Schneider, M., Siller, H.-S., Fuchs, K.-J.

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{michael.schneider, hans-stefan.siller, karl.fuchs}@sbg.ac.at. Abstract. This paper provides an overview of an educational knowledge management system ...
Sharing of and communicating about knowledge in mathematics and informatics education Michael Schneider1, Hans-Stefan Siller1, Karl Josef Fuchs1, 1

University of Salzburg, IFFB – Department for Mathematics and Informatics Education Hellbrunnerstr. 34, 5020 Salzburg, Austria {michael.schneider, hans-stefan.siller, karl.fuchs}@sbg.ac.at

Abstract. This paper provides an overview of an educational knowledge management system which has been developed under the EU project “ABCmaths” (cf. [1]). With its support users will be able to communicate, to share and to exchange learning materials as well as cooperate in the development of these materials. The system is driven by models of knowledge that are grounded on educational concepts. An online vocabulary tool will support ontology engineers and domain experts to extend and administrate the systems knowledge model (ontology). A focus in the system implementation will be placed on making access to the content of the knowledge base and online platform as simple and user-friendly as possible. Knowledge transfer to mathematics and informatics instruction via this system should be as efficient as possible for the users. Keywords: knowledge management, knowledge system, education, ontology.

1 Knowledge management and systems The term “knowledge management” has its origins in economics and is becoming increasingly important in many fields. The task of organising knowledge represents a major challenge, “all too different are the conditions, the use of contexts and modalities of knowledge acquisition, knowledge sharing and knowledge use in the various fields of social action” (see [8], p.11). The current high demand for knowledge and communication as well as the flood of already existing information caused by the rapid development of the internet is directly related to the growth of knowledge intensive activities and their complexity. To effectively manage knowledge and ultimately to ensure the clarity of the collected knowledge, a well thought out concept is required and this is dependent on having efficient technical tools. If knowledge or parts thereof are used collectively, communicated and further developed in a specific discipline by a group of people through a network, substantial advantages in terms of increased efficiency and applied know-how can be brought to an organisation. To ensure the best possible use of knowledge resources, a “knowledge management process model” (see [7]) using the blocks “knowledge

acquisition, knowledge development, knowledge distribution, knowledge use and knowledge retention” should be used. The topic of knowledge management in particular has an important role in education. The terms “knowledge” and “school” can be difficult to separate. Wiater (see [8]) explains how knowledge and the term “learning” are connected and which role it has in education. He stresses the importance of the development of professional knowledge and expertise of teachers in educational fields of action in addition to the personal and social aspects of training (see [1]).

2 Knowledge representation and ontologies When faced with the task of representing and communicating knowledge men principally fall back on their own context knowledge stored in the brain. In addition it is possible to combine knowledge extracted from textbooks, regulations, subject indexes and encyclopaedias with one’s own stored knowledge (see [3]). If machines or computers take on the task of conveying or further processing information, they should require a “representation” of the underlying concepts and their interrelationships. In conventional knowledge management systems information is rarely structured and especially the relationship between the stored data is not described. Therefore it is difficult for a computer system or an application to interpret the context and interrelationships of the information. The saved data needs to be supplemented via a knowledge network to resolve this problem. Specific information should be accessible in this process easily and efficiently. To be able to make decisions regarding the knowledge stored in the database and the exchange of so-called metadata a representation of the underlying concepts and their interrelationships is required (see [3]). For the representation of such knowledge in computer science the term “Ontology”, derived from philosophy, was introduced. The most common definition being “the explicit formal specification of a shared conceptualisation” (see [2], p. 201) is used: “An ontology is an explicit specification of a conceptualization.” An ontology is a knowledge model that represents a network of hierarchies wherein information is linked together via logical relationships (see [3]). This precludes double meanings or ambiguity due to the formalisation. It therefore describes a specific area of knowledge through the use of a standardised terminology and relationships between the concepts described therein. The relationship between a symbol and the related thing or part of the world can only be interpreted correctly when the meaning or semantics of the related symbol are described by the people or by the machine (see [6]). In summary one could say that in principle a formalised model of a thing or a part of our world accepted by a group of experts is mapped by the ontology. Depending on the complexity of the domain to be described, different expressions of the knowledge model may be used. One form often used in practice is the “controlled vocabulary”. It represents a set or collection of terms from which specific content objects in a knowledge management system are assigned clearly.

This in turn means that each object can only be described by a single expression. Hence an important aspect is the avoidance of ambiguities For example, the term “function” may have differing concepts and therefore can be interpreted differently in natural language: Function as a mathematical concept or method in computer science. Thus the quality of a controlled vocabulary depends on the use of synonymous meanings of the expression. It should be ensured that each annotated content object is represented by one preferred term. Alternate terms should be declared explicitly, too. The careful modelling of the relationships between the individual terms plays a particular role. The relationships can occur in various forms here: Synonyms for equivalent terms, taxonomies for specialisation and generalisation of terms as well as associations for semantically linked concepts. The following example illustrates various forms of relationship to a specific term in a controlled vocabulary:

Concept: Derivation Equivalent relations (synonyms): differentiation; Ableitung (German); Hierarchical relations (taxonomies): differential calculus (generalisation); analysis (generalisation); curve sketching: turning points, zeros, inflexion points (specialisation); polynomial function (specialisation); Associative relations (associations): differential equation

Figures 1 and 2 show the graphical representation of the corresponding parts of a semantic network:

Fig. 1. Main Term and alternative terms (synonyms) for the term “derivation”

Fig. 2. Taxonomies (hyponyms, hyperonyms) and associations

The selection of approved expressions in a controlled vocabulary represents a very responsible and difficult task.

3 ABCmaths Knowledge Management System The educational knowledge management system which is developed within the EU project “ABCmaths” (cf. [1]) has the purpose of providing a qualitative set of teaching resources in form of theoretical input, exercises or prime examples. These may include context specific supplementary information related to a single area of content or several related areas of mathematics or computer science. These resources will be offered via a web browser and can be downloaded or printed out on request. Conversely, authorised users have the opportunity to create their own content for the knowledge management system, to annotate these resources and to store them on

the server according to their related context. A special program interface is made available for this purpose. This program is a form of “Content Management System” which allows the user(s) to create and format content easily by the use of a wizard. An additional possibility to create content for the system is through the direct uploading of resources which were previously created on the user(s) own computer. An efficient use of the knowledge management system should support teachers with their lessons preparations and implementations. Thus it allows them to concentrate on teaching methodology. It is up to the individual teacher’s flexibility and decision making skills to assemble the resources for a lesson taking into account the planned teaching objective as well as any specific lesson focus. The form of the lesson as it will be held is aside from the question of its efficient structure. In order to ensure delivery of a quality education, it is vitally important to have a focused selection and creation of the learning content and tasks. Humbert ([5], p. 4) said: “The objective of teaching is often shortened to the question: What should be taught? The question of the goals can only be answered through an intensive study of the dimensions of the objectives, education, themes and content.” In this sense the core objective of the educational knowledge management system is access to online resources that are oriented to the “Big Ideas” within the EU project. These “Big Ideas” are a supplement to support teaching and learning materials for teachers and students (see [1]). The ABCmaths Knowledge Management System should support teachers in finding the most appropriate tasks for their individually designed lessons whilst taking into consideration all cross-references between the different fields of mathematics and computer science. By visualising all relevant cross-references to other areas of mathematics or computer science and by the display of related content and the contexts for these gathered resources the user is assisted in seeing complex relationships faster and more easily. A component of the program is designed for this task explicitly. This creates the possibility to locate significant related resources quickly and to call them up as and when required. This can be done via content criteria and/or the merging of various subject matters.

Fig. 3. Knowledge Management System architecture

1.1 The authoring program The authoring program is a user interface for designing and developing teaching and learning materials which will be conceived by users for accessibility in the knowledge management system. Each authorised user may participate in creating content items in the form of instructional material using the platform’s tools. Users are guided through creating content. Programming skills are not required for developing content items which are available to other users through the system subsequently. The authors of these content objects have privileges to administrate and alter their contributions in a private and closed area within the system. They may then decide if any of their content items are published in read-only mode to other users or user groups of the knowledge base or otherwise excluded from the public. The context of each content item should be described and annotated to the systems knowledge model (ontology). A specially conceived categorisation wizard will help the authors to find the appropriate keywords and to classify any contribution to its educational intentions and guidelines. 1.2 The information platform The online information platform presents information of the educational knowledge management system. In order to receive accurate search results and to arrange the appropriate information efficiently, search components are provided on the basis of semantic technologies. The retrieval of content can be context-sensitive therefore. In many information systems it is mainly down to the skill of the user to formulate a search request. Under certain circumstances this task can become very complicated. A search wizard is made available to remedy this problem. It assists and guides the user(s) in finding the desired content. The operation is the following: A user enters a keyword. The ontology is searched through starting with the entered keyword and all related terms, which can be hypernyms, hyperonyms or synonyms. The results are displayed to the user. At this step the system offers the possibility to select one or more of these terms for the search query. This procedure can be repeated until a satisfactory result is achieved. This method should essentially contribute in optimising a generalised or specialised search query and in optimising the accuracy of the search results ultimately. Therefore it is highly important that an author who creates or maintains content of the knowledge management system annotates resources with appropriate terms and describes the relevance of the content in depth. The implementation of a faceted navigation component will allow the user to manage the process of navigation through the knowledge network more flexibly. Thus the desired goal becomes filtered increasingly and the gradual enlargement and deepening of the search results is made easier. In order to realise this technology, keyword chains are formed which constitute a sequence of relevant characteristics (facets). These chains give an overall picture of the content object. “... Not a

document, but rather an assignation of a precise classification aspect which describes it simultaneously in several different systems” (see [4]). A semantic Wiki will support “Collaborative Learning” (see [9]) in classrooms as well as an online communication tool in the form of a semantic Blog, where users can discuss educational topics or communicate content specific themes. Wiki-entries may be created as well as altered by any system user and are available especially for collaborative learning sessions. A version management assure a good overview of all historic entries to a specific content item. Blog entries may also be created by any system user and can be used in the form of a discussion forum. Each resource retrieved from the knowledge management system can be established in an individual portfolio of teaching staff according to the approach designed for the planned lesson and related teaching goals specifically (see figure 4). These portfolios can be modified at any time, especially during a period of learning, what means that resources can be changed dynamically.

Fig. 4. ABCmaths Knowledge Management System: Custom user portfolio

4 Example scenario The following case study illustrates the interaction between a user and the system during the search of content. The categorisation and classification of resources, created in the authoring program is supported extensively through the use of this technology.

Example 1: Stepwise Search • First step: A search term is entered into the appropriate box. It is possible to choose terms from a list of keywords stored in the system additionally (see figure 5). • Next step: The term is searched in the underlying vocabulary for synonyms, taxonomies and associations automatically. Whenever the system finds synonyms they will be displayed to the user accordingly. • Now the user chooses the most relevant term (here: function mathematics).

Fig. 5. Semantic Web component: entering a search term – response from the system





The selected term is browsed for relationships again and the results will be displayed in the appropriate boxes. Hyponyms will be shown under “Specialisation”; hyperonyms under “Generalization”; associative terms under “Relations” (see figure 6). It is possible to specialise the query furthermore. For instance the user can select a term from the list of specialisation. The system will search for relevant relationships again. Here is the place where the search query reduces the list of terms until an accurate result will be achieved.

Fig. 6. Limit the search by multiple dimensions



4

A search for multiple subjects – in this case representation and (lessons) intention – can be customised to meet the individual needs of a user even more.

Summary and perspectives

A focus on the development of this system is placed on making access to the contents of the knowledge base simple and user-friendly in order to make the transfer of knowledge into the classroom for student(s) and teacher(s) as efficient as possible. Additionally a well thought - out implementation of the individual program features should facilitate a wide acceptance by the user(s) ultimately and promote the integration of this system in everyday teaching therewith. A controlled vocabulary in the expert areas of mathematics education and computer science education ought to exist in addition to the ongoing ABCmaths project [1] in a future work as requested. Further evaluations and field testing of the system will be important for its acceptance in schools and universities. The gradual expansion and maintenance of the knowledge network is planned to ensure the quality of the educational knowledge management system and to optimise it continuously.

Acknowledgements The project ABCmaths is funded with support from the European Commission (503215-LLP-1-2009-1-DE-COMENIUS-CMP). This publication reflects the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein. We acknowledge the cooperation of Sebastian Kuntze, Elke Kurz-Milcke, Anika Dreher, Anke Wagner, Claudia Wörn (Ludwigsburg Univ. of Education), Christiane Vogl (University of Salzburg), Stephen Lerman, Peter Winbourne (London South Bank University) and Bernard Murphy (Mathematics in Education and Industry, UK) who collaborate in the ACBmaths project team.

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