…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 😊
As an Australian, I found this a fascinating insight into American high school mathematics. As a trained high school maths teacher, lecturing in a University, I think our high school curriculum may be more applied. I agree with you that an understanding of spatial mathematics and patterns really enhances knitwear design. It’s always more fun to engage with maths when your passionate about the purpose your applying it for.
Thank you Jo-Ann – I can well believe that about the Australian education system! One of my favourite fashion design books was written by Pamela Stecker, who I believe is a successful fashion consultant. She has a brilliantly integrated and accessible approach to design.
Also (this wasn’t clear in the post, excuse me), I was educated in the U.K. and still live there. The limited insight I’ve had into the US system has been mixed, but so far there’s more evidence of creativity in maths.
Natalie I love reading your blog! And I’m so glad you mentioned that you’d be the keynote for the Fleece to Fashion conference last week — I was able to hear your excellent contribution and some of the late afternoon panels. What an inspiration! So grateful.
Re: USA math ed: I’m posting from Chicago. But my preference in high school was “least amount of math the better.” Observing my kids elementary/high school math education: creativity varies greatly depending on the teacher. Regarding my own math skills: I often find myself trying to do calculations with drawings making a visual version of structures or grouping tick marks for each stitch, not trusting how to divide for spacing out stitch increases… I was sewing a cylindrical duffle bag, trying to hold the cylinder of fabric up to draw the circular end — a friend said, “don’t you remember C = 2πR?” The knowledge is there, how to apply it is lacking.
I agree completely, Karen! And I cannot remember being given any context or real-life examples for maths in school. It wasn’t until I taught the factorials class at VKL that a few of the students (maths postgraduates hiding, I later found out) told me that quadratic equations are generally used in physics. I wouldn’t have known that – and no reference to them was made in my physics class either. Maths needs to be relatable and relevant. I can’t understand why such a creative, relationship-oriented subject is taught so uninspiringly (if that’s a word).
And thank you very much for attending the Fleece to Fashion conference 💕 – I had no way of seeing the virtual attendees, chat or Q&A, so I’m very happy to know you were there and enjoyed the keynote. It’ll have been a very early start; good thing you’re not on Mountain or Pacific time!