…design thinking is abductive; a type of reasoning different from the more familiar concepts of inductive and deductive reasoning. …It is this particular logic of design that provides the means to shift and transfer thought between the required purpose or function of some activity and appropriate forms for an object to satisfy that purpose.Nigel Cross, Design Thinking (Bloomsbury, 2011), p.10. My emphasis.
The applied maths element of knitwear often design elicits dread or fascination. Most people accept that maths is inseparable from knitting, and current practices of separating idea generation and design realisation is a dream come true for some designers. Over the last year or two I’ve come to the conclusion that the level of maths required for knitwear and crochet design is far beyond that covered in compulsory education. Instead of learning and applying theorems, knitwear designers must first identify and create them. Only then can they be applied and tested.
Nigel Cross’ quote is one way of expressing the challenges of knitwear design: How do you choose an appropriate form without a confident grasp of how your design works? You need to understand it mathematically AND visually in order to produce a high-quality pattern. I would argue that maths education, as it relates to knitwear design, is inadequate. Numeracy is not enough; also required is a solid understanding of how mathematical relationships are formed. This is why, despite successfully creating sophisticated visual and structural relationships, knitwear designers often struggle with the mathematical realisation of their designs. Creative methodologies for maths are under-developed because the skills are not taught – and poorly recognised besides.
Maths is all about representation and relationships: the many ways in which relationships can be understood are distilled into numerical form. Yet, most approaches to maths are singular. In school we are often taught only one method of long division, or that we should notate arithmetic in a certain way. Unlike language or vocabulary, where you can describe things using a selection of words according to what best suits your character, intention, what you judge to be appropriate and the words you have learnt through life – you cannot do so as readily with maths.
We speak more frequently than we execute calculations, so we can reach for words such as silence, quiet, peace and stillness to describe a noiseless situation. Maths is also a language, but numeracy skills are more rigidly set according to what you managed to learn in school, and how those skills have been deployed since leaving education.
This rigid context of mathematics is partly what catches my students and some of my colleagues by surprise when I’m teaching sewing, pattern cutting or knitting. I don’t think I’ll ever stop hearing the phrase “There’s a lot of maths involved” until I either retire or leave the profession! But these words are often followed by moments of deep thought, often undetectable from where I’m sitting, but sometimes I like to imagine:
“Maths is EVERYWHERE!”
“I’m bad at maths, but somehow I’m good at this. Why?”
“This is mathematical in a way that I can’t explain.”
“I used to love maths at school, and here it is again – this is so much fun!”
“…SO much counting…”
In all cases, the people I’ve taught have embarked on a new relationship with numbers, completely recontextualised, and familiar numbers establish new relationships amongst themselves. 3 metres can be the quantity of fabric needed to make a dress as well as the width of sofa. 1.5kg can be the weight of your bag of rice of the weight of yarn needed to make a sweater.
These are examples of things that we know or learn as we navigate life, but it isn’t until we stop to think deeply about the rudiments of that knowledge we realise what needs to improve. Just as 3 metres or 1.5kg can change according to context, so we should be able to adapt our approach to mathematics and how we notate it. I have observed that this can be very difficult for people to do – simply because they have never had the tools or tuition to do so.
I suspect this is why applied mathematics is so fascinating, and why so many people perk up at the word ‘applied’. Representation changes everything and brings the numbers alive. You might have dozed off when you learnt about statistics, lottery numbers and predictions, but reawakened when you realised that permutations and combinations are fun and helpful when working out colour schemes or sequences. And – if you’re like me – you got to use the exclamation mark button on the calculator! This came after spending years wondering why it was there, what it could possibly be good for, and why you needed to get a scientific calculator full of buttons you’ll never use for maths GCSE. There’s a reason for everything.
When I taught Fun with Factorials! at virtual Vogue Knitting Live in 2021, I was, to paraphrase, entertaining angels unawares. In this case, the angels were maths postgraduates who knew far more about maths and the remit of the class than I did, but who signed up for the pleasure of seeing the subject they loved applied to the craft they enjoyed. Unsurprisingly, the group was one of the liveliest virtual classes I’ve ever known – and ever since that day I have wondered, reflected, and wondered again. What a huge difference would it make to knitwear design if knitwear designers were as well trained in maths methodologies as they are in visual communication?
I hope I find out one day.
Next time, I will dive a bit deeper and use my Alyssum sweater design as a case in point. I hope you’ve enjoyed this post – let me know what you think, I always look forward to comments! – and see you for part 2 in a couple of weeks 😊