In recent years, an increasing number of analyses in Learning Analytics and Educational Data Mining (EDM) have adopted a "Discovery with Models" approach, where an existing model is used as a key component in a new EDM/analytics analysis. This article presents a theoretical discussion on the emergence of discovery with models, its potential to enhance research on learning and learners, and key lessons learned in how discovery with models can be conducted validly and effectively. We illustrate these issues through discussion of a case study where discovery with models was used to investigate a form of disengaged behavior, i.e., carelessness, in the context of middle school computer-based science inquiry. This behavior has been acknowledged as a problem in education as early as the 1920s. With the increasing use of high-stakes testing, the cost of student carelessness can be higher. For instance, within computer-based learning environments careless errors can result in reduced educational effectiveness, with students continuing to receive material they have already mastered. Despite the importance of this problem, it has received minimal research attention, in part due to difficulties in operationalizing carelessness as a construct. Building from theory on carelessness and a Bayesian framework for knowledge modeling, we use machine-learned detectors to predict carelessness within authentic use of a computer-based learning environment. We then use a discovery with models approach to link these validated carelessness measures to survey data, to study the correlations between the prevalence of carelessness and student goal orientation. [This paper was published in "American Behavioral Scientist" v57 n10 p1479-1498 2013.]