Recently, many countries have considered various assessment methods in order to measure multiple ways of students' thinking skills and problem solving ability. Recently, the Ministry of Education, Science and Technology [MOEST] (2009) in Korea revised the mathematics curriculum, which now more focuses on enabling students to explain mathematically as well as to reflect on their thinking. This method allows students to express or debate on their own ideas in order to extend their mathematical communication skills. The purposes of this study are to introduce the background of such implementation of a constructed-response assessment in Korea as well as to investigate how elementary teachers implement a constructed-response assessment in developing and refining a framework. The developed grading rubric for the constructed-response problems in terms of a holistic approach was introduced. Further, the implication of applying constructed-response items to third-grade students in Korea was discussed.