In Memory of - GCTM · In Memory of Dr. Larry Elbrink 1941 ... Reviewers were able to ... worked at RESA for many years and continued to teach at

In Memory of Dr. Larry Elbrink

1941 - 2005

Vol. LI No. 3 Fall 2005

ReflectionsFall05Web.qxd 8/24/05 9:47 PM Page 1

Vol. LI No. 3 Fall 2005

Table ofContents

SPECIAL REFLECTIONS3 In Memory: Dr. Larry C. Elbrink

4 Closing the Achievement Gap

5 Computation, Calculators and Common Sense

6 How to Make the Most of a Conference

7 Extreme Makeover: Mathematics Edition

8 Rock Eagle: Conference Keynote Speakers

9 Rock Eagle: Conference Major Speakers

10 Eyeball Theorem

12 Using Children’s Literature to Teach Mathematics

14 Factoid Challenge

15 Numberlines: From Infinity to Infinity

18 Why do These Work?

20 Homework: A Key to Improvement in U.S. Mathematics Education

24 Life Members with Comments

27 Congratulations to the Newly-Elected Officers on the Executive Committee

1 President’s Desk

2 Ga. Dept. of Education

19 Al’s Web Sites

28 Exec. Committee/Regional Reps

Mildred Sharkey

NCTM Press Release

NCTM Press Release

Sheree R. Curry

Tom Ottinger

Antonio Gutierrez

Linda Brewer & Deborah Wise

Dr. David Ide

Carol Newman

Cheryl Hughes

Janet Tedesco

REGULAR REFLECTIONS


Making a Difference: You, Me & Larry Elbrink

by Dottie WhitlowGCTM President

1REFLECTIONS FALL 2005

Saving the StarfishA young boy was walking along the beach early one morning. The tide was receding, leaving numerous

starfish stranded on the beach. The boy began picking them up and tossing them back into the water.Engrossed in the task, he didn't notice the old fisherman sitting quietly watching him. He startled the young -ster; asking gruffly, “What are you doing?” The boy enthusiastically replied, “I’m saving the starfish. Thestranded starfish will die if left in the morning sun.” The fisherman laughed at him and launched into ascoffing ridicule. “Look ahead of you down the beach,” he said, pointing to the seemingly endless expanse ofsand and surf. “There are thousands of starfish washed up on this beach. You can’t hope to save them all.You're just wasting your time. What you’re doing doesn’t matter,” he replied condescendingly. The young boystopped, momentarily pondering his words. Then he picked up a starfish and threw it far into the water. Hestood straight and looked him in the eye. “It matters to that one,” he said, and continued down the beach.

—Anonymous

“It matters to that one.” These words haveprovided guidance to me throughout the past20 years through the challenges of work anddaily life. These words have guided my behav-ior to “always try” and “we must try!” Forthose of you who have been in the teachingprofession for some time, you know that therehave always been challenges and struggles. Thefact that we have new struggles should not besurprising. Some of the obvious challenges wecurrently face in our profession are; learning toteach the new GPS, raising the achievement ofall students in our classes and schools, takingnew classes and workshops, helping our stu-dents perform at levels that give them a future,helping our schools make AYP, and the listgoes on and on. We also face challenges in ourdaily lives and our personal quests for growth.There are new challenges every day!As we face each challenge it is easy to wonder

if we can do it and if we can make a difference,and it sometimes feels like there is so much tobe done. All of these things can feel over-whelming and leave us asking, “Where do Ibegin?” Like the boy who was saving the

s t a r f i s h , we begin with small step s, s m a l lefforts, reaching out everyday with enthusiasm,believing in the good of the mission and theidea that “it matters to this one” even if wecan't save everything and everybody today.

Recently several members of GCTM attend-ed the memorial service for our belove dGCTM Executive Director, Larry Elbrink. Ishared with those gathered that we at GCTMknew and loved Larry Elbrink, and he madesuch a difference to GCTM. What we learnedat Larry's memorial is that Larry tried to makea difference in everything he touched. Notonly did he love teachers and mathematics, buthe adopted several children, he loved to growflowers, he advocated for children's rights andprotection, he supported his community the-ater, and he made a difference in so many lives.

At this time I invite you to reflect on the smalland large ways that you make a difference andto make little steps and efforts. Remember, “Itmatters to that one,” one person, one step, oneeffort, and one child at a time. You, me, andLarry; we can and do make a difference.

Thank you and God bless you, Larry.Thank you for making a difference and God bless us all.


by Phyllis MartinMathematics

Education Specialist

[email protected]

From the Georgia Department of Education

REFLECTIONS FALL 20052

Hello from DOE! Carolyn Baldreenow is doing training for the GeorgiaPerformance Standards (GPS) full

time. I was moved into a position as a mathe-m atics education specialist last fa l l . I nD e c e m b e r, the Dep a rtment hired anothermathematics specialist, Claire Pierce, who hasbeen wo rking primarily with the A dv i s o ryCommittee on the new draft of the highschool mathematics GPS and with committeesacross Georgia develop-ing tasks for the GPS.

In March , the Stat eB o a rd ap p roved theposting of the new drafthigh school mathematicsGPS.

Reviewers were able tosend comments online tothe Dep a rt m e n t . A l lcomments were carefullyreviewed by the AdvisoryCommittee at a weekendm e e t i n g — ye s, Fr i d ayafternoon, Saturday andSunday!—at the end of April, and appropriatechanges made.

The Board approved the revised high schoolmathematics GPS at their meeting March 12.Many thanks to all the teachers, mathemati-cians and other educators who worked on theGPS! We now have a completed state curricu-lum in mathematics!

The Department is presently delivering Days4 & 5 Training for the sixth grade mathematicsGPS. Training for Days 4 & 5 began in midMay and continued throughout the month ofJune. Each day of training is repeated at 8-10sites across Georgia for trainers selected by

each school system, RESA, and other educa-tional entities in Georgia. Each school systemhas been encouraged to train every sixth grademathematics teacher—regular, special educa-tion, Title I, remedial—anyone who teachessixth graders mathematics. Training for Days6-8 will occur in the 2005-2006 school year.Also, next year the DOE will begin the trainingcycle for Grades K-2 and Grade 7 mathemat-ics.

Sample Grade 6 mathe-matics tasks have beenposted on our Web site.If you have not visitedour Web site, it isw w w. d o e. k 1 2 . ga.us orh t t p : / / g a d o e . o r g .Student wo rk andteacher commentary forGrade 6 will follow later,as will tasks, s t u d e n twork, and teacher com-m e n t a ry for othergrades.

H aving perfo rm a n c estandards in mathematics is an exciting changefor Georgia. Yes, any change in curriculummeans more work for teachers and other edu-cators. But this change can really make a dif-ference in students learning mathematics.

Research, and the experience of the manyteachers in Georgia already teaching to per-formance standards, has shown us what is pos-sible in terms of improved student achieve-ment. If we work together, as a professionallearning community of learners ourselves, wecan accomplish our goal of helping our stu-dents learn more mathematics in a more mean-ingful way.

Students must be given the

time and the guidance to

construct their own under-

standings of mathematics as

opposed to memorizing the

understandings of others.

—Claire Pierce


In Memory: Dr. Larry C. Elbrink


Dr. Larry C. Elbrink, 64, died Fridayafternoon, July 1, 2005, at his resi-dence following a short illness. He

was a native of Vigo County, Indiana but hadlived in Waycross since 1975. Dr. Elbrink waspreceded in death by his father, the lateFrancis M. Elbrink, his mother the late ElmaJane (Evinger) Bourd e a u x , s t ep - fat h e r,Joseph T. Bourdeaux and his brother, the late Joseph Bourdeaux.

Dr. Elbrink obtained his Bachelor of Arts and Master of Artsdegrees from Indiana State University, followed by obtaining hisPh.D. in Education at Ohio State University. He was a consum-mate teacher, having taught kindergarten through college level aswell as teaching at Ohio State University.

Dr.’s Larry and Donna Elbrink moved to Waycross in 1975where he began work on a government project in Alma. Heworked at RESA for many years and continued to teach atnumerous local colleges and universities. He was an elder for theFirst Presbyterian Church. He belonged to numerous profession-al and civic organizations such as the Georgia Council Teachersof Mathematics(where he served as Executive Director), theNational Council Teachers of Mathematics, and the GeorgiaTechnology Center (where he served as the Treasurer).

Dr. Elbrink enjoyed his association with the Kiwanis Club formany years. He also enjoyed gardening, coin collecting, andstamp collecting. This gentle giant of a man was greatly loved andwill be missed by his wife, family, friends, co-workers, and stu-dents.

Dr. Elbrink is survived by his wife, Dr. Donna S. Elbrink ofWaycross; his daughter, Laura K. Elbrink of Waycross; two sons,Christopher S. Elbrink (wife Janis) of Waycross, Warren N.Elbrink of Nashville, Ga.; grandchildren, Tonia and Amber. Amemorial service was held where many expressed their love forLarry and what he had meant in their lives and the lives of theorganizations they represented. Memorial contributions may bemade to a Hospice Care, the National Association of Wegener’sDisease, or to GMET (Georgia Mathematics Education Trust).

http://obit.musicfuneralhome.com/obit_display.cgi?id=234771&listing=Current

Larry Elbrink is just themost recent death that hasdeeply affected me. Wehave lost John Neff (for-mer GCTM pre s i d e n t ) ,Dwight Love (Fa c i l i t i e sc o o rd i n ator and confe r-ence ch a i rp e rs o n ) , B i l lB o m p a rt (fo rmer GCTMpresident) and now Larry.These men were not onlyoutstanding mat h e m at i c se d u c at o rs, but they we revery dedicated to GCTM.

When I think of the lossof these wonderful men, Ican’t help but pray therewill be other outstandingleaders to help fill the void.Each gave of their time andtalent by not only serving ina leadership role in GCTM,but helped make me proudto be a part of this organi-zation.

As a classroom teacher for30 years, their excitementabout mathematics helpedkeep me going and alwaystrying to do the best, notonly for my students butfor other teachers. GCTMhas a wonderful heritageand I hope the young edu-cators will step up to theplate and help fill the shoesof these wonderful men.

—Mildred Sharkey






by Sheree R. CurrySheree is a graduate

of the University ofIllinois at Urbana-

Champaign. She hasbeen a journalism

instructor at DrakeUniversity and has

written for Fortune,People, the St Louis

Post-Dispatch, and theChicago

Sun-Times.

How to Make the Most of a Conference


Attending a conference is a great way to network, stay current on new products and technologiesin your industry, as well as providing a form of professional education. But when you flipthrough the program guide of that conference, you realize there are many sessions you want to

attend, and unfortunately, some of them even occur at the same time. How can you optimize your timeat panel discussions and still have time to deal on the exhibit floor and press flesh in other settings? Hereare some tips that will help you make the most of your conference experience.

Review Program in Advance“Decide ahead of time which

exhibitors you would like to visitand be prepared to negotiate forspecific products you wish tobuy,” says Karla Krause-Miller,c o n fe rence director at RSAConference of San Mateo, CA.Vendors usually have great flexi-bility at a show to make deals,considering they have to demon-strate that the sales that camef rom the show justified thembeing there. This gives you greatnegotiation power.

Bring Ample Business CardsInevitably you will meet some-

one at a conference who will saythey forgot to bring their cardsor that they ran out. Don’t bethat someone. Constantly replen-ish the stash in your pocke t .Exchanging cards is an importantp a rt of n e t wo rk i n g. M a i l i n glabels work well to sign up fordrawings in the exhibit hall also.

Get MaterialsIf there are sessions you cannot

attend, find the presenter and askfor the handouts they are offer-ing. Some presenters will alsoemail their packet of informationto you, if you can obtain theiremail address.

Ask a Presenter to LunchMany speakers attend confer-

ences alone and have no one toeat or hang out with. If you wantsome free consulting time with as p e a ker you re s p e c t , find outtheir schedule and ask them tolunch or dinner. “I once did apresentation at the beginning andend of a conference and hadreally nothing to do in between,”says Steve McClatchey, presidento f Alleer Training andConsulting of M a l ve ry, PA .“With some consultants rangingin the thousands for consultingtime, it’s worth a shot.”

Apply to be a PresenterWhile the seminars are still

fresh in your mind, start thinkingabout what you can present onnext year. Calls for proposals fornext year’s conference and otherrelated ones can often be foundat the handout tables. Sharing apresentation is a great way to bepositioned as an expert, and it’s agreat way to network. “Whenthere are 200 people attending aseminar, I gather more businesscards there than in the exhibithall,” says Bill Brooks, CEO ofthe Brooks Group, a sales man-agement training company inGreensboro, NC.

Keep Your Program Save a copy of the convention

program. Mark the sessions youattended. Its list of panels, speak-ers and contact information canprove to be a useful reference. Ifyou’re presenting at the confer-ence, you can also use your listingin the booklet in your portfolioas proof of your participation toyour administration when raisetime rolls around, or when posi-tioning yourself as an expert toothers.

Edited from “How to make the most of a Conference”originally appearing in Go!, Airtran Airways’ in-flightmagazine. Reprinted with permission of the author.


Extreme Makeover: Mathematics Edition

Artwork by

Toni DawkinsPalmer Middle SchoolKennesaw, Ga.


The Georgia Council of Teachers of Mathematics Invites You to the 46th Annual GEORGIA MATHEMATICS CONFERENCE!

October 20-22, 2005

Things are changing fast in mathematicseducation. This year’s conference is designedto help you survive and thrive in this environ-ment of change! We have exciting keynotespeakers to get you fired up about mathemat-ics. In addition there are major speakers fromall over the country, as well as our own out-standing Georgia people!

The new Georgia Performance Standardsare on everybody’s mind, and we have numer-ous sessions designed to explore, explain, anduse them. The high school keynote and paneldiscussion Thursday morning will introducethe re c e n t ly ap p roved high school GPS.Sessions are planned at all grade levels to intro-duce the tasks that help explain the standards.Other sessions discuss topics new to a particu-lar grade level and methods of teaching withperformance standards. Most sessions includeideas and activities appropriate for the GPS.

Te ch n o l ogy is ch a n g i n g both wh at weteach and how we teach. Sessions will showyou how to use the Internet in a variety ofways. Other sessions demonstrate the use ofcomputers and calculators at all grade levels.

The school populat i o n is ch a n g i n g.Georgia’s teachers need to be able to teach stu-dents who are not proficient in English, andwe’ve got the help you need. Be sure to lookfor sessions on how to work with EnglishLanguage Learners.

Testing is becoming increasingly importantin this time of accountability. Look for ses-sions about how to teach for understandingand improve test scores at the same time!

Vendors have produced extensive materialsto help you teach effectively. You’ll want tomake time during the conference to visit theexhibits to see what’s available. In addition,some vendors will showcase their materialsduring sessions.

Pa rent invo l ve m e n t m a kes a diffe re n c e.Come visit Saturday’s Math Fair to see howone school successfully got parents interestedand involved in their children’s education.

PRESIDERS NEEDED: Sign up tointroduce a speaker and be guaran-teed a front-row seat. Email Nickey

Ice to sign up ([email protected]).


Conference Keynote Speakers


Thursday Morning Carol Malloy is cur-

rently an associate pro-fessor of mathematicse d u c ation at theU n ive rsity of N o rt hCarolina at Chapel Hill.She has served on theBoard of Directors ofNCTM, as president ofthe Benjamin BannekerAssociation and as a member of the writinggroup for NCTM’s Principles and Standards2000. She is also an author of algebra andgeometry textbooks for Glencoe McGraw-Hill.

Thursday Night Tom Re a rd o n h a s

been teaching highschool mathematics for31 years. He enjoysintegrating appropriatetechnology into his les-sons when possible—e s p e c i a l ly SMARTB o a rds and grap h i n gtechnologies. Tom hasworked with Texas Instruments on developingsoftware: the Symbolic Math Guide and TI-SmartView. A current project is incorporatingComputer A l geb ra Systems in teach i n gAlgebra. Tom enjoys traveling the country anddoing workshops, biking and music.

Friday Night Dr. Monica Neagoy was educated in the

French school system, grades 1-12, in Asia andthe United States. She has a B.S. in mathemat-

ics and philosophyf rom George t ow nU n ive rs i t y, a MA inMathematics from TheCatholic University ofAmerica, and a PhD inMathematics Educationfrom The University ofMaryland. Her expo-sure to many cultures,her mastery of several languages and her pro-fessional involvement in both the arts and thesciences provide her with a unique perspectiveon the learning and teaching of mathematics.

Saturday Morning Jane Barnard is cur-

re n t ly on leave ofabsence from theD ep a rtment ofM at h e m atics atA rm s t rong A t l a n t i cS t ate Unive rsity inSavannah and is com-pleting a PhD at SaintLouis University. She isa past president of the Georgia Council andreceived the Gladys M. Thomason Award in1994. Jane received many awards and has beena c t ive ly invo l ved in GCTM, NCTM andNCSM, and also served as the President of theMathematics Educators of Greater St. Louisthis past year. Having classroom experience atKindergarten through university levels, Janehas a passion for the learning and teaching ofmathematics, with a special love for technolo-gy, communication, connections and mathe-matical photographs and cartoons.


Irina Lyublinskaya has a Master’s degree in Physics and a Ph.D. in Theoretical andMathematical Physics from the Leningrad State University, Russia. During more than 15 yeareof teaching mathematics and physics at high school and college levels, she has received theRadioshack/Tandy award for teaching excellence, NSTA distinguished science teachingaward and Northern Life Unsung Heroes award. Currently she is an Associate Director ofthe Discovery Institute and Associate Professor of Teacher Education at the College ofStaten Island/CUNY.

David Hammett has a B.S. in Mathematics from the University of Georgia and an M.A.T.in Mathematics from Georgia State University. He spent fourteen years teaching at SouthCobb High School in Cobb County, eight of those as mathematics department chair, beforemoving to southern California in 1997. Since then he has served as mathematics teacher anddepartment chair at Oakwood School in North Hollywood and has also acted as a mathemat-ical consultant to a variety of game shows.

Gail Englert is a sixth grade pre-algebra and science teacher at the School of InternationalStudies in Norfolk, VA. A National Board Certified teacher, Gail has received thePresidential Award for Excellence in Mathematics Teaching and was named an All-StarTeacher by USA Today. She is active in her local and state mathematics councils and has justcompleted a term on the National Council of Teachers of Mathematics Board of Directors.

Diane Morren has a B.S. in Elementary Education from the University of Texas at El Pasoand an M.A. from New Mexico State University. After receiving her degrees, she taught lit-eracy and trained teachers in the Philippines, Guatemala, Honduras and Colombia beforereturning to work in the public schools in Texas. Her teaching career there has included ESLteaching—both children and adults. Most recently she has been a full time bilingual readingteacher at the elementary level in Duncanville.

Conference Major Speakers


Jeane Joyner has a B.A. from Mary Baldwin College, M.A. from North Carolina Central, andhas done Post-graduate work at North Carolina State, Sacramento State, and UNC-ChapelHill. She has experience teaching middle school, adults, and has taught in a LearningExchange Lab for K-5. Currently she is a research associate with the Department ofMathematics & Computer Science at Meredith College, Raleigh, N.C. and president of theNorth Carolina Council of Teachers of Mathematics.

Jeane JoynerPreK - 2

Gail EnglertGrades 3 - 5

Diane MorrenESOL

Irina LyublinskayaGrades 9 - 12

David HammettGrades 9 - 12

Antonio Gutierrez earned his B.S. in Electrical Engineering from the National University ofEngineering, Lima, Peru. During his 21 year career in the computer and mining industry,Gutierrez worked in all areas of the computer field. Finally, he retired from the industry topursue teaching in secondary education. He is the creator of the Web site Geometry Step by Stepfrom the Land of the Incas: agutie.homestead.com. This intriguing, multi-award winning site isfilled with facts, problems and interactive puzzles relating to secondary school geometry.

Antonio GutierrezGrades 9 - 12


by Antonio GutierrezAntonio Gutierrez is

from Lima, Peru,where he is a

geometry and computer teacher

and web designer,developing ideas for

popularizing mathematics in a

multicultural teaching and

learning environment.

Eyeball Theorem


Given two circles with centers A and B, draw the tangents AC, AD, BF and BE from the cen-ters of the circles as shown in the diagram. Then the chords MN and PQ are equal in length,where M, N, P and Q are as shown in the diagram.

I found that MN = PQ about 35 years ago whilst exploring new problems concerning circles,tangents and chords. I am convinced that this result has been discovered in almost all cultures.However, a recent Internet search surprisingly turned up only a few relevant references to the“Eyeball Theorem.”

This would be the type of theorem to take on a desert island to exercise the mind because it iselementary, beautiful and surprising. It is designed to improve visual abilities, intuition and proof,thinking and reasoning skills, and above all, the geometric inspiration without which no discov-ery can be made. Like Archimedes, we can draw our sketches in the sand, but without the assis-tance of an ancient Roman soldier, please!

In what follows, I present three proofs of the Eyeball Theorem and a new Eyeball-to-EyeballTheorem with corollary. All are desribed with graphics, as a reflection of how a humble geome-ter thinks. What is the process by which geometers scan, focus, drill down and zoom?

ProofIn sympathy with the noble qualities of “simplicity, economy and elegance,” this proof reveals

the content and the context of the Eyeball Theorem and, by elucidating new relations betweengeometric objects like the cyclic quadrilateral FMPC, leads to further discoveries, such as the newEyeball-to-Eyeball Theorem.



1. ∠AFB = ∠ACB = 90°(a tangent is perpendicular to the radius drawn to the point of contact)∴ AFCB is a cyclic quadrilateral.∴∠BAC = ∠BFC (i.e., β = β’)

2. Let ∠MCP = α, so that∠FBC = 2α(alternate segment theorem, then, angle at center is twice angle at circumference)∴∠FAC = 2α (angles in the same segment)∴∠MFP = α∴ FMPC is a cyclic quadrilateral and∠PFC = ∠PMC (i.e., β’ = β”)

3. So b = b” and hence MP| |AB (pair of corresponding angles).Similarly, NQ| |AB and MPQN is a rectangle.

4. ∴MN = PQ.Q.E.D. (Quod erat demonstrandum).

We are very pleased to announce that Antonio Gutierrez will be speaking this year at theGeorgia Mathematics Conference at Rock Eagle. The proofs of the Eyeball Theorem weretoo lengthy to be published here, but he will be presenting the entire text at that time, as wellas some newly discovered theorems. Also please check our Web site www.gctm.org, whereyou will see the complete proofs soon.


by Linda Brewer & Deborah Wise,

students of Dr. Billy Lacefield

& Dr. Mary Kay Baccallo

Using Children’s Literatureto Teach Mathematics


The following are excerpts from a workshop presented by the students of Dr. Billy Lacefieldand Dr. Mary Kay Baccallo at the 2004 Georgia Mathematics Conference. Each lesson containsactivities that correlate to the NCTM Principles and Standards. We welcome your feedback asyou adapt these lessons to your classroom.

Too Many Pumpkinsby L. White

Holiday House, New York, 1996Lesson plan by Linda Brewer

SummaryEver since she was a lit-

tle girl, Rebecca Estellehas hated pumpkins. Oneafternoon an enormouspumpkin falls off a truckand smashes in her yard.Rebecca Estelle thenshovels dirt over the pieces and forgets aboutthem. But those slimy pumpkin pieces sproutup in autumn, and she finds herself with a seaof pumpkins. She decides to make every kindof dish she can think of with pumpkins. Thenshe carves pumpkins and puts candles in them.She sits back and waits for people to arrive andeat her pumpkin treats.

ActivitiesA l geb ra—Pumpkin pat t e rn s : The teach e r

will cut out pumpkins to use for patterning.The pumpkins can be big and small. The stu-dent is to make different patterns using thepumpkins. Examples: big, small, big, small orbig, big, small, small.

P ro blem Solving— E s t i m ate how manyseeds are in the class pumpkin, graph the esti-mates. Count the seeds to see who was theclosest. Guess how many cups your seeds willfill.

Measurement—Measure the circumferenceof the pumpkin with yarn. Measure the heightof the pumpkin with unifix cubes and othermath manipulatives.

Communication—Have students comparepumpkins to gourds and/or squash. The stu-dents should write in their math journals theirobservations about the pumpkin, gourd, andsquash. After the children observe and write intheir math journals, the teacher will hold a dis-cussion so the students can discuss their find-ings.

N u m b e rs and Operat i o n s— The teach e rwill make pumpkins for the students to use todo pumpkin math. Using pumpkin seeds thestudents will place the number of seeds theteacher directs on one side of the pumpkinand then the number of seeds the teacherdirects on the other. The student will add orsubtract the seeds according to the teacher’sdirections and record the answer on their mathpaper. Then the teacher will do another prob-lem, etc.



Caps for Saleby E. Slobodkina

Scholastic Publishers, New York, 1940Lesson plan by Deborah Wise

SummaryA cap peddler sets out one morning carrying

m a ny diffe rent colore dcaps stacked on his head.He walks up and downthe streets, but by middayhe has not sold a singlecap. He walks into thecountry and takes a napunder a tree. When heawakens, his caps are no longer on his head.He looks up into the tree and his caps arebeing worn by monkeys. He tries many unsuc-cessful attempts to get the monkeys to drop hiscaps. In frustration he throws his cap downonto the ground. The monkeys imitate thepeddler and throw their caps down also. Thepeddler then picks up his caps, restacks themon his head, and walks back into town.

ActivitiesData Analysis—“What color is your cap?”

Students will be permitted to wear a cap tos chool on a designated day. Students willchoose a strip of colored construction paperwhich identifies the color of their cap. A bargraph will be constructed for each cap colorrepresented in the classroom. Students willevaluate the data represented. The teacher willask questions pertaining to the data regardingthe concepts of “most,” “least,” “fewer,” and“more.”

Numbers and Operations—“How muchwill the Peddler Earn?” The book states that

the peddler is selling his caps for $.50. The stu-dents will be given color coded cards repre-senting the different colors of the peddler’scaps. Depending on the number of cards eachstudent re c e ive s, t h ey will determine howmuch money the peddler will make if he sellsall the caps represented by their cards. Theactivity can by enhanced by changing the pricevalue for each color cap, and redistributing thecolor cards. Gray caps can be $.50, brown capscan be $.75, etc. The students will share theirdeterminations with the class.

Connections—“How long did the peddlers l e ep ? ” The students will be divided intogroups of two. Each group will receive a cardwith a word problem relating to how long thepeddler slept. When the g roups have solvedtheir particular problem, they will share withthe class, and the other students will evaluatehow they arrived at their answers.

Problem Solving—“How high are the ped-dler’s caps?” Students will be divided intogroups of two. The teacher willl state a ran-dom measurement for the height of each col-ored cap. Each group will receive cards withnumbers of each color cap. The groups willdetermine the total height of the caps repre-sented on their card and then share with theclass. The class will evaluate each group’sresponses. New cards will be distributed.

Measurement—“How far did the peddlerwalk?” The teacher will indicate the distance infeet which the peddler walked from the townto the country. Students will work in groups oftwo to convert those measurements into yards,miles, and then kilometers. Students will haveaccess to conversion tables for these measure-ments. The class will evaluate and compare thegroup responses.



Factoids

• Canada is the world’s second-largestcountry with an area of 9,971,500square kilometers.

• The rocks on the moon are between 3and 4.6 billion years old.

• The moon has a 15,000-mile tail ofsodium atoms that can only be detect-ed by instruments.

• Hummingbirds fly at speeds up to 71mph.

• Lightning strikes earth somewh e reover 17 million times a day or about200 times a second.

• It takes from 25 to 30 seconds forblood to circulate through the body.

• At birth you start with around 300bones, but by adulthood you havearound 206.

• The American opossum’s ge s t at i o nperiod is 12-13 days; the elephant’s is21.7 months.

The challenge:How can you use these in YOUR classroom?Be among the first 5 teachers to submit the

activity you created using any or all factoids,along with 5 samples of student work (elec-tronically, please), to [email protected].

The reward:You will receive $10 to be used in the exhib-

it hall at GMC 2005 at Rock Eagle.

Factoid Challenge

GCTM Mini-GrantsDo you have an innovative teach-

ing idea, but you need a little moneyto get started?

As a member of GCTM you are elli-gible to apply for a mini-grant of upto $300. The purpose of the grantshould be to fund a creative teach-ing project.

Applications are received duringSeptember, awarded in October,and the project should be imple-mented Octoberthrough June.

Visit our Web siteat www.gctm.orgfor details.

Job OpportunityEditorial assistant for REFLECTIONS. Duties may includeediting, minimal writing, net-working with Georgia teachersto procure writers, photographyat GMC, layout and graphicdesign.Experience welcomed but not required.

All interested parties pleasecontact Cheryl Hughes at [email protected]

by Dr. David Ide


Numberlines: From Infinity to Infinity

by Carol NewmanRincon Valley Union School District

Santa Rosa, [email protected]


CONCEPTS: Number Sense, Measurement GRADES: 2 – 9SKILLS: Ordering numbers, using a rulerMATERIALS: Set of cards with numbers or expressions written on them, adding machine tape,yardstick or meter stick, ruler, Student Activity Sheets (following pages).

BACKGROUND:This activity can help students at many grade levels develop their number sense. It also rein-

forces the concept that the markings on a number line need to be at equal intervals to providean accurate picture of data and the distribution of numbers or algebraic expressions. Usingteacher-made cards, students arrange a set of dates, numbers or algebraic expressions by placingthem in order on a number line. You can use the suggestions given below or make up your ownsets of cards depending on the level and interests of your students.

DIRECTIONS:You can organize this activity for the class or for groups.

• Construct a number line on addingmachine tape (or have students do it)

• Be sure to discuss with students therange of the data so that they will beable to place all of the cards on thenumber line. Also make sure the inter-vals have equal lengths. All of thenumber lines can be the same length,or groups can have different lengths oftape.

• If students are divided into groups,give each group a set of cards. Havethe group arrange the cards in orderand then, using paper clips, place eachcard in its appropriate place on thenumber line.

• Another suggestion is to have studentsmeasure each other’s height and placethese measurements on a number line.Students can construct a number linewith metric measurements on one sideand U. S. measures on the other side.Give students benchmarks such as 4 ft,5 ft, 6 ft, or 50 cm, 100 cm, 150 cm.

• For younger students you could use aset of whole numbers. Depending onthe grade level of your students, you

might want to make different sets ofcards, for example, integers, rationalnumbers including fractions, decimalnumbers, percents, and real numbersi n cluding irrational nu m b e rs likesquare roots and pi.

• A variation that leads to some interest-ing discussions is to use algeb ra i cex p ressions like those on StudentActivity 2. You could use this set ofcards for several days, assigning differ-ent values for x each day.

Be sure to encourage the students to discusswhy they placed the numbers or expressionswhere they did. Have students verbalize theirthinking by asking them questions such as:• How did you decide where to place the

different numbers?• How did you know the placement was

correct?• Which units of measurement did you

find easier to place on the number line?• How does the length of the tape affect

the placement of the numbers?


Numberline Flashcards


2

103

1,473

9,876

102,789

650,821

2,545,499

73

562

4,534

52,491

321,978

1,290,864

5,547,454


Numberlines: Student Activity Sheet 2



Why do These Work?


The following algorithms were found written by a layman (a non-mathematician) who claimsthat they work! Do they always work? If so, why? If not, why not? Could your students help youdecide?

The sum of the integers between 2 integers F (first) and L (last)

Sum = (L squared - F squared + F + L) /2where F > 0 and L > 0,

and L > F

How to find the Fifth RootBegin with any positive number and raise it to the fifth power.

Here is the process:The least significant digit of the big number is the same as the least significant digit of the root.

That is always the case. The following is the list of the first 9 numbers with integer fifth roots.

1 32 243 1024 31257776 16807 32768 59049

Notice the last digit of each number goes up from 1 to 9. You can commit these to memoryto make this process totally mental.

If this is the number for which you are to find the 5th root,459165024, go down the list of memorized numbers until you have found one that is larger

than the 4591. (Yes, you are starting at the right and overlooking the right-most 5 digits to yieldthe 4591.

When you get to a number that is larger than the 4591, you see 7776. The 6 is the only impor-tant digit in the 7776 as the last digit is always one greater than the first digit in the answer.

So the answer is 54.

Here is another example:The problem is to find the 5th root of the number 79,235,168.The one’s digit is 8 automatically. If you discard 35168 and take the 792, and then look at the

list, 1024 is the next greater number with a 5th root. The first digit in the answer is one less thanthe one’s digit of 1024, so the final answer is 38.

Does this always work? Why? Is there an algebraic reason why it works? Is there a more con-cise way to write this algorithm? Send comments and solutions to Cheryl Hughes([email protected]).



Al’s Web sites

Moneyopoliswww.moneyopolis.com/new/home.asp

A free site containing a game to teach stu-dents about investing, banking, and real-lifesituations involving money. Students play thegame and teachers can view their progress.

Mudd Math Factswww.math.hmc.edu/funfacts

Share random fun math facts with your stu-dents by posting them around your room, ontests, on worksheets, on your Web page, etc.Use these math facts to start discussions, fuelwarm-ups, and a myriad of other activities.

Math Tools Techonology POW(Problem of the Week)mathforum.org/tpow

These POWs take advantage of technologyusing Java applets. Printable copies available.Regular POWs available on mathforum.org.

Towers of Hanoi appletmath.bu.edu/DYSYS/applets/hanoi.html

Students will enjoy playing this interactivecomputer game. Hold a contest for finishingin the fewest moves. Even the teacher can win!

ClickMAZESwww.clickmazes.com

This site has interactive mazes and puzzles ofall kinds, with links to the history of the puz-zle or maze. Many include hints for success.

Mathwords: Terms and Formulaswww.mathwords.com

This site provides a great dictionary of inter-active definitions for terms used from Algebrathrough Calculus. There are many 3D graph-ics available to enhance the definitions.

If:• you have an had an “aha”

experience in your classroom

• your students have had greatsuccess at something

• you have used an unusual project with your students

• you have taken your studentson a successful mathematicalfield trip

• you have used anidea you read inREFLECTIONS

We hope you will write an articledescribing your experience. Please seethe writer’s guidelines on page 26.Photos, students work, and samples ofhandouts are welcomed.

NEXT ISSUEDeadline: Oct. 30, 2005

Topics:

• Pi and Pi-Day

• Preparing students for yearly assessment

• Preparing students for competition

• Celebrating mathematics


by Janet Tedesco with M. AtkinsD. Costello

M. DeisterP. Evans

S. JuarezJ. Monson

C. SanderfootL. Winer

Homework: A Key to Improvementin U.S. Mathematics Education


IntroductionThe United States has a serious problem in

mathematics education. Test results show thatbeginning in middle school, the U.S. studentproficiency declines in comparison with otherdeveloped countries throughout the world tonear the bottom by 12th grade [PISA]. TheWorkforce/Education Subcommittee of the

P re s i d e n t ’s Council ofAdvisors on Science andTe ch n o l ogy identifiedtwo principal reasons for

this: too many mathteachers are not

t rained inm at h , and too many mat h

textbooks are inadequate [Herbold].This article suggests a third important con-

t r i buting re a s o n : l ow homewo rk emphasis.The U.S. lags far behind in time spent by ourstudents on homewo rk [TIMMS]. Th u s,improving homework completion at the sec-ondary level may be a significant opportunityfor U.S. math proficiency improvement at thatlevel. This article suggests that new Internetmath homework-help resources may be veryhelpful in getting more students to completeand understand their homework. As an impor-tant by-product, more class time will be avail-able for more in-depth teaching than is cur-rently possible. We identify some of the avail-able resources, discuss their application and thebackground research that supports their use,present comments from several contributingauthors, and present a case study of the use ofone of the Internet resources.

Homework Not Being DoneWithout homework practice, middle school

or high school students cannot fully master theconcepts presented in class. Homework pro-vides an opportunity for the students to extendtheir understanding and directs the students toc o n c epts that need further ex p l a n at i o n .Homework provides an opportunity for stu-dents to make, discover, and correct mistakesso they can learn from them.Students of t e a ch e rs who emphasize the

importance of homework score higher thanstudents of teachers who do not [House].However, teachers are finding that getting stu-dents to actually do assigned homework isincreasingly difficult. Some students, and oftentheir parents, express that homework is a use-less burden. Furthermore, homework com-petes with TV, video games and other activi-ties. A teacher in Northern California had thisto say [Bradley]:

I am a good teacher, as evidenced by my experi -ence, by peer, student and parent feedback, andby advanced certifications that I have earned.Yet, many of my students fail. Most of thosewho failed will say it was because they did not dothe work.

Worked ExamplesThe use of worked-out examples is a stan-

dard practice in classroom lectures and text-books. Some students understand the daily les-son after observing just a few worked-outexamples. Others need more examples thancan be presented during a class period or pro-vided in a textbook section. These latter stu-dents would benefit significantly from addi-tional worked examples, but they might notknow where to find them or have the motiva-tion to seek them out. The research describedbelow shows that providing worked examples



for actual assigned homework problems isbeneficial. The Web sites described belowallow students to view worked-out solutionsfor their assigned homework.

Internet Resources for MathHomework Help Via WorkedExamplesA Web site that provided math homework-

help by showing tutorial (worked-out) solu-tions for actual math textbook homewo rkproblems was first introduced in 2001 [Beall].Other Web sites with the same general capabil-ities have since become available.

Each of these Web sites provides immediatetutorial explanations for math problems. Thus,teachers may assign homework problems forwhich there are explanations (worked solu-tions) available on the Internet. In the case ofEncarta and Hotmath, the explanations arecorrelated to the actual problems assignedfrom popular math textbooks.

Even students who may have fallen behind inmath may be attracted to such Web sites, asthey provide a new avenue for catching up.The help, via computer, with their assignedhomework relieves them of the fear of peer orsupervisory embarrassment. Math teacher JaneMonson noted that more of her students arecompleting homework since they began usingHotmath.com because it answers the question,“What is the next step?” so that students cancontinue on their own. According to Mathteacher Lisa Winer, “I love that this Web sitegives worked solutions to assigned homework,because students who want it can get instanthelp right away on their own. If a student sayst h ey didn’t understand the homewo rk , myresponse is that they should have logged on toget help.”

Scientific research has investigated the use of“worked-out” examples in algebra, and theresults show that this increases effective learn-ing [Carroll, 1992]. A study was done in Texas:two groups of students, one of poor perform-ers and the other of good performers, weretaught together with only one difference; thepoor performers were given their homeworkassignments with 50% of the pro bl e m saccompanied by worked solutions. The goodperformers were given the same homeworkassignments without wo rked solutions.Interestingly, the poor performers achievedhigher scores on the final exam than the origi-nal good performers. In related research, stu-dents in the worked examples group complet-ed their work more quickly while perceivingthe work as less demanding and displayed bet-ter performance on tests [Carroll, 1994]. Theresearchers suggest that the reduced cognitiveload allows the students to process the under-

Students needing assistance on

assigned homework problems

now can find immediate

homework help using an Internet-

connected computer, at Web sites

such as www.aolatschool.com,

www.encarta.com,

education.yahoo.com,

www.calc101.com and

www.hotmath.com.



lying similarity of problems and integrate them e t h o d o l ogy with existing know l e d ge[Grillmeyer, 2001]. They also note that less“wrong learning” results.

The availability of worked solutions also ben-efits advanced students. They can tackle themore challenging problems with more successand move forward with less outside help.Advanced, motivated students can work aheadin their textbook, knowing that an instant tutoris available.

Homework review in class is animportant part of math teach-ing. Teachers need their studentsto ask questions about processes,rules, and properties as a part ofassessing both the students andtheir own teaching. Yet, routinequestions of interest to only a few students canbe a ve ry inefficient use of class time.According to math teacher Marty Atkins, “Asour students have begun to use Hotmath.com…I am beginning to get more ‘Why did theytake that step?’ questions rather than ‘How doI start?’ questions.” A survey of math teachersusing one of the homework-help sites con-cluded that about 20 minutes per class timewas freed up [Grillmeyer, 2004]. According tomath teacher Paula Evans, “We saved classt i m e, wh i ch we immediat e ly re a l l o c ated toactivities which allowed students to developinsight about the material. …We have used thistime to develop in-class activities which askstudents to extend their homework.”

When teachers assign homework problemswith solutions available on any of the listedInternet homework-help Web sites, their stu-dents can receive step-by-step explained solu-tions to their actual homewo rk pro bl e m s.

Students are able to see their mistakes andlearn from them, and parents are in a betterposition to see the methods being taught sothey can amplify them as needed. Use of thesesites is not simply checking or getting answers,but may be considered a directed, self-paced,tutorial experience.

Te a ch e rs justifiably want to balance theamount of available homework help so thatstudents are certain to be challenged. Some

students might mindlessly copy downsolutions if they are available for everyproblem. The research concludes that50% of assigned problems should havethe available help. Two of the Web

sites that provide solutions to actu-al textbook homework problems

(Encarta and Hotmath) only explainthe odd - nu m b e red pro bl e m s, for wh i chnumerical answers are already available in theback of the textbook.

Jesuit High School Case StudyI am a mathematics teacher at Jesuit High

School in New Orleans, LA. This is a privateC atholic urban school with ap p rox i m at e ly1500 students. The student body is primarilymiddle class students from educated, success-oriented families. Our class size averages 25students and 99% of the graduates attend auniversity.

When our math dep a rtment intro d u c e dHotmath.com to our students, only the mostdiligent took advantage of it. As individualteachers and as a department, we learned toapproach the homework review in the class-room differently. Instead of asking, “Whatproblems gave you trouble last night?” webegan to ask “For what problems did you not



understand the solution given on the Website?” and “At what point did you not under-stand what Hotmath did?” Eventually, home-work review went from over 30 minutes a classto under 10. Even better, we saw students’grades improve!

With the extra class time, our teachers wereable to delve into prob lems or topics thatfocused on higher-level thinking skills. Wecould use open-ended problems to stimulatethinking both in a small group setting and toindividual students. Even the lower track stu-dents became more able to think—rather thanjust repeat steps—to attain a solution.

As I listened to and read the experiences ofthe contributing authors, I realized that ourschool’s experiences were not unique. Almost

universally they achieved additional instruc-tional time in class. They found that they couldlimit the amount of time spent on homeworkreview, maintain or increase their rates of suc-cess, and introduce creative classroom activi-ties to stimulate mathematical thinking.

ConclusionIn addition to the re c o m m e n d ation that

t e a ch e rs consider these Internet mat hresources, we feel strongly that our school andpolitical leadership should actively and repeat-edly stress the importance of homework, aswell as the importance of mastering math andscience classes, so as to effect an attitudechange over time that will benefit everyone.

References

Beall, R., Grant, C. & Grillmeyer, O. (2004). “Superior Improvement for Underperformers:Worked Homework Solutions are one Answer,” ComMuniCator, California Math CouncilQuarterly Journal, March 2004

Bradley, Laura (2005). Letter to the Editor, San Francisco Chronicle, January 10, 2005 Carroll, W. M. (1992). “The Use of Worked Examples in Teaching Algebra,” Annual Meeting of

the American Educational Research Association, Apr. 1992.Carroll, W. M. (1994). “Using Worked Examples as Instructional Support in the Algebra

Classroom.” Journal of Educational Psychology. v86, n3, 360-367.Grillmeyer, O. (2004). “A Teacher Survey about Online Worked Solutions to Math Homework

Problems,” www.hotmath.com, 2004Grillmeyer, O. & Chance, S. (2001). “Educational Foundation for Hotmath.com”, Hotmath.com,

2001Herbold, R (2004). “K-12 Establishment is Putting America’s Industrial Leadership at Risk,”

Speech at Hillsdale College National Leadership Seminar, May 25, 2004House, J Daniel (2004). “The Effects of Homework Activities and Teaching Strategies for New

Mathematics Topics on Achievement of Adolescent Students in Japan: Results from the TIMSS1999 Assessment,” International Journal of Instructional Media, 2004,

TIMMS (1999). “Trends in International Mathematics and Science Study, Assessment Report,”National Center for Educational Statistics, 1999

PISA (2003). Program for International Student Assessment, Organization for Economic Co-Operation and Development, 2003


Life Members with Comments


Nadiyah AbdullahMarie AbneyPamela AdamsonGloria AgnewCarol AllenEdith AllenMartha AllenJacqueline AllisonSherry AmmonsDelores AndersonSalvatore AngelicaCindy ApleyDiann AshMelvis AtkinsonCathie AustDeborah BaggsGloria BaileyBrenda BallietJane BarnardRobin BarnesPuttie BarnesPatti BarrettEloise BarronJulia BatchelorNancy BatesEdna BazikTracy BeardGloria Beard

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GCTM Officers are doing a great job carryingon the tradition of quality. I was among thefirst to attend the first meeting at Rock Eagle(1954) and also served on committee of tocompile The History of the Georgia Council ofTeachers of Mathematics, finished in October1984.

—Doris Dickey, Cartersville

I am retiring from North Springs High Schoolin Fulton County in June 2005 and may teachpart-time. I was the Reflections editor for 2years (7 issues) in 78 and 79 when the formatchanged to a journal style over a newsletter for -mat. Wonderful times with Bill Bompart, DoSpypek, and Gladys Thomason.

—Jan Gaylord, Atlanta

I am serving as 6-12Curriculum Director forColquitt County Schools.I sure miss all my mathfriends. We are workingon the standards, tryingto find/craft good per -formance tasks.

—Jenny Funderburk,Moultrie



Gary LeMayPeggy LeonardMary LindquistMichelle LongRita LongJuanita LongPaula LowderLynda LuckieFran LureyLeanne LuttrellJ. LynchAnnie MarksBill MarshDane MarshallPlyllis MarshallEllice MartinNancy MartinPhyllis MartinIris MathisEdith MaxwellFreddy MaynardSara McArthurErnestine McCallPaula McCormickBlanche McElfreshMelissa McGarityJerry McKinneyRegina McKinneyAnne MeinAngie MeredithDenise MewbornNancy MimsRoy MitchellBeth MonfortJanice MonsLaura MontgomeryGrace MooreElizabeth MorrisSheri MorrisScott MorrisRobert MoyerCarol MyersDeborah Najee-UllahLinda NashPeggy NealMary NeffGary NelsonDoris Nelson-JohnsonClare NeSmithSusan NeumanJoan NewellDebra NewsomeMargaret NorthcuttFrances NortonSue NuttingBeth ObergJanet O’BrienDorothy OdellWanda OldfieldDavid O’NeilJudy O’SteenThomas Ottinger

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I do enjoy Reflections and I do follow (viamail) the happenings. I'm now 85+—retiredfrom Atlanta Schools in 1980, did collegework for 6 years—doing just a little free tutor -ing now. You may see my name in the files, asI served as President of GCTM in the mid-seventies as the first Afro-American President.I do miss the activities of both GCTM andNCTM of which I attended several annualand Regional meetings. Good Luck!! I wouldcertainly prefer to improve available resourcesvia conferences and meetings to enhance theteaching skills of teachers.

—Gladys P. Richardson, Atlanta

Even though I am retired, I still enjoy theReflections, to keep up with what is going on atGCTM. For example, I would not haveknown about Dr. Bompart had I not beenreading Reflections. I continue to be interested.If I can assist with something from home, I'dbe happy to do whatever. Continued successwith your work at GCTM.

—Annie Rogers, Augusta

You too cansupport GCTMby becoming a

life member. Seethe membershipapplication onthe inside back

cover for details.


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make a donation to the

Give in honor of a Mentor

Give to perpetuate good teaching

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Submissions to REFLECTIONS should be sent electronically to Cheryl Hughes

at [email protected]. Photos and handouts should be indicated in the ini-

tial email, but sent later after acceptance. Priority is given to those arti-

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Georgia Mathematics Trust


Congratulations to the Newly-Elected Officerson the Executive Committee


Barbara FergusonPresident Elect

Barbara is an associate professor of Mathematics and MathematicsEducation at Kennesaw State University where she teaches and is theMathematics Education Program Coordinator.

Ellice MartinVice President for Honors and Awards

Ellice is an associate professor of middle grades and secondary educa-tion at Valdosta State University.

Patti BarrettSecretary

Patti began her 36th year at Lowndes High (and her 30th year of part-time at Valdosta State) in August. She previously served assecretary of GCTM, as treasurer, registrar, and chair of GMC.

Missy WalkerVice President for Regional Services

Missy is currently the Mathematics Department Chair at Martin LutherKing Jr, High School in DeKalb County.


PresidentDottie Whitlow235 Peachtree StreetNorth Tower, Suite 1700Atlanta, GA [email protected]

V.P. for Constitution & PolicyDon Slater2406 Woodbridge DriveMarietta, GA [email protected]

SecretaryCindy Fielder2322 Glenpark CourtMarietta, GA [email protected]

Council Publications EditorCheryl Hughes50 W Broad StreetFairburn, GA [email protected]

2005 Conference ChairTom Ottinger14 Sprice DriveEllijay, GA [email protected]

V.P. for Awards/HonorsJudy Chambers355 Hampton RoadFayetteville, GA [email protected]

V.P. for Regional ServicesMissy Walker115 Carrington ParkJonesboro, GA [email protected]

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NCTM RepresentativeChristine ThomasCollege of EducationGeorgia State University30 Pryor StreetAtlanta, GA [email protected]

V.P. for CompetitionsDebbie Poss2406 Woodbridge DriveMarietta, GA [email protected]

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WebmasterBryson Payne5489 Highway 19NDahlonega, GA [email protected]

Membership DirectorSusan Craig1011 Stewart AvenueAugusta, GA [email protected]

Regional Representatives

Central East:Amber Donnell920 Highway 80EDublin, GA [email protected]

Central West:Shepard Sawyer6644 Springlake DriveColumbus, GA [email protected]

Metro EastLenisera BodisonCedar Grove Middle2300 Wildcat RoadDecatur, GA [email protected]

Metro West:Ishan Malik818 Willis Mill Road SWAtlanta, GA [email protected]

South East:Mike Clemmons1200 Noel Conoway RoadGuyton, GA [email protected]

South WestSilvana JenkinsSchool: [email protected]

North East:(vacant)

North West:(vacant)

GCTM Executive Committe 2004-2005


In Memory ofDr. Larry C.

ElbrinkExecutive Dirctor


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Indicate your GCTM region: ❏ NW ❏ NE ❏ CW ❏ CE ❏ MW ❏ ME ❏ SW ❏ SE

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Applicant’s Signature (required)_________________________________________________

Mail to: Susan Craig, GCTM Membership Director, 1011 Stewart Ave., Augusta, GA 30904-3151

(Faculty Advisor Signature)


You are invited to the 46th AnnualGeorgia Mathematics Conference!

Rock Eagle

Conference

Center

October 20-22, 2005

is an official publication of the Georgia Council of Teachers of Mathematics

Cheryl HughesLandmark Christian School50 West Broad StreetFairburn, GA [email protected]

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Documents

In Memory of - GCTM · In Memory of Dr. Larry Elbrink 1941 ... Reviewers were able to ... worked at RESA for many years and continued to teach at