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Why is it that the public can read and write but only a few understand statistical information? Why are elementary distinctions, such as that between absolute and relative risks, not better known? In the absence of statistical literacy, key democratic ideals, such as informed consent and shared decision making in health care, will remain science fiction. In this chapter, we deal with tools for transparency in risk communication. The focus is on graphical and analog representations of risk. Analog representations use a separate icon or sign for each individual in a population. Like numerical representations, some graphical forms are transparent, whereas others indiscernibly mislead the reader. We review cases of (1) tree diagrams for representing natural versus relative frequency, (2) decision trees for the representation of fast and frugal decision making, (3) bar graphs for representing absolute versus relative risk, (4) population diagrams for the analog representation of risk, and (5) a format of representation that employs colored tinker cubes for the encoding of information about individuals in a population. Graphs have long enjoyed the status of being "worth a thousand words" and hence of being more readily accessible to human understanding than long-winded symbolic representations. This is both true and false. Graphical tools can be just as well employed for transparent and nontransparent risk communications.

When might a positive HIV test be wrong? Are your chances of surviving cancer better in the U.S. or in England? Learn how to put aside unjustified fears and hopes and how to weigh your real risk of illness-or likelihood of recovery 44 I n a 2007 campaign advertisement, former New York City mayor Rudy Giuliani said, " I had prostate cancer, five, six years ago. My chances of surviving prostate cancer-and thank God, I was cured of it-in the United States? Eighty-two percent. My chances of surviving prostate cancer in England? Only 44 percent under socialized medicine." Giuliani used these statistics to argue that he was lucky to be living in New York and not in York. This statement was big news. As we will explain, it was also a big mistake. In 1938 in World Brain (Methuen & Co.), English writer H. G. Wells predicted that for an educated citizenship in a modern democracy, statistical thinking would be as indispensable as reading and writing. At the beginning of the 21st century, nearly everyone living in an industrial society has been taught reading and writing but not statistical thinking-how to understand information about risks and uncertainties in our technological world. That lack of understanding is shared by many physicians, journalists and politicians such as Giuliani who, as a result, spread misconceptions to the public. Statistical illiteracy is not rooted in inherent intellectual deficits-say, in the lack of a "math gene"-but rather in societal and emotional forces. These influences include the paternalistic nature of the doctor-patient relationship, the illusion of certainty in medicine, and the practice of presenting health information in opaque forms that erroneously suggest big benefits and small harms from interventions. When citizens do not understand the

Over the last two years, we have been conducting NSF-funded research on learning in two biomedical engineering research laboratories. Our goal is to understand the mechanisms that support student learning in such innovation communities. We have identified five characteristics of what we call "agentive" learning environments, which seem to account for the rapid membership and robust learning we have chronicled. In using this term, we refer to students both as agents of their own learning but also as assigning agency to the devices and technologies they encounter in the laboratories. In this paper, we present the five principles of an agentive learning environment with examples of how it unfolds day to day life in the labs. Finally we discuss the implications of these principles and our findings for the development of classrooms as sites of learning which better replicate the agentive learning found in the laboratories.Index Terms -Informal learning, research laboratory, agency. RESEARCH LABORATORIES AND LEARNINGWe are studying research laboratories as part of a larger project aimed at designing optimal learning environments for students in the field of biomedical engineering. This relatively new sub-field of engineering is an instance of what we term an interdiscipline. We use this term to denote an interdisciplinary area that has evolved in such a way that the melding of knowledge and practices from more than one discipline spawns highly unique environments and innovative practices, both cognitive and material.In the case of biomedical engineering, meldings of quantitative/qualitative/descriptive methods and varied forms of model-based reasoning from biology and engineering work together to create new ways of thinking and working towards designing and building medical applications. At present there are almost no textbooks for undergraduate education even though the number of new BME degree programs swells every year. More important, however, is the challenge of creating learning environments that immerse students in truly interdisciplinary contexts. This does not mean taking separate courses in biology and then in engineering with hopes that interdisciplinary thinking will somehow magically emerge. Nor does it mean doing some bio-related problems at the end of the chapter in a traditional engineering class. Rather it means designing learning environments where the various disciplines are explicitly required to solve problems.Our efforts to achieve this have been informed by two streams in the learning sciences community-problem-based learning and model-based reasoning. Very specifically, we are seeking ways to modify the PBL environment for engineering education in such a way that models come to the fore in interdisciplinary problem solving. With that goal in mind, we have been investigating BME research laboratories as exemplars of real-world problem-based learning, which utilize multiple forms of representation and types of modeling to push the frontiers of science.Research laboratories, for some decades now, h...