Points and Angles Online
February 2001

    Table of Contents:

Pushing the Envelope - Reflections on the Difference Between Good Teaching and Really Good Teaching

John Benson
Mathematics Teacher
Evanston High School

The typical MMC audience consists of some of the most knowledgeable, committed math educators in the world.  Mr. Benson would like to start with that set of assumptions and share some of his observations about taking excellent teaching to the next level.  What makes a good problem a great problem?  What makes an effective lesson a memorable lesson?  There will be some mathematics, some problem solving, some specific examples and some philosophy.  Hopefully, John Benson's presentation will nudge us all towards becoming even better than we already are.

As a graduate of Foreman High School in Chicago, Mr. Benson is in his 33rd year of teaching at least five classes a day,  of which 32 years are at Evanston High School.  John also coaches the math team at Evanston and has been president of The North Suburban Math League since its creation in 1977.  John is the regional coordinator of The American Regions Math League at the Iowa site.  He has graded Advanced Placement Calculus exams for ten years.  John was a member of the author team for three textbooks published by McDougal Littell.  John Benson has been attending MMC meetings regularly since 1976 and is past president of MMC.

Please bring with you any high school senior who is strongly interested in becoming a mathematics teacher like us to this event on February 16th!  Looking forward to seeing everyone there!

The 2002 Annual Meeting of the NCTM will be in Las Vegas, Nevada, Sunday, April 21 through Wednesday, April 24.  The major venues will be the Venetian, the Sands Expo Center, and Harrah's.  The theme for this Annual Meeting is "Realizing the Vision of School Mathematics."  The vision is explained in Principles and Standards for School Mathematics which was released in April.  The Program Committee is seeking speakers who can share first-hand classroom experiences in implementing these standards.  A common problem in putting together a national or regional program is the lack of K-12 classroom teachers who propose to present sessions.  We are asking your help in encouraging the best speakers from your state/provincial and regional conferences to submit proposals to speak in Las Vegas.  Information about the types of sessions, criteria for selection, answers to other frequently asked questions, and the proposal form are available online at /meetings or through NCTM's Fax on Demand service, 800-220-8483, document #455.  Proposals must be submitted by March 15, 2001 to be considered.  If you have any questions about the program, please contact the Program Chair, Carol A. Edwards or if you need assistance in submitting a proposal online, please contact our Program Manager, Lorenda Wieder, in the NCTM Conferences Department at <Lwieder@nctm.org>



Date:  Tuesday, February 20, 2001
Place:  Evanston Township High School
   Enter at the Lake St parking lot entrance and follow the signs.
Time:  4:00 p.m. to 9:30 p.m.
Who:  Any student grade 9-12

Tryouts will consist of twenty-four problems.  The problems will be given out two at a time, with a specified time limit for each pair of questions.  Calculators will not be allowed.  The total score for each individual will be the number of questions answered correctly.

The team will compete in the American Regions Math League (ARML) contest to be held at the University of Iowa, leaving in the early evening on Thursday, May 31, and returning the night of Saturday, June 2, 2001.  Each member is expected to travel with the team to and from Iowa.  Each individual is responsible for his/her own cost of $175 per student.

Each member of the All-Star team will be required to do problems he/she is given and to attend four practices at Glenbrook North High School.  The practices are scheduled for the following dates:
  Monday, March 19  6:00 pm - 9:00 pm
  Thursday, April 19  5:30 pm - 9:00 pm with dinner provided
  Tuesday, May 1       5:30 pm - 9:00 pm with dinner provided
  Tuesday, May 22     6:00 pm - 9:00 pm
In addition, we will hold practice in Iowa on Friday, June 1.

For further information, contact Mary Lappan, New Trier High School, 385 Winnetka Ave., Winnetka, Illinois, 60093; (847) 784-6608; FAX (847) 501-6400; email <lappanm@newtrier.k12.il.us>

Here is a sample problem from the 2000 tryouts:
A coin is flipped 1000 times in succession.  Find the probability that all integers a , flip number a  and flip number 2a  will have different results.  [Note that  a  and  2a  must both be integers from 1 to 1000, inclusive.]
ans. 1


Due to the timing of the March 2001 MMC meeting following so closely after the February 2001 meeting, you will not be receiving Points & Angles in time to be reminded of the call-in date for reservations.  So...  MARK THIS DOWN IN YOUR CALENDAR: call Leona Mirza by March 2, 2001 at 773.244-5731 to reserve your spot for the March 9 MMC meeting.  Our speaker will be Monica Neagoy on "A Multimedia Fractal & Chaos Presentation that will Infuse You With Amazement".  Don't miss this one.  Do it today!!

Points from the Interior

 Rather than share my thoughts with you this month, I decided to share the thoughts of
mathematics students from around the world.  Below are excerpts from an article in the January 3rd edition of the Times.  (The Times [e-Services], Wednesday, January 3, 2001.)

 MATHEMATICIANS are fat, scruffy and have no friends in any language.  Youngsters from seven countries, asked to come up with a portrait of the typical mathematician, showed a badly dressed, middle-aged nerd with no social life.  Schoolchildren as far apart as Romania, England and America took part in the study conducted by a researcher from the Centre for Teaching Mathematics at Plymouth University.  The 300 children, aged 12 and 13, also drew pen and ink portraits of the archetypal mathematician.


One English pupil added a caption that read: Mathematicians have no friends,
except other mathematicians, not married or seeing anyone, usually fat, very unstylish, wrinkles in their forehead from thinking so hard, no social life whatsoever, 30 years old, a very short temper.

Most children drew white men with glasses, often with a beard, bald head or weird hair, and shirt pockets filled with pens, who were working at a blackboard or computer.  Finnish children had an even more disturbing view of math teachers: several portrayed them forcing children to do sums at gunpoint.

One has to wonder what our students are thinking about us.  In the next few years, the need for good qualified mathematics teachers is going to increase dramatically.  With images such as portrayed above, filling that need will be a real challenge.  We each need to do our part to change that image.

Equity and Access:  Opening Doors for More Students to Achieve Higher Levels of Mathematics, Kanold and Rauch.

There may be some who think that the title of January's talk "Equity and Access" is incongruous with the teaching environment of the speakers, Tim Kanold and Kathie Rauch of Adlai E. Stevenson High School in Lincolnshire.  Tim addressed this early in presentation, showing how the NCTM Equity Principle applied to all students in all schools.  His review of reforms that are based on student achievement indicated that attitudes of schools were holding many students back from access to high-quality, engaging mathematics and mathematics instruction.  Tim showed the statistics that make Stevenson's mathematics program worthy of study.  In ten years, his department has increased enrollment in Advanced Placement Calculus from 20% of the senior class to the current year's 52%.  AP scores on calculus have remained high, and the increase has been in number of BC Calculus sections as well as AB.  Tim presented five principles that can be applied by all schools to improve access to the upper levels of high school math.  Schools must abandon the selecting and sorting mindset.  The curriculum must have high and clear-cut expectations for all grade levels, starting at least at grade 5 and moving through high school.  Schools must offer strong student support, such as mandatory out-of-class practice and tutoring for kids who fail.  Teachers must aim for engaged learning as the center of their instructional mission.  The school needs to create an environment that promotes teacher collaboration.  Kathie presented three successful techniques from the perspective of the classroom.  What can teachers do to increase the success of their pupils?  The first was vertical articulation: early courses can include aspects of the AP program.  Kathie showed examples of AP-style questions for advanced algebra and geometry.  These foreshadowed AP expectations and exploited AP content early, established exemplars of good assessment, and reduced anxiety about the AP examination.  She emphasized the importance of six-week cumulative review exams as one way students could show mastery of ideas and improve grades.  Kathie emphasized the importance of the teacher using multiple representations of mathematics (including student presentations) to ensure that mathematics flows through all avenues of perception.  Tim and Kathie articulated a clear program for improvement of student achievement that any school can put into effect.  That does not mean that it is easy to carry out.  As Kathie concluded, higher achievement in mathematics requires that students work harder.  To get students to work harder, it is essential for the "teacher to model hard work."         John W.  McConnell, Ph.D.

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