In this study, a conceptual framework of measurement uncertainty was developed and used to guide the development of a multiple-choice concept test for the assessment of students' knowledge integration in learning measurement uncertainty. Based on assessment data and interview results, students were identified into three levels of knowledge integration including novice, intermediate, and expertlike. The reasoning pathways of students at different levels revealed a progression of reasoning from a rudimentary surface level to a deep understanding that can be mapped in the conceptual framework. This work demonstrates the possibility of identifying a quantitative categorization scheme to model knowledge integration as well as its utility in teaching and learning. Overall, the assessments and interviews revealed common and persistent difficulties in students' understanding of measurement uncertainty. In addition, students at different levels of knowledge integration demonstrate unique types of knowledge states that can be represented in the conceptual framework, making it a useful tool for analyzing different reasoning pathways and knowledge structures.