Republic of Mathematics blog

Turning a heel: can knitting contribute to mathematics education?

Posted by: Gary Ernest Davis on: November 14, 2010

Turning a heel when knitting a sock is a big deal for beginning knitters.

The Yarn Harlot (Steph Pearl-McPhee: @YarnHarlot) writes in her book “Knitting Rules!“, that:

Turning the heel is a mythic act, one that sock knitters speak of with reverence. Turning the heel is when you, through an incredibly simple but clever series of short rows …  make the sock change direction and move from leg to foot. I’ve done a hundred socks and I feel smart every time.

Knitting is an intellectual activity: knitters have to think, solve problems, count, and think some more. Yet it is an activity with a physical product: in the case of turning the heel, the product is a sock, or two.


My wife Linda's first sock: turning the heel was a big deal.


From the Yarn Harlot’s words I feel that turning a heel in knitting is a metaphor for many of life’s successful problem solving attempts:  turning the heel is a mythic act, one spoken of with reverence, and one feels smart every time one does it.

Knitting is a very democratic activity. As the Yarn Harlot writes in “Knitting Rules!: “there are no knitting police.”

Knitting is also something that people of all ages –  very young to very old – can do.

Mathematics is full of problems, and problems solving is a major part of mathematical activity. One might argue that all professional mathematicians do is solve problems. Mathematics also has no math police, and people of all ages can successfully do mathematics.

Yet mathematics does not, in general have such physical products as socks, or sweaters.

Generally mathematics is more about analysis, using calculation and reasoning.

So, my question is: “Is there a mathematical activity that corresponds to turning the heel in knitting?”

My colleague Sigal Gottlieb says that for her the mathematical activity that might be close to turning the heel in mathematics is finding the formula for the volume of a sphere by integration.

So, dear reader, is there a mathematical activity that for you corresponds to turning the heel? Or is it just that mathematics consists of a series of intellectual and emotional highs that come from successful problem solving, and that there is no one thing that might correspond to turning the heel?



Leave a Reply