Points and Angles Online
March 2002

    Table of Contents:

Polya’s Problem

Michael Serra

San Francisco, California

When one thinks about visualizing mathematics, one most certainly envisions geometrical objects/figures.  As one visualizes these geometric figures, one can begin investigations that lead to discovering mathematical concepts.  Whether these investigations are done with cooperative groups or individually, the improvement of visual thinking, reasoning and algebra skills is taking place. Do you recall the 1960’s book entitled How To Solve It by Professor G. Polya?   If you do, you may also recall a teacher training film entitled, Let Us Teach Guessing, a film in which Professor Polya demonstrates problem solving techniques and visual thinking skills for which he became famous.  On Friday, March 8, 2002, Michael Serra will reenact the solving of Polya’s Problem, which utilizes problem solving techniques and visual thinking skills.  For over 20 years, Michael Serra has been developing creative ways to visualize mathematics while improving reasoning skills.  Until this last year Michael taught in the San Francisco Unified School District. During that time Michael became known for his publications of Discovering Geometry: An Inductive Approach and Patty Paper Geometry textbooks.  He has been a finalist for California’s Presidential Award for Excellence in Science and Mathematics Teaching, he has also received the Math Teacher of the Year in San Francisco Award in 1996.  Michael has held numerous leadership positions.  He is past president of the San Francisco Mathematics Teachers Association, a consultant for universities, for various California counties, for the California State exam committee, and for the California Department of Education. While outside California, Michael has served as a consultant for over twenty different states as well as the Department of Defense Schools and the U.S. Virgin Islands.  Michael has authored articles for journals and textbooks filled with classroom warm-up activities.  Please join us on Friday, March 8, 2002, at the Fountain Blue Conference Center as Michael Serra will enact the solving of Polya’s Problem.  

                                                                                                - Pat Bowler Johnson

Notes from the MMC Board Meeting:

 Your MMC Board met Monday, February 11th at Berghoff’s Restaurant.  Some of the things we discussed were the Proof Field Trip on April 6th, our current membership of 388 members, what happened to the Eisenhower Funds, 2003 MMC Saturday winter conference, and approval of this year’s ballot.  Please vote.  Your vote does count!  There will be a survey for you to complete regarding the location of next year’s MMC meetings in the May Points and Angles.  This will assist the new president-elect with site location(s). Our next board meeting is May 15th.  If you would like something discussed, please e-mail me at ftribbey@d113.lake.k12.il.us.  I will make sure it appears on the agenda.  Also, if you would like to volunteer, please contact me at school 847.926-9223 or e-mail me at the above address.  I hope to see you March 8th at Fountain Blue to see Michael Serra.  Enjoy!      -Fern Tribbey

MMC New Teacher Workshop

On Saturday, February 9, at New Trier, at about as early as any of us start work during the week, a group of  24 new and pre-service teachers got together at the MMC New Teacher Workshop, lead by Terry Phillips. Much of the morning was spent exchanging ideas for the classroom with each new teacher sharing a favorite lesson, project, or activity. Many of these provided starting points for discussion of our experiences as new teachers. A panel discussion featuring experienced teachers from several schools followed, adding seasoned advice and answering many questions. The program concluded with time for the participants to socialize and network over lunch. Many thanks go to Terry Phillips, Paul Christmas, Alf Estberg, Ruth Dover of IMSA, Don Kim, Patty Bowler-Johnson, Mary Wiltjer, and Myles Whitebloom for the excellent program.  Thank you also to those who participated in the panel and presentation discussions.          -Isaac Greenspan



Submitted by Pat Bowler-Johnson

"Communicating about Mathematics Using Games


Mathematical games can foster mathematical communication as students explain and justify their moves to one another.  In addition, games can motivate students and engage them in thinking about and applying concepts and skills.  This e-example contains an interactive version of a game that can be used in the grades 3-5 classroom to support students' learning about fractions."


 "The Discrete Mathematics Project of the University of Colorado at Boulder"


The use of discrete mathematics has an essential part in the development of students' mathematical power in a society grounded in technology and communication.  In particular, discrete mathematics includes and addresses: Social Decision Making, Fair Division, Election Theory, Graph Theory, Counting Techniques, Matrix Models, and Mathematical, Iteration/Recursion.  This site provides activities on these subjects."


MMC Scholarship

The Metropolitan Mathematics Club of Chicago is offering $1,000 in scholarships for high school students who plan a career in the teaching of mathematics.  Contact Conrad Wayne at Rich South High School,   708-679-3150

The Metropolitan Mathematics Club of Chicago is offering $1,000 in scholarships for high school students who plan 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. 

    The guidelines used for selection shall be:
I.    A. Demonstration of overall academic scholarship with inclusion of at least eight semesters of college preparatory mathematics.  (A minimum cumulative grade point average of 3.0, with A = 4.)

       B. A statement of the intention to pursue a career in mathematics teaching.
       C. Indication of participation in extra curricular activities, especially those which may have a positive influence on a teaching career.

II. Applicants must have a letter of recommendation from a member of the Metropolitan Mathematics Club who is familiar with the applicant’s academic performance and his or her potential as a mathematics teacher.

III. Applicants must submit an essay of at most 400 words explaining why they would like to be a mathematics teacher.

 The scholarship award or awards will be determined by a selection committee of MMC members appointed by the Executive Board.  To be eligible, an applicant must submit the application, have an official transcript sent, and request a letter of recommendation from a member of the MMC such that all of the materials are received by the date on the application.

 The committee will establish its own guidelines for evaluating applications, and will make a recommendation to the Executive Board as to the awarding of the scholarship.  No member of the selection committee may nominate nor recommend a candidate.


Application Deadline:  March 18, 2002
Name:__________________________________________  Date:_________________




School Address:________________________________________________________


Home Phone:(____)___________________  School Phone:(____)________________

Sponsoring Teacher (Must be MMC member):_________________________________

Please complete the following:

Overall Grade Point Average:_________  (A = 4, B = 3, C = 2, D = 1, F = 0)

 Mathematics Courses       Grade          Mathematics Courses       Grade

___________________      _____         __________________      _____

___________________      _____         __________________      _____

___________________      _____         __________________      _____

___________________      _____         __________________      _____

Extracurricular Activities:____________________________________________



In addition applicants must also send:

1.  A letter of recommendation from the sponsoring teacher, who is a member
     of the Metropolitan Mathematics Club of Chicago: **

2.  A current transcript for seven semesters of high school.**

3.  An essay not to exceed 400 words on:  “Why I would like to teach

Please send all information to: Conrad Wayne
      Mathematics Department
      Rich South High School
      5000 Sauk Trail
      Richton Park, IL  60471
      phone: 708-679-3150; fax: 708-679-3168
**(Letters of recommendation and transcripts may be sent by separate mail.)
(Photocopy as needed)

Candidate for president-elect:

Simonette Urbain teaches mathematics at Morton West High School in Berwyn, Illinois and has been an adjunct faculty member at Triton and Elmhurst colleges. She is one of the coaches of the JSM math team and has helped organize and run the district math contest. Simonette also writes the questions for and coordinates the junior high math contest for the district. She has presented at local, state and national mathematics conferences with topics such as writing in mathematics, internet activities for the classroom, hosted sharing sessions on advanced algebra topics, and how to host a junior high math contest in your building.   She has served on organizational committees for NCTM regional (organizing tours) and National meetings (Chicago 2000 volunteer committee chair). Simonette co-chaired the ICTM program committee in 1996 and is currently co-chairing the 2003 program committee with her husband, Bob Urbain. One of her goals is to encourage younger teachers to become more involved in our organization. Sam is very successful in what she does and she is also known for her sense of humor.

 Candidate for president-elect:

Conrad Wayne—Conrad is the Mathematics Department Teacher Leader at Rich South High School and has taught mathematics at Rich South for the past 22 years. He has been an active member of MMC for more than 15 years as well as a member of ICTM (15 years), NCTM (34 years), and NCSM (3 years). Conrad is completing a 3-year term on the MMC board this year. He has served as the MMC Scholarship chairperson for the past 2 years. He has attended NCSM’s Leadership Academy 1 and 2. In 1995, he was 1 of 25 teachers selected to attend a 2-week NASA Workshop at Stennis Space Center in Mississippi. He has been a frequent presenter at MMC Standards Workshops, ICTM Annual Meetings, T3 International Conferences, UCSMP Workshops, and NCTM Regional and National Conferences. He recently did a cooperative learning activity workshop for 30 pre-service mathematics students at Illinois State University. His topics have included graphing calculator, cooperative learning activities, hands-on geometry, and teaching mathematics on a block schedule. He will be doing a TI INTERACTIVE workshop at T3 in Calgary in March. One of his goals for MMC is to increase membership and attendance at meetings, particularly among the newer teachers in the Chicago metropolitan area.



It seems that every year for me and for many other educators at this time of the year, some stress tends to take the forefront of one’s professional life.  We have a great new teacher induction program in our district and also within our high school.  We have had about six meetings so far this school year where the first year teachers at Highland Park High School meet with one of our assistant principals as a facilitator to examine and discuss what we are experiencing.  It almost feels as if we are in group therapy and most of us feel a lot better after our meeting realizing that we are not the only one feeling the stress.  Last month, we were given a “Teacher Stress Test” that included twenty yes/no questions such as “Do you feel you need to slow down?” “Do you consider yourself a workaholic?” ”At the end of the day, do you often feel that you have not accomplished what you had set out to do?” “Do you worry that you don’t spend enough time with your family or friends?” “Do you feel that you have to invent everything new in order to ‘keep up’?”

I wonder how many teachers who are within their first five years of teaching ask, “Is teaching really for me?”   After we had answered these questions, we then split up into small groups and discussed how we are feeling and identified what might be making us feel that way and then discussed the positives of why we are in this field.  Once we saw that we were not alone, we were then able to talk about the positives.  I found myself sitting with another department chair who is new to the school and also an orchestra director who is new and the one thing we had in common was that we have been in the field for at least a couple or more decades.  Time does go by fast!  We really talked about what we did to overcome our beginning years’ stresses.  I often wonder about the young teachers, though.  They do not, as of yet, have the experience to realize that they are in the right field and to remember, through the hard times, to look at their students’ faces when the students understand something and are excited about their learning. The teachers create that student experience!  We are in the right field!  I think that most of us left the meeting feeling better because we ended up on a positive note. 

It is great that our organization sponsored a new teacher’s workshop and a lot of new teachers felt good about their experience.  Kudos to Terry Phillips from New Trier!  We, as math educators in the Chicagoland Metropolitan area have a lot to be thankful for.  We have each other and we have our students!

                                                                                                -Fern Tribbey

What Would the Graph Look Like if . . . ?   A CBL Adventure

Robert Ruzich

Fenton High School

 Bob Ruzich’s presentation, alternately titled “The Adventures of Bob and the Overhead Projector”, gave the evening’s attendees an idea of how teachers can connect the real world of physics to the mathematics students learn.  Inspired by Richard Taylor, a physics teacher from Texas, Bob showed how, by using the CBL, his inductive approach to various topics such as temperature, light, sound, and pressure might evoke the question: “Is there math behind it?” 

  “What would the graph look like” if a temperature probe was immersed into very hot water (for 20 seconds) and then very cold water (20 seconds).  The membership immediately warmed up to this proposal.  Comparisons between graphs drawn by dinner guests and the graph resulting from the CBL data were interesting, and led to a discussion of the difference between Celsius and Fahrenheit graphs.  This, in turn, led to an investigation of the transformation of one graph to the other.  Assuming that students would be familiar with linear functions, and using linear regression to compare the data (Fahrenheit vs. Celsius), the resulting equation F=1.8C + 31.08 heated up the enthusiastic crowd, especially when a few people accounted for the 3% error by rationalizing that we were 600+ feet above sea level!

 Using a different probe in order to shed a little light on the voltage cycle of a fluorescent bulb, Bob demonstrated an application of the study of periodic functions.  We were shocked to see (after having the question posed to us) how placement of the probe alters the cyclical curve.  Even if an individual is in the dark when it comes to electricity, the connection between the physics and the math encourages one to be less resistant to its mysteries.

 Proceeding with a microphone probe, Bob demonstrated how his students have fun with sound—he selected two participants to try to match the pitch of a tuning fork.  After catching a wave from the sound of the fork, former MMC president Suzanne Rzepka tried to match its pitch by humming a few bars and supplying the probe with her “vocal” data.  A new graph was produced, and following some simple calculations comparing the tuning fork’s graph and Suzanne’s graph, it was demonstrated that she can carry a tune and indeed, has perfect pitch!  Former ICTM president Jerry Cummins was asked to perform the same experiment.  When he finished with the exercise, it was determined that Jerry should not give up the day job, and that he also will not be singing “Happy Birthday” at Bob’s new daughter’s party!

 Bob concluded his medley of experiments by utilizing the pressure probe with a syringe to measure how volume affects pressure.  Even though Bob received a little needling about the syringe, he performed very well under pressure with the CBL, and produced data resulting in a graph that demonstrated a beautiful inverse relation between the two variables.  A power regression application reinforced the relation that exists between pressure and temperature.

 Bob Ruzich captivated MMC members and guests with his expertise, enthusiasm, and wit.  Using the CBL (along with the Datamate feature), we enjoyed the experience of seeing how instantly obtained data from the “real world” applies to the mathematics we teach.  His students (and Fenton High School) are fortunate to have a teacher who has a lot of good connections!

                                                                                                            -Harlan Goldberg

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