# Teaching Mathematics with Online Tutorials

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3 The 5-point Likert scale has 1 meaning very poor, 5 meaning very good, and 3 representing neutral. As can be seen clearly from Fig 2, there is a good correlation 1 between student and staff experiences of the technology, and, with the exception of audio quality 2, application sharing, web tours and the webcam, all features got a rating of at least 4 on average. There was an overall technical quality of 4.2 for both staff and students alike. Fig 3 shows the evaluations of staff and students of the Elluminate Live! tools from a learning perspective, throughout the course of the trial. There is a noticeable divergence between the student and staff viewpoint on the usefulness of webcams and of polling, but otherwise there is a good correlation. Again, with the exception of webcams and polling, the responses are at least 4 for both staff and students. With regard to webcams, two things are worth noting. There were relatively few sessions involving webcams and the version of Elluminate Live! used in the trial allowed only a single webcam at a time. This was usually the tutor, which perhaps explains the discrepancy between student and staff perspectives on the issue! The student and staff evaluations of the overall technical quality and learning experience are positive, although not so positive as in survey 1. This is to be expected (especially for the staff results) as all participants were surveyed only once in the final survey, whilst the in-trial results are naturally weighted by the number of sessions held, which are likely to be higher for those who had positive experiences. Fig 4 also shows aggregate results for overall interaction, for convenience, and for comparison with face-to-face (F2F) tutorials. Whilst the view was that online tutorials provide positive interaction experiences, it is perhaps unsurprising that they do not compare well with their F2F counterparts. It is however interesting that both student and staff rate e- tutorials as effective as F2F as a learning experience. The second survey also surveyed those students who had not participated in the online tutorials, so as to ascertain their reasons for not having done so. Fig 5 shows a chart giving the principal reasons cited in the survey. Whilst not Fig 5 Reasons given by students for not participating in the e-tutorial trial Fig 3 Evaluation of the Elluminate Live! tools from a Learning perspective (5 point Likert scale) Fig 6 Optimal tutorial time (in hours) This general picture is supported by the results of the second survey at the end of the trial. Fig 4 shows the results for the second survey. Fig 4 Overall results for the second survey on a 5-point Likert scale 1 We have not conducted a rigorous statistical analysis of the results. 2 The trial used Elluminate Live! v. 8.0; the quality of the audio has been improved in later versions of the system. 14 Teaching Mathematics with Online Tutorials Ben Mestel, Gareth Williams, Tim Lowe and Gaynor Arrowsmith

5 One way round this limitation that has been used by several tutors is to share an application which gives a scrolling whiteboard. However, application sharing is one feature that is very much bandwidth dependent and can be a frustrating slow and disjointed experience for participants on low-speed connections. It is also possible to increase the Elluminate whiteboard size, but this requires action by both staff and students, which can be problematic. Fig 10 Positive comments classified by topic expressed by students during the trial. sessions, as well as the content and preparation of the tutorials by the tutor. The whiteboard was commented favourably on, as was the audio and the features of the Elluminate Live! software itself. However, students audio experiences varied greatly and, in fact, from Fig 11, it is clear that sound problems (including echo) formed the largest number of issues raised by students during the trial. It is worth recording that the second most common cause of complaint was nothing, again illustrating the generally positive student experience of the software. Other issues raised were connection problems and the difficulty of logging on, application sharing and a lack of interaction (despite many students positive experience of interaction during the e-tutorial). Fig 11 Negative comments classified by topic expressed by students during the trial Another major issue was the whiteboard: technical problems, functionality and the tendency of the whiteboard to become cluttered. Since the whiteboard is of major importance for mathematics and statistics teaching, we deal with it in detail. Mathematics and statistics teaching requires extensive board use and one complaint of students and tutors alike was the lack of space on the whiteboard. Although Elluminate Live! has an unlimited number of whiteboards which can be used, navigation between the boards is limited and, in particular, it is not possible to view more than one board at once, even as a thumbnail, so that it is not easy to refer to previous work as one might do, for example, during a face-to-face class. Elluminate Live! has few mathematically oriented tools and the mathematical symbols are insufficient for any serious mathematical work. There is a graphing calculator which can be useful for simple graphs, but for anything sophisticated one would use the application sharing functionality together with a graph drawing program or computer-algebra system. For writing mathematical notation on the whiteboard there are three principal methods, all of which are useful in different circumstances. It is perhaps worth noting that the first two methods require the use of a mathematical typesetting package external to Elluminate Live! It is not clear that such a skill may be reasonably expected of a student who is studying, say, an introductory level course. First, one can prepare mathematical material using, for example, the Beamer class in LaTeX [6], and convert the resulting PDF slide show to the whiteboard. MS PowerPoint may also be used. This is often the most convenient manner and gives structure to the session. However, it is not a convenient method for producing mathematical material on the fly. Second, one can use a mathematical typesetting system (e.g. LaTeX or MS Word) to produce mathematical notation in real time, which is then pasted onto the whiteboard. This can be an effective way to write mathematical notation onto the whiteboard, provided one can typeset mathematics quickly and accurately. However, the third and most widely used method is to write on the whiteboard using a digital pen, most conveniently using a tablet PC. Although some of the tutors successfully used other modes of input (such as USB graphics tablets), the use of a tablet PC seems to be the most successful, both from a quality-of-output viewpoint and from a convenience-for-the-tutor viewpoint. One of the most potentially useful features of Elluminate Live! is application sharing, certainly for computer scientists, but also for mathematicians. During the trial, one of the tutors successfully used the application-sharing feature to teach Mathcad to students [7]. Conclusions Conducting online tutorials in the mathematical sciences using a synchronous communication software tool such as Elluminate Live! can be an effective means of distance learning in mathematics and statistics at university level. 16 Teaching Mathematics with Online Tutorials Ben Mestel, Gareth Williams, Tim Lowe and Gaynor Arrowsmith

6 This is consistent with the results of other smaller scale trials using different systems (see [8], [9]). Despite some technical problems (audio, connectivity, whiteboard design), both students and tutors liked the medium, particularly for the interaction it offers and the convenience of not having to travel to tutorials. Provided important issues of disability and staff preparation time can be addressed, there is likely to be a steady increase of such environments for teaching mathematics and statistics. In the words of one student, Fantastic!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! References The Elluminate Live! Website. Available via: [Accessed 22 April 2010]. MathTran website. Available via: [Accessed 22 April 2010]. Sitmo online equation editor. Available via: [Accessed 22 April 2010]. The Further Mathematics Network. Available via: [Accessed 22 April 2010] MSOR Connections Vol 11 No 1 Spring Term 2011 Lissaman, R., de Pomerai, S., and Tripconey, S. (2009) Using live, online tutoring to inspire post 16 students to engage with higher level mathematics. Teaching Mathematics Applications vol. 28: The LaTeX Beamer class. Available via: [Accessed 22 April 2010]. Kirk, A. (2009) Action Research into Online Support for Computer-Based Work: Examining Student - Tutor Interaction. Proceedings of the Fourth International Blended Learning Conference 2009: Loch, B. I. and McDonald, C. (2007) Synchronous chat and electronic ink for distance support in mathematics. Innovate: Journal of Online Education vol. 3 (No. 3). Reushle, S. and Loch, B. I. (2008) Conducting a trial of web conferencing software: why, how, and perceptions from the coalface. Turkish Online Journal of Distance Education vol. 9 (No. 3): Available via: [Accessed 22 April 2010]. Teaching Mathematics with Online Tutorials Ben Mestel, Gareth Williams, Tim Lowe and Gaynor Arrowsmith 17

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