The Plato project (after Joseph Plateau, a Belgian physicist (1801-1883), whose name is attached to the historic building of the faculty of engineering in Gent - commonly called 'The Platoo' by the students) was launched in October 1996. The target was a relatively small group of students entering our engineering faculty after one to four years of technical education, or after some years of experience in the industry.
Many of these students need remedial teaching in mathematics and most of them have difficulties with attending the lectures and/or the exercise classes: this is due to their very tight class schedule. For many years the main culprit in the first term was the Linear Algebra course, which by the majority of these students was experienced as being highly 'abstract'. Therefore it was decided to develop a Linear Algebra package (a) which is suitable for selfstudy , (b) which contains material for self-evaluation and (c) which covers the same topics as the standard lectures, but offers these in a less abstract way (e.g. putting more emphasis on examples, illustrating the main ideas, rather than on the replication of proofs: the latter can be read in the lecture notes).
It was decided to write the whole package as a collection of hyperlinked Maple worksheets. This choice was directly motivated by the fact that the University was about to acquire a Maple V (release 4) campus license, enabling us to distribute the main 'carrier' software to all students, for use on all platforms. In addition it was felt that a computer algebra system like Maple was best suited to fulfil all our needs at the same time: nicely formatted text and graphics output can be combined with 'hands-on' open exercises and self-evaluation 'tests', the possibilities of which go far beyond those of traditional educational packages, where usually only a literal comparison is made between a student's answer and a collection of standard answers.
No attempt was made to incorporate automatic marking in the package's evaluation modules: for an open package, which can be installed at home, security would clearly be an insurmountable obstacle! Solely for the purpose of self-evaluation a modest attempt was made to restrict access to the system during the 'tests': very short questions, to be solved by a small amount of pencil and paper work, are posed, after which the student's answers are evaluated by the system. Questions and answers, as well as special functions needed to carry out an 'intelligent' check of the answers can be easily provided by the instructor in an ASCII file.
No matter what the quality of a selfstudy package is, the main motivation of a student rests on the number of marks to be gained with it. Therefore three evaluation sessions (about one per month) are organised in a small computer-lab during the first term: herewith a total of 8 marks (out of 20) can be obtained. Each session takes one hour per student: 3 to 4 exercises have to be solved, making use of whatever tools that are deemed necessary (e.g. full access to the Maple library, the course modules and the lecture notes). At the end of the term a traditional examination is organised: two theoretical questions and one more 'abstract' exercise make up the 12 remaining marks.
Preliminary results are very encouraging: students 'like' to do linear algebra in this way (sic!) and a comparison with examination results of previous years indicates a definite progress. Remarkable is the fact that the main group of first year students (who are not using the package so far) appears to obtain a lower marking for the 'abstract' exercises (which are identical for both groups)! These results stimulated us to contemplate also the use of the package by the full group of first year students. Financial support to carry out this program, in a collaboration with the Free University of Brussels (V.U.B., Belgium) and The University of Birmingham (UK) has recently been demanded from the Flemish Ministry of Education (ALICE: Active Learning In a Computer Environment).
The package was written for use with MapleV release 4, but appears to be compatible with release 5 too. No previous knowledge of Maple is assumed, as the use of the necessary Maple commands is built up very gradually. Nevertheless one should take care that the students have had a first look at, for example, the 'Maple New Users Tour', so that they are somewhat familiar with the manipulation of worksheets! A zipped file together with installation instructions can be obtained by email from the address below. The package (a Dutch and English version) should soon be available through the internet too, but will then carry the new name Alice (as Plato is also used by a USA based company, distributing educational material). At the moment a similar package for the theoretical mechanics course is being developed, to be followed by calculus later on.
Norbert Van den Bergh
Faculty of Applied Sciences
University of Gent
Jozef Plateaustraat 22
9000 Gent, Belgium
E-mail: Norbert.VandenBergh@rug.ac.be
Author: Norbert Van den Bergh
Original file location: http://www.math.utsa.edu/mirrors/maple/mplcd02.htm