Televise a Collaborative (Tele-) Tutoring Environment

teleVISE – a Collaborative (Tele-) Tutoring Environment to Support Education e.g. in Mathematics

Thomas Risse, Barbara Grüter, Jörn Loviscach,
Heide-Rose Vatterrott, Ulrike Wilkens

Department of Electrical and Electronic Engineering and Computer Science

Hochschule Bremen, University of Applied Sciences,

Key words: tele-learning, tele-tutoring, CSCW, education in mathematics

Abstract:

To improve the education in mathematics at some departments of our university we set up a hybrid infrastructure allowing students to collaboratively work on application oriented exercises. Students, tutors, and lecturers collaborate online. The exercises together with meta data are stored in a searchable data base for reuse by students and lecturers. Problem solving is assisted by (tele-) tutors. Users input mathematical text via digitising tablets. This input is stored in the data base and it documents the process of solving mathematical problems. By this mobile CSCW support the project teleVISE aims at shifting the focus from calculation to modelling real life problems.
Here, we present the approach, the means and first experiences together with transferability and perspectives of concept and technical system.

1 Introduction

Teaching and learning mathematics in technical fields like automation, computer science, construction, control, and engineering in general is notoriously delicate both for instructors as well as for students.

At Hochschule Bremen, University of Applied Sciences, colleagues in several departments are worried about the quality of the education in mathematics. In the Department of Electrical and Electronic Engineering and Computer Science, we started the project teleVISE – short for Tutorial Enhancement of Learning Environments: Virtual Exercises and Student Expertise – to improve education mathematics, In this project, colleagues from several departments are attacking this complex problem from different angles:

The mathematical content is modularised and tailored to the needs of other disciplines taught in the corresponding degree course (in English and more up to date in German
The didactical impetus in lectures, exercises, and exams favours modelling and disfavours mechanical, dull calculations. We focus on the process of learning mathematics by problem solving (Grüter et al, 2003, [2]).

Tutors assist students working on the more demanding exercises.

Organisation is needed to let students work together among themselves and together with their tutors. Working together in groups may take place face to face or online. A tight synchronisation between lecturer, tutors and students is maintained by a high degree of communication and feedback to make responses on all levels of the project as prompt as possible. As the project evolves evaluation produces additional valuable feedback for optimisation.

Technical provisions let people work together anytime anywhere.

A technical infrastructure has been set up consisting of
notebooks and digitising tablets for lecturers, tutors, and students,
a searchable data base of exercises with web interface,
a data base of documents generated by collaboratively working on exercises with web interface integrating the digitising tablets

Notebooks, wireless LAN, and server based web applications guarantee a high degree of flexibility and mobility.

The paper is organised as follows. In this section we introduce our university, its learning platform and the state of the education in mathematics. This lays the ground and describes the context for the three aspects of the project teleVISE, namely didactics, organisation, and technical infrastructure we discuss in the second section. In the third section we describe our observations of the students learning behaviour, our experiences with tele-tutoring and the adjustments of the technical application after running the project for one semester. In the outlook we indicate the next steps to be taken in the winter term and give future prospects of computer assisted learning at Hochschule Bremen.

1.1 General Context

Hochschule Bremen is a University of Applied Sciences with some 8000 students studying in some (international) 40 degree courses in nine departments one of which is the Department of Electrical and Electronic Engineering and Computer Science.

In 2002 Hochschule Bremen introduced (Wilkens, 2003, [10]) a university-wide learning platform http//AULIS.hs-bremen.de as a portal for all learning units in each degree course in every department. AULIS offers descriptions of all courses taught at Hochschule Bremen together with links to learning materials available on very many various servers. AULIS manages learning units, standardised by different institutions as so called learning objects modules (for an overview see e.g. Risse, 2002, [7], for a critic see (Dodani, 2002, [1]), learners, i.e. (groups of) students, authors, i.e. lecturers and members of staff, and other (groups of) people with specific access rights, e.g. tutors. AULIS also provides e-mail, news groups, etc. In effect, AULIS is the one portal for students and staff of Hochschule Bremen alike: students easily find all learning materials provided by AULIS or via link on other servers run at Hochschule Bremen. Professors make their materials available to their students and can use the very simple authoring environment of ILIAS the open source technical base of AULIS.

1.2 Mathematical Context

Even though education in mathematics at the different technical departments of Hochschule Bremen is rather heterogeneous, all colleagues agree to strive to lay sound fundaments when teaching mathematics in degree courses like

computer science, i.e.
technical informatics,
media informatics, and
digital media
engineering, i.e.
aviation systems engineering,
environmental engineering,
electrical and electronic engineering,
mechanical engineering, and
micro systems engineering

Typical and problematic is the heterogeneity of (incoming) students in all degree courses

 heterogeneous competence levels, and

 heterogeneous attitudes towards mathematics.

Conforming with the findings of the OECD Programme for International Students Assessment, PISA i.e. e.g. a low 20th – 22nd rank of 32 countries in mathematical literacy all members of staff teaching mathematics complain about the lack of basic knowledge and basic skills of incoming students. At the technical departments different initiatives try to overcome students deficiencies in mathematics. For instance, in our Department of Electrical and Electronic Engineering and Computer Science we try to improve the competence of (incoming) students by

online self assessment (in German), comparable to e.g. MyMathTest.com, s. [3], but without proprietary plug-in
preparatory courses
tutorials
learning material on web servers, e.g.
lecture notes, exercises, old exams with solutions and link lists – for examples in German see
interactive documents (Risse, 2001, [6]) , e.g. in basic numerics, cryptography, coding, compression, random number generation etc
integration of computer algebra systems (CAS) like Mathematica, Maple, Maxima or MuPad into teaching, optional courses on CASs later on.

Colleagues discuss and balance the individual syllabuses of instruction and visit other colleagues lectures in order to give hints how to improve their didactics.

At the same time, we try to enhance students motivation and to enthuse them for mathematics e.g. by offering competitions

International Mathematics Competition Kangaroo, e.g. 2001, 2002 and 2003 at Hochschule Bremen, see
Mathematics Olympics in Bremen, see

2 teleVISE – the Project

The project teleVISE (Grüter et al, 2003, [2]) is as hybrid as is learning: ruminative and inventive, solipsistic and interactive, abstract and concrete, in isolation and in groups. teleVISE is

a didactical ambition and pretension realised in class, by (tele-) tutors and by student groups
an organisational achievement (organising students, (tele-) tutors, lecturers in several departments), and
a technical infrastructure (web interface to data base of exercises, data base of collaboration in tutor groups, application to input mathematics via digitising tablets).

Because it supports class room teaching teleVISE is a blended learning (Troha, 2002, [8]) project. Right now, the project teleVISE spans six degree courses in four departments:

Environmental Engineering in the Department of Civil Engineering
Technical Informatics, Media Informatics, Digital Media in the Department of Electrical and Electronic Engineering and Computer Science
Aviation Systems Engineering and Management in the Department of Mechanical Engineering
Women's Degree Programme in Computer Science in the Department of Business Studies

The project teleVISE has been designed and developed and is deployed to support education in mathematics. But it is usable and useful in any degree course in other departments because the organisational structure and experiences can easily be transferred as well as the general Compute Supported Co-operative Work, CSCW, platform which has been developed. This will be corroborated by the following details of teleVISE.

2.1 teleVISE – the Didactics

The project teleVISE is aiming high: lectures and exercises ideally offer

 as little (stupid) calculation as necessary, as much modelling as possible

 whereby retaining application orientation and alertness to match the demands of the practice – typical and characteristic for universities of applied sciences.

Some examples illustrate at least the areas in which application orientation is to be established in, for instance, the degree course Technical Informatics.

Computer graphics or linear optimisation need geometry and matrix algebra.
Electrical networks need arithmetic of complex numbers.
Approximation, interpolation, optimisation, calculation of errors, etc in engineering, physics, etc need calculus.
Audio processors need Fourier series, Fourier integrals, and Fourier transforms.
Physical modelling needs differential equations.
Monitoring and predicting failure rates of computer systems, data compression, etc need probability calculus and statistics.

Although not included in the basic education in mathematics, very many other applications in computer science can not be understood, deployed and modified without mathematics, e.g.

cryptography needs number theory
coding needs the algebra of polynomials

Let two specific examples demonstrate how our didactical requirements are met by certain (types of) exercises.

When students are asked to compute how light rays are reflected first on the x-axis, then on some line through the origin, and at last on any line then two objectives are met and additionally an engineering modus operandi or mathematical method is learnt and applied:

When students are asked to determine the number of additions and multiplications necessary for instance to solve a system of linear equations by the Gauss elimination method and by Cramer's rule then

students explore and program algorithms applied everywhere in engineering
students compare the efficiency of various algorithms solving the same problem
students experience numerical (in-) accuracy, cp. basic numerical algorithms in an interactive document
students make use of formulae like 1+4+9+ ...+n² = n(n+1)(2n+1)/6 which they have proved earlier by induction.

Quite a load of exercises with solutions is provided in a database for students use in exam preparation and for lecturers use in their classes.

Tutors assist students in working on these exercises. They support their students in face to face tutor groups and online via the teleVISE technical infrastructure, keeping in mind the differences of the two settings (Pallow & Pratt, 1999, [4]). By the classification of online education (Paulsen, 2000, [5]) teleVISE tutors serve

organisational functions: structure discussions, pacing, put forward initiatives
social functions: monitor groups
intellectual functions: answer questions, guiding students
assessment functions: give feedback to assignments, correct submissions

Human tutoring combines face to face group tutoring and individual tutoring online or by telephone contact. Video- or audio-conferences may complement our collaboration environment.

2.2 teleVISE – the Organisation

Running the project teleVISE means to

provide students, tutors, and lecturers with notebooks, digitising tablets and software,
instruct students, tutors and lecturers to use the web interface to the system,
schedule online presence of tutors offering assistance,
manage a user help desk,
manage the data bases,
run the technical infrastructure (web servers, network, wireless LAN)

and to constantly evaluate the progress of the project. There is a lot of material available describing the ongoing activities like general evaluation, usability analysis, and the assessment of the didactics of volunteering staff by evaluating lectures recorded on video.

2.3 teleVISE – the Technicalities

The project teleVISE provides two Linux, Apache, MySQL, and PHP (LAMP for short) based data bases, one for exercises and the other for the documents generated by working the exercises (Vatterrott et al, 2003, [9]).

The exercise data base right now contains some 700 exercises in HTML (generated from TeX/LaTeX sources) with XML-markup. In addition to standard attributes like author etc (extending the IMS classification scheme) meta data contains

area of application,
level and time to solve,
type of exercise (calculation, modeling),
Mathematics Subject Classification of the American Mathematical Society, AMS,
references to comparable exercises – exercises for the same mathematical topic which are easier or more difficult.

These meta data make the data base searchable: via a web interface students can find exercises to prepare for exams, lecturers can find exercises for their specific needs and get new ideas for their own classes.

The second data base supports the collaborative process of solving problems posed in exercises. It stores and provides access to documents generated when

students attempt to solve a problem on their own and want to document their various approaches (scratch pad),
students ask assistance of fellow students or tutors to solve a certain problem (cry for help),
students hand in their solution of a problem (solution form),
tutors mark and provide feedback to solutions handed in

Third, a drawing application has been developed as a JAVA applet allowing users to input mathematical text by a digitising tablet. The idea is to provide a way to work on and communicate about mathematical problems as if one had pencil and paper. Working with a digitising tablet and a pen is as close as possible to working with pencil and paper. There are no convincing alternatives to digitising tablets as

equation editors have only limited expression power;
TeX/LaTeX or mathML produce highest quality formulae; but commands have to be memorised and input via keyboard is tedious – or again some TeX/LaTeX- or mathML-front end has to be used;
there is no natural way to generate thumb sketches say of function graphs, of 2D or 3D objects etc.

A screen shot of the JAVA applet illustrates the features of this drawing application.

3 teleVISE – the Status

In anticipation of a serious evaluation of teleVISE end of 2003 we present some first impressions and observations to ponder over, some immediate measures taken in reaction to users requirements, and some examples of responses to supervising the didactics of members of staff.

3.1 Acceptance, Usability, or just the Practical Value

Students attitude towards teleVISE varies extremely as can be observed with respect to

taking advantage of (tele-) tutoring and usage of the application,
acceptance of the projects understanding of collaboration,
response to the idea to reflect not only solutions but the learning process itself.

Let us illustrate the two extremes high and low acceptance of teleVISE by an example each.

The screenshot above shows the usage of the drawing application: e.g. text for the matrix elements, the digitising tablet for big parentheses and special characters, using colours, documentation, reflection of and musing on the own proceeding, interaction with the tutor.

The following screenshot shows that the student has scanned his solution on paper to a file and imported it into the data base. The solution is reduced to (correct) formulae. No explanatory text is provided. Obviously, hardly any interaction with the tutor has taken place.

These two extremes can be characterised as follows:

high acceptance/compliance students

exhibit a neutral attitude towards the application, focus on its functionality,
use the system and explore its features, i.e. maximise use of application,
use the digitising tablet for input,
use online collaboration, i.e. support by peers, by (tele-) tutors,
monitor their own tackling a given problem, i.e. their own learning process

use the archive for exam preparation
and use the system to their best advantage!

low acceptance/compliance students

exhibit a critical and sceptical attitude towards the application, focus on its bugs,
use the system only to hand in their worked exercises, i.e. minimise use of application,
refuse to use the digitising tablet, instead scan their solutions on paper for input,
think online collaboration is too cumbersome,
do not monitor their own learning process using the application teleVISE, so that they can not use the teleVISE archive for preparation of examinations,
perceive the obligatory use of the teleVISE application as an additional burden on top of demanding modelling, so that they try to avoid using the system!

3.2 Fine Tuning the Didactics

All staff participating in teleVISE is encouraged and determined to continue to focus on modelling rather than calculation: students solutions of given problems are documented by the system and selected solutions can easily be presented and discussed in class. This is one example of members of staff changing their didactics by virtue of hints and tips they received from the supervision of their lectures. At the same time we had to realise how demanding modelling is for our students. This observation is taken into consideration in planing syllabuses of e.g. our Bachelor/Master degree courses.

3.3 Adapting the Organisation

Besides the chore to find new tutors for the winter term and to classify the rest of the exercises, a usability study has been initiated and different questions are tackled:

how to improve students motivation for mathematics?
how to stimulate mathematical discussions?

(e.g. by the thought provoking problems like “The Infamous Monty Hall Problem”, cp )

how to teach and how to learn how to model by which examples or exercises?
(e.g. by a continuous problem like transport of material through pipes of different shapes: quantity, optimisation)
how to compare the learning outcome of students in and outside the project teleVISE by questioning lecturers and students alike?
how to assess the possible degree of modelling in relation to the necessary degree of calculation in education of mathematics?

The evaluation is and will be guiding further development of the technical system. Many details can be found in a collection of material.