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LATTICE-VALUED CONVERGENCE: QUOTIENT MAPS
Title
LATTICE-VALUED CONVERGENCE: QUOTIENT MAPS.
Creator
Boustique, Hatim, Richardson, Gary, University of Central Florida
Abstract / Description
The introduction of fuzzy sets by Zadeh has created new research directions in many fields of mathematics. Fuzzy set theory was originally restricted to the lattice , but the thrust of more recent research has pertained to general lattices. The present work is primarily focused on the theory of lattice-valued convergence spaces; the category of lattice-valued convergence spaces has been shown to possess the following desirable categorical properties: topological, cartesian-closed, and...
Show moreThe introduction of fuzzy sets by Zadeh has created new research directions in many fields of mathematics. Fuzzy set theory was originally restricted to the lattice , but the thrust of more recent research has pertained to general lattices. The present work is primarily focused on the theory of lattice-valued convergence spaces; the category of lattice-valued convergence spaces has been shown to possess the following desirable categorical properties: topological, cartesian-closed, and extensional. Properties of quotient maps between objects in this category are investigated in this work; in particular, one of our principal results shows that quotient maps are productive under arbitrary products. A category of lattice-valued interior operators is defined and studied as well. Axioms are given in order for this category to be isomorphic to the category whose objects consist of all the stratified, lattice-valued, pretopological convergence spaces. Adding a lattice-valued convergence structure to a group leads to the creation of a new category whose objects are called lattice-valued convergence groups, and whose morphisms are all the continuous homomorphisms between objects. The latter category is studied and results related to separation properties are obtained. For the special lattice , continuous actions of a convergence semigroup on convergence spaces are investigated; in particular, invariance properties of actions as well as properties of a generalized quotient space are presented.
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Date Issued
2008
Identifier
CFE0002369, ucf:47811
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0002369
Gamification: Badges and Feedback
Title
Gamification: Badges and Feedback.
Creator
Macon, Brian, Fanfarelli, Joseph, Smith, Peter, McDaniel, Rudy, Boustique, Hatim, University of Central Florida
Abstract / Description
Gamification, the implementation of game elements in a non-game context, is a rapidly growing field of research. One element of gamification that has experienced a rapid growth in popularity is the use of digital badges. Despite widespread adoption in educational settings, there are still gaps in the understanding of their effects on motivation, engagement, learning, and other factors. Furthermore, feedback delivered through badges can include a symbolic reward for successful completion of a...
Show moreGamification, the implementation of game elements in a non-game context, is a rapidly growing field of research. One element of gamification that has experienced a rapid growth in popularity is the use of digital badges. Despite widespread adoption in educational settings, there are still gaps in the understanding of their effects on motivation, engagement, learning, and other factors. Furthermore, feedback delivered through badges can include a symbolic reward for successful completion of a task, providing a credential for gaining a skill, or acknowledging mastery of a particular piece of knowledge. This study implemented digital badges in online courses at a large urban two-year college. Badges were used to deliver embedded feedback and analyze the results on motivation, engagement, and learning. An experimental group received badges over the course of a three week module composed of various learning activities targeting course learning outcomes. A control group experienced the same learning activities without receiving the digital badges. Results indicated insignificant differences in perceived motivation, learning gains, and perceived engagement between the two groups. Positive results were observed regarding increased peer-to-peer engagement evidenced by a significant increase in discussion board activity. The increased engagement of peers leads to the subsequent building of a strong learning community. This positive group association can provide a feeling of support which leads to increased effort, persistence, and goal achievement. Potential causes are discussed and suggestions for future research are provided.
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Date Issued
2019
Identifier
CFE0007491, ucf:52641
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0007491