This study is to recognize a problem in the practice of performance assessment in elementary school, and to find out some suggestive points for improvement of teaching·learning method in elementary mathematics through assessment by reducing time restriction according to assessment through the practice of self-assessment, peer-assessment and observation, and then by reflecting the results of assessment on teaching learning plan. For that, the questions of study set up are as follows ; 1. How should self-assessment and peer-assessment be applied to in elementary mathematics assessment? 2. How should the time for 'let's play an interesting game' be managed for assessment of elementary mathematics? 3. How should the results of assessment be reflected on the Process of teaching and learning of mathematics? To solve these problems, a researcher of this thesis performed self-assessment, peer-assessment on 40 students of second grade under her charge as a class teacher, and applied observation in the time management process for 'let's play an interesting game' for a semester. self-assessment was made by mathematics journal, self-assessment chart, peer-assessment was by the analysis of conversation record among students in the situations of assessment, and observation was by observation of activity when playing with the results data of play analyzed. the concrete methods of application as follows ; First, mathematics journal was applied $1{\sim}2$ times by each unit with reconstruction into the level of second grade on the basis of the preceding-study models. Second, peer-assessment was applied to the unit-assessment time and the play-activities time by the method of recording·analyzing the contents of conversation among students in the process of assessment. Third, mathematical attitude & dispositions of students making use of the self- assessment table were examined referring to the teaching learning plan. Fourth, the time management for 'let's play an interesting game' was made through the prior recognition of play method and the joyful play-activities by use of the play-plate. Assessment depended on analysis of play-activities results of students making use of an observation form. Fifth, the results of self-assessment, peer-assessment, and observation were analyzed, and then they were made use of as self-observation data, of teacher her/his self, or teaching·learning improvement data. Students' self-assessment datum (mathematics diary, self-assessment sheets, conversation contents in the process of assessment) and observation materials (check lists, Play-activity result materials, conversation contents in the process of play) obtained in the process of application was analyzed as follows ; 1. From the practice of self-assessment in form of mathematics journal, I could obtain not only datum showing how much students was understanding the learning aims by unit time and to any degree they reached but also information about their response to learning datum and favorable type of learning. 2. Assessment by self-assessment chart was useful in planning the mathematics teaching learning process because it helps ascertain mathematical attitude & dispositions of students. 3. Through the application of peer-assessment, students had the opportunity of communicating with other students looking back on his/her explaining process, and teachers could obtain basic materials for assessment of students. 4, In case of time management for 'let's play an interesting game', there was natural extension of play made through time-security by prior looking into the method of play-activity, and then, for a remained time, by making children play a new game. 5, I could easily record the activities of students by use of the observation. form, and make use of it as basic data for descriptive assessment. 6, Each kinds of data obtained from the results of assessment was helpful for securing self-observation materials in the process of teaching learning and for their betterment in mathematics subject. However, because they were in the second grade of elementary school and there was an individual difference, some students could not make use of mathematics diary or self-assessment form properly. In case of these students, assessment data would be obtained through interview or observation. And for effective operation of play, its purpose & method and matters that demand special attention when play-acting should be clearly guided. Also, when applying an effective play in addition to play activities in textbook, to lessons, interesting mathematics lessons could be guided.