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We propose and implement a novel intelligent tutoring system, called RadarMath, to support intelligent and personalized learning for math education. The system provides the services including automatic grading and personalized learning guidance. Specifically, two automatic grading models are designed to accomplish the tasks for scoring the text-answer and formula-answer questions respectively. An education-oriented knowledge graph with the individual learner’s knowledge state is used as the key tool for guiding the personalized learning process. The system demonstrates how the relevant AI techniques could be applied in today's intelligent tutoring systems.

Introduction: Flow state is a psychological concept used to describe the optimal engagement in different activities. Therefore, the DFS-2 has been developed as an instrument to measure an individual’s dispositional tendency to flow state as a personality trait. Objective: Aiming to obtain an adapted version of the DFS-2 for the Brazilian-Portuguese language (DFS-BR) and for general activities, we performed its forward- and backward-translation, and we validated it. Methods: After gathering answers from 681 Brazilian participants, we performed: (1) the construct validity of the DFS-BR; and (2) the psychometric item quality analysis. Results: the Confirmatory Factorial Analysis (CFA) indicates the best fit for the gathered data is a nine multi-correlated factorial model (χ2/df = 4.23, CFI = 0.94, TLI = 0.93 and RMSEA = 0.069). Reliability tests performed in this structure indicates excellent internal consistency for the DFS-BR. The item quality analysis indicates that its difficulty and discriminating parameters have a good endorsement to estimate the dispositional flow state. Additionally, we proposed and validated a short version of the DFS-BR (composed of only nine items). The validation results indicates good fit (χ2/df = 2.94, CFI = 0.98, TLI = 0.97 and RMSEA = 0.053) and good internal consistency. The Test Information Curve of the short version indicates that it is very informative in the estimation of individual dispositional flow state. Discussion and Conclusions: In view of these results, we conclude that the DFS-BR showed good evidence of its validity to be used with Brazilian people. We also suggest the use of a short version when we need only measure the person’s flow state based on the principle of Occam’s razor. This principle is supported by the analysis presented in this article.

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