Mathematics & Science Institute 2005 Today is July 4, 2009, 4:19 pm   Inaugural Institute: July 24-29, 2005 Courses Offered Choose a Destination... Conference Home Registration Schedule Courses Lodging/Meals Transportation Contact Curr & Inst UNO An Introduction to Bayesian Data Modeling Floyd Bullard, Duke University and North Carolina School of Science and Mathematics, Durham, NC This course is accessible to all, though it may be of particular interest to science teachers and those teaching mathematical modeling. (But note that Bayesian methods are not part of the AP Statistics curriculum.) The goal of the course is for teachers to develop an understanding of Bayesian data modeling sufficient to teach it to students of precalculus, calculus, or beyond. Only a basic knowledge of probability is prerequisite. The course will begin with the basics of Bayesian analysis and conclude with a necessarily brief introduction to MCMC (Markov Chain Monte Carlo) methods. Calculus using only High School Algebra & Geometry Bill Crombie, Relearning by Design, The College of New Jersey, Ewing, NJ The conventional wisdom holds that Calculus as a system of knowledge and technique is an intrinsically difficult subject. Consequently, Calculus as an institution has acted as a filter allowing only some students to move on to higher mathematics and the sciences. A fundamental change in Calculus as a system of knowledge and technique can radically alter the role of Calculus as an institution and effectively act as a redistribution of opportunity for all students completing the high school mathematics sequence. This course will present a fundamental change in the learning and teaching of Calculus by developing the calculus of polynomial functions using only the content of high school Algebra and Geometry. Teachers of Algebra and Geometry will discover that their subjects go much further than anyone previously suspected and that eventually they will teach these subjects much further than anyone presently suspects. Physics for Math Teachers Ira Nirenberg, Ben Franklin High School, New Orleans, LA Historically, the basis for a good deal of secondary mathematics stems from the development of physics. In fact, Isaac Newton invented the calculus in order to solve problems relating to the gravitational force produced by extended bodies in space (namely, the Earth). Our focus here is very basic. Participants will gain a conceptual and mathematical understanding of the physics used in the secondary curriculum. The course is a basic physics college class with mathematics teachers in mind. No previous physics education is necessary. If you had physics a long time ago and remember little to nothing or have never had a physics class, this is for you! Stress level for this class is rated as ZERO! Knowledge of a TI graphing calculator is helpful but not necessary. Topics include: measurements and uncertainty, dimensional analysis, kinematics, dynamics, work, energy and momentum. The Internet Laboratory Amanda Simmons, Nichols School, Buffalo, NY Want to study functions through data analysis but lack the facilities to gather experimental data directly? Perhaps you have experienced the frustration of devoting class time to an experiment that fails to produce good, usable data. Let the Internet be your laboratory! Bring your TI-83, and come learn how to devise interesting projects that explore functions in real-world settings with data collected from the Internet. These applications will utilize trigonometric, exponential, and power functions, and other functions typically studied in algebra 2 and precalculus courses. Statistics Jim Madden, Louisiana State University, Baton Rouge, LA This course provides a deep conceptual treatment of some of the most central ideas of statistics. What is a variable? What is a distribution? What is randomness? What can you infer from data? How certain can you be? These are questions that occur at all levels of statistical practice and theory, from the most basic to the most advanced. We will illustrate with classical examples and activities that can be adapted for a variety of audiences. Participants should come away from this course with the ability to make sense of the most common statistical tests and methods and an understanding of how they are all part of a coherent system of profound, yet very natural, ideas. An "Excel-lent" Adventure In High School Mathematics Jim Marsalis, St. Martin's Episcopal School, Metairie, LA Microsoft Excel is a more powerful and versatile tool for mathematics education than most people realize. Learn how to make scrollbars, animate graphs, and use simple Visual Basic commands to jazz up Excel for exciting classroom demonstrations and meaningful student projects. This is a hands-on course with material appropriate for the entire high school mathematics curriculum, from algebra through calculus. No previous experience with Excel is required. Can Technology Show Us the Path To Reform? David A. Young, Fayetteville HS, Fayetteville, AR Can the deluge of technology be used as a catalyst for reform in mathematics and the sciences? We know of the NSES and NCTM Standards and we all deal with of some form of high stakes assessment so if we are to cope with the new idea of the day, can technology help us? Spend some time learning not just how to use various forms of technology, but to Truly integrate this technology in your quest to move on in the educational continuum. Use of graphing calculators, digital video, wireless networks and data analysis devices will be the canvas as we explore and learn. An Introduction to using Parametric Equations on your TI-83 Ira Nirenberg, Ben Franklin HS, New Orleans, LA Got parametrics? Are you rusty with parametrics? Would you like to easily be able to use your calculator for classroom activities? Then this class is for you. Along the way we'll look at the concepts behind the mathematics and find ways to apply parametrics to modeling real world problems. Lots of activity sheets for classroom use and lots of time to practice what you're learning. This class is for the beginner in all of us! Great Statistics Simulations for Teaching Concepts Floyd Bullard, Duke University and North Carolina School of Science and Mathematics, Durham, NC The best way to teach many statistical concepts is to have students see principles in action. Hypothesis testing, confidence intervals, power, normal quantile plots and other difficult topics will all be explored in this course using simulations; some with manipulatives, some on the TI-83 (or TI-89). Teaching Geometry using Cabri II Michael Keyton, Illinois Mathematics and Science Academy, Aurora, IL Teaching geometry at the high school level has changing rapidly in the last decade. This workshop will provide experiences in investigating mathematics using computer program Cabri II, showing some of the excitement students can attain through discovering mathematics. It also will show some of the necessity for proof. Topics will include those typically found in a high school geometry course with extensions into the unusual. Calculus in Motion — Animating Calculus via The Geometer's Sketchpad, version 4 Audrey Weeks, Calculus in Motion, Burbank, CA This course is designed for those who already use The Geometer's Sketchpad (version 3 or version 4) but who are now interested in expanding its use to the concepts of calculus - after all, calculus is the study of movement and change, so shouldn't it be experienced that way? Participants will learn to animate numerous concepts and applications that are key to any calculus course. All animations will be constructed for direct and immediate classroom use. Although we will use the Windows platform in this course, the work with the Macintosh is identical. Mathematical Modeling in AP Calculus Dan Teague, North Carolina School of Science and Math, Durham, NC This session is designed specifically for teachers of AP Calculus (both AB and BC), but will be of interest to all instructors of introductory calculus. The participants will be engaged in modeling activities that illustrate how mathematical modeling can be used to motivate, develop, and apply the methods of elementary calculus in the AP curriculum. The session will investigate modeling contexts that can be used during the course to develop and apply techniques as they naturally arise during the year as well as modeling contexts that can be used as culminating activities for the course after the AP exam. Mathematical Modeling in Precalculus Mathematics Dan Teague, North Carolina School of Science and Math, Durham, NC The functions studied in Precalculus are the functions we use to describe the world around us. This session is designed specifically for teachers Precalculus who want to add more mathematically engaging, real world problems to their course. The participants will be engaged in modeling activities that illustrate how mathematical modeling can be used to motivate, develop, and apply the functions and algebraic techniques studied in Precalculus. Calculus as the Study of Motion Bill Crombie, Relearning by Design, The College of New Jersey, Ewing, NJ The two founding traditions of the Calculus are due to Leibniz and Newton. Leibniz developed the Calculus through the problem of the tangents to curves and the problem of the area under curves. Newton developed the Calculus through the study of motion. Teaching Physics with Calculus has always required the introduction of the notion of limits. We now know that the central concepts of the Calculus can be built, without limits, from the kinematic concept of uniform motion as a standard of comparison. The required mathematics uses nothing more than high school Algebra and Geometry. Consequently the definition of "Elementary Physics with Calculus" versus "Elementary Physics with Algebra" has become a distinction without a significant difference. During this workshop we will see how and why this is so.