Weaving the Web into Learning and Teaching StatisticsEdwin Redfern
University of Leeds, UK
This article was published in the February 1999 issue of the CTI newsletter Maths&Stats and is re-printed here with permission from the publisher and author.
The Internet has in a short period of time developed into a widely used and versatile hypertext system which has the potential to be a valued addition to the facilities we have available for teaching statistics and a source through which students learn about statistics.
The TLTP program enabled the development of a large source of computer based learning materials. The STEPS project (Bowman et al 1998) was one that contributed to this resource base through the development of 37 standalone modules. Each was designed to introduce or revise a small set of statistical concepts through a problem. One of the problems not fully addressed up to now is how to integrate this material into a teaching environment. Another of these has been how to find time in a traditional course for the use of such material. Knowing that such software is freely available is only the first step. To fully exploit its potential each module needs to be explored, evaluated and its use built into a balanced teaching program. The different modes of learning such modules demand from the students suggest that this is not a formality.
The MEANS project (http://www.maths.nott.ac.uk/rsscse/means/means.html) among its findings emphasised the importance of a practical emphasis in the teaching of the statistics as it provides the source from which theory develops. It was also argued that there should be a more radical approach to assessment and the use of a wider range of techniques, ones that will be more in keeping with the stated aims and objectives of statistical education. This is especially relevant to transferable skills, e.g. communication and listening skills of the type associated with statistical consultancy, working in a team, etc.
This article explores one strategy for addressing some of these issues by describing a first year Joint Honours Statistics course at Leeds University designed around the STEPS material in which the web was used as the linking medium between Lectures, the STEPS modules, MINITAB and other material.
Uses of the web
The web can be used in many ways to assist both the teaching and learning of Statistics (see Figure 1).
Figure 1. Ways in which the web can assist both the teaching and learning of Statistics
As a means of storing material
Handouts, exercise sheets and solutions can be placed on the web as a useful backup resource for students. The amount of paper based information that is given to students can be reduced, with the added advantage that the material is always available without continual reference to the teaching staff.
As a resource for material and information to support the lectures
Lectures are by nature limited in length and the students' needs vary depending on their natural abilities in understanding and developing a comprehension of ideas. The web can therefore be used as a source for further examples on the material covered and supplementary and alternative explanations of concepts. The STEPS glossary (http://www.stats.gla.ac.uk/steps/) is an example of a useful source of definitions.
As a source of explanatory material
Taking the above one stage further, fully exploiting the potential of hypertext and dynamic Java applets leads to the development of on-line texts. Good examples of this are Keith Dear's SurfStat (http://u2.newcastle.edu.au/surfstat/main/surfstat.html) and David Lane's Virtual Lab in Statistics (http://www.ruf.rice.edu/~lane/rvls.html).
As the hub around which a course revolves
If contact between teachers and students is reduced then the web can serve as the focal point of contact between members of the course. It can be easily updated to inform students of activities, deadlines and other issues related to the course as it progresses. It can provide links to interactive learning material, and can contain instructions for using a statistics package and supporting material. Lecture notes can also be made available as a useful backup resource for students allowing them to work through material again at their own pace.
Statistics through application
Statistics through application is a first year course at Leeds University. It is designed to explore and develop a more thorough understanding of some of the basic principles of statistics by using examples and case studies to place them in context. It does this by using some of the STEPS modules (Bowman et al 1998) to revise and extend ideas met in other courses. The use of the different modules is best described through a short summary of the assessment which was done through essays based on themes which can be explored by a range of different modules. These were:
Students are introduced at various stages of their introduction to statistics to some of the principles of exploring data. Frequency tables, histograms, mean and median are part of the National Curriculum. Box-plots are included in some A-levels. This range of tools is developed and extended in introductory university courses to include stem and leaf plots, scatter plots and probability plots. To develop this theme, students are asked to work through at least three of the STEPS modules that explore this theme (Birds of a Feather I, Exploring a Pharmaceutical Company's Behaviour, Exploring a Pharmaceutical Company's Environment, Exploring Dyslexia, Rainfall [Numerical and Visual]). The choice is left to them and facilitates an extended range of subjects making the marking of the resulting essays a more enjoyable task. Having studied the material students are asked to reproduce the analyses in MINITAB and write a report describing the tools and techniques for exploring data, illustrated by examples from the modules.
Estimation, variability and decision making
The principles of hypothesis testing and estimation are covered in The Skinfold Thickness, Birds of a Feather II, Angina, Trials and Tribulations, Rats and IgE modules. These cover a range of issues such as confidence intervals, determination of sample size, estimation, transformations and hypothesis testing as appropriate to the specific problems being addressed. Access to the data for analysis in MINITAB together with macros for simulations associated with the specific problems and for plotting power against both sample size n for fixed standardised scientific error, and standardised scientific error for fixed sample size, was made available.
Earthquakes, plantain and traffic flow
Based around applications of the Poisson distribution this essay is based on the principles explored in the spatial patterns module and data available on the Internet about earthquakes.
An additional part of the course is group based learning. In this the students are formed into groups of 5 and work on an open-ended project. On completion they must submit a single report, a diary of meetings (summarising discussions, decisions and progress) and make a presentation to other class members. Assessment is based on all these aspects and also includes an element of peer assessment.
To free time for the open learning approach only 8 formal lectures were given. These included time for discussion of transferable skills such as report writing. This poses a problem due to the reduced amount of contact. This was overcome by setting up a web site (http://www.amsta.leeds.ac.uk/~edwin/m1830.htm) as the focus point for the course. This was used as a source of information and backup material, as a means of guiding the students on what they should be working on at any stage, and as a means of communicating messages to the students. The other key feature was that the STEPS modules could be launched from links on the web pages.
Construction of web material
This is now relatively easy to do and the problem can be addressed in several ways. Information prepared in TEX, Word97, Excel97 and PowerPoint97 can be easily converted into HTML code. In the case of TEX we use the LATEX2HTML converter developed by Drakos (visit http://www.cbl.leeds.ac.uk/nikos/personal.html) while all the programs in the Microsoft Office 97 suite include the option to save as HTML code. Like most automatic converters the code needs to be edited to enhance the display and tailor it to the users preferences, but a large part of the task is ready almost instantaneously. The code can be edited using the WYSIWYG editors available with Netscape and Internet Explorer, which make some of the tasks like setting up additional links very easy. Note that the final tweaking of the pages' appearance will need to be done by editing the HTML code.
The reaction of the students to this type of teaching was very positive. They particularly liked the freedom to organise their own learning. The access to the web site meant that information was there when required and could not be lost. The use of email meant that they felt freer to ask questions. They found that they had to work harder but most felt that they were learning more as they had to develop their own notes rather than simply record and work on information supplied in lectures. Surprisingly, perhaps, attendance did not drop off from the few lectures presented even towards the end of the course.
The STEPS modules were considered to be an interesting way of learning about statistical concepts, particularly the scope for seeing similar topics in different real situations. Asking the students to duplicate the results in MINITAB for inclusion in the essays reinforced the learning and the application of the ideas. The pages within the site giving guidance on doing this were considered to be useful and successfully avoided the need to spend time in lectures or practical sessions teaching how to use the package. It was consistently used in lectures to demonstrate the principles of data analysis and interpretation.
Structure of the site
The site was divided into three sections. There was the main course outline, statistical support material and a section on operational matters. The latter was intended to support the use of STEPS and MINITAB and provide information about and reminders of what was expected in each of the essays. It also contained details of groups, tutorial times and links to supporting material for the group project.
Figure 2. An example of the weekly student guide
The main feature of the site was the week by week guide to the students of what is expected of them. The example shown in Figure 2 is for the first week of the course. It includes the slides from the lecture, and links to the STEPS module Birds of a Feather I.
Students logged onto the network at Leeds can launch the module simply by clicking on the link on the page. The data from the module is also available to the students on the Leeds network and the description of the MINITAB worksheet is on one of the web pages. The Student notes for the STEPS module have been converted into a web page to which the students can also link.
There are several pages which give support for the use of MINITAB. Figure 3 shows the contents. These cover the relevant MINITAB menus, how to access the package and its operation and how to take information into Word for preparation of the report.
Figure 3. Facilities available in MINITAB
The layout was designed on the basis of frames so that the menu to the main options was always available on the left hand side. This had the further advantage that only the front page could be bookmarked ensuring that the students always passed the message page.
Students' learning benefits
The crucial issue is the benefits of using such a mode of teaching. There was clear evidence in the essays submitted that the students were learning not only about the statistical concepts but about how they were used in problem situations. It allowed students the freedom to express themselves and explore extended ideas related to the theme. Unlike an examination situation feedback was given on all work submitted which the students found extremely useful. In particular it allowed the possibility of correcting misunderstandings in fundamental concepts which is not usually possible following an examination.
Unexpected interesting features were the range of ideas discussed in essays resulting from many students feeling they could extend beyond the limitation of the material covered in the project. Several students also used the Internet to search for more material. An interesting example of this was the group that produced a novel analysis of sentence lengths using quality control methods based on a paper they had stumbled across on the Internet. The methods, which they had briefly been introduced to in an earlier course, were correctly applied and interpreted and the presentation included both an assessment of the paper they had found and a comparison with the more usual two sample tests the other groups covered. This willingness to explore had taken them beyond the scope of what was intended, but had been a valuable learning process to them.
Using the web as a pivotal medium for integrating computer based learning into an organised course has proved to be an interesting and beneficial exercise. It was largely well received although some students found the self-discipline required difficult. They also said that it required more effort on their part but it was usually rewarding and they felt that the learning process was good. This was supported by the evidence in their work. From the viewpoint of the lecturer it had the advantage of bringing one closer to the individual students, through regular email and personal contact. The amount of formal lecturing was reduced to less than 40% but was replaced by a different kind of support for the learning processes. It is clear that this form of teaching has many benefits for the students, however it does not produce large savings in teaching effort. It is however an interesting alternative adding to the variety in the learning experience. It is clearly not suitable for all courses to be delivered in this manner. Indeed there is a strong case for different modules within a course to be delivered in a range of styles appropriate to the content. There is, however, scope for some of the less comprehensive types of web use described above being of benefit to all courses as a support.
Bowman A., Gilmour W. H., Constable G., Davies N., Gilmour S. G. and Redfern E. J. (1998) Computer-based learning in statistics: a problem solving approach. The Statistician 47, 349-364.
UniServe Science News Volume 13 July 1999
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