We reported the major findings of our research based on our own academic achievement tests towards elementary school and junior high school pupils in 2002. We then pointed out the fact that the differences of achievement between social groups have been expanded. Nowadays, that issue is seen to be one of the most serious educational problems in contemporary Japan. Although the differences of various educational outcomes such as academic achievements or educational aspirations between social groups are always emphasized, it is surprising that they seldom discuss about the ways in which those differences could be made smaller. I myself have been exploring the issue in these several years. In this paper, I will describe the progress and the future directions of our academic exploration on this particular educational issue. [This article was translated by Walter Dawson.] (Contains 2 figures, 3 tables, and 1 note.)