Points and Angles Online
May 2001

    Table of Contents:

Developing Proportional Reasoning:  So Important, So Widely Ignored
Steve Leinwand
Mathematics Supervisor
Connecticut Department of Education

This typically up-beat and example-laden talk will focus on the development and ongoing reinforcement of proportional reasoning across the mathematics curriculum.  Moving from stories to poems to everyday problems to not-so-everyday problems and back, we’ll focus on practical strategies that help us emphasize proportional reasoning in many ways and places.

Steve Leinwand has survived over twenty years in this position and weathered the slings and arrows that come with being outspoken.  Steve is also a former president of the National Council of Supervisors of Mathematics and recently
completed a term on the NCTM Board of Directors.

A Programming Note for the May MMC Meeting Rita McGuire of Prentice Hall will be supplying wine for our tables!  Thank you Rita.

See you on May 11, 2001!

Last month’s puzzle, submitted by Leona Mirza.

Two friends, one who lives in an east coast state and the other who lives in a west coast state, were talking to each other on the phone.  They noticed that the time on their clocks, which were both correct, was the same.  How could this happen?  In what states did the friends live?  What time was it?


One friend lives in the panhandle of Florida which is on Central Time.  The other friend lives in the eastern portion of Oregon which is in the Mountain Time Zone.  The time period is during the hour after the time in Florida has changed from CDT to CST and before the Oregon time has changed from MDT to MST.

The election results for the MMC Board are as follows:

 Pat Bowler-Johnson

Board of Directors:
 Randy Pippen
 Mary Wiltjer
 Gwen Zimmerman

Thank you to all of the candidates who ran for office.


Niles North High School will host the final meeting of area Calculus teachers on Saturday, May 19, 2001, from 9:30 am - noon. We shall discuss the free response questions from the 2001 Advanced Placement AB and BC exams, assignments to give next year’s AP students over the summer, textbooks, pacing, and whatever other concerns teachers will have regarding the teaching and testing of AP Calculus. Those new to the teaching of AP Calculus are especially invited and urged to attend.

Niles North is located at 9800 N. Lawler Avenue in Skokie, IL. The building is located just east of the Edens Expressway Old Orchard Road exit. We are just west of Old Orchard Shopping Center and 1.5 blocks north of Golf Road. The meeting will be in room D201. Please park in the large lot just to the north of the building and enter at the auditorium (flagpole) entrance and follow the signs to D201.

If planning to attend, please call George Pryjma at 847 568 3279 or e-mail George at:  <geopry@niles-hs.k12.il.us>  or  <gpryjma@aol.com>

Bagels, donuts, juice, and coffee will definitely be on the agenda.

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

Points from the Interior

It hardly seems possible that our last MMC meeting of the year is just around the corner. In a few weeks, I will pass the gavel on to Fern Tribbey, who has brought in some very interesting speakers this year and will continue to do an excellent job as our President next year. In addition, congratulations to Pat Bowler-Johnson on becoming President Elect and to the other new  board members: Gwen Zimmerman, Randy Pippen and Mary Wiltjer.

This has been a good year for our club. Our speakers have been entertaining and informative. Among them were Donald Palac, who extended our thoughts about space travel, and John Diehl, who provided some guidance on involving more statistics into our curriculum. During the winter, Steve Viktora and Wally Dodge gave us a new and exciting way to approach a traditional problem. John Benson helped us to reflect on what really good teaching means. Our own past president, John McConnell graciously filled in when Monica Neagoy became sick. Now as spring is upon us and we approach the end of the year, we are
invited once again to hear a nationally renowned speaker, Steve Leinwand.

This has been an exciting year for the greater mathematics community. Last spring saw in introduction to the revised NCTM Standards, the PSSM. This year we have seen them gather strength as materials are developed to assist in their implementation, among these materials is the recently released Navigating through Algebra series, which are great resources.

I want to close by expressing my thanks to those who will be leaving the board this year: Joen Flener, who was very helpful to me last year when I was the struggling President Elect; Bill Messersmith, who has been active in the leadership of this organization for as long as anyone can remember; Don Porzio, who graciously volunteered to fill in the remaining year of Fern Tribbey's term as board member; and especially to John McConnell, who has been a leader extraordinary. Take a moment at our May meeting to thank these folks for everything that they have done. They have dedicated their time and energy to our club. Finally, I would be remiss in not expressing our thanks to Suzanne Rzepka and Toni Seidelmann who co-chaired our MMC Conference this spring.

THANK YOU for a great conference!

One last item. For those who feel that we should meet somewhere besides the Como Inn, your wishes are granted. The Como Inn will be closed for renovations from July 1 through the end of November. Exactly where we will meet is yet to be determined; the board is open to suggestions.

Thank you,  -Ron

Dr. John McConnell, Statistics in Mathematics

The only flaw in the evening’s festivities was that our scheduled speaker for March 9, Monica Neagoy, was unable to flee her domicile and fly to Chicago due to a bout with the flu.  Instead, despite all the chaos, Dr. John McConnell pinch-hit and gave a significant talk on “Statistics in Mathematics”.  John spoke with confidence about correlation and regression, citing this tandem of concepts as “ . . .one of the greatest math ideas of the last 150 years.”

Using data to produce a linear model in order to predict outcomes has many applications.  In a brief “tour” of the usefulness of correlation, John shared parts of a “Decisions Through Data” video about a little girl’s abnormal growth rate and how, as a result of charting her growth, her doctor was able to calculate the amount of human growth hormone which ultimately restored her to normal growth.  He also shared a scatterplot of the Palm Beach County election returns which indicated how outliers play a useful role in the regression model of Florida election results—it seems that there is some abnormality regarding Buchanan votes vs. Bush votes.  John rounded off this part of the discussion by using “bouncing ball” data from a CBL as an example of exponential regression.

It was at this point in the presentation of the “Least Squares Method” that John got a little technical.  He was able to show that the cosine of the angle between the explanatory and response vectors is, indeed, the correlation coefficient r.  This model also explains that, as the angle moves from 0 degrees to 180 degrees, why the value of r takes on a range of between -1 and 1 (inclusive).  The proof was quite elegant, but was much more than could fit in the margin of this

Serenaded by the group of outliers in the next meeting room, John concluded his presentation with some history of the gentleman scientist, Sir Frances Galton (1822-1911), who was the father of regression and the cousin of Charles Darwin.
The connection between the two men is obvious—both were involved in studies of “fit”. Although not a mathematician, Sir Frances gathered measurement data of three generations of families, and then showed that a straight-line relationship
exists between the heights of parents and their children: Tall parents have children that are taller than average, but less than their parents (by two-thirds from the mean).  A similar relationship holds true between short parents and their offspring.  Galton was able to do all this without using the method of least squares, and he termed the results of his studies “regression toward mediocrity”.

Karl Pearson (1857-1936), the father of modern statistics, coined the terms “correlation” and “regression” in his studies in data analysis.

Even though there was some variation from the original script of the evening, we appreciate that Dr. McConnell’s influential points were enlightening and entertaining—he certainly didn’t hand us a line!           -Harlan Goldberg
                                            (with moral support from George Pryjma)

Thank you to Rita McGuire of Prentice Hall for helping to discount the cost of our dinner price by $10.00 at the March 2001 MMC meeting.

Equilateral Triangle Puzzle

Given an equilateral triangle with sides S, there is a point P on the same plane within the triangle.  P is 3 units from vertex X, P is 4 units from vertex Y, and P is 5 units from vertex Z.  Find the length of S in units.  (of course, not drawn to scale)  With thanks to my high school math teacher, Joe Mercer (retired), at Glenbrook North.  -Steve Tribbey

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