A focus on mathematical understanding and problem solving in math education has developed a need to implement alternate ways of testing to better assess the students' understanding and problem solving skills. The seventh national school curriculum (MOE, 1997) for mathematics in Korea was revised to the current curriculum (MOEHRD, 2007) to emphasize alternative assessment methods and particularly the descriptive assessment method. However, the implementation process has been slow due to the lack of support to help teachers to prepare, develop and grade the new descriptive problems. In order to help teachers implement the new assessment framework, we carried out a study with students of grade 2, 4 and 6 to test and refine a framework for developing and grading descriptive problems. Analysis and comparison of the data showed that the grading rubric based assessment of the descriptive problems revealed useful information about the quality of problems and the level of understanding of the students. The study showed that a structured approach to descriptive problem assessment can be a powerful tool for improving math education in the elementary school.