An empirical taxonomy of problem posing processes

This article focuses on the construction, description and testing of a theoretical model of problem posing. We operationalize procesess that are frequently described in problem solving and problem posing literature in order to generate a model. We name these processes editing quantitative information, their meanings or relationships, selecting quantitative information, comprehending and organizing quantitative information by giving it meaning or creating relations between provided information, and translating quantitative information from one form to another. The validity and the applicability of the model is empirically tested using five problem-posing tests with 143 6th grade students in Cyprus. The analysis shows that three different categories of students can be identified. Category 1 students are able to respond only to the comprehension tasks. Category 2 students are able to respond to both the comprehension and translation tasks, while Category 3 students are able to respond to all types of tasks. The results of the study also show that students are more successful in first posing problems that involve comprehending processes, then translation processes and finally editing and selecting processes.