Despite decades of research on the close link between eye movements and human cognitive processes, the exact nature of the link between eye movements and deliberative thinking in problem-solving remains unknown. Thus, this study explored the critical eye-movement indicators of deliberative thinking and investigated whether visual behaviors could predict performance on arithmetic word problems of various difficulties. An eye tracker and test were employed to collect 69 sixth-graders' eye-movement behaviors and responses. No significant difference was found between the successful and unsuccessful groups on the simple problems, but on the difficult problems, the successful problem-solvers demonstrated significantly greater gaze aversion, longer fixations, and spontaneous reflections. Notably, the model incorporating RT-TFD, NOF of 500 ms, and pupil size indicators could best predict participants' performance, with an overall hit rate of 74%, rising to 80% when reading comprehension screening test scores were included. These results reveal the solvers' engagement strategies or show that successful problem-solvers were well aware of problem difficulty and could regulate their cognitive resources efficiently. This study sheds light on the development of an adapted learning system with embedded eye tracking to further predict students' visual behaviors, provide real-time feedback, and improve their problem-solving performance.