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Engaging Students with Multiple Representations of Mathematical Models

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Conference

2019 Pacific Southwest Section Meeting

Location

California State University, Los Angeles , California

Publication Date

April 4, 2019

Start Date

April 4, 2019

End Date

April 6, 2019

Conference Session

PSW Section Meeting Papers - Disregard start and end time - for online paper access only

Tagged Topics

Diversity and Pacific Southwest Section Meeting Paper Submissions

Page Count

11

Permanent URL

https://peer.asee.org/31826

Download Count

166

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Paper Authors

biography

Pradip Peter Dey National University

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Dr. Pradip Peter Dey has more than 20 years of experience in Computer Science research and education. His university teaching and professional experience emphasizes mathematical modeling, information extraction, syntax and semantics of natural language, wireless apps and knowledge representation. He has done an M.S.E. in Computer and Information Science and an interdisciplinary Ph.D. from University of Pennsylvania.

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Abstract

Engaging Students with Multiple Representations of Mathematical Models

Abstract Mathematical models of computation such as Turing Machines, Pushdown Automata and Finite Automata can be adequately represented in a tabular form. However, students tend to engage and participate actively when multiple representations including transition graphs, tabular forms and coded strings are used for discussing pertinent issues. These representations can be mutually translated to each other without any loss of formal properties. This paper reports on experiments with multiple representations of Turing Machines for modeling dynamic aspects. Student participation was found to be significantly higher when graphical representations were given using transition graphs in addition to other representations. Most learners liked multiple representations of Turing Machines even when the standard tabular representation was good enough for explaining fundamental aspects of information processing. 87.5% learners preferred multiple representations of a Turing Machine to one representation in a web-based learning environment. The representations of the Turing Machine were used as a supplement to introductory onsite math foundations of computer science course on the following website: http://www.asethome.org/mathfoundations/tmd/. Applications of Turing Machines in other fields were discussed using different representations. Software design tools based on statecharts proposed by David Harel have been very popular for modeling dynamic aspects of software. Statecharts are simplified Turing Machines presented in a graphical notation that is appropriate for explaining software design and development features in an intuitive way.

Dey, P. P. (2019, April), Engaging Students with Multiple Representations of Mathematical Models Paper presented at 2019 Pacific Southwest Section Meeting, California State University, Los Angeles , California. https://peer.asee.org/31826

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