A longitudinal study of students' developing understanding of decimal notation has been conducted by testing over 3000 students in Grades 4 to 10 up to 7 times. A pencil-and-paper test based on a carefully designed set of decimal comparison items enabled students' responses to be classified into 11 codes and tracked over time. The paper reports on how students' ideas changed across the grades, which ways of thinking were most prevalent, the most persistent and which were most likely to lead to expertise. Interestingly the answers were different for primary and secondary students. Estimates are also given of the proportion of students affected by particular ways of thinking during schooling. The conclusion shows how a careful mapping can be useful and draws out features of the learning environment that affect learning. (Contains 7 figures and 3 tables.) [For complete proceedings, see ED496845.]