The Catalan Teaching Tool – A Learning Process Design for Supplemental Instruction and Learning Process Facilitation

ABSTRACTThis paper is based on a supplemental instruction technique aimed at disseminating a difficult concept at the undergraduate level. The software developed as a teaching tool attacks the problem from an intuitive perspective with the aid of visual tools. The tool, run as an experiment, conclusively proves that the original problem of calculating the number of paths from a point (0, 0) to any point (<i>n</i>, <i>n</i>) on a graph might be better understood. The moves can only be east and north in whole number increments and cannot exceed the <i>x</i> = <i>y</i> line at any point. A program is written to produce the graph. Incrementing the value of (<i>n</i>, <i>n</i>), the Catalan number series is produced. Another program is written using the formula which produces the Catalan numbers, and the growth of the series is determined. The teaching tool is created based on the algorithm. A robot is designed which follows the Catalan path is also demonstrated. A survey conducted using this teaching tool shows that it enhances the learning and understanding of Catalan numbers.