Natural language processing (NLP) covers a large number of topics and tasks related to data and information management, leading to a complex and challenging teaching process. Meanwhile, problem-based learning is a teaching technique specifically designed to motivate students to learn efficiently, work collaboratively, and communicate effectively. With this aim, we developed a problem-based learning course for both undergraduate and graduate students to teach NLP. We provided student teams with big data sets, basic guidelines, cloud computing resources, and other aids to help different teams in summarizing two types of big collections: Web pages related to events, and electronic theses and dissertations (ETDs). Student teams then deployed different libraries, tools, methods, and algorithms to solve the task of big data text summarization. Summarization is an ideal problem to address learning NLP since it involves all levels of linguistics, as well as many of the tools and techniques used by NLP practitioners. The evaluation results showed that all teams generated coherent and readable summaries. Many summaries were of high quality and accurately described their corresponding events or ETD chapters, and the teams produced them along with NLP pipelines in a single semester. Further, both undergraduate and graduate students gave statistically significant positive feedback, relative to other courses in the Department of Computer Science. Accordingly, we encourage educators in the data and information management field to use our approach or similar methods in their teaching and hope that other researchers will also use our data sets and synergistic solutions to approach the new and challenging tasks we addressed.