The Learning Environment for Physics Laboratory Activities (LEPLA) is an online resource which is being developed under the EU Socrates Minerva program. LEPLA provides a range of experimental modules based on the use of hand held calculator technology which cover the areas mechanics, electricity and magnetism, heat, light and radioactivity. The materials are targeted at 'A' level and first year undergraduate students. This talk gave an introduction and overview of the materials available through the LEPLA project, and their uses both for classroom demonstrations and student investigations.
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Using blended learning to help motivate students
Diana Mackie, Napier University
Mathematics is not the favourite subject of students studying for a degree in sport and exercise science. Many of those embarking on the course have a poor grasp of basic algebra and geometry, yet these are essential for the study of biomechanics, for example, which requires understanding of vectors.
Poor motivation, often coupled by a lack of confidence in mathematics, can lead to poor attendance at classes, insufficient time spent working through exercises and hence poor results. Many reports have cited appropriate use of ICT as a means of motivating students and encouraging them to learn. ICT can contribute to learning in two ways. Firstly, if resources are available online, students can access them at a time and place suitable to them. Secondly, ICT has the potential to contribute significantly to students’ learning of mathematics by, for example, enabling them to practise and consolidate skills with rapid feedback, making connections between algebraic, geometric and graphical representations of an ‘object’ and working with realistic data sets. ICT can be used to enhance learning both within lectures and, individually, in computer-based classes or in the students’ own time.
This presentation describes how a blended learning approach, combining lectures, tutorial classes, computer-based classes and online resources is used to help motivate students on the mathematics module for sport and exercise science at Napier University. A virtual learning environment provides a single access point to information about the module, learning material and resources for online learning.
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Download the full paper (Microsoft Word document, 46 KB)