The purpose of this study is to compare the preferences of the school mathematical terms of South Korea and those of North Korea by administering a survey for learners, inservice teachers, and pre-service teachers, to establish the criteria of desirable school mathematical terms, and to evaluate the school mathematical terms of South Korea and those of North Korea based on the criteria. According to the result of the survey, the preferred mathematical terms are different from one group to the other, yet the mathematical terms of South Korea are more preferred. In general, terms written in pure Korean and concise terms which are easily understandable are favored. To discuss about the criteria of desirable school mathematical terms, four perspectives were set up, 1) the semantic perspective and the regulatory perspective, 2) terms written in pure Korean and Chinese letters, 3) terms from everyday language and technical terms, and 4) the consistency. Six criteria were followed from the aforementioned four perspectives. Finally, various school mathematical terms of South and North Korea were reviewed in the angles of the four perspectives and the six criteria.