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There is an ongoing research interest to disclose factors that influence problem-posing performance by involving cross-national backgrounds. This research extends that effort by conducting a comparative analysis on the performance of Indonesian and Hungarian prospective teachers in a problem-posing task. A total of eighty-three prospective teachers from Indonesia and Hungary were asked to pose a problem based on the current calendar. For more in-depth insights, an interview was conducted with a representative participant. The obtained data were analysed quantitatively using Fisher's exact test and qualitatively in nature. Their mathematical background seems to influence the characteristic of their proposed problem and the solution approach they utilized. The typical tasks proposed by Indonesian prospective teachers are exercise and mostly related to arithmetic operations, while those by Hungarian prospective teachers are challenging problems and generally connected to arithmetic sequences. Moreover, in solving their problems, Indonesians tend to show arithmetic reasoning while Hungarians often denote algebraic reasoning. These disparities might be attributed to the types of problems that each group typically encounters during their mathematics lessons.

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Covariational reasoning plays a significant role for solving problems. This study examines the covariational reasoning of master program students when solving mathematical problems such as fraction, velocity and acceleration, proportion, and integral. 26 students of mathematics education master program, Universitas Negeri Surabaya, are involved in this study. Generally, mental action of students is more prominent on fraction and proportion than on the other issues. On fraction and proportion problems, most students are able to fulfill all mental actions such as coordinating the value, the direction, and the amount of change of one variable, and also coordinating the average and the instantaneous rate of change of the function. However, on velocity, acceleration, and integral problems most students cannot show their mental actions well. They only fulfill 3 of 5 mental actions of covariational reasoning. Generally, the shape of their graph related to those problems are irrespective with initial point. These findings suggest that learning in mathematics should place increased emphasis on problem involving graph to promote covariational reasoning of the students.