A self-learning package in elementary number theory for HKIED students with the WWW: Its rationale and difficulties in the design and implementation
Yui-Kin Ng, King-Shun Leung and Yiu-Kwong Man
Department of Mathematics
The Hong Kong Institute of Education
Millions of people now have access to the Internet, and the number is increasing every day. The World Wide Web (WWW) is the most visible, graphical and fastest-growing part of the Internet. The role of education in this domain has been studied in recent years.
Some have tried to improve the instruction process through appropriate integration of technology via the WWW. Does the access to the WWW, which can be regarded as an Information Superhighway, deliver the anticipated renewal of teaching and learning? If so, under what conditions? Or to what degree? In this paper, we will focus our attention on the teaching and learning in mathematics and provide a preliminary exploration of the above questions.
A self-learning package in elementary number theory with the WWW has been developed for the pre-service teachers in our Full-time Certificate of Education (Primary) Course at HKIEd. In this paper, we will also explain our rationale in choosing the topics and the difficulties in our design and implementation.
Millions of people now have access to the Internet whose development has initiated a revolution in communication that provides a new way for delivering instruction. As noted by Smith and Bebak (1996), the World Wide Web (WWW) is the most visible, graphical and fastest-growing part of the Internet. The role of the WWW in education have been studied in recent years (See, for examples, Buchanan, 1995; Day, 1994, 1995; Doerr and Hecht, 1995; Golden, 1994; Kelly and Wiebe, 1994; Lindroth, 1996; Shepardson, 1995; Stahl et al., 1995). Some (say, Barron and Ivers (1996)) have tried to improve the instruction process through appropriate integration of technology via the WWW while some (such as Tergan (1997)) have argued that the theoretical assumptions pertaining to the inherent potential of hypertext-based systems as media between text and knowledge basis to support new forms of learning are misleading. Does the access to the WWW, which can be regarded as an Information Superhighway, deliver the anticipated renewal of teaching and learning? If so, under what conditions? Or to what degree?
In this paper, we will discuss the rationale and difficulties in the design and implementation of a web-based self-learning and Chinese-interfaced package in elementary number theory for the pre-service teachers taking our Full-time Certificate of Education (Primary) Course at the Hong Kong Institute of Education (HKIEd). By doing so, we hope it can shed light on the exploration of the above questions.
All pre-service teachers in our Full-time Certificate of Education (Primary) Course at HKIEd are required to take the module "Introduction to mathematics" which aims at broadening the pre-service teachers’ mathematics knowledge so that they can have greater confidence in teaching primary mathematics. The module comprises four main components: propositional logic, elementary set theory, elementary number theory and geometry. Feedback from the students taking this module shows that elementary number theory is often regarded to be the most difficult one amongst the four topics. As the teachers of this module, we are interested in what other feasible modes of delivering instruction, in addition to the tradition mass lectures and tutorials, will support their learning of this topic. In this connection, we decided, in a recent project funded by the Teaching Development Grant, to implement a web-based self-learning, interactive and Chinese-interfaced package in elementary number theory.
It is commonly believed that there are at least three keys to the educational value of the WWW that are important to the instructional design: Hypertext, delivery of multimedia, and true interactivity (Starr, 1977). Some, for instance Jonassen (1990), believe further that the network-like representation of a subject matter in hypertext and the kind of links between information units which support associative browsing correspond to the structure of human knowledge and basic principles of the functioning of the human mind. Elementary number theory is a topic with relatively nonlinear structuring which corresponds best to the presentation of the subject knowledge in the hypertext format.
As Starr (1997) and Quinlan (1997) have noted, apart from deciding on the students' needs and the content, essential considerations for successful instructional design on the WWW must include the Web design features. The cross-platform distribution is one feature that makes the WWW an attractive medium for delivery of instruction. Although we no longer has to worry about producing separate versions of a program for different platforms such as Dos, Windows 3.1, Windows 95, and Macintosh, we are still required to consider the complexity arising from different versions of web browsers. For instance, in order to make sure the Traditional Chinese fonts can be seen by using different browsers, we decided to typeset almost all of our course material in Graphic format instead of Text format (see Figure 1). In designing our webpages, we also follow the design guidelines recommended by Aronson (1994) and Lemay (1995):
A criterion for effective teaching and learning is whether we are able to make material to be taught both interesting and stimulating. Merely drill and practice derived from a text-based format should be prevented (Kennedy and McNaught, 1997). We tried to deliver the course material in a stimulating classroom format . Students browsing the webpages can imagine themselves as if they were attending a tutorial with a mathematics teacher called Gauss. The content are explained, as suggested by Ramsden(1992), by using clear and appropriate language.(See Fig. 2 and 3).
In order to provide opportunities for students to learn by doing, the package consists of some interactive exercises which can simulate students’ applying what they have learned from the courseware to solve similar problem. For example, in the package there is an interactive Jave program testing students’ applying the Euclidean Algorithm to find the GCD of two natural numbers, which would otherwise done by pencil and paper in the traditional learning mode.
Dynamic teaching is another feature of our package. For instance, an interactive Java program illustrating the 'terminating criteria' of the Method of Eratosthenes Sieve, which is difficult to be explained by using chalk and board, is incorporated in our package (see Fig. 4)
Difficulties encountered during the design and implemenation of the web-based self-learning package
Although we have typesetted the course material in Graphic Format, which is indeed a very time-consuming job for us, it doesn’t mean that all of the display problems arising from the diversity of the versions of the browsers have been solved. It is almost an impossible task to ensure the Java programs being support and the display effect being not distorted by all versions of the browsers. Difficulties in designing the package also resulted from the fact that the users have control over many display features on the screen and can override the designer’s setting. For examples, the status line at the bottom of the screen will normally display the pathway and filename of the linked page when the cursor passes over the link and it may thus give the students hint to select the correct response. Also, the students can use BACK to reselect the answer when doing the quiz. We are pressing for a solution of this problem if we want to get reliable students’ results in the quiz.
The number and size of elements in the package will affect the access time while the multimedia components (for graphics, audio, animation, etc) are always of big size. There is always a tension between the minimization of the large files (for graphics, audio, animation, etc) and the maximization of the multimedia components. A compromise is that only those that can significantly enhance the program are used.
3. Concluding remarks
The Internet is a tremendous resource that in the coming year WWW will continue to change the structure of the classroom, extending it beyond a room to a much greater cyberspace, as well as the structure of curriculum, extending it beyond a textbook to hypertext/multimedia-based websites. It is hoped that the above discussion will assist instructional designers in their development of effective websites.
Hypertext, multimedia as well as interactivity are three key features of WWW that afford tremendous opportunities for delivery of instruction. Nevertheless, there are challenges that must be resolved principally. For instances, there are empirical evidences against the assumption that hypertext structure will promote the acquisition of structural knowledge (Joanassen, 1993) or induce learners to adopt a self-regulated constructive learning strategy (Tergan, 1997); the positive effect of using interactive multimedia courseware as an effective teaching or learning aid (Tergan, 1997). It is in fact one of our initiatives to implement such a hypertext/multimedia/interactive courseware so as to compare it with the traditional lecture and tutorial mode of learning of elementary number theory although the collection and the analysis of the students’ feedback are still in progress.
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