Data structures and algorithms in pen-based computingenvironments

Abstract

Data structure visualization (or animation) has been studied for more than twenty years, though existing systems have not gained wide acceptance in the classroom by students and their instructors. The main reason is that animation preparation is too time consuming. A more technical reason is that when a particular data structure is encoded into an animation, it does not have the flexibility often needed in a classroom setting. There is also a pedagogical reason: a number of prior studies have found that using algorithm visualization in a classroom had no significant effect on student performance. We believe that the tablet PC, empowered by digital ink, will challenge the current boundaries imposed upon algorithm animation. One of the potential advantages of this new technology is that it allows the expression and exchange of ideas in an interactive environment using sketch-based interfaces. In this paper we discuss teaching and learning tablet PC based environment in which students using a stylus would draw a particular instance of a data structure and then invoke an algorithm to animate over this data structure. A completely natural way of drawing using a digital pen will generate a data structure model, which (once it is checked for correctness) will serve as a basis for execution of various computational algorithms. In the future, we will extend the above visualization tool to a hybrid theorem prover system. Experience shows that many computer science students have great difficulties with the proofs methods encountered in, say, an advanced course on algorithms. Indeed, often the logical foundation of a proof argument seems to escape some of the students. We propose to transform students’ experience with proofs by incorporating pen-based technology into introductory computer science courses. In particular, we consider formal proofs in Euclidean geometry. The cornerstone of this model is the concept of geometrical sketching, dynamically combined with an underlying mathematical model. A completely natural way of drawing using a digital pen will generate a system of polynomial equations of several variables. The latter will be fed to a theorem prover, based on the Grőbner bases technique, which will automatically establish inner properties of the model. Moreover, once a particular mathematical model is created and then checked for accuracy, it will serve as a basis for logical deduction of various geometrical statements that might follow. Finally, a detailed step-by-step exposition of the proving process will be provided.