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Math insight with MathinSite Peter Edwards Summary Mathematics can be a stumbling block for many undergraduates - particularly in engineering. In recent years, there has been an increase in the amount and variety of support that has become available to help students who find mathematics difficult. MathinSite, funded initially through an internal award from Bournemouth University and more recently though NTFS funding, is just one such resource. Its primary aim is to deepen a student's understanding, and hence enjoyment, of mathematics using visualisations in the form of interactive, dynamic graphical software presentations (applets), theory sheets and tutorial worksheets - all freely available over the Internet from the MathinSite web site. Biography Peter Edwards is Professor of Engineering Mathematics Education, Bournemouth University, and an NTFS Award Winner (2000). With funding from a National Teaching Fellowship award, Peter is currently developing the ‘MathinSite’ website. Its main aim is to help deepen students’ mathematical understanding using Java applets that have a strong graphical content. Keywords mathinsite, mathematics applets, mathematics visualisations, Java applets, reflective learning, student-centred learning, NTFS project Background There are a variety of reasons why some undergraduates have problems with mathematics. Some engineering courses, for example, have dropped the requirement for A-level Mathematics (requiring Physics or Technology instead) and so those who have not studied mathematics in the sixth form will have at least a two-year hiatus in their mathematics education. Taking up mathematics after a gap is not as simple as, say, taking up cycling after a break of several years. Cobwebs have to be brushed aside and, in some cases, certain areas of school mathematics – including, invariably, algebra - have to be reinforced (usually in additional ‘Extra Maths’ classes or ‘Foundation’ years). In teaching this level of mathematics to undergraduates, it is apparent that a bar to learning is often a lack of an understanding of what the mathematics is all about. In these cases visualisations sometimes help. Often this is done by setting problems in a real- world context, or by using graphical visualisations. In the latter case, the maxim ‘A picture is worth a thousand words’ is most appropriate. Even students who have problems rearranging mathematical equations, can, almost invariably, ‘read’, understand and draw graphs. Now, a graph is basically a visualisation of a mathematical equation, whether it is as simple as the straight- line equation or as complicated as the solution of a second-order partial differential equation. Consequently, displaying the graph of (i.e. visualising) an equation can help deepen student understanding of the mathematical processes involved with that equation. During the early 90s Peter wrote and presented for student use some graphical mathematics software using Visual Basic (VB) (Edwards, 1995). It was clear that, through its use, students began to understand better the equations they were investigating - and realised that mathematics could be enjoyable (evidenced, in part, by students talking and enthusing about mathematics and using the software in their own time). Software Development of Mathematics modules The VB software had to be easy to use. Proprietary mathematics algebra packages were not used since they would require students to learn how to use the packages first. Each piece of VB software written had to relate to one, and only one, mathematical topic (e.g. the Parabola, Trigonometrical Functions) with each module taking the form of a PC ‘Windows’ application. The user interface was to be as similar as possible for all modules. There was to be a graphical window, a text window and Windows-type scrollbars to effect data entry. Text box data entry was considered to be inappropriate since there will always be someone who tries, for example, to enter text when they should be entering numbers! With the above philosophy, students soon became adept at using the software. Unfortunately, unscrupulous users were also adept at spoiling the software’s set-up since, at the time, these were placed on individual PCs rather than on a network. With a constant need to reinstall the software, its use declined, even though further VB modules were still being developed. During 1999, funding was obtained locally to review this project, but this time with the potential of having a far more robust and wider disseminated presentation. Java is a programming language that allows the software writer to present programs (‘applets’) to be run through web browsers, such as Internet Explorer or Netscape. Transcribing the existing VB software into Java opened up the possibility of presenting mathematical modules over the Internet – either for local consumption, using an Intranet, or to a wider audience, using the World Wide Web. With local funding, the Intranet path was chosen and during 1999 – 2000 some of the software was transcribed with the resulting applets being made available for student use. Again they were well received, the main student disappointment being that the software could only be accessed from within the university over its Intranet. With students using the applets, this method proved to be a valuable testing ground for the concept and presentation and brought forth suggestions and corrections. There was concern over how this project could continue with local funding coming to an end. Fortunately the National Teaching Fellowship award ensured that the life of the project could be extended by three years. Now with external funding, opening up the project to a worldwide audience became the obvious way forward. The MathinSite website No matter how carefully software is written, bugs will always appear. These may be due to programming errors, or perhaps due to mathematical errors, or even just silly mistakes. So, when one prepares material for a worldwide audience, it is necessarily with some trepidation. However, the applets that had already been developed and rigorously student-tested locally were considered a good, dependable starting point, so in October 2000, MathinSite (http://mathinsite.bmth.ac.uk) was born with its first three applets. MathinSite’s main content is its applets. However, a profound and fundamental philosophy behind MathinSite is that the applets, at least initially, should be used in conjunction with tutorial sheets, also provided through the web site. These tutorial sheets (a) guide the student through the use of the applet, (b) encourage reflection on the mathematics behind the on-screen visualisation, (c) maximise what is learned from the applet and, consequently, (d) help to deepen student understanding of the mathematical topic covered. A most important by-product of this process is that the applets and tutorial sheets effectively pass the ownership of their own learning to the student. Students feel that they are discovering aspects of mathematics on their own. Although the applets have to be run from the MathinSite website, the tutorial sheets can be downloaded and printed by the end user. This provides a permanent, takeaway record of the user’s findings. Also available on the website are Lotus ScreenCam movies that give some indication of the workings of the user interface. How is MathinSite different? Many mathematics lecturers try to enhance their students’ learning experience by visualising mathematics. Technologically, this can range from the use of graphical calculators to the use of software such as Derive or Excel. In fact, graphical visualisations have been used in mathematics since mathematics began – predating the use of computer visualisations by thousands of years! So why MathinSite? • Each applet uses a standard Windows-type display (with which most students are familiar) and, further, all the applets have a common interface and require the same interaction. Ease of use is the key. Students quickly learn how to use the applets; they do not have to traipse up the learning curve necessary when using algebra packages, nor do they need to plough their way through expansive graphical calculator manuals. • Each applet is a self-contained single aspect of mathematics (bite-size chunks). It is not possible to be sidetracked into other areas. • Each applet gives immediate interactive feedback to the student so enabling ‘What if …?’ explorations to be carried out. • The software cannot be corrupted by inappropriate data input since the scrollbars only allow input values for which the applet has been tested. • The working of an applet cannot be changed by the end-user. It has a task to do and points to make, and users cannot alter the program to perform other tasks. • Each applet is accompanied by a worksheet. This is useful for lecturers who want their students to use the applets in something more than a haphazard fashion. Obviously the worksheets provided are not mandatory and there will be those academics who want to write their own. • The applets are immediately accessible anywhere in the world at any time from any computer with an Internet connection. This list makes MathinSite appear to be the panacea that many mathematics lecturers have craved. However, such a panacea does not exist. MathinSite can only be considered as one more tool in the armoury of those who are trying to engage students in the learning of mathematics. Also, MathinSite’s contents are necessarily limited by the time limitations imposed upon the author in writing the applets – even with the modularity and rapid application development capabilities of Java. … and how many lecturers can MathinSite replace? None. MathinSite was never intended to replace the vital face-to-face contact between lecturer and student. The applets of MathinSite do not constitute a self-learning package. Their primary use is in enhancing the learning process and deepening understanding by demonstrating mathematical principles either in lectures or tutorials. Since students use a self-contained website, their access to the site is unlimited and so MathinSite can be used for student investigations in their own time – after they have attended the appropriate lecture. Future development What started out as a requirement for software to help students learn mathematics (and, just as important, learn to like mathematics), has grown into the worldwide resource, MathinSite. Needless to say, it is something of a self-indulgence on the part of the author; ‘My students cover this aspect of mathematics so I need to write an applet on…’ In writing the applets and presenting them through MathinSite, however, the hope is that they will be useful to others. If not, there are plenty of other multimedia mathematical resources – some proprietary, some homegrown like MathinSite (many of which can be found, for example, through the EEVL mathematics resource gateway: http://www.eevl.ac.uk/mathematics/index.htm). With the NTFS funding, the content of MathinSite has grown. It is hoped that further funding can be found to ensure continued growth. A more comprehensive version of this article can be found in the Global Journal of Engineering Education (Edwards and Edwards, 2003). References Edwards, P., (1995) A Visual Approach to Understanding Mathematics, CTI Maths&Stats Quarterly Newsletter, 6(1), 2 - 7. Also available from: http://www.bham.ac.uk/ctimath/reviews/aug95/visual.pdf [Accessed 1/12/00] Edwards, P., Edwards, P. M. (2003) Tackling the Mathematics Problem with MathinSite. In Pudlowski, Z. (ed), Global Journal of Engineering Education, 7(1) pp. 95 - 102. UNESCO International Centre for Engineering Education, Monash University, Australia. Also available from: http://www.eng.monash.edu.au/uicee/gjee/vol7no1/EdwardsEdwards.pdf

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