Points and Angles Online
January 2001

    Table of Contents:

Equity and Access:  Opening Doors for More Students to
Achieve Higher Levels of Mathematics
Tim Kanold                    Kathie Rauch
Director of Mathematics             Mathematics Teacher
Adlai E. Stevenson High School

Authentic program and classroom teaching changes are necessary to move away from a “selecting and sorting” mentality in order to funnel more students into advanced placement mathematics courses by the 12th grade.  Special emphasis will be given to a grade five through twelve course sequence program for students and innovative techniques for teaching calculus.

Kathie Rauch has been teaching at Stevenson for fifteen out of twenty-six years of teaching.  She is currently teaching honors geometry and BC Calculus and coaches the Stevenson Math Team which finished third at the ICTM State Math Contest.  Kathie was a state awardee for the Presidential Award for Excellence in Teaching in 1993 and 1999.  She won the Radio Shack Tandy Award for Excellence in Teaching in 1998 and the Edyth Sliffe Award in 2000.

Tim Kanold received the Award of Excellence from the Illinois State Board of Education for outstanding contributions to education in 1995.  Tim has served on NCTM’s Professional Standards for Teaching Mathematics Commission.  A 1986 recipient of the Presidential Award for Excellence in Mathematics Teaching, Tim served as president of the Council of Presidential Awardees of Mathematics.  Mr. Kanold also is a member of the NCSM’s Board of Directors as the NCTM representative.

Happy New Year and looking forward to seeing you on January 12, 2001.

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 If no boxes are checked, the information you provide here will not be published.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

International studies are an excellent way for us to gauge how well our students are achieving.  With the results of the TIMSS-R coming out, we can evaluate and compare the fourth grade students from 1995 with the eighth grade students of 1999.  The good news is that the eighth-graders in 1999 scored slightly higher than the international average; the bad news is they did worse than they did as fourth graders in 1995.  Our eighth grade students scored significantly higher than 17 other nations, significantly lower than 14 other nations, but about the same as 6 other nations.

More than a comparison of scores, I find the comparison of the curricula and pedagogy of great interest.  Our students are less likely than their international peers to be taught by mathematics majors.  In fact the number of non-mathematics majors teaching in mathematics classrooms has shown a significant and disturbing growth.  We as educators should be encouraging our better students to consider teaching.  In fact, bring them to our February meeting where they can get a brief, but enjoyable, picture.  Consider also, the MMC Scholarship offers a great incentive to pursue a degree in teaching mathematics.  (see the form on page 4)

Ninety-four percent of US. eighth-graders said that their mathematics teachers showed them how to do mathematics problems almost always or pretty often, which was higher than the international average of 86 percent.  It is easy to show students how to do a problem.  The teaching paradigm when I started teaching was just that:  show the students how to do each problem, never ask them something where they might actually have to think, only ask them to do problems where they can mimic what they have been shown.  It is time that we stopped asking our student to mimic and started expecting them to think.

Twelve percent of US. eighth-graders reported using computers almost always or pretty often in mathematics classes, vs. 5 percent internationally.  This is good.  Computers are an important part of our lives and can be a significant educational tool, if used properly.  Similarly, ninety-one percent of the students’ schools had Internet access, compared to 41 percent internationally, which is indicative of our affluence.

Next spring, some results from the TIMSS-R Video Study should be released.  This study involved videotaping and analyzing national samples of eighth-grade mathematics and science teaching in 7 countries.   Reviewing what other nations do in their classrooms can help us improve what we do.

One last item:  THE DEADLINE FOR CALLING IN RESERVATIONS FOR THE JANUARY MEETING IS FRIDAY, JANUARY 5, WHICH IS PROBABLY DURING WINTER BREAK.  Please make an effort to call in your reservations or submit them via email.  You can do this from the MMC web site <www.MMCChicago.org>.  See y’all in January.

Thinking out of the box, by Wally Dodge & Steve Viktora

After several days of battling cold and shoveling snow MMC members who attended the December meeting were rewarded with a presentation by Wally Dodge and Steve Viktora that will be remembered as a classic. Their mathematical problem dealt with the “box problem.” The box problem is one that traditionally appears in calculus courses, and, in various forms, in mathematics courses starting at the middle school level. The problem requires students to start with a sheet of paper, cut out congruent squares from the corners, and fold the edges so that they have a box. The question is “How large should the square cutouts from the corners of the original paper be in order for the box to hold the most?”

Middle school students can do this problem as a lab activity by filling the box with something such as popcorn. They are expected to make different size boxes and analyze the data. By doing this activity with several different size squares, they get a general determination for the cutout size that gives the box that holds the most.

High school students, in a class prior to calculus, are asked to write the volume as a function of x.   v(x) = x(w-2x)(l-2x) where w is the width of the paper and l is the length of the paper. Students then can graph the function using a TI-83 calculator and examine the table to determine the approximate maximum value.

Most calculus students use their differentiation skills and quickly arrive at the maximum volume, and, also, the size of the square cutouts. They stop at this point, but Steve and Wally didn’t allow us to stop. The newly retired Wally had created boxes of various convex shapes and sizes for us to see the types of figures that needed to be cut out. They started with a square and showed us that the optimal size of the square corner cutouts is a/2 where a is the length of the side of the paper. They continued to challenge us to think “out of the box” by having us visualize, with a roll of paper towels, what would happen to the calculations as the width remained fixed but the length was allowed to vary. They continued by posing extension questions, such as, “Is there a relationship between the lateral area and area of the base for the box of maximal volume?” and, “Do the relationships that were discovered for a square also hold true for other figures?”

This presentation by two outstanding mathematics teachers was one that truly should not have been missed. Fortunately, they will be presenting the same talk at the MMC conference in February. If you were not able to attend the meeting in December, don’t miss them a second time.

Leona Mirza

A few words of thanks are in order as we leave the OLD millennium and enter the NEW millennium on 12/31/00-1/1/01.  Thank you Como Inn and our host, Pat Queen, for the wine at the December meeting.  Thank you also to Kristin Sweet of McDougal Littell for the gift bags she gave out at the last meeting of the last millennium.

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