The 2016-2017 school
year is up and running! It’s time for a brand new start with new
classes of students and renewed aspirations of a great year of
student learning. The possibilities are endless, and the
opportunities are great. That’s what the profession of teaching is
all about - the chance to contribute in a substantial way to the
growth and development of young minds with wide-open futures. And,
of course, mathematics teaching and learning affords a tremendous
opportunity to foster students’ analytic thinking and reasoning.
Each and every student
counts within the learning process, though each one is likely in a
different place along the continuum of mastery of the content
standards. This greatly increases the challenges of meeting
students’ needs and accelerating their learning potential. Consider
adding the support of the GCTM as a resource in your endeavors to
meet these challenges for your students.
The reason Georgia
Council of Teachers of Mathematics exists is to promote a high
quality of mathematics education for each and every student.
This statement binds us together in a common purpose and cause,
providing a backdrop for the decision-making processes used for
instruction and assessment.
The members of GCTM
accomplish this goal of promoting a high quality mathematics
education for each and every student by:
active interest in mathematics and in mathematics education
professional development for mathematics education
reward excellence in the teaching of mathematics in the state of
Our Georgia Mathematics
Conference is our flagship professional learning opportunity each
year that helps our members connect with one another and with local
and national experts in teaching and learning mathematics at every
grade level. It is scheduled for October 19-21, 2017, at Rock Eagle
4-H Conference Center in Eatonton, Georgia. The Georgia Mathematics
Conference each year promotes ongoing professional development for
mathematics education as well as encouraging an active interest in
mathematics. The theme for GMC 2016 is Principles to Actions:
What’s in Your Toolbox? Registration is now open! Visit our
to find all the details for this event as well as information on how
Similarly, the GCTM
Summer Academies for 2017 will be offered as yet another opportunity
to connect with teachers from all over the state in high quality
professional learning. Dates and locations will be shared soon on
our website and at the Georgia Mathematics Conference in October.
Stay tuned for registration details early in 2017.
GCTM offers several
awards and honors each year, and the deadline for these nominations
for 2017 is August 31, 2017. This provides an entire year to
intentionally watch for those teachers around you to share this
vision of a high quality mathematics education for every student.
We look forward to all
that this year will bring as you encourage and foster the growth of
Listening Sessions are being held in different locations in the
state. Check the GCTM website
home page and
scroll down to find upcoming sessions. The fourth annual Math Day at
the Capitol is being planned for the 2017 legislative session. The
date will be scheduled when the legislative schedule has been set
and the resolution can be read in the Senate on that day.
Four GCTM Executive
Council members attended the NCTM Affiliate Leaders Conference
in July. Those representatives were Kaycie Maddox, President;
Bonnie Angel, President-Elect; Rebecca Gammill, Publications Editor;
and Joy Darley, Vice President Constitution and Policy. There were
41 affiliates, 90 participants, and 28 states represented. The
following groups were present: Benjamin Banneker Association, Inc.,
National Council of Supervisors of Mathematics, TODOS: Mathematics
for ALL, Women and Mathematics Education, and National Council of
Teachers of Mathematics (NCTM). Our NCTM president, Matt Larson,
served as the keynote speaker throughout the conference.
From left to right: Rebecca Gammill, Kaycie
Maddox, Matt Larson, Bonnie Angel, and Joy Darley
Kaycie Maddox sharing advocacy strategies
with other affiliates.
The Conference Overview
& Goals were as follows:
for inspiring your Affiliate and individuals within your
Affiliate to take action for a high quality mathematics
education for ALL learners
to Actions resources
organizational elements that support the WHY of your Affiliates
Challenge leaders to
be deliberate about equity in your Affiliate’s structures,
practices, and activities
Learn about the NCTM
structure, resources, and initiatives, and participate in
discussions with NCTM President Matt Larson, NCTM Staff, and
Representatives of the Affiliate Services Committee
Develop or revisit a
strategic plan for your Affiliate by integrating ideas gathered
through discussion with Affiliate leaders
Network with other
Matt Larson spoke to the
participants about the qualities of good leadership and emphasized
the following: Good leaders start with why (vision,
values, and purpose) and how (strategy, engagement,
and empowerment) to achieve what (results, outputs,
outcomes, goals, and impacts). Matt Larson’s presentation included a
Ted Talk entitled, How Great Leaders Inspire by Simon Sinek.
job is not to do the work for others, it's to help others
figure out how to do it themselves, to get things done, and
to succeed beyond what they thought possible. (Simon
In addition, we were
reminded that action is needed to implement Social Justice in
Mathematics teachers and leaders must take
multiple actions to create and sustain institutional structures,
policies, and practices that lead to just and equitable learning
opportunities, experiences, and outcomes for children. These actions
must be part of a systemic plan for professional learning that
strives to democratize mathematics education—an education that is
just and equitable for all children. (Joint Position Statement from NCSM & TODOS)
Something new and fun that was presented was
Ignite is a presentation format where a presenter speaks while
slides advance automatically to support them. An Ignite presentation
is exactly 5 minutes and has 20 slides making each slide 15 seconds
on screen. It is promoted under the slogan, “Enlighten us, but make
Knowing your why is an important first step in figuring
out how to achieve the goals that excite members and create an
effective organization. GCTM’s purpose has always been to help all
students learn mathematics and has developed many strategies to
achieve this purpose. Our group has enjoyed quality leadership for
many years and is currently in “good hands.” All of us left inspired
and encouraged to do our very best work in 2016!
The 21 Indispensable Qualities of a Leader by
John C. Maxwell
Character - Be a piece of the rock. Charisma - The
first impression can seal the deal. Commitment – It separates doers
from dreamers. Communication – Without it you travel alone. Competence – If you build it, they will come. Courage – One person
with courage is a majority. Discernment – Put an end to unsolved
mysteries. Focus – The sharper it is; the sharper you are. Generosity – Your candle loses nothing when it lights another. Initiative – You won’t leave home without it. Listening – To connect
with their hearts, use your ears. Passion – Take this life and love
it. Positive Attitude – If you believe you can, you can. Problem
Solving – You can’t let your problems be a problem. Relationships –
If you get along, they’ll get along. Responsibility – If you won’t
carry the ball, you can’t lead the team. Security – Competence never
compensates for insecurity. Self-Discipline – The first person you
lead is you. Servanthood – To get ahead, put others first. Teachability – To keep leading, keep learning. Vision – You can
seize only what you can see.
Because of the efforts of our educators,
the nation is looking towards Georgia and the resources that are
provided for our math teachers. In July, NCTM brought the Summer
Interactive Institutes to Atlanta, dedicating July 11-13, 2016 to
kindergarten through 8th grade educators and July 14-16, 2016 to
high school teachers.
The first of the two institutes featured
several outstanding keynote speakers. Timothy D. Kanold
opened the institute by examining the difference between relevant
and meaningful mathematics for students. Kanold revealed the “six
secrets of effective instruction,” that include: (1) activating
prior knowledge; (2) establishing active peer-to-peer discourse; (3)
using a variety of tasks to engage students; (4) formative
assessment processes in the classroom; (5) becoming great at
balancing the rigor of the tasks you choose; and, (6) designing
great beginnings and endings. Harold Asturias concluded the
first day by discussing ways to provide each and every student with
opportunities to wrestle with, make sense of, and communicate about
mathematics. David Pugalee shared in both institutes a plan
for creating and implementing an effective mathematical writing
program. Robert Berry, III opened up the third day by using
Dylan Wiliam’s framework to focus on three key formative assessment
strategies that support the Standards for Mathematical Practice: (1)
engaging students in discussion, activities, and tasks that elicit
evidence of learning; (2) eliciting feedback that moves learning
forward; and (3) activating learners as resources for one another.
Karen Karp was the closing session speaker. In her session,
Karen shared foundational strategies and conceptual approaches for
effective mathematics teaching for students with disabilities.
Attendees participated Deep Dive
Sessions where discussions on the mathematical practices were
rooted in a content strand. Kindergarten through Grade 2 focused on
place-value structure of numbers, making sense of addition, and
making sense of subtraction strategies. Grades 3 through 5 dove into
understanding the number line. Participants answered questions that
addressed how linear measurement extend from whole to rational
numbers. For example, is 3x5 the same as 5x3? Additionally,
participants used contexts to develop two different
fraction-division algorithms. Grades 6-8 participants chose from a
ratio/proportional reasoning strand, which looked at the Big Ideas
and the ten essential understandings from ratios, proportions, and
proportional reasoning, and a statistics and probability strand,
which focused on data variability, investigating chance and bi-variate
The High School Interactive Institute
was kicked off by Margaret (Peg) Smith, who emphasized
effective teaching practices – a key component that supports
students’ learning - by guiding participants through The Bike and
Truck Context task. Dylan Wiliam enlightened participants on
what formative assessments are (and are not), why formative
assessments should be a priority, strategies and techniques to
implement formative assessments, and ways to support teachers in
changing their practice. Barbara Dougherty described common
misconceptions students have and strategies to help eliminate and
correct these misconceptions. She said we need to “change doing math
into thinking with math.” Cathy Seeley concluded by sharing
her thoughts on “processing and practicing what was learned” during
the institute. She answered the question, “what math do all students
need?” with what she called the Big Three: understanding mathematics
(make sense of it), do the arithmetic (skills, facts, procedures),
and use mathematics (thinking, reasoning, applying, and solving a
range of problems).
Task Discussion Groups met each
day of the High School Interactive Institute. These groups were
divided into Algebra 1, Geometry, and Algebra 2, and provided
participants with rich tasks that can be shared with others and
taken back to the classroom.
Both Interactive Institutes included
Breakout Workshops where math education practitioners engaged
participants in hands-on activities and strategies for implementing
these activities in the classroom. Many opportunities were provided
for networking with math educators across the nation and interacting
with keynote speakers and other presenters.
GCTM had a presence throughout both
institutes by setting up an information booth where participants
could ask questions and join our organization. The outcome was very
positive for GCTM by raising awareness of the benefits of being a
member and forming deeper connections with NCTM personnel. Several
math educators from outside the state of Georgia inquired about GCTM
and at least one joined! Hosting NCTM events in our area provides
opportunities for more Georgia educators to participate in these
wonderful learning experiences.
Congratulations to the
following winners of the Summer Learning Scholarship! These lucky
people received $200 to help defray travel costs to attend the NCTM
Summer Institute in July in Atlanta!
Ellison Sterling Elementary School
Sharpe, Janet Hutto, and Selena Head
Appling County Elementary School
Carver Road Middle
Griffin Spalding County
Arnold Mill Elementary
Clinch County High School
Big congratulations go to the
recipients of the Partners in Professional Learning Grant!
These pairs of educators received $1500 per pair to help pay
travel, lodging, and registration for the NCTM Summer
Institute! (Again, names and schools are in the spreadsheet.)
All three pairs of winners will be sharing what they learned at
the Georgia Math Conference at Rock Eagle!
South Columbia Elementary School
Julie Hernandez Bryan County Elementary
Groves High School
This summer we were privileged to attend NCTM’s K-2 Summer Institute in Atlanta through GCTM’s Partners in Professional Learning Grant. It was an incredibly valuable opportunity that we are very thankful to have been selected for. During our time at the Summer Institute, we learned many things that will help us to better serve our students. However, of all the things we learned, we feel that the most important concept was how our perceptions of certain teaching “tricks” have changed. Much of what changed our perception was due to Dr. Karen Karp’s moving keynote speech that focused on various mathematical rules that many of us teach every year in our classrooms. Unfortunately, many of these rules expire as our students advance into their later grades. One such rule is that “multiplication always results in a larger product”. Not true! For example, when we multiply a factor and a fraction, the product will be smaller than the original factor. Another faulty rule is “the more digits in a number, the higher its value will be”. Also not true! Which number has a greater value: 15 or 1.95?
Teachers do not intend to lay the foundation for students to struggle after they leave their classroom; however, some teaching practices are doing just that! Teachers unintentionally harm students’ learning when they teach tricks, shortcuts, and other rules instead of teaching to ensure a strong conceptual and mathematical understanding! Since we were inspired by this experience at the NCTM’s Summer Institutes, we have decided to share what we’ve learned at the Georgia Math Conference at Rock Eagle. Our session will expose some of the negative aspects of teaching tricks, shortcuts, and other rules in the elementary school setting. If you are interested in removing some of the unintentionally harmful practices in your teaching, we encourage you to join us for our interactive session!
the air will be getting cool, and the leaves will start to turn. The
stores will have pumpkin spiced everything, and we can look forward
to corn mazes, haunted houses, hay rides, and all kinds of ghouls
and goblins! This time of year is special for teachers—we get a new
group of students and all kinds of new beginnings. This time of year
also means it’s time to head to Rock Eagle for the Georgia
Mathematics Conference! Make your plans now! Many school districts
will pay for their teachers to attend conferences. You won’t know if
you don’t ask! GMC will be held this year October 19-21, 2016.
We have a great
conference in store for you. The Georgia Mathematics Conference is
for all mathematics teachers Pre-K-college. There are plenty
sessions at all grade levels. We have three wonderful keynote
addresses planned for Wednesday night, Thursday night, and Friday
will start our conference with a keynote address from Dr. Erica
Walker. Dr. Walker is a product of the Atlanta Public School System.
She taught high school and then earned her doctorate at Harvard. She
is now an Associate Professor of Mathematics Education at Teachers
College, Columbia University. Her opening keynote is “Math
Everywhere: Building Excellent and Equitable Learning Spaces Within
and Beyond Schools”.
evening, our keynote speaker will be Dr. Jenny Bay-Williams. Dr.
Bay-Williams earned her doctorate from the University of
Missouri-Columbia and is now a Professor of Mathematics Education
from the University of Louisville. She is an author of the popular
Elementary and Middle School Mathematics
Developmentally book series. Her keynote address is titled
“Pathways to Procedural Fluency.”
closing keynote address on Friday is from Pamela Weber Harris, who
teaches at the University of Texas. Ms. Weber Harris has a thriving
consulting business and is the author of the book series Building
Powerful Numeracy. Her keynote address is titled, “Building
Powerful Numeracy”. She is also doing some featured sessions, so
you’ll want to check those out!
We have also have great
featured speakers, including James Burnett all the way from
Australia! Other features speakers from right here in GA include:
David Custer, Graham Fletcher, Dr. Marrielle Meyers, Dr. Kevin
Moore, Dr. Pam Seda, Dr. Lisa Sheehy, Miranda Simmons, and Erin
Talley. Be sure to check out these sessions—you will not be
disappointed! See our full list of keynote and featured speakers at
Teachers, get ready to
head to the woods and learn new ways of engaging your students in
mathematics! We look forward to welcoming back old friends and
meeting a lot of new ones! Come fill your toolbox with new ideas
about teaching mathematics today.
June 20 and 21, Virginia Watson, Mary Garner, and Beth Rogers of
Kennesaw State University hosted 15 teachers in a math workshop
supported by the Lockheed Corporation, KSU’s Center for the
Advancement of the Teaching of Math and Science, KSU’s Center for
Excellence in Teaching and Learning, and the Metro Atlanta Math
Teachers’ Circle (MAMTC). The theme of the workshop was “Logistics
is Math” and focused on the logistical problems companies must solve
with the help of mathematics. The culminating event was a tour of
the Lockheed plant.
The workshop began with
one of the most famous problems in mathematics. It is easily
accessible to any student, but actually is unsolvable in its most
general form! It is the “traveling salesman problem.” A simple
version of the problem is shown below:
You must travel to
Macon, Charlotte, Birmingham, Asheville, Chattanooga, and Nashville.
You will begin and end in Atlanta and visit each city exactly
Find the tour of the
shortest length. Remember to explain how you know it is the
shortest length tour. How many tours are possible in this
situation? You can visualize the problem as a vertex-edge graph
with vertices being cities and edges labeled with the distance
between cities. (The distances from Atlanta to Nashville and
from Atlanta to Macon are labeled. Look up the other distances
strategies you used in trying to find the shortest length tour?
Was one strategy more productive than another? Will the
strategies always produce the shortest tour? Why or why not?
Suppose you decide
to add Tallahassee, Florida to the problem? How does the problem
change? How many possible tours are there? Will the strategies
you used above work here?
This problem includes
only seven cities, but you could include any number. There is
actually no efficient algorithm known to solve the problem for any
number of cities, but according to William J. Cook, author of In
Pursuit of the Traveling Salesman, the problem has been solved
for 85,900 cities. The computer code used to solve the problem is
available over the internet and called Concorde; in addition,
the solution was used in a situation where the cities represented
locations of connections that must be cut by a laser to create a
Cook describes a variety
of unexpected applications of the TSP involving mapping genomes,
aiming telescopes, gathering geophysical seismic data and other
problems that are “wildly distant from actual salesmen planning
their tours.” The TSP is one of many “NP-complete” problems. “NP”
stands for non-deterministic polynomial time, and indicates that
there is no known algorithm for efficiently solving the problem in
reasonable computer time (unless you want to run parallel computers
to the end of time perhaps).
The Metro Atlanta Math
Teachers’ Circle meets the second Monday evening of September,
October, November, January, February, and March from 6 to 8 PM.
Dinner is provided. Join us for a fun night of mathematics! Contact
Virginia Watson at
firstname.lastname@example.org if you’d like to join us!
teaching any particular class, I can look out at the sea of students
and see a variety of behaviors. I can see the students who are
intently engaged and hooked on every word I say. They are feverishly
writing down all notes on their paper or tablet. I can see the
students who are listening but not writing. Since I provide the
completed lecture notes after class, they can listen first, then
review later. I can see the students who are staring at the computer
screen. They are probably looking at the lecture notes that I’m
discussing now. I also see the students who are also using their
phones to “take notes”.
How do I know that they
are actually understanding the material? I will ask a question and
give them all wait time to think about it! I ask, “How can we change
this observational study into an experiment?”, and 2 out of the 42
mumble something. “One more time and louder please. Yes!! That’s it.
You have it!” I reply. So what about the other 40? What are they
Keisha Brown is an Assistant
Professor of Mathematics at Perimeter College of Georgia State
University. She completed her Master’s degree in Mathematics
Education from Georgia State University in 2007 and Master’s degree
in Applied Statistics from Kennesaw State University in 2012. She is
interested in research about students’ perceptions of learning.
GCMT would like to
congratulate the team of U.S. high school students for bringing home
a gold medal for their performance at the 57th annual International
Mathematical Olympiad in Hong Kong. For For the second consecutive
year, the US team grabbed the top spot, and this year included two
Members of the winning
2016 U.S. team were Ankan Bhattacharya, Michael Kural, Allen Liu,
Junyao Peng, Ashwin Sah, and Yuan Yao, all of whom were awarded gold
medals for their individual scores. Team members Liu and Yao each
earned perfect test scores. The team was accompanied by Loh and
deputy coach Razvan Gelca, professor of mathematics and statistics
at Texas Tech University.
Find out more about this
winning team through the following resources.
Do you know a teacher of
mathematics that goes above and beyond their job description to
assure their students are successful? Now is the perfect time to
stop and recommend this person for a well-deserved GCTM honor/award.
The rules for making a nomination have been changed to make it
easier than ever to submit the name of a special educator that truly
makes a difference in the lives of their students for a GCTM
honor/award. No longer does the person making the nomination need to
be a member of GCTM, except in the case of the Gladys M. Thomason
Award. This means any teacher, coach, administrator, parent, or
student is now eligible to submit a great candidate for any of the
other appropriate honors/awards.
Gladys M. Thomason Award for Distinguished Service :
Each year, GCTM selects one outstanding individual as the Gladys M.
Thomason Award winner. Selection is based on distinguished service
in the field of mathematics education at the local, regional, and
state levels. To be eligible for the award, the nominee must be a
member of GCTM and NCTM; be fully certified in mathematics,
elementary or middle grades education at the fourth year level or
beyond -- or if the nominee is a college professor, be at least an
assistant professor; and have had at least five years teaching or
supervisory experience in mathematics or mathematical education in
Dwight Love Award:
This award is presented to a teacher in Georgia who models
excellence in the profession and in life and gives much to others
beyond the classroom as mentor, teacher and leader. The awardee is a
master teacher, professionally active, and promotes GCTM and its
John Neff Award :
This award is presented to a member of GCTM who demonstrates
excellence as a full time post secondary educator and/or district
supervisor. The recipient is someone who is an inspirer, a mentor,
and an advocate of mathematics and mathematics education.
Awards for Excellence in the Teaching of Mathematics :
Three awards, one each for elementary, middle, and secondary levels,
are given to excellent teachers who have strong content foundations
in mathematics appropriate for their teaching level, show evidence
of growth in the teaching of mathematics, and show evidence of
professional involvement in GCTM and NCTM.
Teacher of Promise Award :
GCTM recognizes one outstanding new teacher/ member in the state
each year who has no more than 3 years experience at the time of the
nomination and who demonstrates qualities of excellence in the
teaching of mathematics.
Do you have great ideas for activities and lessons for your
students, but just do not have the materials to implement them in
your classroom because there is no money available through your
school, system, or PTA? GCTM can help! GCTM offers mini-grants in
any amount up to $300 and special project grants to support larger
projects that focus staff development, conferences, curriculum
development, task forces, research projects, and other initiatives.
For more information,
please visit the
Grants Page to send us your application. Be sure to make it
simple for those voting on your grant to understand the purpose of
your lesson, why you need the items you are requesting, and why you
need help with funding. GCTM wants to help YOU!
In the Summer Issue of
Reflections, we polled our readers as to the content they were most interested in reading over the next year. Now the results are in! Thank you to all those who took the time to complete the survey. We hear you and hope to include these topics in the near future.
Question 1: What is the most important topic
you’d like to see in Reflections?
Question 2: What is the second most important
topic you’d like to see in Reflections?
Question 3: What is the third most important
topic you’d like to see in Reflections?
Question 4: What is the least important
topic you’d like to see in Reflections?
The least important
topics for our readers included Social Justice and Mathematics,
Student Test Prep, and a Problem of the day.
With respect to
accessibility, 85% of our readers would like the ability to comment
or respond to articles within Reflections as well as be able
to download a PDF of the Reflections Issue. Seventy-five
percent of our readers access Reflections via email while the
other 25% use both email and our website to view Reflections.
Based on this reader
feedback, Reflections welcomes papers, lessons, and
reflections that highlight or focus on the following topics:
Of course, other topics
will always be considered for publication, so if you have a lesson,
research, or a narrative to share with our readers, please send a
Additionally, we would
like to continue to include student mathematical artwork within our
issues. So, if you find your students are creating mathematics in
your classroom, show off their work within this larger forum by
sharing it today. Just don’t forget to include the student release
forms provided by your school district so that we can legally
publish this student artwork in our publication.
School Classroom Resources As you plan for engaging & interactive lessons, remember
that NCTM has a link on its website for Classroom Resources!
You will find:
Illuminations (Lesson plans & Interactives for all
grades, Pre-K through 12)
Explorations in Mathematics
Activities with Rigor and Coherence (ARCs)
Each ARC is a
series of lessons that addresses a mathematical topic and
demonstrates the vision of Principles to Actions:
Ensuring Mathematical Success for All. These lessons
scaffold effective teaching and support enactment of the
eight Mathematics Teaching Practices articulated in
Principles to Actions as well as the instructional
guidance set forth in 5 Practices for Orchestrating
Productive Mathematics Discussions. ARCs integrate a
wide array of NCTM resources to optimize opportunities for
learning, including Illuminations and Student Explorations
in Mathematics. ARCs also include community features that
offer opportunities for social interaction. Engage in online
discussions with other math educators, post a comment, and
give feedback with ratings and reviews.
You may be interested in NCTM’s perspective on Teacher
Evaluation that can be found in a new Position Statement.
NCTM states that teacher effectiveness is one of the most
important factors in student learning and success. Teachers
and students can benefit from a comprehensive system of
teacher evaluation that considers data over time from
multiple domains of professional practice. Evaluation of
teachers should be based on multiple factors, not just one
and the goal of teacher evaluation should focus on the
development and growth of teachers that can lead to
effective mathematics instruction. To read the entire
position statement, visit NCTM.org and click on Standards &
NCTM Annual Conferences – NCTM will be moving its Annual
Conferences from April of each year to September, beginning
April 2017 – San Antonio, TX
April 2018 – Washington, DC
April 2019 – San Diego, CA
September 2020 – St. Louis
September 2021 – Atlanta
New Innov8 Conference
Early bird registration through October 14, 2016.
Check out the newly
revised NCTM website, nctm.org, to learn more about these
NCTM Vision: The National Council of Teachers of Mathematics is
the global leader and foremost authority in mathematics
education, ensuring that all students have access to the highest
quality mathematics teaching and learning. We envision a world
where everyone is enthused about mathematics, sees the value and
beauty of mathematics, and is empowered by the opportunities
mathematics affords. (Approved by the NCTM Board of Directors, October 20, 2012)