Students generally focus only on the mechanics of statistical calculations and graphing. They know how to carry out statistical calculations, draw statistical graphs and charts, and use computer software to produce statistical results, but they are unable to express their statistical works as well as interpretation of the statistical findings. To accomplish these tasks, students need to acquire the ability of reasoning with data and statistical ideas. However, the traditional classroom teaching can hardly help them grasp the essentials of statistical concepts. It is believed that more concrete statistical concepts can be vividly illustrated via computer technology. In this paper, the author discusses how computer technology, for example Seeing Statistics(tm), can be employed to elaborate on statistical concepts, promote interactive instruction, and make e-learning more interesting and meaningful.
A thorough grasp of statistical concepts is essential for developing statistical reasoning skills (Cobb, 1991; Bradstreet, 1996). Traditional blackboard classroom teaching can hardly explain statistical concepts in words and diagrams for the following two reasons. Usually, class time is tight in each lesson, and drawing diagrams takes much time, not to mention that some diagrams are not so easy to visualize. Some particular statistical experiments are not easily carried out in real world situations. But with the aid of computer technology, students are more easily convinced of statistical concepts through their experimentation with data and interactive computer demonstration (Ben-Zvi and Friedlander, 1996).
To accomplish these goals, WebCT is an appropriate authoring tool for developing web-based learning materials. It requires little technical expertise of the developer to create new or edit existing learning materials. Using WebCT as a learning tool, students need not have much computer literacy to interact with the electronic learning materials. Some of its main features include:- supporting multimedia learning environments; creating searchable and linkable glossary; providing on-line quizzes with feedback; keeping each individual student's record of learning progress; managing database of student performance; and facilitating student-student and student-teacher communications.
The major weaknesses of web-based learning materials are the bandwidth problem and the traffic jam in the information superhighways (Nott et al., 1995). Students waste a great deal of time in downloading data during an on-line learning session, whereas learning materials stored in CD-ROM format can provide instantaneous responses. One of the major weaknesses of CD-ROM educational software is that its version may not be up-to-date unless the users are well informed of the release of the latest version.
Fuller (1997) summarizes how to use computer technology to enhance statistics teaching and learning. He also points out that effective statistics teaching still relies on its instructional design, instructional delivery and student's learning strategy.
According to one of Maehr's principles on students' motivation to learn (1984), the design of computer-based learning materials should be well structured and task oriented. A good approach to learning is through a sequence of clear and concise tasks and demonstrations. Students are expected to go through the material of each topic in a systematic manner that leads them to building up their confidence and foundation in mastering statistical concepts and skills. Eventually, they should be able to achieve some specific learning objectives at the end of each lesson.
The rapid development of computer technology enables teachers to create a motivating educational environment for students. They appear to be more motivated when they are working with computers because of the game like atmosphere, exciting visual displays and so on as generated by multimedia technology. Once motivated, students can learn more and at a better pace (Hess and Tenezakis, 1970; Linskie, 1977). Computer-aided instruction enables teachers to make good use of texts, graphics videos, sounds and animation to teach statistical concepts. It makes statistics learning more interesting and contributes to an easy understanding of statistics.
Statistics learning can be considerably facilitated by activities that students regard as purposeful and interesting because most teachers agree that purposeful and interesting activity is the most efficient type of teaching and learning. Students are usually active to participate in activities that interest them. These activities can be in any form, for example, exploration of data or data experimentation and so on. The activities should grow out of problems in real-life situations to arouse students' statistical interest and stimulate their statistical thinking. This also leads to superior learning (Strike, 1975).
One effective learning strategy is to allow a student to directly refer to glossary, images, etc. related to their learning queries. The student can choose the sequence of referencing that best suits his/her own interests and abilities. This is the best time to teach concepts as a student makes inquiries (Velleman, 1998). Accessing the required information in this fashion is to employ hypertext technology to establish hyperlinks between referenced materials within the WWW. This enables a student to jump around the hypertext within and outside the same document. Within the hypertext learning environment, a student can explore and interact with knowledge in a non-linear and interactive way using graphics, videos or audio and so on. Non-linear information delivery is more appropriate because human information processing is in non-linear manner (Richards and Barker, 1994).
Moreover, statistics learning involves both its processes and its products (Biehler, 1993). It should not only ask students to learn procedural knowledge but also helps them develop the ability of statistical reasoning. In fact, more emphasis should be placed on the processes rather than the end products in the teaching of statistics because statistics learning by rote does not lead to deeper understanding of statistical concepts but misconception (Bournaud et. al., 1994). Applying Bruner's ideas in statistics classroom, a teacher should not only help students see connections among various concepts but also organize their experiences into meaningful patterns. Thus, besides teaching mean, median and mode-the three ways to measure the central tendency of data, a teacher should give out some data sets having different distributions for students to develop some guidelines for judging which one of the three ways best represents the middle of a data set. Through discovery journey of learning like this, what is learned is to develop the statistical reasoning. This can be easily applied to other problem, as there are no fixed guidelines in problem solving.
Discovered concepts give students deeper understanding and are easier to retain or recall. In practice, discovery learning is so difficult to organize successfully. However, with the aid of computer technology in preparation of computer-based learning materials, discovery learning becomes ideals.
Learning with Seeing Statistics is under each individual student's control. Each student learns at his/her own pace and can repeat any activity as often as needed. Seeing Statistics uses interactive component to explain and visualize statistical concepts and offers students hands-on practice exercises. It has seven core features: Contents, Calculator, Glossary, Search, References, Comments and Site Help. Contents give an overview of the topics in a lesson. Calculator is an electronic device for simple calculations. Glossary provides definitions of statistical terms. Search allows audience to search a particular term throughout the book. References provide a listing of statistics books. Comments enable the author to hear about what the audience's comments and/or suggestions.
Seeing Statistics enables students to discover statistical concepts, explore statistical principles and apply statistical methods and techniques. Learning takes place in student participation in activities. Concepts discovered by students are easier to retain and recall from memory. This can be readily integrated with understanding of other statistical topics.
Students can use the following interactive tool (see Figure 1) to visualize how changes of mean and standard deviation affect the location and the shape of a normal density curve. This tool allows them to choose different means and different standard deviations to gain true understanding through their hands-on learning experience. Students can see the effect of their actions while they are working.
Figure 1: Normal curve with different means and standard deviations
Figure 2: Area under Normal curve
Figure 3: Sampling Distribution with n=1 and n=2
Figure 4: Normal Approximation to Binomial Distribution
Figure 5: Central Limit Theorem
Figure 6: Exercise
Figure 7: Application
Helping students develop statistical reasoning, teachers should pay close attention to the instructional design and delivery of statistics education. Discovery learning is always more effective than learning from lectures. Students go through their own journey of learning to gain a true understanding of statistical concepts. The concepts discovered are easier to recall or retain, and more readily integrated with practical applications of statistics. However, discovery learning is sometimes hard to organise successfully. With the aid of computer technology, more concrete statistical concepts and principles can be illustrated by providing students with hands-on learning and practice experience.
Trademarks Notice: Seeing Statistics® is a trademark under licence.
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Author: Ken W. Li, Hong Kong Institute of Vocational Education (Tsing Yi) Phone: 852-2436-8573 Fax: 852-2435-1406 Email: kenli@vtc.edu.hk Please cite as: Li, K. W. (2001). Helping students develop statistical reasoning through Seeing Statistics. In L. Richardson and J. Lidstone (Eds), Flexible Learning for a Flexible Society, 420-427. Proceedings of ASET-HERDSA 2000 Conference, Toowoomba, Qld, 2-5 July 2000. ASET and HERDSA. http://www.aset.org.au/confs/aset-herdsa2000/procs/li.html |