# Abstract for "Why Can't Johnny Integrate?"

Mathematics education is (partially) designed to develop skills people need to manage the complex systems of the modern world. Yet while theoretical understanding of complex systems has advanced rapidly, studies of human decision making in complex dynamic systems show that (1) people often perform poorly, (2) performance relative to optimal deteriorates as the dynamic complexity of the environment grows, and (3) learning is slow and often dysfunctional.

Examples from the laboratory include supply chains, capital investment, and markets. Examples from the field include persistent cyclical instability in industries from aircraft to zinc, boom and bust in the lifecycle of new products from vacuum cleaners to telecom equipment, and overexploitation of resources from fisheries to the global climate. To explore the existence and persistence of these problems I report experiments examining people's ability to understand the most basic elements of complex dynamic systems including stocks and flows (integration), time delays, and feedback.

For example, subjects are asked to describe how water accumulates in a bathtub given information on the inflow and outflow. Calculus is not needed to understand that the water rises when the inflow exceeds the outflow, yet highly educated people with extensive mathematics training perform very poorly, often violating fundamental principles such as conservation of mass. For example, most believe the stock of atmospheric greenhouse gases can be stabilized while emissions into the atmosphere continuously exceed their removal from it.

These deficits in our mental models of complex systems are quite robust; I consider implications for public policy and for mathematics education, from the elementary classroom to the corporate boardroom.

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