# On Knitting and Purling

March 24th, 2007 | View Comments

My research focus in grad school is learning and problem-solving, with emphasis on mathematics and implications for classroom instruction. One of the big problems in math education that teachers and education researchers and curriculum developers face today is how to build conceptual understanding of mathematics.

Many students emerge from their K-12 instruction knowing how to multiply, but not really knowing *how* to multiply. Namely, they can execute the multiplication algorithm quickly and flawlessly, but couldn’t, say, tell you why they have to shift every subsequent row one over to the left in order to get the right answer. The relationship between multiplication, place value, and the distributive property never got established during any of those twelve-plus years of schooling, and not understanding these sorts of relationships will probably hurt the student’s chances of applying the math s/he already knows and his/her ability to learn more advanced math.

These are the sorts of things that fill my head when I’m trying to teach someone to knit.

I remember that as a beginning knitter I learned a lot of sequences of motions and knitting facts—procedural and declarative knowledge in psychology parlance. A knit stitch is made like this. A purl stitch is made like this. Garter is knit every row. Stockinette stitch is knit one row, purl one row.

And while knowing these things certainly enables you to knit, I don’t know that just knowing these things means you know *how* to knit, just like knowing the long multiplication algorithm enables you to multiply without knowing *how* to multiply.

I believe that understanding the structure of knitted fabric and knowing how to read your knitting are skills that separate beginning knitters from non-beginning knitters. It’s not that there isn’t any merit in mostly-procedural knitting, because there is. But I think this an important line between being bound to a pattern and being confident in your own ability to make your knitting do what you want and many of my efforts in teaching knitting are in getting beginning knitters to cross this line.

I remember my own epiphany when I discovered that knitted fabric is just new loops pulled through old loops and that the difference between knit and purl is which side of the fabric the top of the old loop winds up on. All of a sudden, it became obvious how to go about picking up a dropped stitch. And how to fix even the slightest mistake, no matter how many rows I’d already knit beyond it. And to prove myself right, I fixed a single flipped stitch two feet into a scarf already five feet long. Dropped stitches stopped being a source of panic and started being my most powerful tool in fixing mistakes.

I was thinking of all of this as I was trying to teach someone to knit today. After learning the mechanics of knit and purl, she started inventing a stitch pattern as she went along, some combination of knit and purl rows, and she wanted to know how she could tell what to do next. We got all turned around in the terminology, because what may appear to be a knit row as you look at the fabric is not necessarily a row that was made with the knit stitch motion, y’know?

I eventually abandoned the knit/purl terminology altogether and told her to just look at the fabric before starting each row and ask herself if she wanted to make bumps or smooth fabric at this point in the pattern. If she wanted smooth fabric, she should knit. If she wanted bumps, she should purl.

I thought I saw a light go on over her head when I said that. I guess I’ll find out next week!

CogKnition posted this on March 24th, 2007 @ 6:52pm in Life as a Knitter | Permalink to "On Knitting and Purling"

This is a very insightful article. You should write more about knitting theory (If it makes you happy).

I do love seeing that light bulb go off when someone “gets it” in knitting.

As a self-taught and mostly solitary knitter (except for the wonders of the innernets), I think I’ve taken for granted that you have to figure these things out or else you won’t get very far on your own. Thank you for writing about this, because it has kind of let me know “where I am”, if that makes any sense. I know what I know, but I probably have no idea what I don’t know. Although stumbling along cluelessly is how I’ve learned most of what I know, so maybe I should just stick with that.

But, yes, if the urge strikes you, please write more about theory!

Yes! Exactly.

I taught my good friend to knit recently, and I basically told her the same things. I also said that even mistakes can be turned into “design elements” if you know what happened, and how to repeat it. Kind of like a science experiment.

Okay, the light bulb just went on in my head (after a year of knitting) when you wrote “knitting is just new loops pulled through old loops…”

Thank you for writing about this. I’m about to teach people to knit in a few weeks and I’m trying to find a better way of explaining it. Your post is very insightful.

i love the idea of a learning project focussed around knit teaching books or resources. I’m currently mid way thru a tertiary teaching post grad dip, but had not thought to apply that knowledge to my knitting. I was reading in a John Biggs book, the chapter on international students that we ‘westerners’ often get confused bewteen rote or proceedural learning and the repitition used to deepen understanding (common in the east)- the knowledge that comes with repeated use. I’m not sure that there is a fast way to get beyond use without understanding. My little look at the published work on plagerism tells me that a copying or rote use is a stage all learners go thru, so I’m looking at ways to optimise and shorten that part of the journey. I teach in ‘studio’ classes on a design degree, so much is problem based learning, but at the opposite end of the spectrum from your maths kids. My own learning comes best from fixing my mistakes, so i give my students time and space to experiment and make mistakes.