Analysis of Steps in Posing Arithmetic Word Problem as Sentence-Integration on Interactive Learning Environment

Abstract

Learning by problem-posing is promising activity in learning mathematics and considered to contribute the understanding of the problem’s structure. If we can clarify how learners are thinking in steps of problem-posing, we will support learning by problem-posing more. This study investigate what learners think during problem-posing as sentence-integration in terms of intermediate products as well as the posed problems as the resultant product. Problem-posing as sentence-integration defines that arithmetic word problems have a structure and problem-posing is a task to satisfy all the constraints and the requirements to build a valid structure. A previous study shows, in problem-posing of arithmetic word problems as sentence-integration, learners try to satisfy relatively large number of the constraints in the posed problems. This study focuses on the violation of constraints in the intermediate products during problem-posing as sentence-integration. If learners have concern with the structure, they will try to avoid relatively larger number of the violated constraints on the way to the resultant posed problems. We conducted Pearson’s correlation test between the occurrence frequency of intermediate products and the number of violated constraints of them. The result shows the negative correlation between them. We consider that learners had an inclination to avoid as many violated constraints as possible throughout problem-posing activity.