This paper considers how the algebra curriculum in secondary mathematics might be reformulated by rethinking both the content of algebra and the approaches to teaching and learning algebraic concepts. It considers how the concept of function can be made a central theme of the algebra curriculum and further suggests that computer software, when designed properly and used with appropriate materials, can provide an opportunity for engaging students in significant mathematical inquiry. After a discussion of the multiple representations of the concept of function, several facets of curriculum innovation involving computers are presented. Some lessons learned from cognitive research involving students' interactions with a variety of graphically based software environments are given. Three examples of software tools growing out of research findings involving visual representations of functions are presented; they are: "The Function Supposer"; "The Function Comparator"; and "The Function Analyzer." Examples of classroom materials developed to engage students in problem-solving and problem-finding activities and to take advantage of new opportunities for learning and teaching made available by the new computer software are presented. Finally, new directions in software environments beyond visualization are explored. One of these, a tool called "controlled dynamic phenomena" is described as an approach that will be a catalyst for new intuitions and understandings of functions. (32 references) (MDH)