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Solving linear equationsEquations always involve one or more unknown quantities which we try to find when we solve the equation. The simplest equations to deal with are linear equations. On this leaflet we describe how these are solved.
Solving simultaneous equations using matrices - Numbas1 question. Solve a pair of linear equations in two unknowns by writing an equivalent matrix equation. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.
Streaming Undergraduate Physicists for Mathematics Teaching in Year OneMany departments of mathematics, physics and engineering now use some form of diagnostic test to assess the basic mathematical skills of new undergraduates [1]. 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 non-engagement with mathematics learning supportsCiarán Mac an Bhaird, Olivia Fitzmaurice, Eabhnat Ní Fhloinn, and Ciarán O’Sullivan (2013). Student
non-engagement with mathematics learning supports, Teaching Mathematics and its Applications, 32
(4), 191-205, doi: 10.1093/teamat/hrt018.
Large numbers of students entering higher education take some level of mathematics as part of their degrees, and it is widely reported that a considerable minority of these students demonstrate a lack of the basic mathematical skills that they require to succeed. A common response has been the establishment of mathematics learning supports to give students the opportunity to reach the levels required. Research has shown that in general, although the supports appear to impact positively on students who avail of them, a significant number of students do not engage appropriately. This article presents preliminary findings from a national survey carried out at nine Higher Education Institutions in Ireland, focusing on the reasons given by students for their lack of engagement with the extra supports. It looks at the students’ mathematical backgrounds; the type of institution they attend, and discusses what these students reported would encourage them to avail of the supports.
Student perception of the impact of mathematics support in higher educationNi Fhloinn, E., Fitzmaurice O., Bhaird, C. M., & O'Sullivan, C. (2014). Student perception of the impact of mathematics support in higher education. International Journal of Mathematical Education in Science and Technology, 45 (7) 953-967., DOI:10.1080/0020739X.2014.892161
Mathematics support in higher education has become increasingly widespread over the past two decades, particularly in the UK, Ireland and Australia. Despite this, reliable evaluation of mathematics support continues to present challenges for those working in this area. One reason is because ideally, properly structured support should function as an integral part of the overall educational experience of the student, in tandem with lectures and tutorials. When this occurs, it makes it difficult to isolate the impact of mathematics support from these other entities. In this paper, the results of a large-scale nationwide survey conducted with first-year service mathematics students in nine higher education institutes in Ireland are considered, exploring studentsâ?? perceptions of the impact of mathematics support upon their retention, mathematical confidence, examination performance and overall ability to cope with the mathematical demands they face. Students were extremely positive about the effectiveness of mathematics support in all of these areas, providing valuable insights into the value of learning support in mathematics.
Student Proctors: A Peer Support SystemThe 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.
Student Support and the Bridging Course at University College LondonUniversity College London has established a wide selection of teaching resources to support a dramatic increase in the number of entrants to the Mathematics Department. This includes a diagnostic test for all entrants, a workbook for students to complete before the first semester and an integrated system of tutorials, lectures and a problem class. An intense Bridging Course also provides students with a valuable and comprehensive perspective of university mathematics.
Student-centred Approaches in MathematicsThe projects highlighted in this booklet have as their key concern the student and have introduced initiatives which recognise the diverse needs of students. All have some element of support tailored to the needs of students, although the projects themselves are quite distinct. The first is focused on supporting mathematics students and the next three focus on student-centred approaches for students from other disciplines. The focus then changes, with three reports on inclusive curricula and students with additional needs. The final report presents an overview of how one might use social media to engage students. This report was edited by Carol Robinson. This report is not made available under a Creative Commons licence but is freely available to UK universities for non-commerical educational use.
Summer internships in sigma-swMatthew Taylor, Ollie Bond, Callum Anderson and Andrew Kennedy. (2012) Summer internships in sigma-sw. MSOR Connections 12(1), 23-27. DOI: 10.11120/msor.2012.12010023
We report on the experience of Loughborough Universityâ??s Eureka Centre for Mathematical Confidence in establishing a small pilot project to provide one-to-one mathematics support for neurodiverse students who attend other local universities and where no such provision is available. We outline the background to the scheme and report on the three students involved.
Support Offered to Natural Science Students at Cambridge UniversityNine 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 â?? most commonly in a group of two undergraduates, sometimes in a group of three and only exceptionally one-on-one â?? 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.
Surds and other roots - part 1This video segment introduces surds, such as the square root of 2.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Surds and other roots - part 5This video segment continues the series of segments on surds. It looks at calculations involving the difference of two roots.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
System of linear equations - Numbas3 questions. First, two equations in two unknowns, second 3 equations in 3 unknowns, solved by Gauss elimination.
The third two equations in 2 unknowns solved by putting into matrix form and finding the inverse of the coefficient matrix.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.
Systems of linear equations - Numbas3 questions. First, two equations in two unknowns; second 3 equations in 3 unknowns, solved by Gauss elimination. The third, two equations in 2 unknowns solved by putting into matrix form and finding the inverse of the coefficient matrix. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.
Teaching Mathematics to 'Science with Management' Students Using A Graphic CalculatorThe 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 SheffieldThe 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 DisciplineNew 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 ApproachAnalysis 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.
The Geometry of a Circle - Part 3IPOD VIDEO:
In this unit we find the equation of a circle, when we are told its centre and its radius. There are two different forms of the equation, and you should be able to recognise both of them. We also look at some problems involving tangents to circles.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
The Geometry of a Circle - Part 4IPOD VIDEO:
In this unit we find the equation of a circle, when we are told its centre and its radius. There are two different forms of the equation, and you should be able to recognise both of them. We also look at some problems involving tangents to circles.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
The Geometry of a Circle - Part 5IPOD VIDEO:
In this unit we find the equation of a circle, when we are told its centre and its radius. There are two different forms of the equation, and you should be able to recognise both of them. We also look at some problems involving tangents to circles.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
The double angle formulaeDouble angle formulae are so called because they involve trigonometric functions of double angles e.g. sin 2A, cos 2A and tan 2A. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
The double angle formulaeDouble angle formulae are so called because they involve trigonometric functions of double angles e.g. sin 2A, cos 2A and tan 2A. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
The Education Drop-in Centre at the University of GlamorganThe 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.
The effectiveness of a special mathematics course for improving the transition from secondary education to higher professional educationThis paper reports upon "the mathematics problem" experienced in some universities in the Netherlands. A mathematics course was designed to tackle the problem. The paper reports upon its effectiveness.
The paper was presented as part of the SoTL conference through the European Association for Research on Learning and Instruction.
The exponential constant eThe letter e is used in many mathematical calculations to stand for a particular number known as the exponential constant. This leaflet provides information about this important constant, and the related exponential function.
