This paper reports on the analysis of concept maps of the nature of science constructed by preservice secondary science teachers during a semester-long reflective process. During the 16-week fall semester of 1996, 17 students were enrolled in a 5-credit course. After analyzing all students' concept maps, students were classified as either good mappers or poor mappers. Two students were selected to investigate conceptual development and change from their initial concept maps to their final reflection paper. These case studies reveal some issues that need to be sorted out, including: (1) students did not revise their concept maps over the semester; (2) the issue of the value of science remained unsettled; (3) students focus more on the instability of scientific knowledge rather than on its stability; and (4) few students integrate the scientific assumptions discussed in class into their concept maps or papers. These findings have the potential to inform understanding of how to prepare science teachers. Contains 19 references. (DDR)