Mathematics education (2005-present)

Work in this area is concentrating on the following areas

Multimedia Learning Resources (2005-present)

Background and motivation

There is a growing need to provide students with learning resources that will help them make the transition from the mathematical skills required at high school to those required at the tertiary level. This problem is made worse by the fact that many students taking service courses in mathematics at university have poor mathematics knowledge and skills, having failed to master high school mathematics.

Students commencing science and engineering degrees at the University of Wollongong are given mathematics skills test in the first and fourth weeks of session. The skills test consists of twenty multiple-choice questions. A mark of 16, or higher, out of 20 is considered to be a pass. Experience shows that students who do not reach this level by the second skills test struggle to pass the course because of their poor ability in performing basic mathematical manipulations and their poor grasp of fundamental concepts. Student answers on the quiz provided clear evidence of a need to create learning resources to assist students in gaining and/or refining basic mathematics skills. In fact, in 2004 only 15% of the class scored 16+ on the first test, indicating that 85% of the class did not have the required command of basic skills.

To assist students master the techniques from high school that are used in their first year at university we have created learning resources that combine visual and audio information. The resources are not intended to provide an introduction to the mathematics, rather they are aimed at providing a theory refresher and review. These solutions permit students to see the development of a solution to a mathematical problem in a step-by-step manner. An audio commentary on each worked solution assists learning by providing students with an explanation of the developing solution. Two methods of video capture were investigated. The first used eBeam, a system to capture pen strokes from a whiteboard. The second method used a video camera mounted on a copy stand. These resources are made available through the course e-learning site, giving students the flexibility of accessing them as and when they need to.

The visual component shows the step-by-step development of the solution. In the audio track the solver explains the evolution of their thought processes as they tackle the question. We expected that this would help students understand the thought processes that lead to the first line of a solution and how to think about problem solving. Research has indicated that the combination of visual and audio components reinforces learning by providing multiple connections that do not occur when the audio is absent (Miles & LeeSing 1999; Mayer 2001; Moreno & Mayer 2001; Veronikas & Maushak 2005). To assist students in learning how to solve mathematics problems, we developed a format in students can watch a video showing the worked solution being developed in real time whilst simultaneously listening to an audio track that explains the thought processes of the solver as they both start and develop their solution. Students may play the video as many times as they wish and may move forwards and backwards within the solution. They may choose to play the solution to a particular point, pause at this place and attempt to complete the rest of the solution themselves. The can then restart the solution and compare their working against that of the remainder of the worked solution.

These resources were developed in 2005 and used for the first time in Autumn 2006. At the end of session students were surveyed regarding their use of the resources. Student comments included

In week one students who were to use the resources averaged 9.7/20 on the test whereas students who would not use the resources averaged 12.6/20. This difference was statistically significant (t74=2.175, p=0.033). In week four the two groups of students averaged 11.95 and 12.4 respectively. This difference was not significant. A paired t-test analysing the change in marks between the two tests found a significant difference between those who used (mean of differences = 2.25, sd = 2.97) compared to the non-users whose marks declined on average (mean of differences = -0.2, sd = 2.97). This equates to about a 12% change in approximate grade. More significantly, this is a change from a fail grade to a pass grade. Thus, by the end of the fourth week, use of the resources allowed the weaker students to catch up with the stronger students. This is an important finding as many teaching innovations are only used by the better students; it is often difficult to provide resources for weaker students.

Although our initial concept was to distribute these resources through a WebCT site we have realised that other mechanisms for their distribution exist such as CD-ROM, DVD and iPod. In fact, we received a number of requests from students to make it easier for them to save the videos.

  1. Mayer, R. (2001). Multimedia Learning. New York: Cambridge University Press.
  2. Miles, C.A., & LeeSing, A. (1999) The relative effectiveness of audio, video, and static visual computer-mediated presentations. Canadian Journal of Education, 24(2), 212-221.
  3. Moreno, R., & Mayer, R. (2001). Getting the message across: The role of verbal redundancy in multimedia explanations. Retrieved April 25, 2006 from
  4. Veronikas, S.W., \& Maushak, N. (2005). Effectiveness of Audio on Screen Capture in Software Application Instruction. International Journal of Educational Multimedia and Hypermedia , 14(2), 199-205.

Published papers

    Refereed journal papers

  1. E. Aminifarp, A. Porter, R. Caladine and M.I. Nelson. Creating mathematical learning resources --- combining audio and visual components. ANZIAM Journal E 47, pp C934-C955, 2007.
  2. Refereed conference proceedings

  3. Elahe Aminifarp, Richard Caladine, Anne Porter and Mark I. Nelson. Online Solutions to Mathematical Problems: Combining Video, Audio and Stills on the Web . In T.C. Reeves and S.F. Yamashita, editors, Proceedings of E-Learn 2006. World Conference on E-Learning in Corporate, Government, Healthcare & Higher Education, pages 2-8 (on CDROM), Association for the Advancement of Computing in Education, 2006. ISBN 1-880094-60-6

Real Time Communication Technologies: Increased functionality to enhance media-rich interactions in teaching and learning (2006-present)

Background and motivation

Modern technologies provide new approaches to tertiary education and will be an increasing component of the educational experience in the future. Their use poses a significant challenge to the design and delivery of teaching and learning as many teachers and students are unfamiliar with them in this context. Over the last decade there has been a very rapid expansion in the capability and usage of Information and Communication Technologies (ICTs) in teaching and learning. To use them effectively there is a need to understand how different ICTs can be applied to learning and teaching. Videconference, Access Grid and Web Conference Applications (WCAs) are now available for use in higher education.

Videoconferencing is a mature technology in teaching and learning. It has been since the early 1990s at the University of Wollongong. Newer technologies such as Access Grid and Web Conference Applications offer additional functionality. These include shared eWhiteboard, presentation sharing, application sharing and saving of resulting files. These functions enhance synchronous teaching and learning and, when recorded for later use, asynchronous learning. Web Conference Applications (WCAs) are defined here as suites of Web-based applications that permit sharing of applications, a computer-hosted whiteboard (or eWhiteboard), videoconference and other collaborative tools. As Web Conference Applications are synchronous, students can take advantage of them to discuss, question and interact. In this way the technology can assist in achieving deep learning. Moreover, if the conference is recorded the files can be used for other purposes such as revising the subject. For clarity the three technologies, videconferenc, Access Grid and Web Conference Applications are referred to here collectively as Real Time Communication (RTC) technologies.

The main motivation to replace video conferences by other Real Time Communications was that videoconference is often limited to discussion between participants and/or short presentations; RTCs offer wider variety of educational tools, such as eWhiteboards and presentations. Furthermore RTC technologies have the potential to increase the efficiency and effectiveness of teaching and learning for a distributed cohort of students. For instance, RTCs can unite a teacher based at one location with students at a number of campuses into a synchronous class, providing access both between the teacher and the students and a mechanism for students' interaction at different campuses.

Our research

We have compared the technologies a view to recommending which ones to implement for teaching and learning (Aminifar et al; 2007). This research has led to the decision that WCAs will not be used in teaching and learning for the next 3-5 years. Video conferencing will be used for teaching and learning for at least the next 3-5 years. During this time further evaluation will determined if Access Grid can replace videoconference for teaching and learning. Within the same time frame, it is also proposed to combine videoconference with technologies that permit the sharing of eWhiteboards and applications. There will be an ongoing evaluation of these developments.

In (Porter et al; 2007) we describe a twenty-four month period in which the School of Mathematics and Applied Statistics at the University of Wollongong moved from first hearing about access grid rooms and finding out what they offer to installing and using an access grid room (AGR) for teaching and research collaboration. We report on the differences between what we had planned to happen and what transpired in practice and account for these differences.

Published papers

Refereed conference proceedings

  1. E. Aminifarp, R. Caladine, A. Porter and M.I. Nelson. Beyond Videoconference: Increased Functionality to Enhance Media-Rich Interactions in Teaching and Learning. In G. Richards (Editor), Proceedings of World Conference on E-Learning in Corporate, Government, Healthcare, and Higher Education 2007, pages 6985-6990, Association for the Advancement of Computing in Education, Chesapeake, VA, USA, 2007.
  2. A. Porter, M.I. Nelson, E. Aminifarp, G. Williams, and R. Caladine. Access grid rooms: the plan, the reality. In C.S. Lim, S. Fatimah, G. Munirah, S. Hajar, M.Y. Hashimah, W.L. Gan, and T.Y. Hwa, editors, Proceedings of the 4th East Asia Regional Conference on Mathematics Education 2007 (EARCOME 4), pages 285--291. School of Educational Studies, Universiti Sains Malaysia, 2007. ISBN 978-983-2700-45-46.

Highlights of research in mathematics education

My collaborators in mathematics education

Ms Elahe Aminifar 2005-PresentMultimedia resources Real Time Communication Technologies  
Dr R. Caladine. 2005-PresentMultimedia resources Real Time Communication Technologies  
Dr A. Porter. 2005-PresentMultimedia resources Real Time Communication Technologies  

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Page Created: 25th April 2007.
Last Updated: 7th March 2008.