If Knitting Was Taught Like Math*

1. In some classes, no one would have any yarn or needles.

   Definition: A knit stitch is the stitch obtained by holding the yarn to the back of the work, inserting the tip of the right needle, while it points towards the tip of the left needle, into the front loop of the first stitch of the left needle and wrapping the yarn around the tip of the right needle (counter-clockwise as viewed from the tip of the needle), pulling this loop through the stitch on the left needle, and sliding the stitch off the tip of the left needle.
   
   Definition: A purl stitch is the stitch obtained by holding the yarn to the front of the work, inserting the tip of the right needle, while it points away from the tip of the left needle, into the front loop of the first stitch on the left needle and wrapping the yarn around the tip of the right needle (counterclockwise as viewed from the tip of the needle), pulling this loop through the stitch on the left needle and sliding the stitch off the tip of the left needle.
   
   Theorem: A purl stitch is isomorphic to a knit stitch when the work is reversed.
   
   Exercise: Show how these results are changed if we assume that the stitches start on the right needle and are worked onto the left needle.
   
   Exercise: Show how combinations of knit and purl stitches can be used to make a sweater [ Hint: consider the case where you have to change the number of stitches. ]

2. In other classes everyone would have yarn and needles. But because you need to start at the beginning, the class would have to start with casting on. Long-tail cast on. Backwards loop cast on. Cable cast on. Knitting on. Provisional cast on. And you can't go forward until you really understand casting on. Students would be left to figure out for themselves how long-tail cast on compares to backwards loop cast on followed by one row of knit stitch.**


3. Students would be shown how to do the knit stitch. They would practice the knit stitch at their desks. They would go home and knit a garter stitch scarf. If they didn't get gauge or if their stitches were sloppy or otherwise imperfect, they would be told to rip it all out and try again. After weeks of this, they would move onto the purl stitch. Years and years of making swatches and scarfs, each demonstrating one stitch over and over and over. Only a knitting super-genius could ever make a sweater.

*Which, obviously it isn't because people take time out of their busy lives to spend their own money to take knitting classes and then will spend still more money on all sorts of zany yarn and will compulsively buy, read, and study books and magazines about knitting. And in the end you have an item -- that to the untrained eye is not much better than what you could buy at a store for $50 -- that took over $100 worth of yarn and hours and hours and hours of someone's time. Unless you are like me, you probably don't know anyone who does math for fun.

**This is based on the math-for-elementary ed class that I taught in Fall 2004 using materials developed by people who had previously taught the class. Using my analogy, I was led to believe that my students already knew how to knit and that they were in my class to fill in the behind-the-scenes details. However, I was misled. Continuing the analogy: they didn't even know what yarn was.