Points and Angles Online
December 2000

    Table of Contents:

Thinking Out Of The Box ... Problem

Steve Viktora and Wally Dodge New Trier High School

Steve and Wally will have us look at familiar problems that we all know and have used with our students.  They will investigate with us how to take these problems and go further with them.  One such problem is the box problem and maximizing the volume not just with a rectangular box but with any n-gon boxes.

Steve Viktora is currently in his tenth year at New Trier High School as the mathematics department chair.  Previously, he taught at Kenwood Academy for sixteen years of which the last six he was the department chair.  Steve was also in the Peace Corp for five years.  Steve is a past president of ICTM and of MMC.  He also has authored math textbooks in his spare time.

Wally Dodge had spent his career teaching mathematics at New Trier High School. This is his first year as a "retired" mathematics educator.  Wally has been awarded the Presidential Award in Excellence in Secondary Mathematics Teaching, recipient of the Tandy Technology Award, and was a Woodrow Wilson National Fellow.  Wally is a past president of MMC and also had authored math textbooks in his spare time.

Please extend a thankyou to Rita McGuire from Prentice Hall for a generous donation to our organization.  This month, McDougal Littell will have holiday gift bags for each of us.

Looking forward to seeing you at our December 14th meeting.

MMC  Membership and Change of Address Form

Mail a check to Mary Wiltjer, 801 Elmwood Ave., Evanston, IL 60202.   <wiltj1@aol.com>
Please use a different form for each person.

Membership: 1 yr ($20)______ Donation to Scholarship Fund __________
New______ 2 yr ($35)______ Donation to Speakers’ Fund __________
Renew____ 3 yr ($50)______ Student/Retired $10 per yr _________
   AMOUNT OF CHECK __________
Please fill in the information below. Check appropriate boxes to indicate what you want included by your name in the next MMC directory. If no boxes are checked, the information you provide here will not be published. The MMC directory is intended for MMC member use only.
 Name  School _______________________
  Address_____________________________  Day phone _______________________
 ________________________________   Night phone_______________________
   E-mail _______________________


 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 scholarship recipients will be honored.

The guidelines used for selection shall be:

I.  A.  Demonstration of overall academic scholarship with an 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 a maximum of 400 word essay explaining why they would like to be a mathematics teacher.

 The scholarship award or awards will be determined by a selection comittee 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 19, 2001

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
                                                    708.747-5500, x220
**(Letters of recommendation and transcripts may be sent by separate mail.)
(Photocopy as needed)

Points from the Interior

Those who attended the November meeting thoroughly enjoyed listening to Glenda Lappan discuss the new PSSM document and especially the CD that is available.  Both the document and CD contain important material that should be influencing what we teach, how we teach, and how we expect our students to learn.  If you have not taken the time to review both of these, I strongly recommend that you do it.

Although everything may be settled by the time you read this (at least hopefully everything will be), a comment on the election is appropriate.  The discussions on the Electoral College and voting should be of great interest to every mathematician and mathematics teacher.  It provides an opportunity to discuss our system of voting, how it could prevent a popular candidate from winning and how other systems of voting (e.g., be allowed to vote for more than one candidate) may actually be better.   If the Electoral College is dispensed and a straight popular vote is instituted, would a plurality be necessary (in which case, a candidate with less than 50% of the vote could often be the winner) or do we require a majority?  There are numerous resources available to aid in this discussion.  Among them are three modules produces by CoMAP (www.comap.com):  Fair Voting - Weighted Votes for Unequal Constituencies, The Apportionment Problem: The Search for the Perfect Democracy, and The Mathematical Theory of Elections.  These would be good topics for a math club.

On November 14, your Board held its fall meeting.  The major topic of discussion was membership: how can our membership be increased and how can more members be encouraged to attend the dinner meetings.  We are submitting a proposal so that MMC can be a provider for professional development units, CEU's and CPDU's.  Fern Tribbey has been busy talking with publishers.   McDougal Littell has offered to provide favors for everyone who attends the December meeting, and, as usual, the main course will be prime rib.  The February meeting is "Senior Night".  Because of the success last year, we are again encouraging everyone to invite high school seniors who are interested in pursuing mathematics education careers.

Here is hoping that everyone has a good holiday season and as part of it, come out and have an enjoyable evening listening to Steve and Wally.

Summary by  Conrad Wayne

Summary of Nov. 17 Talk


Glenda Lappan
University Distinguished Professor
Department of Mathematics
Michigan State University

 MMC was very fortunate that Dr. Lappan had time in her busy schedule to share her thoughts on the revised Standards (PSSM). As the former president and current past president of NCTM, she is extremely qualified to share those thoughts. She also served as Chair of the middle school writing group for National School Mathematics (1989) and Chair of the Commission that developed the NCTM Professional Standards for Teaching Mathematics  (1991).

 What is reform all about? It’s about modernization, improvement of curriculum instruction, and assessment of student progress that supports student learning. To accomplish this reform, we need programs that are developmentally responsive, academically excellent and socially equitable. To help students accomplish the goals of this reform, we need to connect to their interests, look at the logical and experimental sides of mathematics and create a tool-rich environment for learning mathematics. We also need to listen to our students to understand what sense they are making of mathematics.

 Dr. Lappan then spent a few minutes describing the procedures in developing the PSSM, who was involved (teachers, administrators, mathematics supervisors, university mathematicians and mathematics researchers), issue clusters, solicitation and collection
of reactions to these issues, conversion of these reactions to some manageable data and ways to code this qualitative data. Some of the features of the PSSM are mathematical tasks, illustrations of uses of technology in teaching methods, student work, classroom episodes and research episodes. There are ten different content standards and are organized so that teachers can see how the level of depth and rigor evolves from grades K-12.

 PSSM is available in the traditional book form which was mailed to every NCTM  member last April. It is also available on CD-ROM. This disk was mailed to all NCTM members who returned the request card contained in the book. Teachers can also go to NCTM.org for information on PSSM. Dr. Lappan also suggested that the teachers then go to the ILLUMINATIONS link for some very good and interesting problems for students. She showed two examples:
1) (grades 6-8) A family has $60 to spend for dinner at a restaurant. They know that the total cost after adding tax and tip will be 25% more than the menu prices. What can be ordered so as not to exceed $60? To turn this into a small group activity, collect some carry out menus from some local restaurants and have the students order for the family of four while staying within the constraints of the problem.
2) Geometry- Paper Pool Problems. Students work with pool tables of various dimensions with the drawings of the tables divided into squares (e.g., a 3 by 5 table would have the table divided into 15 squares). The ball always starts from the same corner. The only holes are at the four corners and the ball must start out at a 45? angle. The questions that the students are to answer are: a) what hole the ball will end up in and b) how many paths the ball will follow to end up in the hole. Students are then asked to draw the paths.

The PSSM are supported by fourteen professional organizations such as the National Council of Supervisors of Mathematics and the National Research Council. If you have not taken the time to get familiar with PSSM, Dr. Lappan strongly urges you to do so. She also mentioned the NCTM PSSM workshops that are now being offered at different locations around the country during the school year as well as in the summer. Information on these workshops can be found on the NCTM website as well as in their various publications.

Thank you, Glenda Lappan, for a very entertaining and informative presentation!

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