This paper presents a transformative modeling framework that guides the development of assessment to measure students' deep understanding in physical sciences. The framework emphasizes 3 types of connections that students need to make when learning physical sciences: (1) linking physical states, processes, and explanatory models, (2) integrating multiple explanatory models, and (3) connecting scientific models to concrete experiences. We carried out a 2-phase exploratory study that helped further develop and refine the framework. In the first phase, we developed 3 items on sinking and floating and pilot tested them with 18 undergraduate students. Analysis of student responses revealed various student misconceptions and the different connections students made among science ideas. Based on the findings, we revised the assessment, modified the instruction, and collected data from another cohort of 26 students. The second cohort of students showed significant improvement of understanding of sinking and floating after instruction. Implications and limitations of how our assessment framework can be used to improve students' conceptual understanding in science are discussed.