Aggressive driving behavior is one of the leading causes of road accidents worldwide. One way to ameliorate this situation is to collect and analyze driving patterns with the intention of promoting driving awareness, a task that has been called driving analytics (DA). DA employing the driver’s smartphone has attracted attention from the community given its good capabilities to capture, via its integrated sensors, data that could be exploited to infer driving style. Most works in the related literature have represented this sensor information either as statistical scores or in raw format that are later fed into threshold-based heuristics or machine learning (ML) approaches. Based on the hypothesis that better data representations do exist, in this paper, we propose a second-order representation, based on the bag-of-words’ strategy, to model accelerometer timestamps associated with aggressive driving maneuvers. We evaluate this representation in two scenarios and three data sets against the best reported work in each of them. In the first scenario, we classify accelerometer samples as either belonging to aggressive or safe driving style. In the second scenario, we approach a multi-class problem, where we are now interested in identifying the exact aggressive maneuver that the accelerometer sample represents. The results show that this novel representation outperforms both state-of-the-art works with 6% and 15% in F-measure for each scenario, respectively. To further investigate the strength of our representation, we make a comparison against similar second-order strategies that have also proved to be successful. Overall, this analysis suggests that this representation constitutes an attractive method for driving behavior classification, boosting discriminative performance of ML approaches.