ection 1.1
Laboratory Abstracts and Laboratories
Laboratory Abstracts
Lab 1 — Turning Brownfields Green
In this lab, students are asked to investigate groundwater pollution at a brownfields site in their region, to develop ways to measure and model groundwater pollution, and to evaluate alternative means of remediation. The problem may be supported by geometry, proportions, basic algebra, concept of a function, predictor equations, cellular automata, and modeling software.
Lab 2 — Time Delay in Telecommunications
This lab addresses the problem of transmission delay in the context of a satellite-based telecommunication system. Questions may involve the nature of satellite orbits, Newton's laws of motion, the law of universal gravitation, Kepler's laws of planetary motion, geosynchronous and geostationary orbits, latitude and longitude, orbital coordinate systems, measurement of time, speed of light, and calculations involving distance and angle measurement.
Lab 3 — Landing on Mars
This lab requires use of resources such as Geographic Information Systems (GIS) to identify and evaluate landing sites for Mars Exploration Rovers. Students will use coordinate systems, latitude, longitude, transformations, and properties of conics to determine equations of elliptical landing sites.
Lab 4 — The Robot Race
Student teams will commence by researching the field of robotics. Then, they will design, build, and test a robot in accordance with specified criteria. The lab involves ratios, proportions, gear relationships, the Pythagorean Theorem, loops and conditionals in programming, and an understanding of light and touch sensors. The project will culminate with a contest between teams.
Lab 5 — Blood Spatter Analysis
Forensic science forms the framework of this lab. Students will analyze representations of bloodstain patterns to determine the victim's location and the nature of the wounding instrument. The analysis will include use of the circle and ellipse, right triangle trigonometry, a frequency distribution, regression, metric and customary systems of measurement, and different coordinate planes.
Lab 6 — The Big Chill Refrigerator Factory
Subject to a number of constraints, students will design an assembly line and arrange a parts-delivery schedule so that the production process runs as efficiently as possible. This problem requires careful analysis, scale drawings, manipulation of the distance-time formula, repeated application of the trial and error method, and use of tables.
Lab 7 — Water Quality, pH, and Acid Rain
Students will research the significance of pH in diverse situations, explore pH level as an indicator of pollution, carry out serial dilution to construct a response curve, and use the curve to determine the concentration of a pollutant. Supportive mathematics tools include percents, graphing, functions, regression, and logarithms.
Lab 8 — The Ride of Your Life!
This lab requires students to design an amusement park ride that satisfies a number of research-based specifications, conditions, and constraints. These may include safety, capacity, space, degree of interactivity, appearance, environmental impact, building codes, handicap access, legal issues, building costs and operating costs.
Lab 9 — Hemodialysis
The context for this lab is hemodialysis for End Stage Renal Disease and the need to develop a way for determining patient-specific doses of an anticoagulant. After initial research, students will work with a differential equation that models heparin clearance. Students will calculate appropriate heparin doses for hemodialysis treatment that take account of the coagulation sensitivity of individual patients.
Lab 10 — I've Got Your Number
This lab explores several aspects of the cellular phone industry such as: what a cellular phone is and how it works, cellular tower placement, health and safety issues, and consumer education. Helpful mathematics tools involve the geometry of circles and polygons, graphing techniques, topics from introductory statistics, and piecewise functions.
Laboratories
The Laboratory Plan approach for either a course or club is evolutionary in that it weaves together a number of strands already present in courses with mathematics reform elements. The approach is revolutionary at the two-year college level because students are expected to work in teams to address open-ended technology problems by doing research, engaging in scientific inquiry, and reporting their results in accordance with accepted academic protocols. The degree of open-endedness varies among the labs, and each technology problem can be developed in a multitude of ways and at different levels of complexity.
Students are expected to apply the process of scientific inquiry – the scientific method (problem, question, hypothesis, test, decision) – in each lab they undertake. The scientific method should be applied in a way that supports learning, explanation, and understanding; it should not be applied in a pro-forma or mechanistic fashion. Since there is wide variation among the labs, the scientific method may apply more intensively and extensively to some than others. Also, the points in the labs at which the elements of the scientific method are introduced will differ from lab to lab. In some cases, the scientific method will be helpful near the beginning; in others it may extend throughout the lab; and in still others, it may be applied to best advantage near the end. Furthermore, in labs that lend themselves to multiple hypotheses, the scientific method may be used repeatedly.
In addition to inter-lab variation, there is inter-team variation. Two teams doing the same lab may develop different solutions, present their findings differently, and apply the scientific method to different questions. In spite of such variation, it is very important to keep in mind that while the technology problems are open-ended, the solution process should be guided by the Mathematical Journeys I framework.
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