Happy Birthday CRMCHappy Birthday CRMC

20 Years!20 Years!

Happy BirthdayHappy Birthday

20 + Years!20 + Years!

In mathematics there are In mathematics there are VARIABLES and CONSTANTSVARIABLES and CONSTANTS

During CRMC’s During CRMC’s twenty year history twenty year history there have been there have been many variables, many variables, but one constant.but one constant.

Ruby A. Ruby A. TuckerTucker

RR Responsible: Whatever task was asked of Ruby, Responsible: Whatever task was asked of Ruby, I was ALWAYS sure it would be well done.I was ALWAYS sure it would be well done.

UU Unassuming: Ruby is a wonderful unassuming Unassuming: Ruby is a wonderful unassuming person…there is not a pretentious bone in person…there is not a pretentious bone in her body! And she is always ready to give her body! And she is always ready to give credit to others.credit to others.

BB Beautiful spirit: It was a privilege to get to know Beautiful spirit: It was a privilege to get to know Ruby. She is a beautiful spirit and is the first Ruby. She is a beautiful spirit and is the first to see the beautiful spirit in other, especially to see the beautiful spirit in other, especially children.children.

YY Young at heart. Ruby’s energy keeps us young Young at heart. Ruby’s energy keeps us young at heartat heart

Helen P. CollinsHelen P. Collins

Whenever I think about my time at CRMC – Whenever I think about my time at CRMC – even beyond the PRIME camps – the one even beyond the PRIME camps – the one face I see every time is that of Ruby Tucker- face I see every time is that of Ruby Tucker- her smile, bright eyes and eager-to-be-of-her smile, bright eyes and eager-to-be-of-assistance-demeanor. The thing about assistance-demeanor. The thing about Ruby – you never really had to ask her to do Ruby – you never really had to ask her to do anything: by the time you’d figure out anything: by the time you’d figure out something needed doing, Ruby was always something needed doing, Ruby was always busy getting it done! What a real jewel!busy getting it done! What a real jewel!

Susan PruetSusan Pruet

Ruby is CRMC's value-added resource. She has a love and Ruby is CRMC's value-added resource. She has a love and appreciation for the great lessons and activities whose appreciation for the great lessons and activities whose dusty pages might be passed over for the glossy print. dusty pages might be passed over for the glossy print. Ruby always cheered when I dug out some of my favorite Ruby always cheered when I dug out some of my favorite activities on yellowed, faded pages or even purple ditto activities on yellowed, faded pages or even purple ditto sheets. She is a champion for the best mathematics for sheets. She is a champion for the best mathematics for every student. She has cheerfully served as a mentor and every student. She has cheerfully served as a mentor and coach. She has earned an advanced degree in cutting and coach. She has earned an advanced degree in cutting and pasting and an award for best supporting actress in the pasting and an award for best supporting actress in the Phillips/Tucker Road Show. Ruby's service to the Phillips/Tucker Road Show. Ruby's service to the mathematics community proves that the best things in life mathematics community proves that the best things in life and at CRMC are free. and at CRMC are free.

Thanks, Ruby.Thanks, Ruby. Kitty FoucheKitty Fouche

I was blessed to be able to work alongside I was blessed to be able to work alongside Ruby when I came to the Collaborative as Ruby when I came to the Collaborative as the secondary resource teacher. I learned the secondary resource teacher. I learned so much from her example then. I am so much from her example then. I am especially blessed, as is everyone especially blessed, as is everyone associated with the Collaborative that Ruby associated with the Collaborative that Ruby continues to be a shining example for all of continues to be a shining example for all of us. She is both a mentor and a friend! us. She is both a mentor and a friend!

Kenneth JonesKenneth Jones

Ruby A. Tucker PRIME ScholarshipRuby A. Tucker PRIME Scholarship

This scholarship, This scholarship, administered by the administered by the CSU Foundation, will CSU Foundation, will provide financial provide financial assistance to help assistance to help girls with financial girls with financial need attend PRIME need attend PRIME Camp.Camp.

CRMC First DirectorCRMC First Director

Helen Purks CollinsHelen Purks Collins1989-1995, 19981989-1995, 1998

CRMC…the earliest daysCRMC…the earliest days

1989: The Ford Foundation1989: The Ford Foundation

$ 8,000 matching grant $ 8,000 matching grant

to create a local urban math collaborative to create a local urban math collaborative

1989: The Ford Foundation 1989: The Ford Foundation

Existing Mathematics Collaboratives: Existing Mathematics Collaboratives:

ClevelandCleveland Minneapolis-St. PaulMinneapolis-St. Paul San Francisco San Francisco Philadelphia Philadelphia Los AngelesLos Angeles PittsburghPittsburgh New OrleansNew Orleans St. Louis St. Louis Raleigh-Durham Raleigh-Durham MemphisMemphis San DiegoSan Diego

We needed to We needed to write the grant…the original collaborative was write the grant…the original collaborative was

for high school teachers for high school teachers enlist area school system supportenlist area school system supportcreate a board of business and industry create a board of business and industry

leaders and educators (the collaboration)leaders and educators (the collaboration) raise $ 8,000raise $ 8,000

CADRE of TEACHERS CADRE of TEACHERS

Chattahoochee Council of Chattahoochee Council of Teachers of Mathematics, Teachers of Mathematics,

NCTM affiliateNCTM affiliate

Former Mayor Bill FeighnerFormer Mayor Bill Feighner Hosted luncheonHosted luncheon Helped develop the boardHelped develop the board

Gene Demonet,Chairman of the Gene Demonet,Chairman of the BoardBoard

Frank BrownFrank BrownJim BallengeeJim BallengeeJohn BolandJohn BolandJoyce LeeJoyce LeeGlenn VaughnGlenn VaughnRolla BaumgartnerRolla BaumgartnerBob BushongBob Bushong

Now what?Now what?

Birds of a FeatherBirds of a Feather

Ford Foundation Ford Foundation

$10,000$10,000

““NRM”NRM”

C to Shining CC to Shining C

Collaborative to Shining CollaborativeCollaborative to Shining Collaborative

$10,000 Travel Grant$10,000 Travel Grant

PRIMEPRIME

Positive Reinforcement Positive Reinforcement

in Mathematics Educationin Mathematics Education

Kitt Lumley Kitt Lumley

Ruby TuckerRuby Tucker

Woodrow Wilson FoundationWoodrow Wilson Foundation

Pam CoffieldPam Coffield

Statistics and Data AnalysisStatistics and Data Analysis

GeometryGeometry

Mathematical ModelingMathematical Modeling

Business and Industry

Mathematicians

Mathematics Teachers

Multiple grants per yearMultiple grants per year

High School TeachersHigh School Teachers

Middle SchoolMiddle School

ElementaryElementary

The Knight FoundationThe Knight Foundation

$30,000 for Prep PRIME$30,000 for Prep PRIME

Telephone call from KnightTelephone call from Knight

Think BThink BIIGGGGEERR

$250,000$250,000Algebra for AllAlgebra for All

Provided leadership Provided leadership

for initiatives for initiatives

for the state of Georgiafor the state of Georgia

Project ’92Project ’92SYNERGYSYNERGY

CRMC CRMC

$ 3,511,419.00

Birds of a FeatherBirds of a Feather

Improve math education for our students Improve math education for our students

Develop Teacher LeadersDevelop Teacher Leaders

CRMC!CRMC!

CRMC Second DirectorCRMC Second Director

Susan PruetSusan Pruet 1995-19971995-1997

CRMC Events 1997-1999CRMC Events 1997-1999

Great New Hires!Great New Hires! Elementary Math/Science CampsElementary Math/Science Camps MathFestMathFest CSU-Math Department/CRMC grantCSU-Math Department/CRMC grant

College Algebra through College Algebra through Mathematical ModelingMathematical Modeling

CRMC moved to Center for Excellence CRMC moved to Center for Excellence in Math/Science Education (CEMSE)in Math/Science Education (CEMSE)

My Favorite Problem from My Favorite Problem from ColumbusColumbus

FractionsFoodAnd…ughhDieting

Just in time for Thanksgiving!

Susan’s diet allows her to eat ¼ pound of Susan’s diet allows her to eat ¼ pound of turkey breast. She ordered ¼ pound of turkey breast. She ordered ¼ pound of turkey from the local deli.turkey from the local deli.

The sales person sliced 3 uniform slices, The sales person sliced 3 uniform slices, weighed the slices, and said, “This is a weighed the slices, and said, “This is a third of a pound.”third of a pound.”

So, how many of the 3 turkey slices could So, how many of the 3 turkey slices could Susan eat and stay on her diet and get to Susan eat and stay on her diet and get to eat as much as she is allowed?eat as much as she is allowed?

The Turkey ProblemThe Turkey Problem

CRMC Third DirectorCRMC Third Director

Ann AssadAnn Assad 1998-20041998-2004

Connecting the Dots: Seeing Connecting the Dots: Seeing the Whole Picturethe Whole Picture

Ann Assad Ann Assad

Austin Peay State UniversityAustin Peay State University

Clarksville, TennesseeClarksville, Tennessee

Emerging research and recently Emerging research and recently published documents guided published documents guided our work.our work.

National Council of Teachers of National Council of Teachers of MathematicsMathematics

Principles and Standards for Principles and Standards for School Mathematics School Mathematics (2000)(2000)

Emphasis on the Process StandardsEmphasis on the Process StandardsProblem SolvingProblem SolvingReasoning and ProofReasoning and ProofCommunicationCommunicationConnectionsConnectionsRepresentationRepresentation

Integration of Six Guiding Principles across the Integration of Six Guiding Principles across the StandardsStandards

• EquityEquity – high expectations and strong support – high expectations and strong support for all students.for all students.

• Curriculum Curriculum – a coherent curriculum, well – a coherent curriculum, well articulated across the grade levels.articulated across the grade levels.

• TeachingTeaching – challenging students and – challenging students and supporting their learning.supporting their learning.

• LearningLearning – actively building knowledge through – actively building knowledge through experience and prior knowledge.experience and prior knowledge.

• AssessmentAssessment – providing useful information for – providing useful information for both teacher and student.both teacher and student.

• TechnologyTechnology – influences the mathematics that – influences the mathematics that is taught and enhances students’ learning.is taught and enhances students’ learning.

Education Development CenterEducation Development CenterK-12 Curriculum Summaries K-12 Curriculum Summaries (1998, (1998,

2005)2005)

Provides information about research-Provides information about research-based curricula for elementary, middle based curricula for elementary, middle grades, and high school.grades, and high school.

Education Development CenterEducation Development CenterChoosing a Standards-Based Choosing a Standards-Based

Curriculum Curriculum (2000)(2000)

Provides guidance in reviewing standards-Provides guidance in reviewing standards-based curricula and for selecting and based curricula and for selecting and implementing curricula.implementing curricula.

Based on these documents, along Based on these documents, along with current research, CRMC with current research, CRMC developed a vision of P-12 developed a vision of P-12 mathematics education that mathematics education that integrated curriculum, teaching, integrated curriculum, teaching, and learning both horizontally and learning both horizontally (within grade levels) and vertically (within grade levels) and vertically (between grade levels).(between grade levels).

The implementation of this vision was the development of The implementation of this vision was the development of three integrated projects funded by Improving Teacher three integrated projects funded by Improving Teacher Quality State Grants (formerly Eisenhower).Quality State Grants (formerly Eisenhower).

High SchoolProject

Middle SchoolProject

Early ChildhoodProject

Teachers came together to share and learn.Teachers came together to share and learn.

Students and Students and teachers teachers worked together worked together in camps and in camps and classrooms.classrooms.

We relentlessly solved problems (and still do).We relentlessly solved problems (and still do).

A Question: What is the relationship A Question: What is the relationship between the area of a great circle of a between the area of a great circle of a sphere and the surface area of the sphere?sphere and the surface area of the sphere?

Data Collected by StudentsData Collected by Students

Area of Great Circle

(A1)

Surface Area of Sphere

(A2)

Ratio of A2 to A1

5 20.5 4.1022.8 88 3.86

12 41 3.423 12 4.00

1.25 5.25 4.20 Average 3.92

Data Collected by StudentsData Collected by Students

Area of Great Circle

(A1)

Surface Area of Sphere

(A2)

Ratio of A2 to A1

5 20.5 4.1022.8 88 3.86

12 41 3.423 12 4.00

1.25 5.25 4.20 Average 3.92

Area of a circle Area of a circle AAcc = = ππrr22

Surface area of a sphereSurface area of a sphereAAss = 4 = 4 π πrr22

A Ass÷A÷Acc = 4 = 4

Compare our results to the formulas for area.

Some problems to think about.Some problems to think about.

What is the minimum number of angle measures you need to have in order to know the measures of all the angles in the triangles represented here?

From Fostering Geometric Thinking: A Guide for Teachers Grades 5-10 by Mark Driscoll

Find four points in a plane that Find four points in a plane that can serve as the vertices for two can serve as the vertices for two different but congruent different but congruent quadrilaterals. quadrilaterals. ● ● ● ●● ● ● ●

From Fostering Geometric Thinking: A Guide for Teachers Grades 5-10 by Mark Driscoll

CRMC Fourth DirectorCRMC Fourth Director

Kitty FoucheKitty Fouche 2004-20052004-2005

““Wrap a string around the blob. Wrap a string around the blob. Then use the string to form a Then use the string to form a rectangle. Find the area of the rectangle. Find the area of the rectangle. This area will be the rectangle. This area will be the same as the area of the blob?” same as the area of the blob?”

I would say this was a very I would say this was a very creativecreative way to come up with the way to come up with the solution to this problem. I would solution to this problem. I would commend himcommend him for his for his intelligentintelligent and creative thinking.and creative thinking.

I would say he has I would say he has definitely definitely understood the concept of areaunderstood the concept of area..

I would tell him that his answer I would tell him that his answer was was very brilliantvery brilliant and would and would congratulate himcongratulate him..

I would say the student was I would say the student was rather rather ingeniousingenious to have thought to have thought of the method to find area. It of the method to find area. It shows he’s shows he’s thinking aheadthinking ahead and and knows what he is doingknows what he is doing. I would . I would praise him on his work.praise him on his work.

First I would comment that he/she has First I would comment that he/she has done a done a good jobgood job, and that this way is a , and that this way is a possibility. possibility. However, there is a simpler However, there is a simpler wayway. Simply do what she/he has done to . Simply do what she/he has done to start but a start but a rectangle may be difficult to rectangle may be difficult to formform. Simply form the string into a . Simply form the string into a square square or a triangle or even better simply or a triangle or even better simply measure the piece of string on a ruler and measure the piece of string on a ruler and the measurement will give you the areathe measurement will give you the area..

A very good start Karen! You are on the A very good start Karen! You are on the right track. right track. Isn’t that blob shaped more like Isn’t that blob shaped more like a circle?a circle? (Karen agrees and proceeds to (Karen agrees and proceeds to find the area of the circle.find the area of the circle.

Mouse and Elephant: Measuring GrowthMouse and Elephant: Measuring Growth

Middle Grades Project Middle Grades Project

byby

Fitzgerald, Phillips, Lappan, Winter, and Shrover Fitzgerald, Phillips, Lappan, Winter, and Shrover

Spaghetti and Meatballs for AllSpaghetti and Meatballs for Allbyby

Marilyn Burns Marilyn Burns

NCTM Illuminations LessonNCTM Illuminations Lesson

Apple PiApple Pi

A very good start Karen! You are on the right track. Isn’t that blob shaped more like a circle?

(Karen agrees and proceeds to find the area of the circle.

Finding the Area of a Circle: Use Finding the Area of a Circle: Use a Cake Pan and Leave Out the a Cake Pan and Leave Out the

PiPi

Arithmetic TeacherArithmetic TeacherMay 1986May 1986

bybyWalter Szetela & Douglas T. OwensWalter Szetela & Douglas T. Owens

Method 1Method 1

Counting squaresCounting squares

Take mean ofTake mean of

UnderestimateUnderestimateandand

OverestimateOverestimate

Developing an Area Formula for Developing an Area Formula for a Circle with "Goldilocks and the a Circle with "Goldilocks and the

Three Bears"Three Bears" Jerry A. AmeisJerry A. Ameis

Mathematics Teaching in the Mathematics Teaching in the Middle SchoolMiddle School

November 2001, November 2001, Volume 7, Issue 3, Page 140Volume 7, Issue 3, Page 140

Method 2Method 2

Inscribed and circumscribed Inscribed and circumscribed squares squares

Take mean of

Underestimateand

Overestimate

Method 3Method 3

Octagonal (Egyptian) methodOctagonal (Egyptian) method

Method 4Method 4

Weighing methodWeighing method

Method 5Method 5

Random numbersRandom numbers

Method 6Method 6

ParallelogramParallelogram

Area of Rectangle = Area of Rectangle = L WL WL ≈ ½ the circumferenceL ≈ ½ the circumference

L ≈ ½ (2 L ≈ ½ (2 ΠΠ r) r)W ≈ rW ≈ r

Area of Rectangle ≈ ½(2 Area of Rectangle ≈ ½(2 ΠΠr)rr)r

Area of Circle = Area of Circle = ΠΠ r r22

Method 7Method 7

Marble rectangleMarble rectangle

Understanding the area of a Understanding the area of a circle formula is as easy as Pi.circle formula is as easy as Pi.

Let’s get cooking.Let’s get cooking.

Title ??????Title ??????

Mary LindquistMary Lindquist

CRMC Fifth DirectorCRMC Fifth Director

Kenneth JonesKenneth Jones 2005-20??2005-20??

Where are the answers?Where are the answers?

Do we answer the Do we answer the questions or question the questions or question the

answers?answers?

How has CRMC survived for 20 How has CRMC survived for 20 years?years?

We’ve stood on the shoulders of giantsWe’ve stood on the shoulders of giantsWe’ve had the support of local school We’ve had the support of local school

systems, CSU, local businesses, and the systems, CSU, local businesses, and the local communitylocal community

We’ve been responsive to changeWe’ve been responsive to changeWe’ve empowered teachersWe’ve empowered teachersWe’ve questioned the answers rather than We’ve questioned the answers rather than

answering the questionsanswering the questions

Where do we go from here?Where do we go from here?

We have to continue to We have to continue to

Navigate the Trails of ChangeNavigate the Trails of Change

Navigating the Trails of ChangeNavigating the Trails of Change

A Mathematical ProblemA Mathematical Problem

From the NCTM Illuminations website. The complete lesson is available by going to www.nctm.org, going to the Illuminations section and searching for “maze.”

ImplicationsImplications

Even small changes can make a big Even small changes can make a big differencedifference

Big changes make and even bigger Big changes make and even bigger differencedifference

New paths are being added and old paths New paths are being added and old paths are being removedare being removed

It is not the strongest of the species that survive, nor the most intelligent, but the one most responsive to change.

- Charles Darwin

Vision is perhaps our greatest strength.. it has kept us alive to the power and continuity of thought through the centuries; it makes us peer into the future and lends shape to the unknown.

- Li Ka Shing

We have to continue to We have to continue to

Navigate the Trails of ChangeNavigate the Trails of Change

To provide more, and better mathematics for ALL students!

You know a dream is like a river, ever You know a dream is like a river, ever changing as it flows.changing as it flows.And a dreamer's just a vessel that must And a dreamer's just a vessel that must follow where it goes.follow where it goes.Trying to learn from what's behind you Trying to learn from what's behind you and never knowing what's in store and never knowing what's in store makes each day a constant battle just makes each day a constant battle just to stay between the shores.to stay between the shores.

And I will sail my vessel 'til the river runs And I will sail my vessel 'til the river runs dry.dry.Like a bird upon the wind, these waters Like a bird upon the wind, these waters are my sky.are my sky.I'll never reach my destination if I never I'll never reach my destination if I never try,try,So I will sail my vessel 'til the river runs So I will sail my vessel 'til the river runs dry.dry.

Too many times we stand aside and let the Too many times we stand aside and let the water slip away.water slip away.To what we put off 'til tomorrow has now To what we put off 'til tomorrow has now become today.become today.So don't you sit upon the shore and say So don't you sit upon the shore and say you're satisfied.you're satisfied.Choose to chance the rapids and dare to Choose to chance the rapids and dare to dance the tides. dance the tides.

Garth Brooks,Garth Brooks, song "The River" co-written with Victoria Shawsong "The River" co-written with Victoria Shaw

20 Years of Mathematics 20 Years of Mathematics along the Chattahoochee--along the Chattahoochee--

Let’s keep it going!Let’s keep it going!