I had to the chance to talk with Valentyna Pikalova, Kharkiv National Pedagogical University, Ukraine. She is currently doing here Ph.D. on pedagogical aspects of math education. Among others she is collecting and categorizing mathematical problems e.g. distinguishing easy, medium, and difficult problems or well-suited/ inappropriate problems for math teachers. She has experience on different education technologies as she has been using various system to put her materials online, a potential candidate seems to be GeoGebra.
From our discussion I have a better understanding of the workshop’s community. Please note that the following notes are my personal perspectives on the workshop and do not necessarily reflect the actual characteristics of this community.
Most of the international participants seem to be researchers of mathematical education, while there are also many Norwegian teachers attending the event. Challenges of these mathematical education researchers seem to include the following questions:
- Which technologies have been successfully used in math education?
- Can technology improve the learning experience?
- What are drawbacks and pitfalls when using technology?
- When should teachers make use of technologies? Are there situations that are more appropriate then others?
- Does the use of technology change mathematical practice? If yes, can this have negative impacts on the mathematical learning experience and resulting mathematical skills?
- Should traditional teaching methods really be fully replaced or advanced/ enriched by technology?
In contrast, our group provides the technological basis for education technologies. We are working on …
- Change management of various (semi-structured) materials - potentially this is also useful in an eLearning scenario to maintain and collaboratively edit corpora of course material.
- A (intelligent) database for mathematical content providing services such as change management or the adaptation of documents
- A discussion platform for course material
- A wiki for collaborative content creation
- A search engine for mathematical content
- and the theoretical foundations for all our projects (such as the methodology and theory of change management, the development of our document format for mathematical document, and work for allowing easy integration and linking of mathematical theories, …)
- panta rhei - used as precourse and course system for our General Computer Science lecture
- SWiM - soon used to edit OpenMath Content Dictionaries
- and the improved version of locutor - a Subversion Client with change management features
In consequences, we seem to provide fundamental technologies that could be used in mathematical education at some point of time. However, although we are making progress, most of our technologies are still very prototypical. Some system I could imagine to be of interest soon are …
So I believe this community can be seen as potential end-users of our systems. Talking to the participants can be very valuable to use in order to gather real-live requirements and feedback as well as experiences in evaluating technologies. Overall, showing that we produce useful approaches and technologies is an important part of our work we should not neglect.
However, what I also realized is that the understanding of mathematical eContent strongly differs to our understanding. Standards/ terms like OpenMath, MathML, Content Dictionaires or our own document format OMDoc are not necessarily known by the participants. So we need to do a good job in explaining and motivating our work in order to successfully present it to the community. Moreover, the benefits of semi-structural documents/ the markup of the structural semantics of documents has to be clearly stated. Currently, most participants store their materials in system-specific formats/ Word/ (sometimes) TeX - transformation into OMDoc will be tedious.
Knowing this now, my talk was really missing relevant preliminaries in order to be understandable and acceptable by the workshop community. It would have been helpful to include a motivation and introduction of our group’s interest (or the common goal of the Mathematical Knowledge Management community in general) as well as our basic methods/ ideas/ assumptions.
Thanks for this insightful summary! It’s always been a hard exercise for me, maybe even more than for you, to try to understand how the teachers in the JEM project think and what they want. We would have so nice possibilities, but sometimes “we” (the technical guys) and them speak a completely different language, even about the basics.
A crucial experience for me was the program of the “repositories” track of the 3rd JEM workshop in Barcelona (January 2008): We think that a repository is an intelligent semantic database like TNTBase, whereas for a math teacher a repository is rather like a directory of HTML or Word documents with some educational metadata on a file server or web server.
Conclusion: We need to try harder :-/