Momentum is a foundational concept in physics. Although it is often taught in introductory mechanics courses, there are a limited number of studies on this topic in the literature. The results from these studies have consistently shown that students have difficulties in understanding momentum, especially the connections between net force, time, and change in momentum, which are signs of fragmented knowledge structure and poor knowledge integration. This study adopts the conceptual framework representation to model student understanding and guide the design of an assessment test on momentum. Informed by the previous work on knowledge integration, the conceptual framework maps out the key concepts and their connections within a student's knowledge structure. Recent studies have shown that a conceptual framework can be used as a guide to create assessment items that follow different reasoning pathways, probing various misconceptions and student difficulties. In this study, an assessment of momentum was developed and tested among a large number of U.S. college freshmen and Chinese high school students. Based on testing and interview results, students' understanding is separated into three progression levels of knowledge integration including novice-like, transitional, and expert-like. Furthermore, the comparison between the two countries' curriculum and momentum test results indicates that an emphasis on the central idea of impulse-momentum theorem can be an essential instructional strategy to help students make the necessary connections within their knowledge structure, leading to a deeper conceptual understanding of momentum.