A Visual Modeling Tool for Mathematics Experiment and Inquiry

Abstract

The Function Machines Language Programming languages are potentially powerful tools for helping students develop mathematical ways of thinking. However, helping students acquire fluency in developing mathematically rich programs, especially in a way that they find engaging and pleasurable, is a nontrivial task indeed. Even Logo, the most accessible functional language, poses significant conceptual barriers to the acquisition of the necessary knowledge and skill. The mechanisms for passing data and transferring control between procedures, particularly iterative and recursive control structures, are particularly difficult for beginning students. The Function Machines computer language was expressly designed to overcome these barriers through the use of visual representations that make control structures and program operation more transparent and accessible. Work with Function Machines enhances students’ development of the notions and art of mathematical modeling and model-based inquiry.