Points and Angles Online
October 2000


    Table of Contents:



Statistics Throughout the Secondary Curriculum
John Diehl
Mathematics Department Chair
Hinsdale Central High School

          John will share with us suggested content and technologies that can be incorporated into algebra, geometry and precalculus courses that can prepare our students for an AP Statistics course.  John will excitingly  challenge us with this integration of content.
           John Diehl has taught high school for twenty-three years, twenty of these years at Hinsdale Central High School.  Mr. Diehl serves as an AP Statistics reader (grader), College Board faculty consultant (workshop leader) and a member of the AP Statistics Development Committee.  John has co-authored TI-83 Enhanced Statistics and is a T-cubed instructor.  He is also one of the coordinators of the summer MathTech Institute.  John is a Presidential Awardee for Excellence in Teaching Mathematics.  He was one of the original Teachers Teaching With Technology instructors and has greatly influenced a lot of us with how we facilitate mathematical learning in our classrooms today!

            BEFORE YOU LEAVE FOR ICTM, be sure to call in your MMC reservation so you don't forget while at ICTM.

            See you October 27th.



AP Calculus Meeting

         Niles North will host a meeting of Advanced Placement Calculus teachers (both AB and BC) on Saturday, November 4, 2000. The meeting will begin in room D201 at 9:30 am and conclude at "noonish." Those new to the teaching of Calculus are especially encouraged to attend along with colleagues who have had the joy and challenge of teaching AP for years. Topics will include the grading of the 2000 exam free response question (graders of the exam-- PLEASE attend!), insights from Test Development Chair Tom Dick's one-week summer workshop on AP Calculus at the International Conference of Advanced Placement held this past summer in Honolulu, and a variety of resouces used to help in the teaching and learning of AP Calculus.
           If you are planning to attend this meeting, please call host George Pryjma at 847-568-3279 or e-mail me at geopry@niles-hs.k12.il.us or FAX me at 847-568-3166. I need to provide a sufficient quantity of bagels, donuts, and coffee to please my guests.
           Niles North is located at 9800 N. Lawler Avenue in Skokie. We are just west of the Old Orchard Shopping Center with easy access from Golf Road or the Old Orchard Road exit of the Edens Expressway.

           George Pryjma
           Niles North High School
           9800 N Lawler Ave
           Skokie, Il 60077
                   847.568.3279
                   847.568.3166 (Fax)



MMC Scholarship

 Every year the Metropolitan Mathematics Club of Chicago offers a scholarship for senior high school students who will be entering their first year of college next year and are planning a career in the teaching of mathematics.  The selected students, their parents, and their sponsoring teachers will also be invited to the May meeting of the MMC at which time the recipients will be honored.  Begin thinking about students whom you think might benefit from applying for this scholarship to pursue their goal of the noble career of teaching mathematics.  More detailed information and application forms will be published in subsequent issues of Points & Angles.



New Teacher Workshop

           Terry Phillips from New Trier is looking to see if there is any interest in organizing some new teacher workshops.  Specifically he needs help with the marketing and administration of it.  He is also hoping to recruit someone with internet skills in his plan.  Terry can be reached at 847.784-6614 or <phillipt@newtrier.k12.il.us>



Points from the Interior

           "In an age now driven by the relentless necessity of scientific and technological advance, the current preparation that students in the United States receive in mathematics and science is, in a word, unacceptable." Thus starts the Executive Summary of BEFORE IT’S TOO LATE -- A Report to the Nation from the National Commission on Mathematics and Science Teaching for the 21st Century, commonly called the Glenn Commission Report, after its chair, Senator John Glenn.  However not all is "gloom-and-doom".  Indeed, there are some bright spots and some very strong recommendations.
Among the bright spots are the reasons that the report gives for studying mathematics and science:  " Above all, mathematics and science impart three qualities that define our human world and enable us to meet its challenges.

                       • First, mathematics and the sciences bring order, harmony, and balance to our lives… [Their] analytical tools … and investigative skills … are also foundational skills for lifelong learning, in other words, for creating progress itself.
                      • Second, science and mathematics continually shape and reshape our history and culture, giving rise to new ideas and inventions.
                      • Third, as science and mathematics provide human beings with powerful tools for understanding and continually reshaping the physical world itself, they teach us again and again that Nature’s secrets can be unlocked—in short, that the new is possible."

            Powerful words that I find encouraging.  To me, mathematics has always been an exciting arena.  It is a language for describing our world, but also a collection of concepts and ideas worth studying for their own intrinsic value.  Through our teaching, we have a wonderful opportunity to transfer our enthusiasm for mathematics to our students.
            Another bright spot is found in "Evidence for the Effects of Reform." The report states, "This analysis provides strong evidence that math scores from 1990 through 1996 … increased in most states for public school students by statistically significant amounts."  I interpret this to mean that the NCTM Standards have had a positive effect on mathematics education.  I anticipate that the new standards will have a stronger effect.  This is good.
           I would also like to think that, at least within the Chicago Metropolitan area, MMC has been a promoter of quality mathematics teaching.  An important goal of MMC has been the improvement of mathematics education.  We accomplish this through our annual winter workshop and through our regular meetings where we meet to exchange ideas and hear from outstanding speakers.  I was impressed at our September meeting with the announcements about extended meetings:  A new teacher group, an AP statistics group, an AP calculus group.  All meeting to assist us to become better teachers, to promote quality mathematics education in our schools.  Last year we dedicated one meeting to our students who expressed interest in becoming mathematics teachers.  I hope that we can do this again, as we must continually encourage our better students to enter this field.
           MMC has always been a dynamic and highly respected club.  But in fact, it is only a reflection of its membership.  I look forward to seeing you at our October meeting.  Don’t forget to register early and don’t forget to bring a friend.



Summary by George Pryjma

            The 2000-2001 MMC dinner program truly blasted off on Friday, March 22nd, with a superb talk and Power Point presentation entitled MARS PATHFINDER “By the Numbers”. Our very practiced presenter was Donald Palac, a project manager at the NASA Glenn Research Center in Cleveland, Ohio. Born in Evanston and raised in St. Charles, Don said it was great to be back home in Chicagoland. Don’s background includes teaching religion to middle school students and volunteer tutoring in mathematics. Don thanked us for sharing our knowledge with students, saying “please don’t give up your commitment (to teaching); some of us appreciate you.” Don noted that the students who don’t learn their mathematics now will eventually have to (as NASA often does) hire consultants that “cost us up the wazoo” .
            Don announced that the space program is “IT’S ALL MATH”. Then he admitted that he tells physics teachers that “it’s all physics” and chemistry teachers that “it’s all chemistry”. He also joked that he doesn’t know what to do with biologists.
            Don has been a project manager with NASA for 15 years, adding that he therefore hasn’t done any real work for all those years. Don studies aero-astronautics at Purdue, where he admired the beautiful and then-unsolvable air flow equations that described air flow and turbulence in a jet engine. These equations drove him from aeronautics into a career in space travel, where “things are nice and Newton is King”.
            Two of NASA’s challenges are how to do things better and how to do them more cheaply. For example, currently the cost of launching a 100 pound payload by rocket is 10 to 15 MILLION dollars and about $12,000 per pound via a space shuttle. NASA has goals to reduce these costs by a factor of 10 by 2010 and by a factor of 100 by 2025. Today the Russians are offering flights to the MIR Space Station (one-way?) for $10,000,000. By 2025, NASA may offer flights into outer space for a mere $10,000 to $25,000. (Just think of all the frequent flier miles you’ll get!)
            Don discussed the failures of two previous NASA missions to Mars. Because some of the technology on both the Polar Lander and Climate Observer missions had not been fully tested, neither mission should have been launched. Additionally, the Climate Observer used data from both a newton/meters table and a pound/foot table for landing trajectory calculations. The effect was a 60 mile (or was it kilometers?) error deeper into the Martian atmosphere than required that resulted in a crashing conclusion to the flight.
            In contrast, the Mars Pathfinder mission was “an exciting and glorious success”. The technology used in this mission was fully tested, partly at the expense of cancelled experiments, with the money diverted to testing.
            With a beautiful set of Power Point “slides”, Don took us through a history of man’s views of Mars. Galileo, who first invented the telescope, thought he saw a variety of features on Mars. Chaparelli, in the 1700’s, drew pictures of Mars that featured systems of canals. Astronomer Percival Lowell also drew detailed pictures of canals and described the changes in vegetation that he saw on Mars, looking through his 3-foot mirror optics. The pictures transmitted from the Mariner 9 Mars fly-by showed all these to be illusions created by minds that naturally try to create order out of fragmentary parts. Even the famous “face on Mars” is an illusion created in part by the grid on the camera lens that took the picture. Don said it is thanks to mathematics that data can be digitized, transmitted, and recreated. This digitized data does not lie!
            The Mars Pathfinder transmitted a wealth of information about Mars. The planet is more like the moon (quite dry) than it is like earth. The daily weather report may read “another great day with a beautiful pink sky (thanks to iron oxide in the atmosphere) near the horizon and a great view of the stars above”. The Pathfinder also sent pictures of the Martian surface that showed ground formations more consistent with past flow of water than of volcanic lava. With water available on Mars, a mission to the planet could use this water to create fuel, air, and drinking water that would sustain a crew of human visitors.
            Don spent much time describing the need for mathematics in calculating flight trajectories, “entry corridors”, and landing footprints (targets). Students could be challenged with the question of why a space vehicle’s landing footprint target is elliptical, while that of a missile warhead is circular. Displaying the equations of various conic sections, Don stated that lives have literally been saved by the correct choices of a, b, and c in calculating re-entry paths. Incorrect choices could result in being bounced off the earth’s atmosphere into deep space or being incinerated while hurtling towards crashing impact with the ground. Don recalled the dangers of space travel that were highlighted in the film “Apollo 13.” The astronauts were protected upon re-entry by a heat shield. The Mars Pathfinder used a parachute to slow its descent into the Martian atmosphere and tetrahedral airbags that deployed and allowed the lander to cushion its contact with the Martian surface. Mathematics was also used to engineer the ramps that the Martian Rover (about the size of a microwave oven) needed to move off the lander and onto the Martian surface. Because Mars gets only 1/3rd of the light intensity form the sun that earth does, calculations were needed to design solar panels large enough to meet the electrical needs of the Rover and of the Pathfinder itself.
            Don’s Power Point presentation also had pictures of a meteorite that was found on top of a miles-deep ice field in Antarctica. Because of its location, the “rock” had to have come from outer space. Chemical analysis of the meteorites internal gases showed them to be of a composition identical to that of the Martian atmosphere. Even more astounding was the finding of what appear to be fossils of bacteria! Was there once life on Mars? Does it still exist?
            Don provided much more fascinating information and enlightening comments than I can fit into this humble summary of a great presentation. Fortunately Don provided MMC with a copy of his Power Point presentation. Thanks to our webmaster Kevin Wiland, this presentation is available on the MMC website www.MMCChicago.org under the 2000-2001 Meeting Schedule. Don also listed the following websites as useful for teachers and students interested in NASA activities: www.stci.edu/ toda@NASA.gov Spacelink.ms.fc.nasa.gov/ www.mars2030.net and www.jpl.nasa.gov/
 Thank you, Don, for a most delightful and educational evening. Thank you, Fern, for such a great beginning of our program for 2000-2001.


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