This research I selected a data set that fulfilled the following criteria: 1. It is data collected from human experimental participants, 2. the problems use examples of visual analogical problem solving, and 3. they provide constraints for the visual abstraction language.
In David Craig's experiments (Craig, Nersessian, & Catrambone in press) participants solved problems similar to the fortress/tumor problem. They saw diagrams showing the solution to the source problem and were asked to draw diagrams describing their solutions to the target problem. This data set fulfills the above criteria in that it is human participant data, it's an example of analogy with both visual input and output, and the diagrams drawn provide information about what to put in the visual abstraction language. I assume that the diagrams and descriptions the participants wrote down reflect, to some degree, the thinking process that went on when they solved the problem.
The first example is the lab/weed-trimmer problem.
This is the solved source problem given to the participants: ``Please read the two problems below. At the bottom of the page, please try to solve Problem 2. Draw a diagram to show what you're thinking. The solution to Problem 1 may be helpful in solving Problem 2. Problem 1: A computer chip manufacturer has designed a special lab for manufacturing microscopic devices. They have taken great care to seal off the lab from the surrounding environment in order to keep the air inside the lab free of dust and undesirable gases. The problem, though, is that whenever lab workers enter or leave the room, the seal is broken and contaminated air is allowed in. The company is trying to design a door that will allow workers to enter and leave the lab easily, while minimizing the amount of contaminated air that is let in. Solution: Have workers enter a vestibule space before entering the lab.'' A diagram of the intermediate room is shown. It is a plan (a roofless top view), where the walls are represented with lines and the doors as unfilled rectangles.
The unsolved target problem is: ``Problem 2: In order to trim the weeds that grow along the side of the road, the department of transportation has designed a weed trimmer that attaches to the end of a long pole sticking off the side of a truck. As the truck drives down the highway, the trimmer is extended about 6 feet to the right, perfectly positioned to trim the weeds at the side of the road. The problem is that the 6-foot pole is obstructed by sign posts that are positioned at the curb in certain parts of the city. The weed-trimmer pole, in fact, is exactly 2 feet too long to clear the sign posts. Although the wee-trimmer pole could be retracted or lifted out the way to clear the sign posts, this would interfere with the weed trimming. And although the pole could bend over the top of the sign posts, this would be impractical since in some areas the signs are 15 feet tall. The Department of Transportation is trying to design a pole that can pass through the sign posts without stopping or changing the position of the trimmer. In the space below, try to design a weed-trimmer pole that can pass through sign posts. Draw a diagram to illustrate what you're thinking.''
The solution to the first problem is to make a set of redundant doors so that air can't go through both at the same time because one is always closed. Some of the participants came up with the analogous solution for the weed-trimmer problem, which is to have a redundant support mechanism for the trimmer. That is, have double door-like support mechanisms, one of which is always closed, holding the trimmer together.
The second analogy problem given is the furnace/factory problem.
``Problem 1: A blast furnace at a steel mill requires a steady stream of fresh air to keep the furnace burning at a suitably high temperature. The problem, though, is that as fresh, oxygen-rich air enters the furnace, stale air must exit, taking a considerable amount of heat with it. The fresh air comes from the surrounding environment and this is several hundred degrees cooler than the furnace. Although the engineers at the steel mill have considered heating the incoming air before it reaches the furnace, this would be very expensive and wouldn't solve the problem that valuable heat is lost when stale air leaves the furnace. The engineers are trying to design a system that will solve the heat-loss problem. Solution: Run the input and output streams close to each other so that the hot output stream warms up the cool input stream.'' A diagram is shown of the air input and output shafts up against one another, connected to a square furnace at the bottom. Arrows indicate the direction of air flow.
The target problem follows: ``Problem 2: Citizens of a small island nation in the South Pacific are forced to pay taxes directly to the King. Most citizens work in a shoe factory at the center of the island. To insure that taxes are properly paid, the King has set up a provisional tax office in the basement of the factory. On payday, workers leaving the factory at quitting time are ushered down the stairs into the office. When it's their turn, they empty their pockets of the coins they were just paid (all workers are paid the same- 10 small silver coins a month) and the King takes eighty percent. On a typical payday, the scene is pretty grim: Happy workers walking down the stairs to the tax office pass those walking up 80% poorer. Most of the citizens have grown tired of being taxed so heavily. Unfortunately, though, there doesn't seem to be a way out of paying the tax. There is only one exit to the factory, and workers are not allowed to leave before going down to the tax office. Ideally, the citizens need a way to avoid being so heavily taxed but they all still need to go through the tax office on payday so the King doesn't get suspicious. In the space below, try to come up with a scheme that will help the factory workers avoid being taxed so heavily. Draw a diagram to illustrate what you're thinking.''
The analogous solution is to have the workers pass money to each other as they pass on the stairwell, as the air in the furnace ducts pass heat.
