Abstract:

Fostering an understanding of the local principles underlying emergent phenomena is a goal of science education. The present study examined the effects of prior experience observing emergent phenomena on rule discovery. To investigate this question, we used Conway’s Game of Life, a two-dimensional cellular automaton in which cells change between two states according to the states of neighboring cells. Each cell takes one of two states, 0 or 1 (represented as black and yellow, respectively, in this experiment). The state of each cell is determined by the states of the eight surrounding cells in its Moore neighborhood. Under the original rule (“23/3”), a yellow cell remains yellow in the next generation if two or three of its neighbors are yellow; otherwise, it turns black. Conversely, a black cell turns yellow if exactly three of its neighbors are yellow; otherwise, it remains black. Despite these simple rules, higher-order patterns can emerge when the initial configuration is appropriately designed. For example, a group of cells may move together across generations, forming a pattern known as a “spaceship.” The two experimental conditions differed only in whether participants had prior experience observing emergent phenomena: a prior-observation condition and a no-prior-observation condition. In the experiment, participants completed two tasks: a training task and a main task. In each task, they were asked to discover the rules of the Game of Life by observing changes in cell patterns. In the training task, participants completed two trials, each consisting of an observation of 13 generations. After each trial, they were asked to report the rule they had identified. In the main task, participants completed seven trials. The training task used the “23/3” rule. In contrast, the main task used a different rule, the “2/2” rule. Under both rules, emergent phenomena such as still lifes, oscillators, and spaceships can be observed when the initial state is configured appropriately. During the training task, in which participants were required to discover the rule, the initial state in the prior-observation condition was configured to produce numerous emergent phenomena. In contrast, in the no-prior-observation condition, the initial state was configured so that no emergent phenomena appeared. The two conditions differed only in the nature of the training task. At the end of the training task, participants in both conditions were informed that the rule was “23/3.” They then proceeded to the main task, in which the rule was “2/2,” and were required to discover it. In the main task, participants began their observations from an initial state in which emergent phenomena could be observed. The reported rules across the seven trials of the main task were compared between conditions using survival analysis. The results showed that the no-prior-observation condition facilitated rule identification compared with the prior-observation condition. This result suggests that prior observation of emergent phenomena may have directed participants’ attention toward higher-order phenomena, thereby weakening their focus on the local relationships necessary for rule discovery. These findings imply that instruction for exploring emergent phenomena should not only highlight global patterns, but also explicitly encourage learners to attend to the hierarchical relationship between local rules and the higher-order patterns that emerge from them.

Keywords:

Emergent phenomena, Game of Life, prior experience, rule discovery.