Jang Hye won, 2015), and Jeong Hye rim et al.(2016) confirmed that teachers are having difficulties in the liking cube teaching due to lack of alternative strategy and proper expressive system for 3D objects. The purpose of this study is to present the turtle representation system as an alternative to solve the difficulties of the linking cube class and to investigate the educational changes when it was used in the class. The turtle representation system can be used not only as a symbolic expression that compresses spatial information, but also as a cognitive strategy to solve spatial tasks. Therefore, two studies were conducted regarding the use of turtle representation system and examined the effect of turtle representation system in linking cube class. Study 1 focused on the use of turtle representation system as a cognitive strategy to solve and explain spatial tasks. Study 2 focused on the use of turtle representation system as a representation of 3D objects.Study 1 focused on activities to solve spatial tasks, analyzed how students use strategies to solve and explain them, and then examined what kind of changes occurred when they used the turtle representation system. As a result, students used imagistic strategy mainly in terms of processing aspect to solve and explain the liking cube task. In terms of approaching aspect, strategy that students used primarily was different according to the type of the linking cube item. In the rotation type, the ratio of holistic approach and partial approach was similar. But in the combination type, the ratio of holistic approach were higher than partial approach and in decomposition type the ratio of partial approach were higher than holistic approach. In addition to the processing aspect and approaching aspect, the strategy used to explain the solution of the linking cube task was also analyzed in terms of the reference frame aspect. The ratio of using strategy to transform objects was higher than perspective taking strategy. Thus, it was found that students were intuitive to solve and explain the linking cube task.After using the turtle representation system, there was a change in the achievement and communication of the liking cube task. First, the achievement of the linking cube task increased after the use of the turtle representation system. Particularly, the higher the difficulty level, the higher the percentage of correct answers. But the reaction time increased after using the turtle representation system rather than before, and the difference was especially significant in the rotation type with low difficulty level. When the achievements were compared by dividing groups by level, the low level group showed the greatest increase in the percentage of correct answers compared to the high or middle level group. Thus it was found that the higher the level of difficulty, the more effective the turtle representation system is and that turtle representation system can be suggested as an ;;alternative strategy;; for students who have difficulty using imagistic strategy. Second, in communication, before using the turtle representation system there was confusion to understand its meaning due to use of own non-mathematical expression. However, after using the turtle representation system, the communication became much more accurate and concise. This is because the turtle representation system played a role of ;;mathematical expression’ in which the meaning was agreed.Study 2 focused on the activities to communicate 3D objects, and examined the differences in communication according to whether turtle representation system was used or not. As a result, the groups using the turtle representation system was easier to communicate than the groups not using it. The reason for this is that the turtle representation system played a role of expression in which the meaning was agreed to 3D objects. But, even if groups use the turtle representation system, there were difficulties in the communication if they were confusing the meaning of the tortoise expression system or unfamiliar with it. So this study can reveal the limitation of the turtle representation system that unless sufficient learning of the conventions of symbol was preceded, it will interfered with communication. In this way, the turtle representation system can be used to communicate spatial information and solve spatial tasks. This study is meaningful in that it showed an alternative of linking cube class. In particular, ;;gesture’, which is the embodied aspect of the tortoise expression system newly proposed in this study, makes intuitive understanding and quick learning about the tortoise expression system by raising the embodied cognitive effect. Also it makes the turtle representation system availabe as an ;;mental tool’ without any external tools such as linking cubes or computers. Therefore, it is expected that the turtle representation system will be helpful to teachers who have difficulties in linking cube class at the school site.
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