Visualizations of problem-posing activity sequences toward modeling the thinking process

Problem-posing is well known as an effective activity to learn problem-solving methods. Although the activity is considered in contributing to the understanding of the problem's structure, it is not clear how learners could understand it through the activity. This study proposes a method to offer a visual representation for analyzing the problem-posing activity sequence in MONSAKUN, a digital learning environment for problem-posing of arithmetic word problems via sentence integration. This system requires users to pose a problem through combinations of given simple sentences based on the requirement. The system writes every single action into logs as sequences of problem-posing activity. The sequences are considered to represent the thinking processes of learners. The thinking process reflects their understanding and misunderstanding about the structure of the problems. This study created visualizations of learners' problem-posing processes from the data obtained through the practical use of MONSAKUN, including the states in which many learners had difficulties finding the correct answer. In this study, we refer to such states as "trap states." In MONSAKUN, a trap state is a combination of simple sentences where many learners tend to make and need relatively more actions to obtain the correct answer. As the result of the visualization and analysis of the data, some trap states have been identified, and they changed for each trial in the same problem.