Function Machines

Abstract

Function Machines is a visual environment expressly designed to support the learning and teaching of mathematical modeling. The Function Machines language employs 2D visual representations—graphic icons—in contrast with the symbolic textual expressions used for representing mathematical structures in standard programming languages. Function Machines supports learners in a rich variety of mathematical investigations. Its visual representations significantly aid students’ understanding of function, iteration, recursion, and other key computational concepts. It is especially valuable for developing mathematical models. To understand a model, students need to see the model’s inner workings as it runs. At the same time, they need to see the model’s external behavior—the outputs generated by its operation. Function Machines supports both kinds of visualization. The use of these duallinked visualizations has unique and valuable learning benefits.