The aim of the ISHTAR project is to build tools on the Web to help students learn physics using hypermedia. The course is mainly intended for students of life sciences such as Medicine, Biology or Pharmacy, not requiring an in-depth knowledge of mathematics.
The package we present, elaborated within the didactics of physics, is divided in two levels designed to fit different students' backgrounds. It first develops the most important concepts of statistics, probability theory and error analysis, and the ultimate goal is to provide an exhaustive treatment of these subjects.
The package exploits the Web capacities in terms of communication and includes Java applets created to improve the interactivity level.
We are, at present, also developing two chapters on mechanics and thermodynamics.

ISHTAR (Innovative Software for Higher-education Telematics Applications R. & d.) is a project under development at the Department of Physics of the University of Bologna.

The purpose of this work is to create interactive tools on the Web to help students learn some chapters from the physics course. Initially the ISHTAR project had more ambitious goals, such as producing a virtual laboratory, in collaboration with the Physics Departments of the Universities of Athens, Bologna, Florence and Lisbon.

The project starts with a software package about the study of diffusion processes in solutions (Fig. 1 shows the starting page of the package), presented at the Third World Wide Web Conference, Darmstadt, 1995 [1].

Fig. 1

The first software package was developed to make it possible for a student to follow in detail parts of the program of a General Physics course and to obtain a working knowledge of specific arguments using a sort of virtual experiment.
The group working on the project includes people involved both in software-engineering and education. In this way we hope to build good software tools and also easily understandable interfaces for the students.

We are currently working on a new hypercourse chapter devoted to statistics, probability theory and error analysis (Fig. 2 shows the cover page of the chapter [2]).

Fig. 2

The educational material has been divided into two courses: the first for students who face these arguments for the first time; the second for general physics or non-physics students who have already some knowledge of the subjects. The two courses have separate structures but share common parts such as notes, mathematical details, applets, etc. In spite of this, it is impossible to jump from one course to the other. We have done this to prevent students from finding themselves in trouble wandering into a package with too many links and possibilities.

We have used the usual multimedia techniques typical of Web documents and here is a brief description.

- The text (hypertext) starts from a Table of Contents and has main pages and others containing notes and more detailed information (comprising mathematical details) [3 , 4].

Figure 3 shows an example of four pages taken from the package. They include text, links, pictures and forms, as frequently found in a Web document.

- Inlined figures have been introduced to help users to understand the text using graphs, plots, histograms, etc.

- Formulas have been written first in LaTeX [5]and then converted in inlineable images through the use of the LaTeX2HTML [6] package.

- Java applets have been introduced to show statistical behavior and to check pseudo-random number generators. Figure 4 shows the applet built to discover the correlation between randomly generated numbers: this applet has been downloaded from the net and improved by the members of ISHTAR [7].

The applet creates and reads a file of pseudo-random numbers generated, and plots a noise sphere of the data. Poor random number generators will show clear patterns. It is possible to select a random number generator from four different kinds: the java random generator, the additive method, the multiplicative method and the mixed method random number generators.

Fig. 4

Another applet (see Fig. 5), downloaded from the net and improved by the members of ISHTAR [8], shows how the sample mean tends to the population mean as the sample size increases. It is possible to test it for three different distributions: uniform, exponential, and normal distributions.

Fig. 5

- Scripts in conjunction with the use of forms have been created to plot histograms and functions. In this way students can compare different distributions and verify their behavior by changing the parameters.
Scripts have been created using HBOOK [9], HPLOT [10] and HIGZ [11] routines from CERN software libraries to produce Postscript files, and then the IMAGEMAGICK [12] package was used to obtain inlineable GIF files (see Fig. 6).

Fig. 6

This interactivity should stimulate students to repeat experiments, make comparisons, and develop their own conclusions on the different effects generated with different parameter values.

This package was developed to give an exhaustive introduction of the main concepts of statistics, probability theory and error analysis: we have also paid special attention to errors in simulations. Students are often not able to understand the meaning of error analysis in a simulation environment: they are inclined to neglect the errors, being misled by the idea that a computer is a perfect machine and behaves in a "deterministic" way.

The philosophy, as with the previous package about diffusion, is not to abandon students in front of a computer but, on the contrary, to exploit its capacity and that of the Web, using them as very useful tools for educational activities.

To understand the impact of the hypercourse, we are testing our packages with first year students of Medical Chemistry at Bologna University.

We are also working on other chapters of the physics course, and hope to provide two new didactical software packages about mechanics and thermodynamics.

Acknowledgements

We would like to thank Maria Cecilia Coperchio for her help in building Java applets, Riccardo Veraldi for some help in programming, and Ivan Nanni at the Department of Statistics of Bologna University for his suggestions on the topic.

References

1

M.C. Coperchio, F.L. Navarria, T. Rovelli
`` Simulation of the diffusion process on the Web''
Third International WWW Conference, 10-14 April 1995, Darmstadt, Germany
in `` Computer Based Training'' section.
http://axdel 1.bo.infn.it/pub/art/abs_wwwconf/abs.html

2

The "BallDrop" applet on the cover:
``The normal distribution: an illustration of basic probability''
http://www.cco.caltech.edu/~ekrider/Finance/BallDrop/BallDrop.html

3

R. J. Barlow, Statistics, J. Wiley, New York, 1989.

4

J. R. Taylor, An introduction to error analysis: the study of uncertainties in physics measurements, University Science Books, 1982

5

L. Lamport, LaTeX, a document preparation system, Addison-Wesley, 2^nd edition (1994)

6

Nikos Drakos
``LaTeX2HTML''
http://cbl.leeds.ac.uk/nikos/tex2html/doc/latex2html/latex2html.html

7

Chuck McManis
``NoiseSphere applet''
http://web.professionals.com/~cmcmanis/applets/noise.html

8

Suresh Srinivasan
``Sample Distributions''
http://ttis.thom tech.com/~suresh/java/sample.html

9

Application Software Group - Computing and Networks Division
``HBOOK - Reference Manual''
CERN - Program Library Long Writeups
http://wwwcn.cern. ch/asdoc/hbook/HBOOKMAIN.html

10

Application Software Group - Computing and Networks Division
``HPLOT - User's Guide''
CERN - Program Library Long Writeups
http://wwwcn.cern.ch /asdoc/higz/HIGZMAIN.html

11

Application Software Group - Computing and Networks Division
``HIGZ - User's Guide''
CERN - Program Library Long Writeups
http://wwwcn.cern.ch /asdoc/higz/HIGZMAIN.html

12

John Cristy
``ImageMagick''
ftp://ftp.x.org/ contrib/applications/ImageMagick/