Problem posing has received increased attention among researchers and educators. One of the most important aspects is to understand the cognitive process of problem posing. In this study, we conceptualized a framework for the cognitive process of mathematical problem posing in three stages: (a) input--understanding the task, (b) processing--constructing the problem, and (c) output--expressing the problem. In this paper we focus on examining the role of task format (i.e., the presence or absence of specific numerical information, with or without context) in 669 students' problem posing and behaviors during the three stages of problem posing and problem solving. The major findings were that students' performance was better when the task contained specific numerical information (i.e., the task with context) than when it did not (the task without context) during the problem-posing stages of understanding tasks and constructing problems. Students' behaviors during the stage of expressing problems did not show a significant difference under the task format with (or without) numbers, but students could express problems more clearly under the task format with context than under the task format without context. Moreover, students who were able to solve the problem correctly were able to pose more mathematical problems and more solvable problems than those who couldn't solve the problem. In particular, students who were able to solve the problem correctly had a better understanding of the problem-posing task. However, students who were unable to solve the problem correctly were still able to pose solvable and complex problems.