Minutes of Working group 5
Thursday 9th - Friday 10th October 1997
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Present | Alfredo Moscardini, Ossi Nykanen, Paul Tammela, Otu
Vaarmann,
Jan Lellep, Jaagup Kippar
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Aim |
The aim of the working group was to design a timetable and
mobility plan to implement the construction of a web
based course entitled " Foundations of
Mathematical Modelling"
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Discussion of the content of the course
Alfredo began the meeting by discussing what was meant by mathematical
modelling and its separate identity to Mathematics. He also emphasised the
difference between studying built models and the process of modelling. The
new course was to establish the process and not to teach any new
mathematical techniques. Students, when building models would be encouraged
to use the mathematics that they already knew. In this way, the course
could be attractive to a wider student audience than usual.
In Alfredo's view, the process of modelling involves three principal stages
- analysing the problem, building the model and implementing a solution.
Each stage has various sublevels which were discussed. Mathematics or
software is needed at the solution stage but this should be placed in
context and seen as only part of the whole process - one brick in the wall.
It would not be an objective of this course to teach detailed numerical
analysis.
Not everyone agreed with this immediately - in particular Otu wanted some
numerical analysis to be taught. The opinion was also expressed that
without mathematics - no mathematical modelling could take place. This of
course true, but the student has many courses to improve his mathematics.
Perhaps there should be one course which just uses what mathematical
knowledge is present and concentrates on the wider implications.
Alfredo also thought that it was important that students had a clear idea of
the philosophy and nature of mathematics itself and then its relationship
with modelling. He saw modelling as a subset of problem solving whilst
containing applied ( and pure ) mathematics. Modelling skills are not
identical to mathematical skills and different modes of thought are needed.
Often the precise, logical thinking that is mathematics is not suitable at
the initial stages of the modelling process - alternative methods of
thinking are available and should be explored.
A discussion followed and at the end of the morning session, it was agreed
by all that the aim of the new course would be.
" To enable the student to understand the role of mathematics in modern
society and for them to build, evalute and criticise their own models"
Its content should be:
- Philosophy of Modelling ( 1/4 )
- Building Models ( 1/2 )
- Case Studies ( 1/4 )
The case studies could be taken from mathematics, physics, chemistry,
biology, ecology or economics. REach should have the same format:
- A Statement of the problem ( not neccessarily precise)
- A set of assumptions used
- The construction of the model
- Solutionm and anaysis of the model
- Validation of the model
- Criticism of the model
Delivery of the Course
The course should be prepared in three ways:
- document form with overheads
- for use with a data projector
- for use with the web.
To physically put the document form of the course on the web was a purely
routine task which did not require any particular technical expertise and
was not thought to be any more beneficial than just handing out photocopies
of the document form. This was not exploiting the potential of the Internet.
A discussion followed as to the major advantages of the web and it was
agreed that the major ones were:
- an immense store of information
- the ability to support group work
- multimedia capabilities
- its monitoring capacity
The discussion centred on how these qualities could be best utilised by our
course.
It was decided that the members of the group should search the web for
suitable data and then these references would be incorporated into the
course. This would provide the student with a much larger database than he
would normally be exposed to.
In the classroom, students are taught the modelling process in small groups
of four. It was decided that Ossi would design a web structure ( which
would then be implemented by Jaagup ) that would allow the tutor to
supervise similar groups but consisting of students from different
countries.
At present the multimedia aspects of the web were not thought to be a
priority and would not be implemented. If video conferencing was available
in the future, some aspects could be incorporated to utilise this.
The structure would be so designed as to allow the tutor to monitor the
students who use the material. Factors such as number of accesses and time
spent on various parts could be used to supplement the student profiles.
Tasks Assigned
The following tasks were assigned:
- Mutual familiarisation of an agreed modelling process
As a modelling course was being taught in Sunderland by Alfredo at
the present moment, it was thought desirable that the Estonians visited
Sunderland as soon as possible., It was decided that Jan and Paul would
both come for one week in November. The purpose of the visit would be to
obtain as much feedback and materials as possible so they would understand
the problems of implementing it on the web. Otu would visit with Paul in
the next semester to agree on the final structure ( Paul would stay for
three weeks to supervise the visiting Estonian students ) This task was
allotted three months.
- The design of a web based structure
This was to done by Ossi in discussion with Alfredo. It was
timetables for one months work. Money was allocated for Jaagup to visit
Sunderland in early January to discuss the implementation and also for him
to visit Tampere to discuss with Ossi. It was suggested that Ossi visit
Sunderland but that would depend on his other activities. It was hoped that
the main design could be agreed by mid-November.
- Data provision.
All staff should be engaged in searching the web for suitable
material. This process could not start till the end of task one and would
take one month.
- Implementation of the web structure.
This would be the responsibility of Jaagup and would take four
months. It is hoped to be finished by the end of May
- In May/June, a selected group of students would test the material.
- Before the February meeting in Tartu, the working group will an
agreed understanding of the content, a written version of the course and the
detailed design of the web structure. By the summer meeting, the web based
course would have been implemented, tested and will be demonstrated at the
meeting.
Activity Plan
Ossi and Alfredo completed the forms for the activities and mobility for
next year. These were handed to Seppo