Zoltan Kovacs

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 problemposing appeared in the Hungarian Complex Mathematics Teaching Experiment (1962-78) led by Tamás Varga.

This study is guided by the question: Can systematic instruction in problem posing strategies increase teachers' flexibility in the way they look at textbook problems? The participants in the study consisted of a group of math teacher trainees in the last semester of their training. They got experiences with problem posing strategies during their training. After solving a textbook problem, students explored the problem more deeply by using the “What-If-Not” strategy. Three different solutions appeared in the classroom. I analyze these approaches based on Pólya's steps of problem-solving and Ernest’s categorization of inquiry methods.

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 ...

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Can teacher trainees use inductive arguments during their problem solving activity? Eszter Kónya, Zoltan Kovács

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

The use of difference and differential equations in modelling is a topic usually studied by advanced students in mathematics. However, difference and differential equations
appear in the school curriculum in many direct or hidden ways. Difference equations first enter the curriculum when studying arithmetic sequences. Moreover, Newtonian
mechanics provides many examples for differential equations, and numeric solution leads to difference equations which can be treated easily with Computer Algebra or Dynamic Geometry Systems. My hypothesis is that numerical methods supported by technology serve as a tool that helps the early
introduction of modelling concepts.

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 ...