Engaging Students with Multiple Representations of Mathematical Models

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.