Teachers’ predictions of students’ mathematical thinking related to problem posing

In this study, we used two pattern-related problem-posing tasks to investigate the mathematical problem posing of fifth-, sixth-, seventh-, and eighth-grade Chinese students. We also explored their teachers’ predictions about their students’ problem posing. We found that students in higher grades were more likely than those in lower grades to pose problems that involved functional relationships in both posing task situations. A posed problem involves a functional relationship when a mathematical function is the basis of the problem. We also found a mismatch between the problems that the students generated and those that their teachers predicted they would pose. Compared to the actual problems posed by the students, the problems predicted by the teachers were more likely to involve functional relationships about the pattern and less likely to involve a particular term in the pattern. Moreover, at the higher grades, the mathematical thinking related to problem posing predicted by the teachers was of a higher order than was evidenced by the problems posed by the students. Implications and future directions for research are discussed.