Visualization of Solution Processes to Reach the Correct Answer in Online Math Tests

Unlike multiple-choice online tests, in a system where students submit mathematical expressions as answers and they are automatically marked, it is possible to evaluate not only correct and incorrect answers, but also various other aspects, including partial marks. If an environment is prepared where students can take the test as many times as they need to get the correct answer, it is possible to visualize the process of arriving at the correct answer, and we can expect to obtain information about the process of understanding. We adopted STACK as an automatic mathematical expression grading system and visualized the solution process from the answer data. In order to visualize the situation of approaching the correct answer, it is necessary to define the distance between the answer and the correct answer, and we used two methods for visualization: one was the distance based on the classification of incorrect answers using the Potential Response Tree, which is one of the functions of STACK, and the other was the distance between the answer and the correct answer based on the Tree Edit Distance. Through these visualizations, it was found that it was easy to grasp things like students who are approaching the correct answer in an orderly fashion even if they don't get the correct answer the first time, and the process of getting to the correct answer through trial and error, with the distance to the correct answer becoming closer or further away.