Structure and Dynamics of Knowledge
Knowledge is a Network
The structure of knowledge can be better described in terms of a network, as in a semantic network, is the point of departure of the lab's work. Meaning of any concept that we harbour or any activity that we do as cognitive agents is generated out of links between concepts or activities. No node in such a network is meaningful on its own right, but only by virtue of the links the node has with the neighbouring nodes. Nothing will be considered a bit of information unless it is linked to others.
We use this framework to study the problem of conceptual change in both ontogeny (individual cognitive development) and phylogeny (history of ideas). By studying the nature of changes in the knowledge network we wish to capture the dynamics of knowledge, and each snapshot of the network at any given time as the structure of knowledge. This is how we are approaching the problem of structure and dynamics of knowledge.
In concrete terms we undertake research and development work in the gnowledge laboratory, where we are currently investigating on the following topics.
Developing GNOWSYS, a node oriented computing system (an official GNU project.).
Studying the nature of dependency relations in a cognitive system (working paper).
Using dependency relation to develop a unique roadmap of all knowledge (this project is now online at www.gnowledge.org.) This will eventually develop as an atlas of knowledge. This is our version of knowledge cartography.
Refined concept mapping for science education, for teaching, learning and assessment.
Testing the hypothesis that rigor develops by minimal use of relation types, and not by refining the concept. This is also the basis of our cognitive development model where agents begin with procedural, implicit, modular knowledge and develop declarative, explicit and non-modular knowledge.
- A characterisation of scientific knowledge as procedurally re-described reproducible knowledge.
Refined Concept Mapping (RCM) is an extension of Novakian concept mapping for representing scientific knowledge. Any concept map can be turned into an RCM by using well defined and non-redundant linking phrases (relation names). One of the main assumptions for trusting this approach is that science is a pursuit to advance rigor (clear thinking) so that all subjects hold onto the same meaning to the extent possible.
Some of the tasks that we are currently working using this approach include:
re-representing the domain of Cell Biology at the school, college and undergraduate level using RCM
developing a minimal set of relation names for representing scientific knowledge
studying the possible use of RCM for teaching and learning science
to compare the representations of novice and expert
to study conceptual change by focusing on the linking phrases (relation names)
- Heather D. Pfeiffer, Dmitry I. Ignatov, Jonas Poelmans and Nagarjuna Gadiraju (Eds.) (2013). Conceptual Structures for STEM Research and Education, Proceedings of the 20th International Conference on Conceptual Structures, Mumbai, India January 2013. Springer-Verlag, Berlin.
- Nagarjuna G. & Meena Kharatmal (2011): A Proposal for Developing a Primer for Constructing and Analyzing Conceptual Structures. In S. Andrews et al. (Eds.), Lecture Notes in Artificial Intelligence: Vol 6828. Conceptual Structures - Learning Teaching and Assessment. In International Conference on Conceptual Structures: Conceptual Structures for Discovering Knowledge (p. 402-405). Berlin, Germany: Springer-Verlag. Doi: 10.1007/978-3-642-22688-5_36
- Meena Kharatmal & Nagarjuna G. (2010): Introducing rigor in concept maps. In M. Croitoru, S. Ferre, and D. Lukose (Eds.), Lecture Notes in Artificial Intelligence: Vol. 6208. International Conference on Conceptual Structures 2010: From Information to Intelligence (p. 199-202). Berlin, Germany: Springer-Verlag. Doi: 10.1007/978-3-642-14197-3_22
- Nair, R., Nagarjuna, G., & Ray, A. K. (2014). Finite-size effects in the dependency networks of free and open-source software. Complex Systems. 23, 71-92.
- Meena Kharatmal (2009): Concept Mapping for Eliciting Students’ Understanding of Science . Indian Educational Review. 45(2), pp. 31-43.
- Meena Kharatmal & Nagarjuna G. (2013): Representing Change Using Concept Maps. In G. Nagarjuna et.al. (Eds.) Proceedings of epiSTEME 5 -- International Conference to Review Research on Science, Technology and Mathematics Education, p. 124-131. India: Cinnamonteal.
- Meena Kharatmal & Nagarjuna G. (2011): An Analysis of Growth of Knowledge Based on Concepts and Predicates---A Preliminary Study. In S. Chunawala & M. Kharatmal (Eds.). Proceedings of epiSTEME 4 -- International Conference to Review Research on Science, Technology and Mathematics Education, p. 144-149. India: Macmillan.
- Meena Kharatmal & Nagarjuna G. (2009): Refined Concept Maps for Science Education: A Feasibility Study In K. Subramaniam & A. Majumdar (Eds.) epiSTEME 3 Third International Conference on Review of Science, Technology and Mathematics Education. Mumbai: MacMillan Publishers Ltd.
- Meena Kharatmal & Nagarjuna G. (2008): Exploring the Roots of Rigor: A Proposal of a Methodology for Analyzing the Conceptual Change from a Novice to an Expert In A. Canas, P. Reiska, M. Ahlberg, J. Novak (Eds.) Concept Mapping: Connecting Educators. Proceedings of the Third International Conference on Concept Mapping. Tallinn, Estonia & Helsinki, Finland.
- Meena Kharatmal & Nagarjuna G. (2007): An Alternative Proposal for Eliciting and Assessing Students’ Knowledge Structure In C. Natarajan & B. Choksi (Eds.) epiSTEME 2 Second International Conference on Review of Science, Technology and Mathematics Education. Mumbai: MacMillan Publishers Ltd.
- Meena Kharatmal & Nagarjuna G. (2006): A Proposal To Refine Concept Mapping for Effective Science Learning In A. Canas, J. Novak (Eds.) Concept Maps: Theory, Methodology, Technology. Proceedings of the Second International Conference on Concept Mapping. San Jose, Costa Rica.
- Meena Kharatmal & Nagarjuna G. (2004): Understanding Science Through Knowledge Organizers In J. Ramadas & S. Chunawala (Eds.) epiSTEME 1 First International Conference on Review of Science, Technology and Mathematics Education. Mumbai: HBCSE.
Structure and Dynamics of a Model Semantic System
A semantic interpretation has been given to the dependency network of a free-software operating system. To preserve uniqueness of operations in this network, the nodes (software packages) obey an exclusion principle, with no two nodes being exactly alike in their functionality. From a semantic viewpoint this implies that the meaning derived from a particular node is defined uniquely only by its dependency neighbourhood. The frequency distributions of links in this network follow a scale-free power-law behaviour for the intermediate nodes, but the extremal nodes exhibit a saturation behaviour as a result of the finiteness of semantic possibilities in the network. Across two generations of free-software network, the saturation properties of the in-degree and the out-degree distributions are affected oppositely. The primordial nodes of the out-degree distribution are the foundation of the entire network, and in a semantic sense, meaning flows from these nodes to the derivative nodes. In a mature network, semantic variations are more likely in the weakly-linked derivative nodes than in the primordial nodes (where all axioms are founded). The notion of a semantic system, based on dependency relations, and behaving like a scale-free network, has been extended to understand the structure of knowledge in general.
Making of an atlas of knowledge
The article is about a new online resource, a collaborative portal for teachers, which publishes a network of prerequisites for teaching/learning any concept or an activity. A simple and effective method of collaboratively constructing teachinglearning sequences is presented. The special emergent properties of the dependency network and their didactic and epistemic implications are pointed. The article ends with an appeal to the global teaching community to contribute prerequisites of any subject to complete the global roadmap for an altas being built on similar lines as Wikipedia. The portal is launched and waiting for community participation at http://www.gnowledge.org.
Kharatmal Meena & Nagarjuna G. (2009) SELF Platform---A teacher-centric collaborative authoring system, Journal of Applied Collaborative Systems, 2 (1), 2009.
- Nagarjuna G. (2009) Collaborative creation of teaching-learning sequences and an Atlas of Knowledge Mathematics Teaching-Research Journal Online, 3 (3).
- Nagarjuna G. Kharatmal, M., Nair, R. (2010): Building Dependency Network for Teaching-Learning Conceptual Structures. In Polovina, Simon; Andrews, Simon; Hill, Richard; Scharfe, Henrik;
Øhrstrøm, Peter (Eds.) Proceedings of the First Conceptual Structures
– Learning, Teaching and Assessment Workshop (CS-LTA) at the 18th
International Conference on Conceptual Structures (ICCS 2010),
Published by MIMOS BERHAD » Technology Thrust Areas » Knowledge
Technology (ISBN: 978-983-41371-5-1), Kuching, Malaysia.
- Divya, S., Gajbe A., Nair R., Gajre G., Nagarjuna G., (2009) GNOWSYS-mode in Emacs for collaborative construction of knowledge networks in plain text, Proceedings of 8th International Semantic Web Conference (ISWC), October 25-28, 2009, Washington, D.C.
- Divya S., Gajbe A., Nair R., Gajre G. and Nagarjuna G. (2009) GNOWSYS-mode: An Emacs based Text Editor for Semantic and Structured. Document Editing Proceedings of Workshop on Collaborative Construction, Management and Linking of Structured Knowledge (CK 2009), October 25-28, 2009, Washington, D.C.
- Gajbe A., Nair R. (2009) Node Oriented Knowledge Management, Proceedings of National Conference on Open Source Software, 25-27 May 2009, C-DAC, Navi Mumbai.
- Kharatmal M. (2009) SELF-Platform---A Teacher-Centric Collaborative Authoring System, Proceedings of National Conference on Open Source Software, 25-27 May 2009, C-DAC, Navi Mumbai.
- Nair R., Nagarjuna G., Ray A (2009)., Semantic network in a free-software computer operating system, Proceedings of the Annual Conference of Vijnana Parishad of India and National Symposium on Recent Development in Applicable Mathematics and Information Technology, Jaypee Institute of Engineering & Technology, Guna.