Xmath Objectives

The participating institutions have for many years been using mathematical software and multimedia documents in their teaching of mathematics. Governmental authorities have plans for the integration of new technology in education. The coordinating institution has recently closed the national project "Open learning systems in mathematics" (http://kurs.hibu.no, http://www.emr.hibu.no/mathstream/default.htm) and the post-doctoral work "HyperMath" (CD-ROM, attached document). Mathematics has been especially focused for some years. In many european countries both the number of students in mathematical courses (university) and the number passing the examination have reached a "dangerous" low level and industry and schools are complaining.

To meet this challenge the pedagogics and methods of communicating particularly higher mathematics will have to undergo an innovative process where new technology is important. The connection between mathematical pedagogics and ICT has to some extent been underestimated. The improvement of understanding mathematics by using interactive and personalized documents in a non-linear and event-driven manner could turn bad trends for mathematics. And the problems assosiated with girls and mathematics also have to be emphasized through the selection of applications.Mathematics and ICT is in its very birth. One very important factor of this shortcoming has been the difficulties with distributing mathematics on the internet. Until now this has in fact not been possible due to technological problems and the lack of standards. Mathematics on the net has NOT been mathematics but images.

The development of the new standard for describing documents on the net, XML (MathML), has now made it possible to include REAL mathematics on a web page and to introduce this brand-new technology in connenction with mathematical education. MathML will convert "frozen images" to "live materials", the main difference between ordinary books and multimedia documents. Introducing MathML will be an important strategic factor in the development and innovation of mathematical and scientific education on the net and represents a "quantum step" in rendering mathematics in a web browser.

The objectives of Xmath is first of all to design a framework making it possible to use MathML in mathematical education on the net and making it possible to evaluate the pedagogical advantages of netbased education in mathematics. One of the key elements of netbased pedagogics generally is connected to the communication process student-student and student-teacher over distance (synchronous and asynchronous). The framework then has to include a management system and communication resources understanding MathML documents. One of the participants has developed the very first system for e-communication using mathematical symbols, operators and shapes (ScientificTalk). The framework also has to include sofrware making it possible to generate MathML code automatically and to evaluate (calculate) content markup (WebMathematica coming including a special WEB-server)).

To demonstrate the use of MathML and to be able to evaluate the pedagogical impact of using it, a pilot course in university mathematics has to be developed. Since MathML is not generally well known because this is a brand-new technology or even more important the lack of browsers to render it, the project partners have to take responsibility in connection with dessimination of both MathML itself and the envisaged outputs of the project. It is expected that the use and interest for MatmML will be increasing both in education and publishing. The project group will have as an objective to create and maintain virtual rooms concerning the use of MathML and WebMathematica (www.Xmath.org) in education and publishing.

The innovative elements of the project lie in the technology itself. As earlier mentioned MathML will make it possible, for the first time, to render real mathematics in a web browser. This will have influence on both the presentation and the semantics of mathematical symbols and operators and the impact of this technology on netbased pedagogics in mathematics will be explored. The project group has to design the course in the front line of web-based research and development and the course will be one of the first using MathML. For the first time it will also be possible, due to one of the participants, to communicate student/student and student/teacher using mathematical symbols, operators and shapes (ScientificTalk, MathML based) and in this context using innovative pedagogical methods where the use of small groups e-communication and collaboration will be essential.

Mathematical education has traditionaly two main goals: to train students in logical and abstract thinking and to give students an ability to use mathematical knowledge in fields other than mathematics itself. Achieving, in particular, the last goal will require what we call understanding and the understanding of understanding will be important. We need to let the student feel importance in a wider context than the upcoming examination. The use of interactive and event-driven documents will enhance understanding and allow an explorative and personal way of working. These documents are efficient and direct and may combine different kinds of hypermedia. MathML content markup and animated graphics (ShockWave) will make this possible in mathematical education.

This is expected to enhance mathematical pedagogics on the net and will stimulate activity, independence and collaboration, and may also prevent sharp distinctions between girls and boys using ICT. In this way the teacher will be more of an instructor rather than a professor.Representing mathematics using MathML content markup will make it possible to include semantics which means that mathematical expressions may be evaluated in site or by pasting the expression into mathematical software. The student may then "play" with the expressions rather than only looking at them. The history of evaluation may be accessed by the student and it will be possible to draw graphs and to make simplifactions.Special focus will be put on the communication process which is one of the main differences between ordinary teaching and distance learning.

The communication process is critical and mathematical didactics has to deal with these kinds of problems. We hope that the use of MathML documents in mail and chat will enhance communication. The use of MathML will strongly support one of the most important parameters here: the exactness and unambiguousness of the communication. Innovative pedagogical methods in connection with virtual rooms for group activities will be evaluated by using small groups to look for advantages connected to the the group size.Due to the software ScientificTalk developed by one of the participants, the very first communication software using mathematical symbols, operators, drawings and graphs, such an excatness and unambiguousness will be possible in mathematics for the first time. Important differences between netbased pedagogics and traditionally pedagogics lies in this communication process and in the ability to monitor the students work . You then have to use a management system which may be called a vertical portal for distance learning. The framework earlier described include such a portal.

The portal may let the instructor get information about the frequency of using different parts of the course documents and may include what is be called a "Course café": virtual rooms as chat and news and quizzes evaluated automatically. The evaluation of these new "pedagogical elements" will be important.

The project group will design a framework for distance learning. The use of this framework will be described in detail and all kinds of personal in education may take advantage of this. The mathematical course developed and the pedagogical evaluation of it will be free to use both in the countries involved in the project and beyond these countries.

The target groups for the framework and the pilot course are initialy the students of the participating institutions including ODL students. As described mathematical education has reached a low level of both the number of students and the number of students passing the exams. We hope that bad trends will turn using the results of the project and that the learning oportunities for mathematical students will be enhanced.These bad trends for mathematics are serious. It can make european countries disabled to meet new challenges and to get run over. Mathematics has had and will have impact on the technological and the economic development. A student has to personify mathematical knowledge and to make it her/his own. We have to avoid a development were information is increasing but as a result the knowledge is decreasing. We hope that Xmath will contribute here.