Natural Sciences: Mathematics on the WWW
Heikki J. Mäenpää
Tampere University of Technology
Digital Media Institute
Introduction to Pythagoras
Hypermedia laboratory of Tampere University of Technology is actively developing distance learning material for mathematics. One of the current projects is to build an environment for learning mathematical statistics. 'Pythagoras' project is a part of larger 'Distance Learning in Multimedia Networks' project and done in co-operation with several schools in Tampere area.
Principles of Design
The mathematical statistics course is aimed for senior high school students. The covered topics are statistical survey, classification of data, graphical presentation, means, variances and correlation. Making a survey was decided to be the key topic of the course. The students design their own survey, collect answers and analyze them. The motivation to learn the mathematical theory should arise at least when the collected data must be analyzed.
Ease of use is a requirement for any modern learning environment. In Pythagoras it means that the environment is comprehensive. It contains all the tools needed for studying the theory, making the survey and communicating with other students and teachers. Only a web browser, no additional software, is needed to use the environment. The tools and the material are embedded into KUOMA framework which is a WWW environment for project learning. KUOMA integrates WWW material and communication tools into a package that is easy to use [Leinonen, 1997].
The environment is composed of four components: theory, exercises, survey tool and teacher's tool.
Theory contains definitions for statistical concepts such as distribution, correlation etc. Theory of designing and analyzing a survey is provided as well.
Exercises test what student has learned. The architecture of all the exercises is the following: Some requirements are shown and the student must enter a set of data that will meet the requirements. For example, if values for mean and standard deviation are shown the student must form a distribution with the given characteristics.
Survey Tool can be used to design a simple survey. The survey is composed of multiple-choice questions. The same tool is also used for answering the questions and for retrieving the answer data.
Teacher's tool enables a teacher to observe the students' learning. The tool shows graphically what exercises each student has done.
All the software is based on Java technology. It enables WWW pages to have interactive content [Sun, 1997]. The basic architecture is shown in Figure 1. On a single WWW page there are multiple applets that communicate with each other. One main applet is responsible for controlling the other applets on the page and communicating with the servers. The chosen architecture breaks the application into separate objects that all have an independent
task to do. It is also possible to reuse code efficiently because most of the modifications involve only the main applet.
Figure 1: Software Architecture
Exercises, teacher's tool and survey tool
When the WWW page contains an exercise the main applet first asks an identification from the user. After the identification has been checked by the administration server the exercise is started. On start-up the applets are linked together. Each applet is told which dependent applets it should update when its state changes. For example when the user inserts some data into distribution applet the diagram applet should update its display automatically.
When the page contains an exercise one of the applets is constantly checking if the exercise has been completed or not. When the completion is detected it sends a message to the main applet. The main applet then contacts the administration server. The server makes a mark that the user has accomplished the exercise.
The main applet in the teacher's tool page retrieves user data from the administration server. The page also has a diagram applet. When the data is retrieved the main applet asks the diagram applet to display the data graphically.
In the survey page the main applet is used for maintaining the surveys. A separate applet is activated for creating and modifying a survey. The page also has an applet for displaying the survey data graphically. The main applet communicates with the survey server. The surveys and the answers for them are stored in the server.
The servers are standalone Java applications and are accessed using Remote Method Invocation (RMI). By using RMI client can manipulate server objects in a simple way. Accessing a remote object is similar to accessing a local one [RMI, 1997].
Pythagoras server processes and the WWW server process must run in the same computer. This is because
an applet cannot make network connections except to the host that it came from [Campione, 1997]. This might cause some problem in the future if each school would like to have their own servers. Distributing the servers nearby the users could make system maintenance easier. However this alternative has not been tried yet.
Pythagoras is an interactive environment for learning the basics of mathematical statistics. Using a web browser the student can study the theory, design and publish a survey and analyze the survey data. A teacher can monitor the students' progress by checking what exercises they have accomplished. All the time integrated communication tools are available for tutoring and discussing. Java applets that use Remote Method Invocation (RMI) is a the way to build this kind of distributed learning environment.
[Leinonen, 1997] Leinonen, Teemu (1997). Hypermedia Learning Materials for Comprehensive Schools (The KUOMA -pilot). http://matwww.ee.tut.fi/kamu/kuoma
[Sun, 1997] Sun Microsystems (1997). Java Home Page. http://java.sun.com
[RMI, 1997] Sun Microsystems (1997). RMI Documentation. http://java.sun.com/products/jdk/1.1/docs/guide/rmi/index.html
[Campione, 1997] Mary Campione (1997). The Java Tutorial http://java.sun.com/docs/books/tutorial/applet/security/security.html