# Teaching: October 2008 Archives

## Introducing Embroiderers to their Inner Math Wizards

Anyone familiar with embroidery, quilting, or knitting knows that some heavy duty math can come into the craft, depending on the pattern. Last night I was teaching a project called Optical Color Blending which is a showcase of mixing colors of embroidery threads.

Embroidery floss is actually made up of six smaller threads. Normally, you use strands of the same color, but can actually stitch with floss made of different colored threads (this is called blending). The Color Blending design is a triangle with each corner a different soliid color. In between are blends of two or three colors arranged in a mathematical pattern (almost like wave ripples). From a statistical point of view, the squares in the triangle represent all possible combinations of three colors in a piece of six-stranded floss.

The challenge was if I could explain this pattern to my fellow stitchers. I suggested they find their inner mathmetacians, but that just induced panic.

Instead, at the last moment, I decided to try an "active cognitive" exercise. I gave users a blank chart with only a few specifications filled in. I said that the edges were stepping from color 1 to color 2 in one thread increments, then I gave an example and asked them to project the rest (which they did quickly).

The tricky part, of course is figuring out what happens on the inner part of the triangle where three colors were involved. Interestingly though, just before I was about to give an answer for one triangle, someone guessed it correctly. The rest of the time was spent quickly filling in the chart, with some students helping others a little behind (embroidery would die without peer-to-peer learning).

Even though everyone swore they had no "inner mathematician", they all figured the pattern very quickly and seemed to enjoy the chance to outsmart the chart. It was an interesting case how people can be very mathematical outside a formal math class.

In any case, I found it a very enlightening "teachable moment" - in this case letting people deduce the pattern on their own was much more effective than my trying to explain it (partly because I think math sometimes defies traditional verbalization). In fact, one of the group noticed a pattern I had missed before (cool).

I've had mixed success in having people "figure things" out independently, but I'm hoping this will encourage me in the future. It was certainly a lot more fun than me lecturing while pointing at a tiny diagram for 20 minutes.

I have been an instructional designer at Penn State since 2000.

See my List of Current Projects for more details.