In this article, the author discusses the advantages and the disadvantages of using surprise elements in teaching mathematics. According to the author, there are three key ideas concerning the element of surprise: (1) The ethical aspects of teachers' manipulation of their students in order to construct surprise; (2) Every mathematical task generates a different kind of surprise and some of these are related more closely to cognitive aspects of the mathematical task than others; and (3) The ability to cope with surprise in terms of its emotional charge may not always be present. She discusses her reservations about using surprise in her teaching, founded on the fact that these strategies risk the loss of students' trust. However, she also believes that the power of surprise to excite and stimulate thinking has tremendous potential both as a motivator and probably as an aid to memory. Sample activities are used as examples. (Contains 6 figures.)