In order to capture the nature of problem posing, our model (Figure l) incorporates
forms of semi-structured and structured situations (Stoyanova, 2000) in which
students are asked to generate problems from a presented stimulus (presolution
phase). The stimulus situations involve quantitative information, which contain
representations either in the iconic or in the symbolic form. For example, students
posing problems based on a picture are handling information in iconic form.
Similarly, students are handling quantitative information in iconic form if they are
given graphs and diagrams. Students posing problems based on words or phrases or
calculations are handling quantitative information in symbolic form. Examples of the
tasks that correspond to each cognitive process are shown in Table l.
The purpose of the present study was twofold: First, to validate the proposed model,
i.e., to confirm that problem posing consists of the proposed cognitive processes, and
second to search for a possible developmental trend in students’ abilities to pose
problems based on the editing, filtering, comprehending, and translating cognitive
processes and to find out meaningful differences in students’ thinking in generating
problems. However, in this paper, due to space limitations, we present the results of
the first aim of the study.