After 10 years of teaching rule-driven, procedure-based, algorithm-oriented mathematics, an elementary teacher describes how she began to rethink her teaching style after returning to school for a graduate degree. Her rethinking is based on the first of four student teaching events that spanned an entire school year in which she used the Comprehensive School Mathematics Program (CSMP) and its pattern system. The start of her change was her recognition that the CSMP teaching guide was only a guide, not a step-by-step procedure to follow without deviance. After 3 years of teaching as a graduate student, she came to realize that mathematics is a science of patterns, and it is the search for these patterns that drives mathematicians. Understanding these patterns helps children understand mathematical relationships, not just find the right answer. Recognizing, describing, and creating a wide variety of patterns provides the foundation for exploring these relationships in numbers in later grades. By way of conclusion, Mark Twain's "Life on the Mississippi" is used to construct parallels between Twain's early learning experiences and the teacher's, mainly in the sense of his growing understanding of the nature of what he needed to learn and the usefulness of a text in doing the work. What the teacher took from her project was the need for a new sense of purpose, the questions she would need to ask, and an understanding of why this sense of purpose is important in the kind of math teaching she had been learning to do. (Contains 46 references.) (NAV)