How Plankton Swim: An Interdisciplinary Approach for Using Mathematics & Physics to Understand the Biology of the Natural World

The authors have developed and field-tested high school-level curricular materials that guide students to use biology, mathematics, and physics to understand plankton and how these tiny organisms move in a world where their intuition does not apply. The authors chose plankton as the focus of their materials primarily because the challenges faced by plankton are novel problems to most students, forcing adoption of new perspectives and making the study of plankton exciting. Additional reasons that they chose plankton to focus on include their ecological importance, their availability to most teachers and students, the ease with which they can be collected and observed, and the current focus of some scientific researchers on their movement and behavior. These curricular materials include a series of inquiry-based, hands-on exercises designed to be accessible to students with a range of backgrounds. Many of these materials could be adapted for use by middle-school, and/or college-level students. In this article, the authors describe sample lessons, summarize what worked well, and flag obstacles they encountered while integrating mathematics and physics into the biology classroom.

Digital Vertical Aerial Camera System for High-resolution Site Inspections in Conservation Easment Monitoring

A three-level satellite to ground monitoring scheme for conservation easement monitoring has been implemented in which high-resolution imagery serves as an intermediate step for inspecting high priority sites. A digital vertical aerial camera system was developed to fulfill the need for an economical source of imagery for this intermediate step. A method for attaching the camera system to small aircraft was designed, and the camera system was calibrated and tested. To ensure that the images obtained were of suitable quality for use in Level 2 inspections, rectified imagery was required to provide positional accuracy of 5 meters or less to be comparable to current commercially available high-resolution satellite imagery. Focal length calibration was performed to discover the infinity focal length at two lens settings (24mm and 35mm) with a precision of O.1mm. Known focal length is required for creation of navigation points representing locations to be photographed (waypoints). Photographing an object of known size at distances on a test range allowed estimates of focal lengths of 25.lmm and 35.4mm for the 24mm and 35mm lens settings, respectively. Constants required for distortion removal procedures were obtained using analytical plumb-line calibration procedures for both lens settings, with mild distortion at the 24mm setting and virtually no distortion found at the 35mm setting. The system was designed to operate in a series of stages: mission planning, mission execution, and post-mission processing. During mission planning, waypoints were created using custom tools in geographic information system (GIs) software. During mission execution, the camera is connected to a laptop computer with a global positioning system (GPS) receiver attached. Customized mobile GIs software accepts position information from the GPS receiver, provides information for navigation, and automatically triggers the camera upon reaching the desired location. Post-mission processing (rectification) of imagery for removal of lens distortion effects, correction of imagery for horizontal displacement due to terrain variations (relief displacement), and relating the images to ground coordinates were performed with no more than a second-order polynomial warping function. Accuracy testing was performed to verify the positional accuracy capabilities of the system in an ideal-case scenario as well as a real-world case. Using many welldistributed and highly accurate control points on flat terrain, the rectified images yielded median positional accuracy of 0.3 meters. Imagery captured over commercial forestland with varying terrain in eastern Maine, rectified to digital orthophoto quadrangles, yielded median positional accuracies of 2.3 meters with accuracies of 3.1 meters or better in 75 percent of measurements made. These accuracies were well within performance requirements. The images from the digital camera system are of high quality, displaying significant detail at common flying heights. At common flying heights the ground resolution of the camera system ranges between 0.07 meters and 0.67 meters per pixel, satisfying the requirement that imagery be of comparable resolution to current highresolution satellite imagery. Due to the high resolution of the imagery, the positional accuracy attainable, and the convenience with which it is operated, the digital aerial camera system developed is a potentially cost-effective solution for use in the intermediate step of a satellite to ground conservation easement monitoring scheme.