Last Friday afternoon I experienced one of the most joyous moments of my thirty years in education. I took three fifth grade girls (along with their classroom teacher chaperone) out to lunch. That’s right. We walked right out the front gate of the school, into the sunlight, crossed the street, walked down the block and had a leisurely 90-minute lunch at the restaurant of their choice – regrettably the crime against gastronomy (and pizza), California Pizza Kitchen.

A few weeks earlier, I had challenged the 5th graders to write a computer program in MicroWorlds EX that would draw fractional representations of a circle for any fraction a user requested. Feeling a bit cheeky, I said that I would buy lunch for the first kid or group of kids to write a successful program. After a few class sessions dedicated to the challenge, three fifth grade girls were the first to succeed.

I know. I’m a hypocrite.

I reject behaviorism and its evil friends; grades, punishment, bribes and rewards. However, this felt different. The kids were going to join me for lunch like colleagues celebrating an accomplishment. Best of all, their classmates continued working on the programming challenge, without hard feelings, even after “winners” had emerged. Perhaps they knew that their turn would come. I routinely bring treats from my travels into the classroom. If I worked in an office, I might stop occasionally and buy Dunkin Munchkins for my co-workers. I do the same with my students. Why not?

I loved telling the girls that they could order anything they wanted and learning about their dietary habits and favorites. Conversation covered sick babies, interior decorating, roller coasters, face blindness and Khan Academy. The last two topics were introduced by a girl who matter-of-factly stated, “I watch 60 Minutes.” I was jealous of their classroom teacher who knew more about their parents, siblings, friends and neighbors than I do, but a good time was had by all. The genuine gratitude expressed by the girls (including their teacher) made it all worthwhile.

Perhaps the highlight of our lunch was watching the girls color their kid’s menus at a lunch celebrating their computer science prowess.  Once again, Seymour Papert is correct.

Below is the program the girls wrote. It required figuring out how to “teach the turtle” to draw a circle and utilized a bunch of mathematical concepts, including radius, fractions, variables and angle.

For those of you lacking the skills of a 5th grader and can’t read a Logo program, I’ve included a video demonstrating their program at work.

to Pie
 repeat 360 [fd 3 rt 1]
 end

to fraction :n :d
 cg
 setc "black
 pd
 Pie
 pu
 rt 90
 fd 172
 rt 90
 pd
 repeat :d [fd 172 bk 172 rt 360 / :d]
 repeat :n [rt 360 / :d fillit ]
 end

to fillit
 setc color + 5
 pu
 rt 5
 fd 20
 fill
 bk 20
 lt 5
 end

to mem
 repeat :n [fillit pu rt 1 fd :l / :d lt 1]
 rt 1
 bk :n / :d * :l lt 1
 end

 .

An old friend of mine, Dr. Barry Newell, is an astrophysicist who was was the Administrator (in the NASA sense) of Mount Stromlo and Siding Spring Observatories of the Australian National University. He now works on the dynamics of social-ecological systems. In his spare time (back in 1988), he wrote two classic books on Logo programming and mathematics, Turtle Confusion and the accompanying book for educators, Turtles Speak Mathematics. Turtle Confusion features 40 challenging turtle geometry puzzles in a mystery format and Turtles Speak Mathematics helps educators understand the mathematics their students are learning.

I was reminded of the books when Sugar Labs, the folks behind the operating system for the One Laptop Per Child XO laptop, featured the challenges as an activity to accompany TurtleArt software on the XO.

The books’ author, Dr. Barry Newell, gave me permission to share digital copies of the book for personal, educational and non-commercial use. Click here to go to the download page.

These books are best used with versions of Logo such as MicroWorlds EX or Berkeley Logo. Some of the puzzles are very difficult or impossible to solve in Scratch, but it’s worth trying if that is all you have. SNAP! is another potential option. TurtleArt is another possibility. Although, mathematical programming is often easiest and best achieved through the use of textual language (IMHO). A bit of dialect translation might be necessary. For example, CS is often CG (in MicroWorlds EX).