Research on Mathematical Problem Posing: What We Know and Where We Are Going = Research on Mathematical Problem Posing: What We Know and Where We Are Going

다국어 초록 (Multilingual Abstract)

There is a long history of integrating mathematical problem solving into school curricula. In contrast, problem-posing research is a relatively new endeavor. Nevertheless, there have been efforts to incorporate problem posing into school mathematics at different educational levels around the world in the past two decades. These efforts indicate interest among many researchers and practitioners in making problem posing a more prominent feature of classroom instruction. In this plenary, I will present the current state of knowledge in problem-posing research and suggest some directions for future study. In particular, my discussion will be organized based on the following ten questions: (1) Why is problem posing important in school mathematics? (2) Are teachers and students capable of posing important mathematical problems? (3) Can students and teachers be effectively trained to pose high quality problems? (4) What do we know about the cognitive processes of problem posing? (5) How are problem-posing skills related to problem-solving skills? (6) Is it feasible to use problem posing as a measure of creativity and mathematical learning outcomes? (7) How are problem-posing activities included in mathematics curricula? (8) What does a classroom look like when students engage in problem-posing activities? (9) How can technology be used in problem-posing activities? (10) What do we know about the impact of engaging in problem-posing activities on student outcomes? Each of these questions represents a rich area for problem-posing research and I will summarize what we know as a field, and then point out possible future directions of research on mathematical problem posing.