Problem Posing in Mathematical Investigation

This paper reports on the types of problems that high-achieving students posed when given investigative tasks that were constructed by opening up some mathematical problems. A teaching experiment was conducted to develop the students' thinking processes during mathematical investigation, and each student was videotaped thinking aloud during a pretest and a posttest. The findings show that some students were unable to pose the original intended problems and what Krutetskii (1976) called problems that "naturally follow" from the task, including extending the task to generalise. The implications of the difficulty encountered by these students for teaching and research will also be discussed.