Uses of the Internet in Teaching and Learning of Statistics |
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| Abstract: The purpose of this paper is to explore the importance and advantages of using the Internet in teaching and learning of statistics courses at the university level, by providing instructors and students with examples of hands-on experiment with the Internet. The paper also shows how statistical resources from around the world can be brought into the classroom, and very important it also answers the questions: Why statisticians use the Internet? How statisticians are using the Internet. At the end there are selected web links to a wide variety of resources of use to instructors and students. Introduction The Internet was developed to permit researchers at universities and colleges to freely communicate their ideas and results with others doing similar research. This was accomplished by connecting the universities by an electronic network called the Internet and providing a method for sending messages called Electronic Mail or E-mail. E-mail works fine for simple text messages. However, transmitting results of research often requires the capability of transmitting formulas, graphics, and pictures and occasionally even sound and video. Tools to accomplish this were developed and the Internet, with these capabilities, is called the World Wide Web or, more simply, the Web. Instead of directly transmitting this more complex information between two researchers, say Faisal and Rania, it was decided to allow Faisal to deposit his results on a machine at his institution and let Rania obtain them from this machine. This made Faisal's results not only accessible to Rania but also to anyone else in the world who had access to the Web. This resulted in a remarkable new way to share information. Common usage now uses the terms Web and Internet interchangeably. The enriched Internet was such a success that it was extended to allow the same kind of transmission of information by the general public and industry. Although the Internet has grown to have all of the best and worst elements of any society, it is still a wonderful way to achieve its original goal: to allow academics to freely share information. E-mail still works very much like it did in the beginning and continues to be a natural and useful way to communicate. When we write a letter, we imagine this letter may be kept as a permanent record of our thoughts. For this reason, most of us take a some care in the way we express our thoughts in a letter. E-mail is much more informal--it is not a sin to misspell a word or make a grammatical error. You usually are just writing to ask someone a technical question, help a student, give a colleague a reference to a paper, and so forth. Most of the time, when you receive an e-mail message, you reply and never again look at the message. Somewhat the same philosophy has been applied to putting materials on the Internet. People often put their first thoughts on an issue onto their Web site, almost like a first draft of an article or book. However, unlike e-mail, this material stays where it is and can be viewed by anyone in the world. In this paper we explore the following questions and issues: „h Why statisticians use the Internet? „h What are the uses of the Internet in teaching and learning of statistics courses at the university level? „h Some examples on the use of the Internet in the statistics classroom. „h What are the benefits to the students who use the Internet? „h Encouraging students to use technology in their learning of statistics? „h What are the useful Internet resources for teaching and learning of statistics? Why statisticians use the Internet? Statisticians already have considerable expertise in traditional ICT (Information & Communication Technologies) because of their importance in facilitating data analysis. Statisticians also typically work in relatively small groups, and need contact with other statisticians, so the more recent trend to convergence of communications and information technologies is underpinned by the needs of professional networking and updating. Then although statistics is a small discipline, its applications involve a great range of data and work with a wide variety of subject disciplines and professions. Finally the cost effectiveness and speed of ICT based communications, has led to their adoption, first in the academic and research communities, and now more widely. Uses of the Web for Teaching and Learning of Statistics The Web can be used in many ways to assist both the teaching and learning of Statistics . „h 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. „h 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. „h 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://surfstat.newcastle.edu.au/surfstat/) and „h As the hub around which a course revolves If the number of points of 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, 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 to work through material again at their own pace. Examples of Interactive Demonstrations for Statistics Education on the World Wide Web Bin Width for Histograms The histogram is one of the first procedures discussed when teaching students graphical techniques for describing data. One important consideration for the construction of a histogram is the choice of the bin width (or equivalently the number of bins) for a given dataset. Choosing too few bins often hides valuable information, and choosing too many bins leads to a messy plot from which little information can be obtained. Many students have a difficult time grasping the effect that bin width has on the shape of a histogram. An applet, located at allows students to interactively see this effect. A histogram of the Old Faithful dataset (Azzalini and Bowman 1990) is given when a student loads the applet. Students may interactively change the bin width by clicking and dragging the arrow underneath the bin width scale. The histogram automatically adjusts to the new bin width as the student slides the arrow. The student will quickly see that the bimodal nature of the dataset is hidden when the bin width is too large, and that the histogram reduces to a spike at each data point when the bin width is too small. Influential Points in Regression One important topic often mentioned when teaching students about basic regression analysis is that extreme observations may have a large effect on the regression line for a particular dataset. An applet, located at Interactively shows students the effect of various influential points on regression analysis. When the applet is loaded, students are given a plot of five data points and the resulting estimated regression line, as well as the equation for the regression line underneath the graphic. By clicking the mouse button, students may add an additional point to the plot. Each time the student adds a point, the new regression line is plotted in red and the equation of the new line is given underneath the original regression line equation. Students are instructed to add points close to the existing regression line and also far from the line. Students will learn from this interactive graphical procedure how individual points can affect the regression line and which outliers exhibit maximal effect. Central Limit Theorem One concept that students often struggle with is the central limit theorem. To illustrate this concept in a way that would not be feasible without using computing power, the applet located at The applet performs a simulation in which a user-specified number of virtual dice can be "rolled." Each time the dice are rolled, an updated histogram of the sum of the dice is constructed. Students can study the way the shape of the histogram changes as more observations are generated. When students get bored repeating the dice-rolling experiment only once for each mouse click, they can select to replicate the experiment more times per mouse click -- up to 10,000 -- so that they can see the convergence in "fast motion." This applet also demonstrates that the central limit theorem applies only when the sample size is relatively large. When students roll a single die repeatedly, the histogram will never get bell-shaped -- it will more and more closely resemble the uniform distribution. Similarly, with two dice, the histogram will tend to resemble a "witch's hat" as the experiment is repeated many times. But for more dice, the histogram will tend to take on the satisfying bell shape, allowing students to see the central limit theorem in action. What are the benefits to the students who use the Internet? „h Develop the technical skills required to use the Internet for communication and Information gathering. „h Acquire geographic awareness based on understanding the global nature of Internet connections and communications. „h Improve their ability to learn and understand new and changing information technologies. „h Learn to evaluate the validity of information acquired through Internet Resources. „h Learn to synthesize data acquired through the Internet into a meaningful whole. „h Develop the skills required to rate information for relevence in meeting a specified need. „h Understand and Know How to use at least one Web Browser. „h Understand differences and similarities among search engines. „h Understand how to ue a variety of search engines. „h Develop strategies for finding and evaluating new Internet growth and use. Techniques to encourage students to use technology in their learning of statistics? One of the specific educational goals at many universities is for students to achieve technological competence, by which is usually meant facility with the tools of information technology. Here are some ideas and techniques that will encourage the achievement of this goal. A particularly attractive factor of these techniques is that most are self-assessing: completion of the assignment by the student demonstrates that the student can use the tool or perform the skill. „h Require students to use email to send at least some of their homework, papers, projects, comments, questions, or assessments. A useful assignment is to have students write and mail a narrative evaluation of a paper, reading, or class session they completed. Email can be used effectively by requiring students to submit paper topics early in the term. The professor can simply use the reply function to make comments and suggestions. „h Use email to send students individual assignments or comments and require that they respond to the assignment (even if it means merely printing out the letter or replying to it). Comments about papers, in-class presentations, or current grade status can be sent to students, together with a request for a response. For small classes, unique regular or extra credit assignments can be sent through email only, followed, if necessary, by a brief mention in class ("Did you check your email recently?"). „h Require students to get assignments online. Post assignments or other information on a web page, intranet page, or shared drive folder. Particular sites with pertinent information might be mentioned in class or listed in an assignment or syllabus, with the requirement that students visit them and obtain certain information from them. „h Use electronic reserves. Instead of photocopying materials for library reserves, put those readings on your class web page for students to read. That way, students do not have to go to the library to read the reserve material, several students can read it at the same time, and you can leave it on reserve indefinitely or update it regularly. The electronic format not only gives students practice in using technology, but it can simplify their use of the material by allowing them to cut and paste quotations with their word processor. (Note: Be sure to secure the appropriate permissions to post any copyrighted material. You may wish to ask for permission to post only to the campus intranet rather than to the Internet at large. Get all such permissions in writing and include a declaration of permission and notice of copyright on each page or document posted.) E-reserves can include documents, pictures, video, audio, or links to materials from libraries, museums, or other sites all over the world. „h Require students to search the Internet and make use of one or more Internet sources as part of their research assignments. Books, journals, newspapers, magazines, organizational sites, corporate sites, museums, and a host of other information sources provide a truly staggering amount of useful information. (But plan also to discuss source evaluation with your students because some show a surprising lack of caution in accepting as true whatever they find. As part of their research, you might have them locate some articles on the Net relating to source evaluation or direct them to my article, "Evaluating Internet Research Sources".) „h require students to make use of one or more articles in electronic form as part of their research assignments. These forms are usually on CD-ROM and include encyclopedias, magazines, newspapers, and various abstracts and databases. „h Require students to find research information through other specified technologies, such as online library catalogs, CD-ROM indexes, microform materials, videocassette sources, etc. „h Require students to subscribe to an Internet mailing list relevant to the class and to turn in one or more useful postings together with an evaluation of it and the mailing list in general. You might even require that the students propose a posting of their own. „h Require that all papers be written using word processing software. Require the use of some additional functions, such as headlines or subheads, font changes, drop caps, tables, graphs, inserted pictures, boxes, and so on. Help students to stretch themselves and their knowledge of how the word processor can help them present information in a clearer, more effective way. (Note: Make the requirements specific to the skill you want demonstrated. For example, "Present your data in an outlined table inserted into the text and not attached at the end"). „h Require that students use presentation technology such as overhead projectors, data projectors, presentation software, or „h Include spreadsheet and graphing assignments relevant to your course material. Remember that spreadsheets will do averages, percentages, forecasting, goal seeking, trend lines, graphing, correlation, comparison charts. A physical education class might have students graph times or scores, a business class might chart stocks. Any class that has several grades (quizzes, exams, papers, homework) can require students to keep their own point scores on a spreadsheet and turn it in from time to time. Comment: Not only will the use of a spreadsheet give students technological skill, but it will increase their number fluency, something needed by many students. „h Require students to create their own Web pages and to post their papers or reports to them. Not only will they learn to use technology for the dissemination of information, but they will have a lesson in sharing the fruits of their intellectual labors, and perhaps be more motivated by the thought of a larger audience than the professor. A sampler of „h General Guides to Statistics Resources „h Statistics Lists and Newsgroups „h Search Engines „h Software & „h Online Journals „h Online Texts & Teaching / Statistical Education „h Learning Technology Initiatives in the UK „h History & Context of Statistics „h History of Mathematics Archive: „h Sources of Data „h National & International Statistical Offices: http://europa.eu.int/en/comm/eurostat/serven/part8/8som.htm Recommendations „h The author recommends that all Palestinian Universities offer to statistics teachers as part of professional development a computer literacy training at no cost to the teachers to include the following: „h One should be able to utilize word processing software. „h Be comfortable with installing and configuring common software. „h Be familiar and use regularly a computer modem. „h Be able to access a computer bulletin board or on-line service. „h Be able to send and receive messages, assignments, and exams via electronic mail. „h Be able to upload and download computer files with ease and be able to print from the computer. „h Be able to use Internet and e-mail. „h Be able to use scanner, digital camera, etc. „h The author recommends that statistics educators encourage students to use technology in their learning of statistics using the ideas and techniques presented in this paper. Conclusion Educational institutions must recognize that the world has changed. Employers and students have needs that our current delivery system is not meeting. We face financial constraints that will not quickly disappear, as well as both global and private competition. Doing more of what we are currently doing will not solve these problems. To survive these challenges, we must find new ways to deliver education to our students. The use of academic computing in general and the Internet in particular can contribute to solving some of these problems. The use of technology combined with other measures will dramatically change the nature of the teaching/learning process. References „h Active Learning ( 1995 ). Using the Internet for Teaching. Active Learning, Special Issue, 2. „h Azzalini, A., and Bowman, A.W. ( 1990 ). A Look at Some Data on the Old Faithful Geyser. Applied Statistics, 39, 357-365. „h 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. „h Garfield, J. ( 1995 ). How Students Learn Statistics. International Statistics Review, 63 (1), 25-34. „h Hog, R.V. ( 1990 ). Statisticians Gather to Discuss Statistical Education. Amstat News, 19-20. „h Kumari, S. ( 1998 ). Teaching with the Internet. Journal of Information Technology for Teacher Education, 7 ( 3 ), 363-377. |
Thursday, January 7, 2010
Uses of the Internet in Teaching and Learning of Statistics
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