The concept of intellectual need, which proposes that learning is the result of students wrestling with a problem that is unsolvable by their current knowledge, has been used in instructional design for many years. However, prior research has not described a way to empirically determine whether, and to what extent, students experience intellectual need. In this paper, we present a methodology for identifying students' intellectual need and report the results of a study that investigated students' reactions to intellectual need-provoking tasks in first-semester calculus classes. We also explore the relationship between intellectual need, affective need, and students' learning. Although the overall percentage of students who reported experiencing an intellectual need was low, we found positive associations between intellectual need and learning.