Mathematics Metadata Working Group

Dedicated to the research, development, implementation, and standardization of metadata for educational and research mathematics.

News AMS Panel discussion: Wednesday, January 19. Ballroom Balcony A, Marriott Wardman Park Hotel. 2:15 - 5:15. Immediately followed by American Mathematics Metadata Task Force Meeting.

This document reports on work done and decisions made at a meeting held August 10 and August 11, 1999, in Berkeley, California. Please see the last section for acknowledgments and a list of attendees. This document was prepared by Robby Robson

Issues covered: The issues covered in the main part of this report are
a mission statement of the Mathematics Metadata Working Group (MMWG)
a brief report on IEEE Learning Object Metadata Standards
the decision to classify mathematics using three separate taxonomies
the detailed structure of these taxonomies
a discussion of other LOM tags and their relevance to the MMWG. Includes rough proposal for which tags to use.
Implementation, work, and cooperation commitments timelines and commitments for the completion of a first public release of mathematical metadata standards
Attachment: Attached is an annotated version of the LOM 3.5 base scheme.
Requests for comments and notes by the author. Comments on any and all aspects of this document are welcome.

Mathematics Working Group

I Mission Statement.

The following mission statement is proposed for the MMWG. It is important to have such a statement for setting future agendas and for explaining MMWG work to potential partners, contributors, and funding agencies. Comments are welcome. MISSION The mission of the Mathematics Metadata Working Group (MMWG) is to analyze, formulate, disseminate, and facilitate the implementation and acceptance of metadata standards that support and enhance mathematical research, education, publication, and software development. Standards developed and promoted by the MMWG will be compliant with accepted international standards. The MMWG is an open group that welcomes the participation and seeks the cooperation of all professional societies, commercial interests, academic institutions, government agencies and individuals who have an interest in its work or a stake in its results.

II IEEE Learning Object Metadata Standards

Until recently there have been several organizations developing potentially completing standards for pedagogic metadata. Over the past six months the situation has changed dramatically. The IMS project and ARIADNE have both agreed to use the IEEE Learning Object Metadata, or LOM, as their standards. The latest LOM specifications, together with annotations, appear as an attached document. It should be pointed out that there are some difficulties in mapping IMS metadata to LOM and that, at least in the opinion of the MMWG, there are portions of the LOM base scheme that are too restrictive or have not anticipated the full range of learners and learning environments. The MMWG struggled with this and eventually decided to follow the lead of NEEDS and to judiciously define the necessary extensions to LOM. These decisions will be explained and communicated to the IEEE Learning Technology Standards Committee and to the IMS project. The structure of LOM. The LOM base scheme is divided into nine categories defined as follows (source: LOM v3.5):
General. Context-independent features of the resource.
Lifecycle. Authorship, ownership, etc.
Meta-metadata. Describes what metadata scheme(s) are being used.
Technical. Describes the format and the technical requirements needed to use the resource.
Educational. Educational and pedagogical features of the resource.
Rights. Refers to intellectual property rights.
Relation. Describes the relation of the given resource to other resources.
Annotation. Allows for comments on the educational use of the resource.
Classification. Taxonomic classification of the resource. (Could be subject matter, educational objective, accessibility requirements, etc.)
The MMWG has decided to work only on those portions of this scheme that need special attention for the purpose of cataloging and searching mathematical materials. But other parts of the base scheme must be included in software that implements metadata, e.g., that tags documents with metadata or that uses metadata to retrieve documents. The most immediate implementation will be as part of the SMETE portal under development by NEEDS, and most of the more general tags have already been addressed by NEEDS software that will be modified to handle mathematical resources.

III The Classification of Mathematical Content.

The MMWG proposes to classify the content of mathematical resources using three taxonomies corresponding to three different levels of vocabulary. Whereas it might be tempting to view these taxonomies as correspond roughly to American grade levels, they should be thought of in terms of vocabulary usage rather than in terms of subject matter. History of This Decision. The first idea for classifying mathematical content was to extend the MSC to encompass grade school, high school, and college mathematics. This was quickly seen to be a poor option for a number of reasons:
The meaning of identical vocabulary can change both subtly and radically across levels of mathematics. It would be very hard, if not impossible, to fit lists of vocabulary used by existing digital libraries into the MSC in a consistent fashion.
There are vocabulary terms, such as "times tables", that decidedly would not fit in with the MSC but which might be important to a large user group interested in finding mathematical resources.
It is not clear that the two-level tree structure used by MSC is the appropriate taxonomic structure, and in fact it is not the one proposed by the MMWG.
There is no organization which has as its natural responsibility of maintaining, disseminating, and updating a classification spanning all of mathematics.
During its June meeting the MMWG abandoned the idea of extending the MSC and proceeded to propose a division of mathematics into four or five separate taxonomies based on progress through the traditional American educational system. Several issues were left open for further consideration: should some of the levels be merged, what were appropriate names for the levels, and what should their internal structure be.
Further Considerations. At this August meeting the MMWG tackled these issues. The following points were made:
The audience for mathematical resources extends well beyond the traditional student taking a traditional class at a traditional stage of schooling. Today’s cadre of learners includes large numbers of adult learners, returning students, students with disabilities, distance learners, and self-directed learners. Neither the taxonomies nor the names for the taxonomies should assume otherwise.
Metadata-enabled searching and learning is of interest to students, teachers, corporate trainers, researchers, editors, and the general public. It is by no means limited to mathematicians or to people studying mathematics as a discipline.
It is better to have fewer rather than more taxonomies. Simpler is better as well. It is not the responsibility of a classification scheme to imbue intelligence into search engines. Rather, it is the responsibility of a classification scheme to provide a basic structure which increasingly intelligent search engines and agents can use and extend.
There are other metadata tags, primarily in the Education category, that can be used in conjunction with any content classification to further describe a resource. Good search and retrieval schemes will rely on a rich combination of metadata tags to define the context in which a classification scheme will be interpreted.
There is nothing precluding labeling a resource with multiple taxonomies. This will be necessary for resources that naturally fall near the boundary between two levels and perhaps will be done as a matter of routine.
Metadata tags will likely be invisible to the general user. They have to make sense to authors and catalogers. This observation should guide the way in which tags, taxonomies, and terms are defined.

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