Abstract:

Problem-solving competence is defined as the capacity to engage in cognitive processing to understand and resolve problem scenarios where a solution is not obvious. Computer-based assessments usually provide an interactive environment in which students can solve a problem by choosing among a set of available actions and taking one or more steps to complete a task. All students’ actions are automatically recorded in system logs as coded and time-stamped strings. These strings are called process data. The process data have multi-level structures in which the actions are nested within a single individual and therefore they are logically interconnected. Recently, researches have focused on characterizing process data and analyzing the response strategies to solve the problem.

This study proposed an extended MMixIRT model which incorporated the multilevel structure into a mixture IRT model. It can classify latent groups at process level that have different problem solving strategies, and estimate the students’ abilities at the student level simultaneously. This model takes the accumulated response information as the specific steps at the process level and defines a more free matrix to determine the weight information used for ability estimation at the student level. Specifically, in the standard MMixIRT model, the student-level latent variables are generally obtained from the measurement results made by the process-level response variables, while students’ final responses are used to estimate their problem-solving abilities in the extended MMixIRT model.

This research applied process data recorded in one of the items (Traffic CP007Q02) of problem solving in PISA 2012. The samples were 3196 students from Canada, Hongkong-China, Shanghai-China, Singapore, and America. Based on the log file of the process record, there were 139,990 records in the final data file. It was found that (1) The model can capture different problem-solving strategies used by students at the process level, as well as provide ability estimates at the student level. (2) The model can also analyze the typical characteristics of students’ strategy in problem-solving across different countries for targeted instructional interventions.

It is concluded that the extended MMixIRT model can analyze response data at process and student levels. These analyses not only play an important role in the scoring, but also provide valuable information to psychometricians and test developers, help them to better understand what distinguishes well performing students from the ones that are not, and eventually lead to better test design.

Key words: computer-based dynamic assessment, problem-solving strategy, process data, the extended MMixIRT model