A one-on-one dialogue-based mathematics intelligent tutoring system (ITS) for learning multiplication and division of fractions was developed and evaluated in this study. This system could identify students’ error types and misconceptions in real-time by using a block-based matching method. The adaptive dialogue-based instruction was supported by a response-driven tutoring model, which was constructed based on the diagnostic teaching methodology. Instructional strategies including provoking cognitive conflict, problem simplification and representational teaching were used in the tutoring model of the system. Effectiveness of the math ITS in remedial instruction was evaluated through a quasi-experimental study. The participants of the study were 66 sixth graders chosen from central Taiwan. They were divided into an experimental group of 35 and a control group of 31. One week after the pretest, the experimental group received 2-h one-on-one instruction via the math ITS, while the control group took a 2-h conventional teacher instruction with the same teaching content in the classroom. All participants took a post-test within 2 days after the remedial instruction. The results showed that the experimental group using the math ITS significantly outperformed the control group. Further analysis indicated that the math ITS had a significant effect on the lesser-performing group (the lower 75% in the pretest score). In addition, a usability and user experience survey showed that students were willing and likely to learn mathematics using the dialogue-based math ITS.

The current study explores students’ collaboration and problem solving (CPS) abilities using a human-to-agent (H-A) computer-based collaborative problem solving assessment. Five CPS assessment units with 76 conversation-based items were constructed using the PISA 2015 CPS framework. In the experiment, 53,855 ninth and tenth graders in Taiwan were recruited, and a multidimensional item response analysis was used to develop CPS scales and represent the students’ collaboration and problem solving performance. The results show that the developed H-A approach is feasible for measuring students’ CPS skills, and the CPS scales are also shown to be reliable. In addition, the students’ CPS performance scores are further explored and discussed under the PISA CPS framework.

This study established an online game-based assessment to explore third and fourth graders’ performance of computational estimation in addition and subtraction. Students’ computational estimation strategies could be automatically recorded and classified in this assessment, and the Higher-Order DINA model was used as a measurement model in order to provide more information of individual learning status. A total of 729 students in Taiwan participated in this study. 349 third graders and 380 fourth graders randomly selected from two elementary schools. Results showed that (a) successful problem-solvers tended to perform computational estimation with good intuitive number sense or relied on item content to adopt effective computational estimation strategies, (b) fourth graders’ estimation ability in addition and subtraction was significantly better than third-graders’ ability, and (c) students at different ability levels used different computational estimation strategies and mastered different computational estimation skills.