How should River City use three pieces of newly acquired land: a closed-down military base, a 300-acre farm, and a mine? Residents are split between development and recreational advocates–and their final choices must minimize costs to the city. Students at Boston’ s Fenway Middle College, a CES member school, will soon be working out the answers as they learn to combine mathematics with governmental know-how.
The pilot Interactive Mathematics Program, developed at the University of California’ s Lawrence Hall of Science and San Francisco State University, poses just such open-ended problems in a high school curriculum with regional centers in three states. Funded by the National Science Foundation, it aims to replace the traditional year-by-year progression (algebra-geometry-algebra 2-trig- precalculus) with one that uses substantial, complex applications to emphasize concepts and connections among these branches.
The “meadows or malls” dilemma, for instance, can be expressed using a system of linear inequalities, which lends itself to a solution by means of linear programming (a topic introduced in the second-year curriculum). A key step is to find various points of intersection of the graphs of corresponding equations, which in turn leads to the need to solve systems of linear equations. To solve the problem, students use inexpensive graphing calculators, which allow a stronger intuitive understanding of how the linear programming model works. Along the way they must also wrestle with the dilemmas governments face as they calculate the costs and benefits of improving the land for various kinds of use.
IMP aims to broaden the scope of who takes challenging math courses, expand and enrich their content, and replace traditional pedagogy with investigations, projects, and new technology. IMP’ s goal is to teach students to use mathematics in a meaningful context and to assess them on that basis.