A secondary mathematics curriculum of open-ended non-routine problems developed by a teacher of high school math over 10 years is described. An open-ended non-routine problem is one that requires problem recognition and orientation, effort, and persistence. It is open-ended in that it allows for various solutions, and requires the student to evaluate a variety of approaches and solutions. Every student can solve the problem, and each solution requires at least a few hours of work. In a sense, it corresponds to an essay in the language arts. A 4-year high school curriculum of non-routine problems has been developed and field tested. The core is a set of 60 non-routine problems, 16 for each year. Each item gives the student a chance to practice problem solving. In field tests over 10 years with the instructor's students, the problems have been refined. Students who have practiced these problems demonstrate "mathematical maturity" in their problem-solving approaches. Appendix A summarizes the non-routine problems for each grade level. Appendix B gives sample problem statements. Appendix C is a draft of teaching suggestions. (SLD)