This paper looks at the analysis leading to and design of a Web-based "hint system." The hints are designed to help middle-grade teachers participating in a mathematics professional development effort, called InterMath, achieve a high degree of success when working open-ended mathematical investigations. The model upon which InterMath is based assumes that teachers who experience learning in a rich, exploration-based environment will more readily transfer these kinds of experiences to their classrooms. The centerpiece of the InterMath experience and Web site is an extensive set of open-ended mathematical investigations that can be explored using various technologies. These investigations form the central experience of the 15-week workshop as teachers are encouraged to explore a particular set of explorations, choose problems that intrigue them, work those investigations, and write-up the solutions, along with extensive activities. The paper discusses the issues and processes involved with designing this system, paying special attention to the different types of hints and the limitations of the system. It concludes that the use of a Web-based hints system is a potentially valuable tool for supporting teachers in tackling complex math problems, that there are limitations with this plan, but the just-in-time help of a static system can be combined with the asynchronous support of a wider community as a viable option for promoting the development of mathematical thinking. (Contains 19 references.) (Author/AEF) Reproductions supplied by EDRS are the best that can be made from the original document. PERMISSION TO REPRODUCE AND DISSEMINATE THIS MATERIAL HAS
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