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.

We report on the results of a professional development programme involving four Hungarian teachers of mathematics. The programme aims to support teachers in integrating problem solving into their classes. The basic principle of the programme, as well as its novelty (at least compared to Hungarian practice), is that the development takes place in the teacher’s classroom, adjusted to the teacher’s curriculum and in close cooperation between the teacher and researchers. The teachers included in the programme were supported by the researchers with lesson plans, practical teaching advice and lesson analyses. The progression of the teachers was assessed after the one-year programme based on a self-designed trial lesson, focusing particularly on how the teachers plan and implement problem-solving activities in lessons, as well as on their behaviour in the classroom during problem-solving activities. The findings of this qualitative research are based on video recordings of the lessons and on the teachers’ own reflections. We claim that the worked-out lesson plans and the self-reflection habits of the teachers contribute to the successful management of problem-solving activities.

Based on the literature, Pólya was influential in problem-posing research. The present paper draws attention to a book written with Pólya's collaboration, which has not yet received sufficient emphasis in the problem-posing literature. On the other hand, Pólya's impact on mathematics education in Hungary has been significant, including the problem-posing paradigm. Two works, published only in Hungarian, that rely heavily on problem-posing are highlighted. Furthermore, it is presented how problem-posing appeared in the Hungarian Complex Mathematics Teaching Experiment (1962-78) led by Tamás Varga. Subject Classification: 97D50

Problem-posing is an essential component of mathematics education because, among other reasons, when students are given the opportunity to pose their problems, they can take ownership of their learning and become more engaged in the given subject. Thus, problem-posing can lead to a deeper understanding of the studied mathematical concepts. In a collaborative action research study, the authors explored whether well-structured problem-posing activities could be incorporated into classes with students of mixed ability in mathematics. This question is addressed by examining the correlation between students’ mathematics grades and problem-posing success. The problem-posing approach used in this paper relies on problem solving as a parallel activity. Hence, the study also focuses on the relationship between problem posing and problem solving. The paper presents the results of a classroom experiment with 86 sixth-grade students and their teachers from Hungary and Romania. After evaluating the students’ problem-posing products and problem-solving performances, the results show that problem posing, based on a worked-out model problem, is a feasible challenge for most students. Moreover, this experiment identified a direct relationship between successful problem posing and problem solving.