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We would like to talk with others trying to address the needs of teachers and in order to prime the conversation we offer a few of our observations about what might be done.

**SCHOOL TEACHERS**

Our experience has been that many teachers would like specific lesson plans (for the faint of heart the more spelled out the better, even to the point of black line master printouts). It's also important to have suggestions as to how to use them in class, especially the experiences of teachers who have actually used them. Discussion groups might also help both the users and the producers a lot.

Some very good teachers develop large collections (books even) of useful supplemental material. With a bit of help, some teachers can transform materials into Web pages with content.

Teachers also find very useful interactive material that engages their students, such as our Problem of the Week, Ask Dr. Math, and MathMagic. This is splendid stuff, but very labor intensive. We need to find more volunteers - do you have a whole stable full?

It seems that enough good material is being developed that students can browse the Web for special projects, provided they have effectively organized, selective annotated lists of worthwhile sites.

**COLLEGE TEACHERS**

Our guess is that college teachers would sometimes like to look over others' course outlines and lecture notes, but are not particularly interested in daily lesson plan structures. On occasion many spend time developing supplemental material: applications, examples, computer projects, visualization tools. Quite a few college teachers should be interested in using good quality materials developed by others--provided they could easily find them and they were easy to use.

It might be good to have a more sophisticated program called something like Ask Professor Math, which allowed students to submit higher level problems (they'd be culled for apparent homework problems). A lot of answers would invoke the Socratic Method, and might prove enjoyable to a few mathematicians who have the time and social conscience to agree to participate.

Some college teachers might appreciate data banks of exam problems, provided they were appropriately graded by level. Both teachers and students might want access to graphing and symbolic programs which reside on a remote machine but return images or computations via the Web. There is also some good material out there suitable for elementary to sophisticated projects.

**SCHOOL AND COLLEGE TEACHERS TOGETHER**

There is substantial overlap in the upper level high school and lower level college curricula: pre-calculus, calculus, algebra (school and remedial college), and geometry (the college intro to geometry course, often intended for future teachers). There should be much each group can learn from the other, e.g. school teachers will often have worthwhile ideas to contribute on pedagogy.

We have had some experience which indicates that teachers with a reasonable number of college-bound students are quite interested in what college teachers would like their students to know. Indeed, some of the changes in school mathematics appear to be brought about by the school's perceptions of college desires. Some of these perceptions may not be entirely accurate. For example, mastery of pocket calculators (many college teachers might prefer the ability to have some arithmetic sense, plus mastery of small number arithmetic), and new courses in discrete mathematics, probability and statistics (most teachers would prefer that the college bound have a firm grounding in fundamentals--most might even wish that schools were not in the calculus teaching business if they couldn't do it really well).

Thus, two important areas for interaction would be the teaching of overlapping courses and discussing what schools should be doing to prepare students for college (as well as to be citizens). We expect that by having a virtual math center which combines materials useful to each group, there will be many opportunities for serendipitous interactions when people browse to see what's going on in the other world.

11 October 1995