Middle-grade preservice teachers’ mathematical problem solving and problem posing

Empirical data were gathered from 51 middle-grade preservice teachers who were randomly assigned into one of two groups. The fi rst group solved a task and then posed new problems based on the given fi gures, and the second group completed these activities in reverse order. Rubrics were developed to assess the written responses, and then thoughts and concerns related to problem-posing experiences were collected to understand their practices. Results revealed that the preservice teachers were profi cient in solving simpler arithmetic tasks but had diffi culty generalizing and interpreting numerals in an algebraic form. They were able to pose some basic and reasonable problems and to consider important aspects of mathematical problem solving when generating new tasks. Thus, teacher educators should provide substantial educational experiences by incorporating both problem-solving and problem-posing activities into engaging instruction for preservice teachers.