Introducing MATLAB into Basic Mathematic Lectures Using a Custom E-Learning System Florian Judex1, Günther Zauner2, Felix Breitenecker1 Institute for Analysis and Scientific Computing, Vienna University of Technology Wiedner Hauptstrasse 8-10, 1040 Vienna, Austria 2 'Die Drahtwarenhandlung' Simulation Services Neustiftgasse 57-59, 1070 Vienna, Austria
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Abstract. To counter the decreasing interest and understanding in the basic mathematic lectures in geodesy, it was decided to supplement these lectures with MATLAB. Due to licence issues, the MATLAB web server was used, changing the lecture to a blended learning course. A special interface for the web server was created for a better separation of content and web server, and the system has proven satisfactory.
Keywords. E-learning, MATLAB, Moodle
blended
learning,
1. Introduction The last decade simultaneously saw the advent of computer algebra systems embedded in calculators, together with a dramatic increase of the knowledge in many applied sciences due to the information age. This lead to a shift in the curricula of many engineering programs. Lectures on fundamental topics, like mathematics and physics, which are the foundation of most natural and technical sciences, have to be considerably slimmed down to allow basic introduction in all the sub-fields in an engineering discipline. Therefore, the lecturers have to present a great amount of content in a short time, often being forced to rush through their lectures sacrificing comprehension for sheer amount of information. This, in turn, leads to students, incapable to understand the importance of, for example, higher calculus or group theory in the bachelor course for Geodesy, as they will need this knowledge in later terms of their studies. These basic courses are thus often seen as a necessary evil, only needed for the degree. The aforementioned advent of cheap graphical calculators, often including even basic CAS software, and the embrace of this by the public
education system, leading to phenomena, such as classes or schools, where mathematics is taught with the emphasis on these calculators, further strengthening the believe of many first year students that the knowledge taught in the calculus classes is not important for them as t anything can be derived by only using computers nowadays. This situation is a great challenge for those lecturers in mathematics, who are not prone to uses their exams as devices for selection, as they have to instil the students with not only the material of mathematics, but also the use and the limits of available computer software.
2. E-Learning at the Vienna University of Technology Like at most universities, early attempts in elearning at the Vienna University of Technology (TU Wien) were simple systems for the submission of students’ work, e.g. the programs for informatics exercises. These early attempts were neither coordinated between the university and the organizational unit using it, nor between organizational units. This lead to a multitude of simple solutions, each for a single purpose for only one or a few lectures, carefully tailored to the preferences and special needs of a single user.
2.1. TUWIS++ In 1998, the ‘TUWIS+ (TU Wien Information System) was introduced, which, at first, was only an online catalogue of offered lectures and a tool to govern the payment of lecturers for their lectures. Soon, a simple first form of e-learning was made possible, offering a discussion forum for each lecture. As in many official forums, though, the secure knowledge that the lecturer also reads
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Proceedings of the ITI 2008 30 Int. Conf. on Information Technology Interfaces, June 23-26, 2008, Cavtat, Croatia
these forums limited their usage to organizational details.
with experience in e-learning had to be found by a small group of relatively inexperienced users more willing to try out a new system.
Figure 1: the TUWIS++ system
Figure 2: The TUWEL System
The next step was an upgrade to the TUWIS++ allowing the upload of files only available to students registered with the corresponding lecture, and the administration of smaller groups of students within an exercise. This included the direct transfer of grades to the central administration via the TUWIS++, using a TAN code system like the one usually used in ebanking nowadays. Therefore, the TUWIS++ system had, apart form the aforementioned forums, no way for the student to interact with the system, sacrificing the possibilities of e-learning for a better security.
3. Introducing MATLAB into a basic Lecture The Curriculum of the students of the Geodesy and Geomatics Engineering already includes some very basic courses in applied computer science and information technology, mainly to prepare them for the use of geo information
2.2. TUWEL With the TUWEL (TU Wien e-learning platform), an e-learning platform developed basing on the open source e-learning software “moodle” [2], a dedicated software platform was introduced in 2005. It offers a good range of the possible moodle features, including automated testing and grading. It uses the same central LDAP server as the TUWIS++, and allows to limiting the access to of the course information to registered students, which cannot be done in the TUWIS++ system, as it is the official university calendar of the TU Vienna. In the first one-and-a-half years, usage was sparse. Lecturers, already running their homegrown systems, kept using them, as the new elearning platform still had a few bugs. This set a bad example for the rest of the lecturers, who often refused to use it, referring to the more experienced users who should try it first. This lead to a vicious circle, which took some time to unravel, as the bugs that kept away the lecturers
Figure 3: an example with graphic output
systems or a possible master study in geoinformation and cartography. On one hand MATLAB, although one of the most important pieces of software today, was not part of the curriculum. On the other hand, as mentioned in the introduction, students had more experience working with CAS and graphical calculators. Furthermore, in 2004 the curriculum was changed, cutting down the mathematics lectures by 20 percent and in 2005 the lecturer of the two basic mathematic lectures for Geodesy and Geomatics Engineering was emerited. This change offered the chance to introduce MATLAB both as a tool to help with the lecture,
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as well as including a basic course in MATLAB into the accompanying exercises. As the vice chancellor of studies approached all lecturers with a call for an increase in elearning activities, at approximately the same time it was also decided to use the TUWEL system too.
Figure 4: an example using only textual input and output
4. Didactic Concept When planning to include basic MATLAB knowledge into the courses Mathematics I and Mathematics II, two main goals where defined. First, MATLAB should be used by the lecturer in the lecture especially for the quite large amount of geometric drawings occurring in a mathematics lecture for geo science, as those where either incredibly time consuming or not precise enough to satisfy students in this field of work. Using overhead projectors or slides for this purpose were never flexible enough, as they could only be used for pre-made examples, or were as inflexible as the blackboard.
Figure 5: the different input files defining an example. Explanation in section 5.1.
This would also allow the students to use these examples at home, to practice for the exams, as they can generate solutions to common
problems on their own, therefore being able to test their own solutions. This can be extended to quite complex examples, including calculus, as MATLAB also has a toolbox for symbolic computation, which allows it to be used as CAS as well as for numerical tasks. On the other hand, education in MATLAB was to be included in the lectures, as using a software without explaining it in depth to the students would only increase their belief that almost everything today can be computed using software, increasing their stance towards mathematics mentioned in the introduction of this paper. Therefore the MATLAB files used in the lecture had to be distributed to the students as well, allowing them to get a feeling for the computations taught in the lectures, as well as improving their own MATLAB skills by learning from these scripts how certain problems, or classes of problems, can be approached using this software.
5. Implementation At the time the idea of the lecture was created, MATLAB was not readily available to the students for use at home, as the student licence is still quite expensive if purchased individually. It was well known that pirated copies were readily available, but this, of course, could not be used as a base for the implementation. The then-current MATLAB release 2006a, though, still included the MATLAB web server, which could be used for the implementation of the MATLAB examples used in the lecture. It is an ideal compromise, as files written for the server do only need small changes in order to be used on a workspace version of the software, decreasing the time for the development of the examples. This also makes the step back - using the file from the server at a workstation at the university or at home for the exercises – much easier for students. It was briefly discussed if two versions of the file should be supplied, one for the students’ use and one on the server, but this idea was discarded, the reason being that it would greatly improve the stance of the students towards MATLAB, providing them with the sure knowledge that the file shown and used on the server was really nearly as small as the one they receive to work with.
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commandos as well. A single image can be returned by MATLAB to be displayed. This image will be written in a temporary file, but is put together using the usual MATLAB commands, needing only one addition line of code to create the file from the picture. As a third alternative, an error message, which can be created by MATLAB as well as by the programmer, can be displayed, overriding the other output structures.
5.1. The custom Interface To further ease the usage of the webserver, a simple frame work was developed at ‘Die Drahtwarenhandlung – Simulation Services. One of the most important features is to provide the MATLAB web server with an access protection system, which was one of the demands of “The Mathworks” to allow the usage of the server for lecture purposes. As the web server is available from every computer simply connected to the internet, without using techniques like IP access, measures had to be taken so that the server could not be used by anybody, but only by users authorised via the TU Vienna. This was accomplished by only linking to the webserver from within a TUWEL course, and issuing passwords for each course via this system. More important, the somewhat cumbersome interface provided with the server was replaced. A basic layout was designed, and a PHP interface created, which simplifies the task for the user providing examples. The custom interface allows users proficient in MATLAB to use the web server without a great deal of knowledge in web programming. Except from the piece of PHP code used to create the input structures, only text files have to be supplied. Figure 5 shows the basic layout of every example, where the following elements are placed: (A) A file in the chapter folder containing a description of the chapter. This file can contain HTML code as well, if wished. For the sake of simplicity, a further file contains the headline of the chapter. (B) Each example has its own directory. This directory includes a file containing the name of the example, which is placed here as a navigation link. The option for sorting and numbering is included, but this goes beyond the scope of this paper. (C) Every example has a description file as well, which, similar to the description file of the chapter, can include any amount of HTML code including pictures. This file also has to include a short piece of PHP code, creating the input form. (D) The results of the computation are displayed here. There are three possible forms of output: Text is just returned by the MATLAB file as a string which can contain HTML
5.2. Implemented examples Based on this custom interface, over a hundred examples on about 20 topics have been implemented for the two lectures. Each is defined as an own chapter on the web server, and has a direct link from the moodle platform. By now there are over 90 examples implemented in the moodle courses for mathematics I and II. Topics include, but are not limited to -complex numbers -coordinate systems -basic linear algebra -linear algebra applied in geometry -interpolation -basic derivatives -Fourier series.
Figure 6: Linear algebra applied in geometry: rotating a circle
6. Experiences As the first of the e-learning augmented lectures, Mathematics I, was already read for a second time, and almost all of the students have taken the exams, the benefit of the use of MATLAB in the lecture could be proven.
6.1. Usage by the lecturer
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As many lecture rooms at the TU Vienna are not equipped for simultaneous use of the blackboard and the digital projectors, this proves that using the examples during a conventional lecture was too time consuming. To counter this, the schedule of the lectures was changed, introducing one special lecture in the early evening, where mostly the MATLAB content was presented. While not intended initially, this improved the quality of the lecture, as the removal of the time consuming computations from the main lecture helped the students to understand the overall picture instead of struggling with large computations like matrix inversion, which do not facilitate understanding, as they are only a large series of basic calculations. Since March 2007, MATLAB is also available for students of the TU Vienna for usage at home at a reduced price. Therefore, the amount of MATLAB exercises could be greatly increased, as the students were no longer limited to use the workstations provided by the university. The workstations providing MATLAB are still sparse at the university, given the costs for licences, therefore a time contingent policy is implemented on those workstations, allowing only a limited number of weekly hours by students. This problem was, of course, nearly eliminated by the affordable student licence. This increase made it possible to hand out more complex MATLAB tasks in the exercises accompanying the lecture. This student version does not contain the MATLAB toolbox for symbolic computation; therefore those examples can only be used either on the web server or on the workstation mentioned above. This is due to the fact that the symbolic calculation toolbox is only licensed by Mathworks from the CAS vendor Maplesoft.
6.2. Usage by the students Contrary to the expectations, the students did not use the system as much during the term as at the end of the term and/or the recess between terms, apparently to prepare for exams. This changed in the second year, as the knowledge of MATLAB was not only needed for the exam of the lecture, but also for a mandatory part of the accompanying exercise course. The logging features of moodle proved to be insufficient to track the activities of the students of the MATLAB web server, as many of them prefer to use bookmarks in their personal
browser instead of the links provided in the TUWEL system, to circumvent one of the password protection layers. All modern web browsers include password storage, and the chance to copy the password from the page provided by moodle into the password dialog of the MALAB web server is no longer a necessary feature. The MATLAB files, though, written by the students contain code that was obviously taken from the web server and modified for the use in the example. This definitely improves the quality of the files written by the students for their exercises, as they are introduced to quite advanced features from a familiar context, easing the comprehension of, for example, vector based manipulation instead of flow control constructs. With carefully chosen examples, they were able to get the notion of doing basic calculations before programming, avoiding numerical errors or unnecessary computations.
6.3. Usage for other lectures As interface created for the MATLAB web server can be used for many kinds of computations, the next step was to integrate it into lectures, which traditionally already use the software. Most notable are the lectures in modelling and simulation technique, where MATLAB is a very basic tool. Small models for simple dynamic systems, like transfer functions, are implemented on the server, allowing the students to get a feeling for model parts before starting to put together their own models.
7. Conclusions and Outlook The blended learning approach definitely raised the quality of the two lectures in mathematics. The average grade of the students and their programming skills improved, especially with respect to the interaction between calculation and programming. Current plans include the augmentation of the MATLAB server with a dedicated Maple TA elearning server. This will allow the use of professional CAS software for instruction and testing, allowing the students to test themselves to greater extends, especially due to the grading system provided by this software. Eventually, some of the content of the MATLAB course could be re-implemented in the Maple TA
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software, strictly separating the numerical and symbolical tasks. The interface proved to be versatile enough, though, to be directly transferred to other lectures held by the Institute for Analysis and Scientific Computing, especially all those with modelling and simulation content. Other faculties also expressed their interest in using the MATLAB interface. MATLAB is, for example, one of most common tools for signal processing, making the web server an obvious tools for these lectures as well. TUWEL, as expected, simplified the organisation of the lecture and the exercises, but was only used for static content, although its ability to directly translate latex code into properly formatted web pages was priceless in the course design.
8. References [1] www.mathworks.com [2]www.moodle.org
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