The purpose of this research is to explore the aspects of abilities of mathematics communication of grade two students in the elementary school, including spoken understanding and as well as written and figural understanding. This researcher adopted action research, having the investigator implemented two months teaching. After referring to mathematics teaching materials grade two, the researcher designed four units. During the period of research, the teacher utilized a variety ways to collect data, such as; video recording, audio recording, questionnaires, reflective notes, observation records and student activities sheets. Eventually, the teacher made qualitative analyzes and explored methods of improvement on her ways of teaching. The results of this research illustrated seven aspects of spoken language expression of understanding. The students were weak in listening; dare to express their opinions; put forward queries regarding teacher's or schoolmates¡¦ questions; some were unable to raise conceptual related questions; when students made exchanges they needed help from the teacher, students spoke with low or vague voice; and, finally, students replied intermittently or silently. Besides the above seven findings on spoken language, there are four findings of phenomena in written and figural understanding. First, students were able to examine mistakes or others¡¦ mistakes according to the record on blackboard. Moreover, the students even can put forward the queries on others¡¦ problem solving records. Yet, they were capable of understanding others¡¦ mathematics records and explained others¡¦ ideas.