This article describes several approaches to assessing student understanding using written explanations that students generate as part of a multiple-document inquiry activity on a scientific topic (global warming). The current work attempts to capture the causal structure of student explanations as a way to detect the quality of the students' mental models and understanding of the topic by combining approaches from Cognitive Science and Artificial Intelligence, and applying them to Education. First, several attributes of the explanations are explored by hand coding and leveraging existing technologies (LSA and Coh-Metrix). Then, we describe an approach for inferring the quality of the explanations using a novel, two-phase machine-learning approach for detecting causal relations and the causal chains that are present within student essays. The results demonstrate the benefits of using a machine-learning approach for detecting content, but also highlight the promise of hybrid methods that combine ML, LSA and Coh-Metrix approaches for detecting student understanding. Opportunities to use automated approaches as part of Intelligent Tutoring Systems that provide feedback toward improving student explanations and understanding are discussed.