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I have just returned from a trip to India. Whilst there I spent several days working with groups of teachers looking at what we really mean by ‘active learning’.
Discussions included statements like ‘active learning isn’t necessarily hands-on, but it is most definitely minds-on’. We considered what it means to be an active learner and that being active does not necessarily lead to new learning. Activities have to be carefully designed to ensure they offer value to a lesson.
During these discussions, I used my current crochet project to talk about activity vs active learning.
I’m currently making a crocheted bed spread which consists of 252 hexagons, each crocheted separately and then sewn together. I’m at the stage now where every day I spend time adding a white outline to my coloured hexagons. I repeat the same process again and again and again...and again. In fact, I can now perform the task whilst speaking, watching TV, even without looking at what I’m doing – using my muscle memory can reproduce the same pattern easily. Whilst doing this I am being active, but am I learning anything new? I have become more fluent and can perform the task effortlessly, but is this making me a better crocheter? What do we mean by ‘better’? More skilled? Faster? Neater?
I find this fascinating as it offers me a wonderful metaphor for learning maths. I am improving my performance in terms of fluency – but I am not constructing any new knowledge. I appear more proficient because I can perform the stiches more quickly and whilst multi-tasking, yet my ability to produce new patterns and designs is negligible: I am not learning any new stitches and I would say that I’m not really being challenged.
The way I learn to become a more accomplished crocheter is by trying out new stiches. I do this by looking at videos, books and experts demonstrating stiches, having a go at them, going wrong, seeing that I’ve gone wrong, undoing the work until I know it’s back to a point at which it’s correct and then having another go. Quite often I do this multiple times, looking at multiple sources for support. I’ve learnt that I do not get better at crochet by handing my work to an expert and getting them to undo, mend and pass it back to me, no matter how tempting that may be at times!
As my repertoire of stiches increases, I become more confident, I try out new patterns and challenges and start to design my own patterns. I start to recognise the stitches which have been used to create other people’s work. I may even support and advise other crocheters.
It’s worth saying that practising the same stiches in my current bedspread project has its uses. It is making me more fluent and may indirectly help me hone my skills in that some stitches have similarities to others, and I am becoming adept at noticing this. I am however completing it in parallel with other projects – otherwise to be honest I would be bored to tears and would probably stop constructing the bedspread.
The links between this craft and mathematics do not end there. I can revisit earlier stitches using different threads and with different hooks. I can use a thinner thread and a small hook to create a delicate fine pattern in much more detail. This is much like re-visiting a piece of maths with a new viewpoint, refining arguments, offering more formal solutions.
Additionally, crochet patterns come in many forms: written using a form of shorthand, diagrammatically, and in pictures. I’m learning how to work with all of these and convert between them. Interestingly the shorthand used depends on the origins of the pattern. The same terms in the US and UK often mean different stitches, so I have to look in detail at what I’m reading and take this into account.
People often look at my work in awe. They talk about how they cannot crochet but wish they could. I explain that it has taken hard work, learning some simple skills which I now piece together to make more complicated stitches. These in turn allow me to create designs and larger works. I was not born with the ability to crochet: I’ve developed and learnt it through trial and error, support, and perseverance. Anyone can learn, although for some the hand-eye coordination may take longer. Some may have unusual techniques for handling the hook; some may need to use thicker yarn and larger hooks; others will be able to work at the finest level of detail.
There’s an obvious parallel here with being an innately ‘maths’ person or not, but something to think about in more detail is the ability of most people to ‘see’ the beauty in my bedspread, but not in my mathematics. This is particularly interesting to consider if you think that the beauty they perceive in the bedspread may be partly due to its mathematical structure.
Do people admire and require maths as much as bedspreads?
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