teleVISE–a Collaborative Environment to Improve Education not only in Mathematics.doc

teleVISE a Collaborative Environment to Improve Education not only in Mathematics Thomas Risse, Barbara Grter, Jrn Loviscach, Heide-Rose Vatterrott, Ulrike Wilkens Department of Electrical and Electronic Engineering and Computer Science Hochschule Bremen, University of Applied Sciences, Flughafenallee 10, 28199 Bremen, Germany rissehs-bremen.deAbstract 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 modeling real life problems. 1. IntroductionTeaching 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, Germany, 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 http:/www.teleVISE.hs-bremen.de 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 rmatik.uni-leipzig.de/theo/cps/index_2.htm and more up to date in german rmatik.uni-leipzig.de/theo/lpv/pgs/dt/Verbund/index.html). The didactical impetus in lectures, exercises, and exams favours modeling and disfavours mechanical calculations. We focus on the process of learning mathematics by problem solving (Grter, 2003). 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 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 next section. In the conclusion we describe our experiences gained in the first half of the project, indicate the next steps in the second half and give future prospects of computer assisted learning at Hochschule Bremen. 1.1 The University Hochschule Bremen http:/www.hs-bremen.de is a University of Applied Sciences with some 8000 students studying in some 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) 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), for a critic see (Dodani, 2002) , 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 www.ilias.uni-koeln.de, the open source technical base of AULIS. 1.2 The Education in Mathematics at Hochschule Bremen 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 most 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 /knowledge/chap3/intro.htm all members of staff who teach 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 http:/www.weblearn.hs-bremen.de/risse/MAI/docs/vorkurs.pdf (in German), comparable to e.g. (MyMathT), but without proprietary plug-in preparatory courses tutorials learning material on web servers, e.g. lecture notes, e.g. http:/www.weblearn.hs-bremen.de/risse/MAI/docs/MAI1.pdf http:/www.weblearn.hs-bremen.de/risse/MAI/docs/MAI2.pdf exercises and old exams with solutions http:/www.weblearn.hs-bremen.de/risse/MAI/docs/klausur/ http:/www.weblearn.hs-bremen.de/risse/MAI/docs/uebungen/ interactive documents, e.g. http:/www.weblearn.hs-bremen.de/risse/MAI/docs/numerics.pdf http:/www.weblearn.hs-bremen.de/risse/MAI/docs/epuzzles.pdf link lists http:/www.weblearn.hs-bremen.de/risse/MAI/links.htm integration of computer algebra systems (CAS) like Mathematica, Maple or MuPad, into teachings, 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 Mathematics Competition Kangaroo, /ksf/index.html, e.g. latest one in March 2003 at Hochschule Bremen, 2003: http:/www.weblearn.hs-bremen.de/risse/MAI/docs/kanguru3.pdf 2002: http:/www.weblearn.hs-bremen.de/risse/MAI/docs/kanguru2.pdf 2001: http:/www.weblearn.hs-bremen.de/risse/MAI/docs/kanguru1.pdf Mathematics Olympics, e.g. latest one in February 2003 at University Bremen, http:/www.uni-bremen.de/campus/campuspress/unipress/ 2. The Project teleVISEThe project teleVISE 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 and by (tele-) tutors 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 classroom teaching telVISE is a blended learning (Troha, 2002) 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 Womens 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 modeling 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 modeling 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 Cramers rule then 1. students explore and program algorithms applied everywhere in engineering 2. students compare the efficiency of various algorithms solving the same problem 3. students experience numerical (in-) accuracy, cp. basic numerical algorithms Available: http:/www.weblearn.hs-bremen.de/risse/MAI/docs/numerics.pdf 4. students make use of formulae like 1+4+9+ .+n = 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). By the classification of online education (Paulsen, 2000) 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 submissionsHuman tutoring combines face to face group tutoring and individual tutoring online or by telephone contact. Video- or audio-conferences are may complement our collaboration environment. 2.2 teleVISE organisational Running the project teleVISE means to provide students, tutors, and lecturers with notebooks, digitising tablets and software, instruct students and tutors 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 (network, wireless LAN, web servers) at Hochschule Bremen, and to constantly evaluate the progress of the project. 2.3 teleVISE technical 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. The exercise data base right now contains some 500 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 /msc 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 /Math/ 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 thumbsketches say of function graphs, of 2D or 3D objects etc. A screen shot of the JAVA applet illustrates the features of this drawing application.One easily identifies the exercise given in german and the drawing applet with text in english input via the keyboard and graphics input the digitising tablet. 3. teleVISE in Operation3.1 teleVISE - Where we are Since August 2002, in the first half of the project teleVISE, in the winter term the didactical objectives were established in a suitable style of lectures and of issued exercises, cp. http:/www.weblearn.hs-bremen.de/risse/MAI/docs/Uebungen (in german); tutors were hired, briefed and trained; tutor groups established; online availability of tutors scheduled; the project acted as a broker to provide students with used notebooks and new digitising tablets; the technical infrastructure was set up: the exercise data base with some 500 exercises and web interface, the collaboration data base with web interface, and the drawing application, a JAVA applet, provides an unshared whiteboard. At www.teleVISE.hs-bremen.de, a link to the teleVISE application including the drawing applet is provided to a user guest with password guest for demonstration. 3.2 teleVISE Where we will go Up to now, the collaboration within groups of students or the collaboration of students and tutors is asynchronous. The next and essential step will provide synchronous collaboration by extending the drawing applet to become a shared whiteboard. Also, the teleVISE software has to be integrated into AULIS/Ilias to benefit from the user management of AULIS/Ilias, to offer the integrated e-mail and news groups, and to be able to seamlessly integrate exercises into the learning units already provided by AULIS/Ilias. End of 2003, at the end of the project, the teleVISE infrastructure will be mature enough to think of transferring it to oth