Treasureworld:A Computer Environment for the Study and Exploration of Feedback

Aaron Brandes and Uri Wilensky

Introduction: Feedback as a Powerful Concept

Feedback is one of the mechanisms we use in daily life, yet we may be unaware of it. We are constantly using feedback to act and navigate in the world. The thermostat, for example, operates on a feedback principle. A desired temperature is set. The actual temperature is then measured. If this temperature is lower than the desired temperature, the heating system is turned on. If the temperature is higher, the heating system is turned (or left) off. If there is a cooling system, the corresponding appropriate actions are taken. Yet many people believe that the thermostat is like a valve, and they will therefore turn it up higher than the desired temperature to get the room to heat up more quickly (e.g., Kempton, 1986). Thus we may miss opportunities to learn about feedback from mechanisms around us through misapprehension of how they work.

It is also possible that the sheer effectiveness of these devices suppresses any need to understand them. We may think, for example, "the thermostat keeps the room at the right temperature." No explanation is needed. In a similar way, it is easy to steer a car without conscious thought about the feedback process involved The hands turn the steering wheel, the wheels of the car turn, and our eyes detect any difference between where we are heading and where we want to go. The difference between the desired state and the actual state is usually detected without our conscious attention. Just as subconsciously, our hands respond to the difference, adjusting the position of the steering wheel. Conscious thought enters only when a problem arises.

Our focus here is on "negative feedback loops," in which the response to the feedback decreases the difference between the current state and the desired state. In contrast, in a "positive feedback loop" this difference is increased. Consider, for example, a sink or shower with its hot and cold faucets reversed. Sensing that the water is too cold, a person will turn the "hot" faucet. Since this is really the cold faucet, the water will get colder, and the person may continue turning that faucet on more, or turning the other faucet off. The expectation of a negative feedback loop is so strong and unconscious that it interferes with understanding the situation. Interesting system behavior can also result when two negative feedback mechanisms with differing goals interact. It has been observed, for example, that on average Italians prefer to be physically closer to people they are talking to than do the English. An Italian and an Englishman in conversation may therefore perform quite a "dance." As the Italian moves closer, the Englishman will back away, provoking the Italian to continue the pursuit.

The approach of our research is to put children in a negative feedback loop. Making explicit part of the feedback loop provides the student in the loop an opportunity to learn about feedback, while simultaneously allowing us to observe and study the development of this learning process. The game, Treasure, is the tool we developed to accomplish these goals. In our research we were interested in whether there would be stages in learning to play the game, and what differences in style could be observed. Although learning and understanding feedback was our initial research focus, during our research other concepts-of strategy, information, and model building-became important to our assessments as well.

Before discussing our methods and results in detail, here is a brief summary. We found that the group of children (primarily fourth graders) we studied were able to use sensory feedback to find a hidden treasure. Nevertheless, this was a nontrivial task. Most children went through a common set of stages in mastering the search for the treasure. Differences in style in mature play were also observed.

What is Treasureworld?

Treasure begins by asking the player for his/her name. The player's name is used to give the game a number of personal touches. The player is given an option to get directions for the game. There are four commands available to move the turtle: "cfd," "cbk," "crt," and "clt." These are analogous to the LOGO commands "fd," "bk," "rt," and "lt" which move the turtle forward or back, and turn the turtle right and left. For each command, the distance to be moved or the angle to be turned must be specified. To help the player interpret the color feedback a line of turtles showing the colors from hottest (red, pink, ...) to coldest (..., gray, dark gray) appears at the top of the screen. In the current implementation there are 14 different colors. The turtle begins at the home location (Figure 1). The game proceeds with the player issuing commands to move the turtle. The turtle then gives color and sound feedback based on its distance from the treasure. When the turtle comes to within 5 units of the selected location, the treasure has been found. The player is then congratulated by name, and treated to a display of graphics (including a treasure chest opening and coins coming out) and music (the theme music from "Looney Toons" cartoons). The player then has an opportunity to have his/her moves replayed (see Figure 2a). This is possible because we created software which stores a log of all of the players moves (see Figure 2b). As researchers, we found the logs to be a valuable tool for capturing and examining data.

Figure 1: Initial Screen

Each of the turtles in the "strip of turtles" at the top of the computer screen is a different color ranging from red (hottest) to dark gray (coldest). The "action turtle" is white, and positioned at the Logo "Home" position (x=0; y=0). The bottom of the screen is the Logo "Command Center," where the user types commands to move the turtle in search of the treasure. As the user starts the game, he/she is asked to enter his/her name, which appears at the top-center of the screen throughout the game.

Figure 2a: Example of a Replay of Moves

Figure 2b: Example of a Log

The player also has an option to display a map of the colors corresponding to the regions of the screen (as seen in Figure 3 below).

Figure 3: The Color Regions on the Computer Screen (With a Replay of Moves)

These options give the player a chance to review what they have done, and to learn from the experience. This option can be thought of as second order feedback because it is feedback on the strategy as whole, not the individual move.

In designing Treasureworld, our goal was to create an environment for the study of feedback in which students with a variety of styles could be successful. We learned from other microworlds that the principles of low threshold and syntonicity would be valuable for engaging the children (Papert, 1973, 1980). Since we wanted children to reflect on their actions, we would provide them with opportunities to view things from different perspectives.

Feedback requires response to "differences which make a difference" (Bateson, 1972). In a rich and complex world, selecting which differences to attend to and interpret is a complicated (and often subconscious) task. In our microworld, the significant differences (change in sensory feedback) are made explicit. The player can then concentrate on interpreting the difference and responding to it.

We chose sensory feedback (sound and color) over words or numbers to encourage syntonicity. Syntonic learning, in contrast to dissociated learning, is learning that engages a person's sense and knowledge of something familiar. Sensory feedback is directly engaging; the turtle can be experienced as trying to communicate with the child. Using both color and sound increases access for children of different cognitive strengths.

Low threshold means that it should be easy to begin playing. We achieved this by using a small number of commands. These commands are very similar to LOGO turtle commands. Since the children were familiar with the LOGO environment, the directions could be focused on the goals of the game. The meaning of the feedback is constant from game to game. Although location of the treasure is chosen randomly at the beginning of the game, it remains in the same place throughout the game. These regularities support an incremental learning process.

During the game, children respond to the feedback, possibly drawing on previous experiences during that game. Reflection from a more global point of view is encouraged at the end of the game by optionally replaying all of the moves and feedback responses. Children can see where they repeated an action, or took a circuitous route. Looking at a map of the different color feedback zones offers another shift in perspective. Children can see the relative size of the zones, their shape, and how far each zone is from the treasure.

Our basic goals led to the design decisions and criteria just described. These criteria influenced further decisions. For example, we considered having motion commands for big, medium, and little steps. The child would then not have to make number selections. The resulting world would be simpler (in terms of choices), but less rich. We did not want to encourage unnecessary limitations. By encouraging exploration, we hoped a fuller learning experience would result.

Another important decision involved whether the feedback should be continuous (any change in the distance to the treasure changes the feedback, with small changes corresponding to small feedback differences) or discrete (all positions within a certain range of distances from the treasure result in the same feedback response). Having a small, discrete set of feedback responses also makes the problem of feedback interpretation much simpler, because different responses are easily distinguished. This puts more emphasis on the response to the feedback. It is possible to have a continuous feedback channel (for example sound or number) in addition to a discrete one (for example color ). However, we wanted these modes to complement each other. Furthermore, we did not want to make things unnecessarily complicated. Because the feedback responses are not continuous, some information theoretic aspects (such as how frequently to sample) enter more strongly into the game.

Research Phases

Individual Interviews Phase

Methodology. We worked with the children one at a time, outside the classroom. Some of the students had seen the game, and were eager to try it. Other children were selected by the classroom teacher. We aimed for a mix in gender and ability. We introduced ourselves and the game to the children. During and after the game we asked questions to evoke their thoughts and feelings. Why did you do that? Where do you think the treasure is? Could you find it again, no matter where the computer hides it? Did you like playing the game? Results. These initial observations were very encouraging. The children were very enthusiastic about playing the game.They showed great persistence in searching for the treasure, often taking well over a hundred moves to find the treasure. Typical patterns in the process of learning to play the game were observed. Differences in style also became apparent.

Classroom Phase

Methodology. Children in the class already knew us from work we had done with them earlier. We initiated our new phase of work with the class with a series of "pretest" interviews. The purpose of the interviews was to give us a baseline sense of each of the children in the class. At this point we also selected five children for closer observation according to their gender, ability, and personality.

We then met with the whole class to explain what we would be doing for the next few weeks. Treasure had developed a good reputation by word of mouth, so the children were looking forward to playing. The game was explained as being a computer game similar to the game of "hot and cold." The goal was to find a hidden treasure. We stressed that the process of how they looked for the treasure was interesting to us. To encourage self-reflection, we gave them notebooks we had designed for them to record their experience. During the first few sessions with the game, much of our effort was spent helping the children resolve their technical problems in using the software, and making sure they understood how to play. From then on, the children played the game twice a week for four weeks. We gathered information on the children's process through three sources: direct observation, the logs created when the children played the game, and their notebooks.

During a typical day, a cacophony of computer beeps rang out as the children played Treasure, in the Headlight computer pod. The computers were arranged in a large circle, and also linked in a local area network. Some children talked to each other, and others bragged about how many times they found the treasure. We helped the children with technical difficulties, and observed their play of the game. No attempt was made to "instruct" them in finding the treasure. After playing, the children were usually given time to write in their notebooks. We also worked directly with the class in a discussion format to explore the concept of strategy. More will be said about this in the results section.

We concluded our class sessions with a competition, in which the children formed five teams of three or four children. The teams were instructed to work together to find the treasure in as few moves as possible. The children were enthusiastic about the team competition. All the teams did well by some measure (e.g. one team found it the greatest number of times, one had the best single game, one had the best average, etc.).

We conducted post-interviews with five of the children we had followed closely, and held a competition among them to see who could teach Treasure the best. The competition involved teaching Treasure to other children. The other children were introduced to the game, and allowed to play for half an hour, in order to get a baseline for their ability. Only one of them was able to find the treasure. Next, each was paired with one of the experienced children. These sessions took place one at a time, enabling us to observe and videotape the process. The children who were teachers were told they could use whatever method they wanted to teach the other children. This competition had a clear winner.

Results. Observations of stages and styles in the play of the game will be presented in separate sections. A few notes on our classroom discussions of strategy follow.

In our classroom discussions we found that the concept of strategy seemed difficult for the children, especially in the context of games. We had more success when we asked them for strategies they might use to get a sibling to do a chore for them. Among the ideas they came up with: offer them something they wanted, threaten to tell the parent on them, take something away from them until they did what you wanted. They seemed to particularly enjoy being able to express the "sneaky" plans.

The classroom teacher was away at a conference during our class discussions of strategy. After her return, she was surprised when one of the girls in the class asked her "Do you think about us after school?" This provoked a discussion in which the children raised such questions as "Do you have strategies to make us learn?" and "Do you do use tricks to get us to react in a certain way?" This was a novel way for the children to look at things, and provides a concrete example of how they brought experiences from the game into other areas in their life.

Developmental Sequence of Stages

Sometimes we asked the children to guess where the treasure might be. Not only did they not have a guess, but the question appeared strange and sometimes amusing to them. It appeared that the concept of a fixed but invisible location for the treasure was foreign and hard to grasp.

In the next stage, children moved the turtle in a straight, usually horizontal, line. Some children did this the very first time they played Treasure, skipping over the first stage. Typically, the children moved the turtle to the right, and when encountering the end of the screen, "wrapped" to the leftmost edge and then continued in the same direction. They were content to watch the turtle move and retrace its steps over and over. Initially, while the turtle may have passed over the same trail, it may not have landed on precisely the same spots it had before, so the feedback pattern may have been different for each pass across the screen. However, the children often used the same numeric arguments to the movement commands, so the turtle did land in exactly the same places as before, resulting in the same feedback pattern. Assuming a stable world, a world in which treasures stay put and distance means what we expect it to, no new information can be gained by going back to the same locations. Yet, this perseveration persisted. Indeed, perseveration was not limited to this stage alone: it occured at virtually every stage of Treasure proficiency.

In the next stage, we observed a very marked change. The children began to respond to the feedback with corrective action. If the result of the previous move is to make the turtle "colder," the child immediately moved the turtle back to where it was before. Often, we observed expressions of excitement when this discovery was made. They had gained a measure of control over the environment. They could undo the undesirable. They had discovered the reversal rule. As this stage progressed, the colder regions were experienced as extremely unpleasant. One child demonstrated her discomfort particularly dramatically. When she moved away from the treasure (in her words "I got colder"), she would exclaim, "oh no," and bury her face in her hands. After a few moans, she would peek back up at the screen and when seeing the colder color again would repeat the performance. Sometimes it would take a few minutes for her to get the gumption up to move again. The discouraging feedback was experienced as pain. (Getting colder "is bad.")

In the transition period between the reversal stage and the next stage, the children seemed literally stuck. They typically moved in only one dimension and since moving away from the warmer sections was experienced as painful, they therefore found the warmest sections of the line, and just stayed there basking. After a few moments of contentment, a child might attempt a small move out of the warmth, but when this is inevitably followed by a colder turtle, she hastily returns to her spot.

In the next stage, we again noticed a crucial moment. Frustrated by her immobility, the idea suddenly dawns that she can move out of her comfortable line into a new dimension, to start exploring the plane. In all observed cases, this meant that the child turned ninety degrees and searched perpendicularly to the line she had been traversing. Acclimation to the new line proved rapid, and soon she would find the warmest region on this new line. This procedure is then iterated as the child spirals in to the treasure region.

At this juncture there was an observed divergence in the class. Some of the children continued to play as they had before responding to the local feedback. However, some children began to look at things from a more global perspective. They paid greater attention to the map of the colors displayed at the end of a game (which by now they had seen a few times from "lucky" strolls into the treasure area) and began to construct mental maps of the domain. Before making their next move they would visualize the color map and hypothesize a specific location for the treasure. Often they would point to a specific spot on the screen and say: "I think the treasure is here." This is in marked contrast to their earlier puzzlement if asked where the treasure might be.

The next obstacle that the children encountered was passing the treasure by. By using the spiraling strategy, the children entered a zone of proximity to the treasure. However, because they had gotten accustomed to moving the turtle in large steps, they often leaped right over it and landed on the other side. In large part, this is due to the progressive reduction in color region size, the closer one gets to the treasure. Initially this was very confusing to them. They had gotten used to the idea that they could find the best color on a line by moving in a hotter direction. Once they got colder, they would reverse their heading and thus converge on the best color. This, however, only works if the step you are taking is smaller than the size of the region. When you are close to the treasure, the regions are not very wide, so if your step size is too large, you will miss it. It was while struggling with the frustrations of this stage that some children first asked us: "How big is the treasure?"

The solution to this dilemma led to the next stage, which we call step size refinement. The children learned to reduce their step size as they got close to the treasure. In many cases, the trigger for this response seemed to be arriving in the pink region, the second hottest area. In the teaching competition, for example, one child explicitly invoked this rule saying: "When you get to the pink, you gotta use a lower number" (of turtle steps).

The situation is further complicated by the following fact about Treasureworld. The radius of the innermost feedback region, the red color zone (which sounds the note high c) is ten units, but the zone of the treasure, the region which triggers the animation and announces you have won, has a radius of five units. This means that while you are in the red region, you can no longer use feedback to find the treasure, you must either search the whole space, or develop a more sophisticated strategy for deducing the treasure location. One such strategy is to take very small steps while in the red zone, and notice at which point you entered it and at which point you exited. Then you can go back half the distance you traversed and you will be in the middle of the red zone, on top of the treasure. This strategy can be generalized.

Recall the stage at which the children made the breakthrough and learned that they can move off of a line by turning ninety degrees. Typically, a child had been moving along a line in a warmer direction, when suddenly he encountered a colder color. Knowing now that he had just gone past the best color on his line, he applied the reversal strategy, returning to where he was, and then turned either right or left. This dynamic had the effect of making the turns happen at the edges of color regions. Figure 4 illustrates the path of a child proceeding in this manner.

Figure 4: Example of an Edging Path

As we can observe, the child has taken a circuitous path due to this "edging" effect. In some cases this pattern can lead the child to loop around the treasure, always very close, but ever just out of grasp. One child solved this problem by discovering the generalization alluded to above. Whenever you have found the best color on a line, note where you entered that region and where you exited it, and go half way between. Only then make your turn. Following this "centering" strategy results in a much cleaner and shorter path to the treasure, as shown below in Figure 5.

Figure 5: Example of a Centering Path

By the time children have attained the latter stages of this developmental sequence, they have achieved a level of mastery of Treasure. In the process, they have moved from the stance of "getting colder is bad" indicative of the reversal stage, to the new stance of "getting colder is information." Now, when they are moving towards the treasure and encounter a colder region, they no longer hang their heads and moan. Instead they say "Oh, ok, it's the other way," and head in a new direction.

Discussion of Children's Learning

Another component of the children's enjoyment arises because it is reassuring and satisfying to find a hidden object. There may be an analogy with children's delight in playing peekaboo and hide-and-seek. These games tap into fears and desires that lie beneath the surface of our consciousness. The game also possesses an element of "moderate novelty" (Piaget, 1952). There is novelty in that the treasure is hidden in a new location each time the game is played. At the same time, strategies and insights from previous games can be applied. This recognition of something familiar in something new is also pleasurable. The treasure location is random, hence there is a small chance that it will be the same from one game to the next. As one child observed in her notebook, "Today I learned that the treasure can be in the same place."

Learning about Feedback, Strategy and Information

What did the children learn about feedback? A key question is, what is going on in the early play of the game when children do not respond to the feedback by retreating if the feedback indicates that they are getting "colder" (further away from the treasure)? One hypothesis is that they are exploring the situation, "smelling the flowers." While that may be an aspect of their behavior, our hypothesis is that the main reason for their behavior is that they do not initially understand feedback, and its value in the process of playing the game. Evidence for this is that although adults may experience some difficulties in finding the treasure, they generally respond to the feedback by attempting to move in a direction which will decrease their distance from the treasure. However, the children needed to first learn that it is important to interpret the change in feedback. When asked, the children were able to correctly interpret whether the change in color and sound feedback meant they were getting "hotter" or "colder." They did not, however, necessarily make this interpretation spontaneously. Furthermore they had to learn to act in response to the feedback. The child who was most successful in the teaching competition made this an explicit rule. Once children realized that the feedback required interpretation and appropriate response, they attempted to use the feedback to get closer to the treasure. As we mentioned earlier, this was not always an easy task: when children were near the treasure, but stepping over it, frustration was frequently the result.

The experience that using feedback can get them to a goal was new and powerful for the children. During their initial play of the game children often expressed discouragement, seeming to believe that they would never find the treasure. However once they found the treasure, most were confident that they could find it again. Even if they encountered difficulties in their subsequent searches, they did not abandon the strategy of responding to the feedback as a way of finding the treasure. As they refined their understanding of the game, they came to see that they could have a general method of play, which would work no matter where the treasure was hidden. The children learned to use information. The sensory feedback is information, if one knows how to interpret it. Knowing that one has moved away from the treasure helps one learn more about where the treasure is. Initially, however, many children react to the moving away as a negative thing. One of the girls, for example, was so afraid of making a mistake that she was initially almost unable to choose a move. Later, the children realized that they could use this information to take corrective action. This is an example of learning from "mistakes." Children were able to experience mistakes as a natural part of the learning process.

Models can be useful in interpreting and assimilating information. As mentioned in the observations section, the question "Where do you think the treasure is?" seemed initially to take children by surprise. They were looking for the treasure precisely because they didn't know where it was. If the feedback indicated that they were far from the treasure, they looked elsewhere. However, as indicated in the discussion of perseveration, they often returned to cold regions. Their earlier understanding of where the treasure was diminished with time. As some players developed, they began to build up more of a sense of where the treasure might be. A "sense" can include an association of an area of the screen as being near the treasure, a mental image of the map of colors, and other possibilities. In the team and teaching competitions, children were frequently seen pointing to where on the screen they thought the treasure was.

Along with building up a model, some children began to make and test hypotheses. In the early stages of a game, this means going to an area where the player thinks the treasure might be, and exploring there. The idea might be disproven, in which case the child tries somewhere else. If the child thinks he/she is getting very close, an exhaustive search of the area might be started. Children varied in their ability to search an area systematically. The frustration of children who had unsuccessfully searched an area where they believed the treasure to be was very evident.

Making and testing their own hypotheses in the school environment was a new thing for many of the children. The children tended to rely heavily on adults for validation of their progress. In this reliance, the classroom teacher conjectured a cultural factor. Most of these children come from Hispanic families in which the adults make all of the decisions. Many parents chose what their children eat and wear. These children face fewer decisions than many other children their age. This game offered these children an opportunity to make decisions on their own. Initially however, many children took the approach of trying to get hints about the treasure's location from us. Telling them that the computer had hidden the treasure, and that we didn't know where, helped to shift the task to one of their engagement with the computer.

What do we mean when we talk about the children's learning? We do not claim that they have assimilated a series of abstract principles. We do believe, however, that they have contacted these principles in a meaningful way. This is manifested in the increasing stability of their understanding of the game. Lack of such stability is linked to the recurrence of perseveration. The most striking perseveration was noticed during the phase of one-dimensional play. The child finds the point on the line closest to the treasure. Failing to reach the treasure, the child continues to move along the line. Consider another situation. The child reaches the "pink" region, and is quite near the treasure. By taking steps that are too large, the child steps over the treasure. The inexperienced child may explore the area, and then suddenly go off looking in another area. This pattern may repeat. A child with a stronger sense that the treasure must be nearby may become rather frustrated, but is not likely to wander off to a cold area.

There is some structure of understanding which develops in the child's mind. One of the goals of our future research is to explore this process more fully. We believe that the understanding developed in playing the game supports the development of a set of "mental muscles." The experience of playing the game promotes an ability to take advantage of a number of regularities in the Treasure microworld which reflect regularities in the world. The complexity of events in the world may hide such regularities. Feedback is in operation all around us, yet we may not be aware of it. Information given to children in school is often so balkanized that it would be difficult to build up a coherent model of it. Treasure is simple enough to allow construction of a model of where the treasure is, and how distant from the treasure the different color/sound feedback zones are. Furthermore, the use of this model is rewarded by greater ease in finding the treasure. Treasureworld thus provides a positive, concrete experience of model building with which other similar experiences can begin to resonate. We believe that the kind of learning discussed in this section is a valuable contribution to the development of the children's meta-cognitive skills. The convergence of experiences of success based on internalizing or operationalizing the abstract principles discussed here will foster a sense that there is another way of looking at things. This process is analogous to the childrens' insight that "teachers have strategies." Discussions with the classroom teacher support our view that growth of this sort occurred.

Styles in Treasureworld

The first of these, which we shall call the flat position, essentially says: Any individual differences detected in approaches to problem domains are reflections of the person's unique gifts and perspective. All approaches are equally good. Any approach can lead to success in any domain. The educational mission of a teacher holding this position is to work with and encourage the development of the student's individual style; to provide an environment in which it can flower (e.g., Turkle & Papert, 1989).

The second of these, which we shall call the hierarchical position , says: For each problem domain there is one right approach, one right way to solve the problem. Any problem solving effort that does not use this approach is inferior. The educational mission of a teacher holding this position is to impart the correct approach to the student, to ferret out the student's bad problem solving approaches and to replace them with better ones (e.g., Brown et al., 1983).

We came to this study with a prejudice to steer a middle course between the Scylla of indiscriminate acceptance (flat) and the Charybdis of judgmental rigidity (hierarchical). In Treasureworld we were convinced that a number of very different styles would be successful. However, we believed that the nature of the domain would lend itself to a style that favored abstraction over concrete representation, focusing on higher level goals (black-boxing) over absorption in detail, and an ability to shift perspectives over a less differentiated view of situations.

Another confusion that often arises in discussion of style relates to the level of description to which the word style is applied (Falbel, 1985). In one such level, a style is synonymous with a strategy. In this sense an individual can choose from his grab-bag of styles the one most appropriate to the particular situation. At a different level, a style is almost synonymous with a personality. It is fixed and immutable, coloring the individual's actions through all situations.

In order to elucidate the manifestation (or emergence) of styles in children playing the game, it will be useful to contrast the play of two children.

Thomas and Jose: Two Styles in Treasure Play

Jose notices us playing the game in a prototype version, and attracted by the music and the colors, asks if he can play. He understands what to do immediately, and with great confidence he grabs the keyboard. At first he moves only in horizontal or vertical lines, but then he begins to make turns and thereafter speedily attains the treasure. When asked if he can do it again, he says "of course." At the beginning of the second game, when asked where he thinks the treasure is, he points to the location where he had just found the treasure. After one move in that direction gave him disconfirming evidence, he immediately turned around and spontaneously told us that the treasure was on the opposite side of the screen this time. Jose played three times his first day and found the treasure in less than 60 moves each time.

- Development (over next three weeks) Both Thomas and Jose learn to vary their step size. Thomas, however, soon settles on selecting from a palette of three step sizes: 10, 3, and 1. Jose varies his step size considerably, sometimes choosing steps as large as 100, and often choosing step sizes between 1 and 60. Thomas soon formulates explicit rules to govern his motion of the turtle. He says: "If you are going forward and the sound gets lower, turn back. If it gets higher, keep going until it gets lower again, then go back one move and turn." Of all the children, Thomas notices the sound feedback most consistently, and responds to it rather than the color. Indeed, during phase 3 of the project, when he is teaching another child to play the game, he admonishes him: "Don't look at the colors, listen to the sound."

In contrast, Jose can not articulate how he moves the turtle. When asked to explain his strategy, he responds with a list of the places he has recently visited before arriving at the treasure. Jose is perceived by the class to be an expert at Treasure. Class members often direct questions about the game to him and he is happy to help them. His help usually consists of wandering over to their terminal, seizing the keyboard and solving the problem on his own. Then he cocks his head and says "see, it's easy, that's how you do it." Thomas, on the other hand, is not highly regarded. He is a peripheral class member and not often questioned about Treasureworld.

- Teaching Others During phase three of the project, five students were selected to teach five novice Treasureworld players how to play the game. Thomas and Jose were among these five. Jose was paired with Ahmed, the only novice child who was able to find the treasure in the pretest encounter with the game. Thomas was paired with Brad, a child who seemed to flounder during the pretest.

Just before Brad came into the room, Thomas asked us "How do you want me to teach?" When we replied that "he was the teacher and he could teach any way he wanted," he said with a determined expression on his face: "I'm not going to be a normal teacher."

Thomas began by telling Brad; "I'm going to play a game first and you watch me, then you'll play." As Thomas played, he stopped to point out whenever he was applying a rule. After he had won, he asked Brad to play. He watched carefully as Brad played. Whenever Brad made a move that violated Thomas's rules, Thomas immediately corrected him, pointing out which rule he was violating. In some cases, however, he actually gave Brad "bad advice," i.e., advice which led him down a longer path to the treasure.

Jose, on the other hand, did not offer Ahmed a chance to play by himself. Jose took charge of the keyboard and found the treasure rather speedily, stopping at various points to "explain" why he turned in a particular situation. An example of Jose's explanations: "It's easy, you see. Do you get what I'm doing?" Ahmed invariably replied that he did.

Even though we were convinced that Thomas's teaching had been much better than Jose's, we were nonetheless expecting Ahmed to win. We did not believe that Thomas's superior teaching would overcome the large handicap that Brad had begun with. To our surprise, Brad won first place and Ahmed tied for second. While Ahmed showed some improvement in his game, Brad's improvement was dramatic.

- Dichotomies We would like to make two distinctions of style implicit in the discussion of Thomas and Jose. The first of these uses the word style in the "strategy" sense, the latter more in the "personality" sense.

The first distinction is between those who use many different step sizes in moving the turtle (the variable-step-sizers), and those who use only one or a few step sizes (the fixed-step-sizers). From the above cases, it is evident that Jose is a variable-step-sizer and Thomas a fixed-step-sizer.

A typical first "rule" learned by the Treasureworld player is what we call the reversal rule. It says: if you are going in a certain direction and you get "colder," go back to where you were. Fixed-step-size players apply this rule rigidly and go back to exactly where they were. Variable-step-size players reverse their heading but, because they may step back a different quantity than they went forward, usually do not return to the exact same place from which they came. In some cases they may vary their step size a great deal in this situation, and jump a whole range of colors.

Different styles lead to different difficulties in finding the treasure. A child, for example, who has a fixed step size (a step size of 5 is a common one), may endlessly repeat the traverse of a rectangle surrounding the treasure. In Figure 6 we can see how Sula is stuck in such a loop.

Figure 6: The Traverse of a Rectangle Surrounding the Treasure

Sula starts off at point A. The first step gets her to point B, which turns the turtle pink. Feeling like she's getting closer, she takes another step in the same direction, to point C. Now she has crossed over the red zone without knowing it, since the turtle does not change color. Another step in the same direction now gets her to point D, where she hits the yellow. Seeing that matters have gotten worse, she turns and continues around the rectangle, never getting to the red. Notice that even if she applied the reversal strategy, going back to the pink (point C in Figure 6) before turning, she would still be stuck in such a rectangle, albeit a tighter one. The combination of the "bad luck" of point of entry into the pink region and a fixed step size has doomed her to this Sysiphian circumnavigation. Children with a variable step size strategy do not as often get into this particular bind. Once they are in such a rectangle for a while, they will vary their step size and break the pattern, thus increasing the likelihood that they will wander into the red.

One factor that influences the choice of style in this case is comfort with moving the turtle. Most children begin as variable-step-sizers. However, after encountering difficulties with controlling the turtle (for example, getting it back to exactly where it was before in order to verify an hypothesis) they narrowed their selection of steps and became fixed-step-sizers. Many were therefore able to solve the problem of controlling the turtle by making use of a restricted set of options with which they felt comfortable.

A second distinction of style that emerges from the previous discussion is between the "rule-based" style, and the "situational" style. We would say that Thomas's style in playing Treasureworld is "rule-based," while Jose's style is "situational." Jose's confidence in his ability to get out of any bad situation that he might encounter in Treasureworld did not foster a need to reflect on his strategy and explicitly formulate a set of rules. While it might be said that he was still following rules, just a large number of very specific situational rules, Jose was never able (despite great efforts on the part of himself and the researchers) to express what those rules were. Thomas, on the other hand, did not initially feel confident in his ability to win at Treasureworld. It may be surmised that this lack of confidence and consequent desire to protect himself from failure led him to step away from the game a little, to stop the ceaseless activity of playing, and to reflect on what he could do to ensure that he did not get into trouble. This led to the formulation of explicit rules. We found that "rule-based" treasure players tend to be fixed-step-sizers, and "situational" players tend to be variable-step-sizers. The initial lack of confidence that characterizes the rule-based players leads them to adopt the more controlled fixed-step-size. In this way, a style in the sense of personality shapes the "lower-level-style" (strategy) of the players.

In addition, much of the difference that we observed in the play of rule-based players vs. situational players, is captured in the recent literature on situated action (e.g., Agre, 1989; Suchman, 1987). Agre, for example, contrasts the traditional AI view of planning with the notion of "situated activity" in the following way.

In the planning view of everyday activity: "If an agent's activity has a certain organization, that is solely because the agent constructs and deploys a symbolic representation of that activity, namely a plan. Everyday activity is fundamentally planned; contingency is a marginal phenomenon. An agent conducts its everyday activity entirely by constructing and deploying plans. The world is fundamentally hostile. Life is a series of problems to be solved."

In contrast in the situated activity view: "Everyday life has an orderliness, coherence, and laws of change that are not the product of any representation of them. Everyday activity is almost entirely routine, even when something novel is happening. Everyday activity is fundamentally improvised; contingency is the central phenomenon. An agent conducts its everyday activity by continually redeciding what to do. The world is fundamentally benign. Life is a fabric of familiar activities" (Agre, 1989. p. 11).

The parallel between the style of Jose and the situated action model is striking, similarly that of Thomas and the planning model. Agre goes on to argue the superiority of the situated view over traditional planning models. This however, is not our contention here. Of greater relevance is his observation of the marginality of the situated view in traditional AI and cognitive psychology. Similarly, we discovered that Jose had been marginalized by the traditional academic school system. Indeed he had been classified as learning disabled and had stayed back two grades.

Further Research Directions

Our work with Treasure, however, has also left us curious about many questions that arose out of the details of the game. We plan to experiment with a number of variations. The next paragraph is a quick summary of some of these ideas.

What would happen if the turtle left a trail when it moved? The children would no longer have to remember what the feedback told them last time, they would be able to see it on the screen. Would this alter in any way their perseveration behavior? What differences might we observe if we chose to separate the feedback channels, one game with sound feedback, another with color feedback? Will some kids learn to auditorize their environment instead of visualizing it? Treasure provides fourteen gradations of feedback. What if we provided continuous feedback? Would this change eliminate looping behavior? Would the traversal paths be less ragged?

We would also like to work with a broader range of children. With older children we would like to work on writing programs for the turtle to find the treasure (Abelson & diSessa, 1980). What additional power would be gained from this concretization, the reifying of strategy? Would situational style players be interested in writing such programs? Would they be able to write such programs without abandoning their style? Another research question is at what age do children begin to respond to feedback in Treasure the way adults do?

The children we worked with were primarily Hispanic. The Hispanic culture has been characterized as a ñsoftî culture (Turkle, 1984), which may be associated with a more situational style. Would the same style dichotomies be observed in a different cultural milieu?

Lastly, we plan to develop the other games in Treasureworld. Among these are one dimensional and three dimensional analogues of Treasure, variations in which various obstacles (both linear and planar) are placed on the terrain, and worlds in which the treasure moves. One interesting variation involves changing the meaning of the feedback from a measure of distance to the treasure to a measure of height above sea level. The treasure would be "buried" on the highest mountain, Everest. In this variation, following the feedback would be much more complex. One might climb up a very tall hill, the Matterhorn, only to find that one can't get any higher, and have to descend in order to find another slope.

Another variation moves closer to the original "hot and cold" game by providing relative feedback. Only two feedback signals, ñcloserî and "farther" would be given, so no absolute measure of distance could be calibrated. Still another game involves putting two children in the feedback loop, one to interpret the feedback and one to give it. The could play on two computers across a network, and the feedback giver would be constrained to give non-linguistic cues. Through their interactions, they would develop a feedback language in which to have a conversation about feedback. A final variation is one in which the goal of the game is changed. Instead of finding the treasure, the child is asked to draw a color picture of the "world" as he has understood it from the feedback obtained. This variation could be very interesting for exploring some of the epistemological issues involved in the construction of worlds.

We all navigate through the world usually receiving feedback only from the narrow range of our senses. Yet somehow we construct a more or less coherent picture of the whole, though we may not know where the treasure is located.

Acknowledgements

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