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Manas Hardas |
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Research interests: Manas Hardas – Research Statement
2008-09 In the academic year of 2007-08 I was
able to publish two papers and present them at conference such as 5th
Atlantic Web Intelligence Conference (AWIC 2007 Traditional learning theories can be
broadly divided into behavioral, connectionist or cognitive theories. I am
particularly interested in the cognitive explanations for learning because
they fit well with the traditional graph theoretic approaches of computer
science. We envision the learner’s mental map as a complex graph of concepts
linked with relationships labeled with different kinds of semantics. I our
representation we symbolize the mental map as a constructively developed map
with newer concepts formed over the knowledge of previous concepts.
Constructivism is a cognitive theory of learning given by the acclaimed
psychologist Jean Piaget which explains how knowledge is acquired by a learner
by the means of assimilating and accommodating newer knowledge into already
existing structures of knowledge [1, 2]. It says that newer knowledge is
built on existing knowledge with the advantage of experience. Of course
educational psychology fails to address their specific explanations in the
context of graph theories which are firmly grounded in computer science with
sound mathematical basis. I plan to model the phenomenon of constructivism as
seen happening in everyday learning and give it a mathematical explanation.
In the previous published work, we have been able to get our representation
of knowledge framework critically evaluated in various conferences [2, 3].
The basis of this representation again is engrained in the theory of
constructivism. In our representation the knowledge required to understand a
particular concept is given by the children concepts. Thus a constructively
developed bottom-up map is formed where in the leaf concepts constitute the
knowledge of their parents, which constitute the knowledge of their parents
and so on. Using this as the basis of our knowledge structure I plan to
define the exact operations which contribute to “learning”. We define
learning as a “demonstrable acquisition of the expert knowledge map by the
learner”. Using this definition I will conduct experiments where I can test
different cognitive learning theories with a mathematical basis. The research project can be broadly divided
into three phases: 1. The very first phase in the project
is to ready the expert knowledge map for hypothesis testing and
experimentation. We have decided to compose the expert knowledge map for the
field of Computer Science, with 7 basic topics namely, Operating systems,
Computer Architecture, Data Structures, Programming Languages, Discrete
Structures, Algorithms, and Computer Networks. The granularity of the
knowledge map will be refined as time progresses and finer concepts and links
are added and deleted from the knowledge map. Standardized text books are
used to create these knowledge maps, the granularity of concepts ranging from
the high level concepts from the index to low level concepts extracted from
actual lines of text. Creating a comprehensive map of Computer Science
knowledge is the first phase of the project. 2. In the first phase we develop a
mathematical model for explaining the process of learning defined by a
learning theory from educational psychology. The backbone representation for
this model is the constructively developed graph, also called as the
learner’s mental map, which adheres to the original graph representation. The
act of learning is said to have occurred when there are changes made to this
graph by the learner as a response to a particular stimulus. We define an
array of plausible operations like add link, delete link, add node, delete
node, merge node, split node, reinforce link etc. that are used to make
amendments to the learner’s map. Once we have all the plausible operations,
we go further and try to analyze in a step by step process the actual metamorphosis
of the learner’s mental map from M1 to Mn as the
learner acquires the expert map through the medium of instruction. For the
time being we restrict the medium of instruction to text excerpts from
standardized text books. The next step in this phase is to mathematically
explain the processes of assimilation and accommodation as described by Jean
Piaget. By the theory of constructivism, assimilation of knowledge occurs
when a student acquires new knowledge and it does not conflict with previous
conception. However if it does conflict then a learner moves into a state of
disequilibrium (or confusion) and to recover from this state the learner has
to change this preconceptions to accommodate the new knowledge. These two
theories fit very well with the graph theoretic point of view. 3. In the second phase, we develop
mechanisms to understand individual student learning process and consequently
guiding the process of learning based on the mathematical model from phase 1.
This phase is loosely divided into two experiments: · In the first experiment
I plan to map the learner’s mental maps before, during and after the process
of learning. The mapping of the gradual metamorphosis of the mental map of a
student can give great insights into exactly how human mind works while
learning. We use the technique interviews-about-instances (IAI) to roughly
map the student’s alternative conceptions, or naďve conceptions (learner’s
initial mental map) at different times of the experiment and using the
operations defined in phase 1 try to visualize the actual learning process.
The IAI technique is carefully designed so as to exactly figure out which
operation is the learner subconsciously executing at exactly which instance
of learning activity. · In the second experiment we streamline the
process of learning itself by controlling the process of instruction. By
algorithmic means, based on the specific learning theory, the sequence in
which particular topics need to be taught can be generated. The algorithm
travels through the predefined course concept space generating a sequence of
concepts which need to be taught. Unless the learner demonstrates that he/she
has acquired the concept knowledge, the algorithm does not proceed. Then the
student can be recursively accessed for the acquired knowledge, making sure
at every stage of instruction the student acquires the correct mental
structures. This research has a lot of implications
to education psychology and machine learning. Until now, nobody in either of
the field has looked at learning as a metamorphosis of a concept map.
Educational psychologists do have theories for learning and instruction by
conceptual transformation but none of them have graph theoretic approach and
therefore lack the soundness of mathematical proofs. By treating the process
of learning more objectively than subjectively we can tap into the vast
knowledge of computer science and use it to explain to some extent the
subjectivity in psychology. This research grant will help me pursue this
multi disciplinary research project for the next year and hopefully I will be
able to come up with some ground breaking results. References: [1] Piaget, J. (1971). Biology and
Knowledge. [2] ATHERTON J S (2005) Learning and
Teaching: Assimilation and Accommodation [On-line] [3]
Javed Khan and Manas Hardas, “A Technique for Representing Course Knowledge
Using Ontologies and Assessing Test Problems”, pp. 174-179, 5th Atlantic Web
Intelligence Conference 2007, June 25-27, 2007 - [4] Javed Khan and Manas Hardas,
“Hierarchical Course Knowledge Representation Using Course Ontologies”, in
IICAI 2007, the 3rd Indian International Conference on Artificial
Intelligence, December 17-19 2007,
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© 2005-2006 Manas Hardas, Mail to: mhardas (at the rate ) cs (dot) kent (dot)edu |