This study aims to investigate understanding of meanings of division, quotitive division and partitive division, by the third graders and preservice elementary teachers. To do this, we analysed and compared mathematics textbooks according to 9 mathematics curricula, gathered information about their understanding by questionnaire method targeting 5 third graders and 36 preservice elementary teachers, and analysed their responses in relation to recognition of division-based situations, solution using visual representations, and awareness of quotitive division and partitive division. In Korea, meanings of division have been taught in grade 2 or 3 in various ways according to curricula. In particular, the mathematics textbook of present curriculum shows a couple of radical changes in relation to introduction of division. We raised the necessity of reexamination of these changes, based on our results from questionnaire analysis that show lack of understanding about two meanings of division by the preservice elementary teachers as well as the third graders. And we also induced several didactical implications for teaching meanings of division.