Meanings of "surprise" are wide and include uplifting and engaging facets like wonder and amazement on the one hand as well as ones that may be of the opposite nature like interruption and disrupt on the other. Pedagogically, educators who use surprise in class activities are focusing on students being "taken aback" by a situation, hopefully causing them to "look again" and spurring them to further effort to resolve an anomaly. In this sense, surprise implies facing something unexpected, out of place, counterintuitive, or somewhat "not fitting". It implies that the learner has met the elements of the situation separately before, but is now associating them for the first time, as in much of learning. It also implies that there is some emotional charge, in the sense that the person is intrigued enough to make the further effort. In this article, the author reflects on the role of surprise in mathematics classrooms. He discusses the personal and social aspects of surprise, the requirements for increasing chances of surprise, the different types of surprise, and the role of motivation. (Contains 2 footnotes.)