One of the more interesting aspects of working on the Cambridge Maths framework is the opportunity to fall down the rabbit hole and see where it leads. The "Quantity" chapter in "On the Shoulders of Giants" threw up a reference to "Computing & Mathematics", a book published in 1984. Ellen, our fabulous research officer, quickly sourced a copy from its home in the British Library. Scanning the slightly yellowed pages, it was clear that conversation about the impact of computing on the study of mathematics has barely moved on since the early 80s. Many of our discussions at Cambridge Maths concern how the affordances of technology in support of conceptual understanding can be balanced with the need to ensure procedural fluency in mathematical techniques. It is absolutely vital that our framework encapsulates the advantages that the "black box" of software can provide, without throwing the numerical baby out with the bathwater.
Back to the rabbit hole, a paragraph in "Computing and Mathematics" identified a course developed in the late 1960s by the "Colorado Schools Computing Science Group" entitled "Second Course in Algebra and Trigonometry with Computer Programming", which can now be found on the web here:
https://archive.org/details/ERIC_ED041746
The course begins with very basic procedural design using flowcharts, introduces some basic BASIC commands, and proceeds to develop programs exploring simple ideas such as subsets, sequences and tests for divisibility.
The language used is now obsolete and many of the later mathematical ideas explored have fallen out of favour in modern curricula, but the core of the idea contained within this course seems more relevant now than ever. Recent government reform has seen a big push towards developing coding ability in students. The adoption of the Python language by many educational providers and its inclusion in computing GCSE, and even some mathematics A-level units, mean that in the next few years students will be better coders than ever before.
As a teacher, I often fiddled around the edges of coding in mathematics, teaching a series of lessons to KS3 students using "Gamemaker" to produce mini games such as "shoot the prime number". These were always a lot of fun, but suffered from the barrier that in order to explore the mathematical ideas, the programming and software had to be taught from scratch (there is an accidental pun in this sentence for those who know!). In an era where students are gaining experience in the use of Python, now seems like an ideal time to revisit the concept of a course in mathematics using programming, in which ICT departments and maths departments (often already sharing staff) can work together to deliver lessons in which the coding challenges set in ICT are given purpose and reinforce mathematical ideas, and mathematics exercises can explore structural concepts either by writing code or by translating examples of code into mathematical processes.
The rabbit hole beckoned once more - my curiosity was piqued and I decided to explore how easy it would be to create a program that would find the Highest Common Factor of two numbers. The slight fly in the ointment was that I had absolutely no idea how to use Python, nor even how to get started. A brief google located a beginner's guide at https://automatetheboringstuff.com/ and after half an hour of scan reading, trial and error, and absolutely no swearing at all, I managed to produce the following code.
![](data:image/png;base64,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)
Amazingly and very satisfyingly - it works! It got me thinking, how much of the maths that we cover with students at KS3 and KS4 could be explored using this approach? And if a comprehensive guide existed, would it be a useful and beneficial tool in a teacher's toolkit?