The amount of substance and its unit the mole is a basic concept in chemistry. However, previous research has shown that teaching and learning the concept are challenging tasks for both teachers and students. The purpose of this study was to pinpoint the problems which emerge in the teaching and learning process, and provide integrated suggestions for classroom instruction. By means of videotaping and interviews, the case studies explored how the mole is presented and conceptualized in two secondary classrooms in two different countries, Australia and Taiwan. Data analysis was based on a concept map and focused on how two key ideas were presented in the lessons and perceived by the students: (1) the definition of the mole, and (2) the concept of molar mass. The findings show that during the lessons on the mole, most of the time was spent on solving stoichiometric problems. Conceptually, the number aspect of the mole, that is, Avogadro's number, was emphasized; the concept of molar mass was introduced without meaningfully connecting it to the concept of relative atomic/molecular mass. Although the students were able to solve relevant problems, they could not coherently explain the relations among the concepts. Two critical components for a conceptual understanding of the mole emerged: (1) the number aspect of the mole needs to be justified by its mass aspect, and (2) the connection between molar mass and relative atomic/molecular mass needs to be explicitly explained. The two components provide one explanation for students' algorithmic learning and their confusion in learning about the mole, and serve as concrete suggestions for improving classroom instruction. The study once again manifested the significance of teaching for conceptual understanding in science education. It also exemplifies how a concept map of a specific scientific concept can also be a useful analytical tool in educational research. © 2015 Wiley Periodicals, Inc. J Res Sci Teach 53: 181–214, 2016.