Problem-posing research in mathematics education: new questions and directions (original) (raw)
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CEPS Journal, 2022
Problem solving and problem posing are leading mathematical activities that stimulate mathematical thinking. From the theoretical point of view, these activities are very complex, partly due to the various issues that describe/define problem solving and problem posing and their role in the process of teaching and learning mathematics. Problem solving and problem posing are interrelated activities; we could say that they are in an interdependent relationship: we solve the problems we pose, we pose the problems in a way that we can solve them. However, the two processes are not equally present in every situation. Research into problem solving focuses mainly on the following areas: the basic characteristics of a mathematical problem; the nature (conceptual, procedural) and role of representation (interplay between internal and external) of a mathematical problem; mental schemas for problem solving; heuristics as principles, methods and (cognitive) tools for solving problems; types of generalisations and reasoning (abductive, narrative, naïve, arithmetic, algebraic); problem solving as a challenging activity for mathematically gifted students; and the role of the teacher in guiding problem solving as a way of implementing student problem solving in the classroom. Regarding problem posing, there are also some critical questions: How can the existing definitions of problem posing be categorised? How is problem posing conceived by the research community in relation to other mathematical constructs? What are the possible ways of implementing problem posing in research and teaching settings? Regarding problem solving, problem posing is formulated/used in research findings for generating (formulating, finding, creating) new problems; reformulating existing problems; creating and/or reformulating problems; raising questions and viewing old questions from a new angle; and an act of modelling. Research has demonstrated and frequently confirmed that (mathematical) problem posing and solving possess great potential for learners, but the reality in terms of teaching practice, external examinations, teaching material, and mathematics curricula seems out of alignment with the research findings. In this focus issue, we have considered two aspects of problem posing and problem solving: conceptualisation and implementation in the mathematics classroom. This issue contains five articles that address the issues of problem posing and problem-solving. The authors come from different backgrounds (Greece, Croatia, Hungary, Germany), which means that diverse perspectives and research
Problem Posing in Mathematics Education Research: A Systematic Review
International Journal of Academic Research in Progressive Education and Development
Students' critical thinking skills, attitudes, confidence, and understanding of mathematical concepts can be improved through problem-posing activities. However, teachers' and students' skills in problem-posing are still at a moderate level. This study aims to review the concept of problem posing and explore empirical research results on mathematical problem posing. The criteria for selecting empirical studies are publications between 2015 and 2020, the main focus of studies on mathematical problem posing, conducted in educational institutions, and sample empirical studies among students and teachers. Twenty articles were selected through a systematic search of the "ERIC" database. The findings show differences in mathematical problem posing, creating a new problem statement, producing new questions, formulate meaningful mathematical problems posing new mathematical questions, a distinctive problemsolving process, mathematical imagination, and creative thinking between multiple answers. The research results show that eight research on problem posing was done on primary school students, where the remaining were on secondary school students. A total of 12 articles on problem posing were studied on teachers, were 8 of them were preservice teachers, and another three are on qualified teachers, and one was on both. The results of school students showed a mostly positive impact on students' achievements, creative thinking, critical thinking, and learning motivation in their respective domains. For teachers, out of the eight researches done, five articles imposed a negative result. Teachers had conceptual difficulties in problem posing. The problems they posed were the inappropriate, error, or failure to establish a part-whole relationship, and some posed problems that required an irrelevant strategy. Implications of the study are discussed.
Mathematical problem posing : from research to effective practice
2015
Mathematical Problem Posing Practices and Research: 1970-2010.- Problem Posing From a Modelling Perspective.- Conceptualizing Problem Posing Via Transformation.- Developing a Problem-Posing Pedagogy From the History of Mathematics.- On the Relationship Between Problem Posing, Problem Solving and Creativity.- Is Problem Posing a Tool for Developing Mathematical Creativity?.- Using Digital Technology for Mathematical Problem Posing.- Problem Posing in Mathematics - The Relevance of Philosophy for Children (P4C).- Problem Posing as Lenses for Understanding and Improving Students' Learning of Mathematics.- Examining Problem Posing in Different Grade Levels: How Students Posed Problems-To-Solve.- Problem Posing by Way of Mediated Activity at Grades Four and five.- Enhancing the Development of Chinese Fifth-Graders' Problem Posing and Problem Solving Abilities, Beliefs and Attitudes: A Design Experiment.- If You Don't Know Why Do You Ask?.- Problem Posing to Provide Students w...
Problem Solving in Mathematics Education
Encyclopedia of Mathematics Education, 2014
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Australian Journal of Teacher Education, 2013
Problem posing is one of the most important topics in a mathematics education. Through problem posing, students gain mathematical abilities and concepts and teachers can evaluate their students and arrange adequate learning environments. The aim of the present study is to investigate Turkish primary school teachers' opinions about problem posing applications for students, the mathematics curriculum and textbooks. A 30-item questionnaire was developed by the researcher and administered to 18 primary schools. Altogether, 277 primary school teachers participated in the study. The results showed that Turkish primary school teachers have positive views about problem posing applications related to students but negative opinions about the mathematics curriculum and mathematics textbooks.