Conceptual Mathematics via Literate Programming

TL;DR

This paper advocates for a literate programming approach combining types and functions to improve mathematics learning, demonstrated through a collaborative solution to the Josephus problem.

Contribution

It introduces a novel programming methodology integrating types and functions to enhance mathematical education, contrasting with traditional Scratch programming.

Findings

Literate programming improves understanding of mathematical concepts.

The approach effectively solves the Josephus problem.

Enhanced engagement in mathematics learning through programming.

Abstract

Recent developments in computer programming and in mathematics suggest that there is a strong case for a new way of introducing programming to enhance the learning of school mathematics. The article describes a collaboration of mathematics and computer science teachers to solve the Josephus problem. We demonstrate how a programming approach based on both types and functions can make a vastly improved contribution to learning mathematics than the less successful use of conventional computer programming in Scratch.