My goal in this tutorial series is to illuminate the beauty in the mathematics that most of us study in our youth. This formal language for self expression enables us to communicate ideas clearly–so clearly that computers can interpret those ideas and respond to them. Seymour Papert, a pioneering educator and researcher, imagined teaching children to “talk mathematics” in his classic book Mindstorms.
The idea of “talking mathematics” to a computer can be generalized to a view of learning mathematics in “Mathland”; that is to say, in a context which is to learning mathematics what living in France is to learning French.
A Little Background
The Wikipedia entry on mathematics begins by highlighting core topics like quantity, structure, space, and change. Whether you’re into creating things or exploring the limits of knowledge, mathematics is a useful lens through which to view the world.
In 1936, two mathematicians named Alonzo Church and Alan Turing wanted to determine what functions could be computed; they ended up laying the foundation of computer science. It’s fitting that computational thinking–thinking about problems in terms of systems, models, data, and algorithms–is a powerful approach to learning and applying mathematics.
The International Society for Technology in Education (ISTE) outlines the following core components in their computational thinking competencies.
Systems that enable decomposition.
\(\mapsto\) Models that distill essential features.
Data that computers can understand.
Algorithms that computers can execute.
These tutorials emphasize these components as part of a structured problem-solving process.