Visualizations: Algorithm

• Peanut butter and Jelly
  [This is due to a teacher from the States, I neglected to write down her name, if she is reading this: please let me know so that I can attribute it to you!]
  Props: Jar of Peanut butter, Jar of Jelly, Butter, Loaf of sliced Bread, knife, paper towels
  Description: Ask the students to help you make a peanut butter and jelly sandwich. Everyone knows how to make one! Your job is to do exactly what they say, that is, to misinterpret the statements that have multiple meanings. For example: If a student says "Butter the bread" then butter the bread still inside the bag using your fingers! Or if they say "Butter one side", then you choose a crust side. Once you get to the point of having a slice with peanut butter on it and a student says "Put it down", then you put it down with the peanut butter side down. Makes an awful mess, but everyone is focussed on this and they laugh a lot. They will remember this for a very long time! Develop the properties of an algorithm after wiping up the mess.

  Lynn Andrea Stein, Professor at MIT, uses the Peanut-Butter-and- jelly Model for describing sequential programming in her "Rethinking CS101"

  1999-08-01, Malmö högskola: I finally used this for real in a college class instead of just talking about it. I make quite a mess! And I had to work hard to misunderstand what was being asked of me, as they were very exact about taking the bread out first and using a knife. But I managed to butter the top crust, and when they said "Turn it over!" I turned it over and buttered the bottom crust. I opened the jam jar with the lid down, getting rasperry jam all over the place, and the student who already knows everything about computers just said "put the slice down", so I slapped it down on the peanut-butter side, this was quite amusing.
  Their assignment was to write down an algorithm explaining an aspect of Swedish life to a Martian, and going through the aisles we kept using the PB&J example to explain again the fine points of what an algorithm is.
  So it even works in a college situation, not just at school.

  1999-09-02: Carl G. Alphonce writes: "Since Debbie issued a dare, I felt I had to take up the challenge: yesterday my class instructed me on how to make PB&J sandwich! I took Debbie's advice and brought lots of paper towels (this is, I might add, very good advice). The demonstration certainly got the class involved and paying attention! As the demo went on, they became more careful about how to phrase their instructions to me, trying to anticipate and short-circuit my silly interpretations of their commands.

  This was our first meeting for the semester, and it set the tone well. We spent the first little while speaking about the boring formal things we have to discuss in the first class (what constitutes cheating, what will happen if they cheat and so on), and the demo was wonderful counterpoint to the dull administrivia."
  
  October 2004: Now that mobile phones have cameras, we have a picture of me making PB&J, with my Martian ears on. Thanks to Christian Niermann for the picture!

• Marionette
  Since people don't know what a peanut butter and jelly sandwich is here in Germany, I sometimes use a marionette (an "absent minded professor" I once found in a toy store!) instead. I set it on the table, and ask the students to help me get the professor off the table and walk him to the door. I misinterpret all that they say, it is interesting, but not quite as drastic as above. They remember it for many semesters, although some students who already thought that they could program found it silly.
  
  
• Cleaning the board
  Ulrike Jaeger from the FH Heilbronn in Germany reports having her students tell her how to clean the board as a first algorithm. She suggests wearing a raincoat for doing this...

  Back in my second semester at collage Thomas Wolff and I wrote up the algorithm for cleaning the board for the student newspaper because we had a professor who couldn't clean the board properly and kept writing in the chalk detrius from a previous proof. If I ever find it again I'll retype it here. Should be in the Fachschaftszeitung Mathe/Inf/Physik der Universität Kiel, SS 1977, if someone should find it before I do .-)

• Monte-Carlo methods
  In order to demonstrate Monte-Carlo algorithms, I calculate an approximation of π I use the document cameras that we have in our lecture rooms to show what I am doing. You need: a bag of rice corns your husband made you throw out because the use-by date was 5 years ago; a square piece of paper with a circle inscribed on it in felt pen; a scale that weighs in grams; a brush; and a container. I put the formula on the board: the circle has radius r, so we have π r² / 4 r² = π / 4. You now scatter rice evenly over the square, noting that each rice corn is two random values between 0 and 1, the x and the y coordinate. When the square is more or less evenly covered, use the brush to carefully brush the excess corns away. Then you determine the tare weight of the container, brush off the four corners and put the rice into the container, and weigh it. Put this on the board as a. Now take the rice from the circle and weigh it, putting this on the board as b. The area of the circle in proportion to the area of the square is b / (a+b). Calculate it out, multiply by 4, and you should get at least one digit of precision, if not two! I even got three one year, strangely enough using lentils, which are larger than rice corns.