Open-ended problems

The International Journal for Mathematics Teaching and Learning has recently published an article called: "Teaching and Evaluating 'Open-Ended' Problems". The article is written by Rama Klavir and Sarah Hershkovitz, and it is freely available in pdf format. Here is the abstract:

This paper focuses on an open-ended problem. The problem comprises a group of four numbers from which the students are asked to find the one that does not belong. Each of the numbers can be selected as not belonging, each one for different reasons. The problem was given to 164 fifth-grade students. The paper suggests tools for teachers to analyze and evaluate the work of their students when dealing with problems of this kind.