Patterns of Life: Integrating Mathematics with Science, Culture, and Art

We offered undergraduate students an interdisciplinary course Patterns of Life that develops mathematical reasoning strategies to solve complex problems. In its most essential form, mathematics is the study of patterns; and mathematical (patterned) reasoning is the ability to think with a plan and a purpose. Students personally experience and use patterns of reasoning in diverse disciplines, and then work in groups to form a valid strategy for solving a selected problem. Patterns of Life is designed as guided, on-site, active-learning experiences, in cooperation with local scientific, cultural and fine arts communities. Course goals for students include: (1) to increase mathematical understanding, find mathematical thinking more relevant to their own programs and build mathematical perspectives and strategies to become more confident problem-solvers, and (2) to develop a life-long ability to reason more effectively on a wider variety of problems, including those that may be unfamiliar or seem to have no answer. The following four activities were an integral part of Patterns of Life: (1) biologists at the Golden Gate Raptor Observatory engaged students in the study of the raptor population crossing the Golden Gate section of the Western Flyway; (2) National Park Service scientists, students and instructors studied ecological, environmental and cultural patterns in Yosemite National Park; (3) students studied structure and vitality of traditional human cultures through their use of mathematical patterns: model and map-making, navigation, time, recording devices, networks, linear programming, probability, geometric growth rates, binary codes, fair division and appointment, measurement and systems of influence and power; and (4) with members of the San Francisco Bay Area Fine Arts Community, students discovered patterns in artistic expression, including symmetry, balance, scale, repetition of motif, and geometry in visual arts and architecture