In current national survey (Japan), approximately 70 percent of recent secondary school graduates recommended that schools provide more instruction in mathematics. It is well recognized that our current instructional system needs to be much improved to achieve our goals. No one denied that the goal of teaching is to master learning. Yet, in fact, there have been relatively few successful systematic attempts to determine the effectiveness of specific teaching methods or to design methods that maximize positive results and minimize negative results. One of the important purposes of this study is the development of new instructional system based upon recent learning strategies...... a system which is most suitable for the actual situation in mathematics of elementary school. As an effort to bring about this purpose, the diagnostic and remedial instructional system was developed. This system differs from conventional classroom instruction in (1) its emphasis on the mastery of each of a series of learning units, (2) its frequent testing to diagnose learning difficulties, and (3) its systematic feedback-corrective procedures through error analysis for helping slower learners overcome learning errors. In this system, an instructional unit is defined as a learning task or tasks requiring approximately six to fifteen lesson hours of instruction. Since the system was emphasized in individualized instruction, the tests used were almost exclusively criterion-referenced. Mastery is demonstrated on these measures by attaining a prespecified level of achievement on each instructional objectives. The flow chart in Figure 1 illustrates the use of testing in guiding pupils through units on individualized instrcution. Here Figure I The instructional system has been developed through continuous experimentations over a period of three years. The instructional system was more effective compared with the conventional system, and the instructional materials including teacher's manuals and remedial programmed programs were successfully used without any particular difficulties encountered in using them. Four units in arithmetic from four elernentary grade levels were selected for use in this study. The results are as follows: (1) According to summative testing results, for the lower grades 90 percent of the pupils belonging to the mastery learning groups achieved 90 percent mastery. (2) Remedial learning for low achievers (identified through arithmetic achievement and/or readiness tests) was improved significantly. (3) For the higher elementary grades, 80'. percent of the students attained an 80 percent or higher level of mastery of the instructional objectives. (4) Overall results showed that the instructional materials developed for this study were significantly more effective than regular instruction.