Mathematics in Context: Focusing on Students

This chapter presents nine case studies in which school students engage in chal- lenging mathematics outside their immediate classroom environment. In each case, students are encouraged to collaborate in investigations that go beyond the standard curriculum and creatively use the ingredients of the particular context. In Italy, students visit a mathematical laboratory to understand and utilize mathemat- ical machines. Morning assembly at an Indian school brings students from many classes together in the solution of mathematical problems. Four of the projects are from France: students analyze the configuration of a heap of sand, pursue astro- nomical investigations with software, obtain a flavor of research by having sec- ondary school teams investigate interesting problems, and are presented at all le- vels with open-ended research problems. There are three programs from the United States, the first an advanced geometry sequence for secondary students completing the regular syllabus early, the second, activities arising from exhibits in an art museum, and the third, using the school lawn to deepen student under- standing of geometric constructions. All such activities need to be evaluated for their effectiveness, so that they move from just being initiatives of dynamic indi- viduals to serve as the foundation for systemic improvements in the way in which students learn, understand and use mathematics. In the early part of this chapter, we briefly mention how research into such activities might be approached.