The purpose of this study was, first, to understand the item hierarchy regarding students' understanding of scientific models and modeling (USM). Secondly, this study investigated Taiwanese students' USM progression from 7th to 12th grade, and after participating in a model-based curriculum. The questionnaire items were developed based on 6 aspects of USM, namely, "model type," "model content," "constructed nature of models," "multiple models," "change of models", and "purpose of models". Moreover, 10 representations of models were included for surveying "what a model" is. Results show that the "purpose of models" and "model type" items covered a wide range of item difficulties. At the one end, items for the "purpose of models" are most likely to be endorsed by the students, except for the item "models are used to predict." At the other end, the "model type" items tended to be difficult. The students were least likely to agree that models can be text, mathematical, or dynamic. The items of the "constructed nature of models" were consistently located above the average, while the "change of models" items were consistently located around the mean level of difficulty. In terms of the natural progression of USM, the results show significant differences between 7th grade and all grades above 10th, and between 8th grade and 12th grade. The students in the 7th grade intervention group performed better than the students in the 7th and 8th grades who received no special instruction on models.