This graphic was created by Editor Cheryl Hughes using THINGLINK.com, a convenient tool to combine many media on
one topic. Check out all the links as you mouse over the
much is currently going on in mathematics in the state of Georgia!
The Common Core Georgia Performance Standards for Mathematics have
been revised for all grades, new courses have been created for high
schools, and some standards in the current high school courses are
being moved up to later courses. Additionally, the Georgia Milestone
Assessments will be implemented this spring for the very first time.
They will emphasize the appropriate rigor of the standards, and
students will be given the opportunity to write about their
conceptual understanding of the standards through constructed and
extended response questions. And, as if that’s not enough, classroom
teachers continue to face the challenges of finding or developing
exemplary resources and pedagogical strategies to best serve the
learning needs of our students.
The Georgia Council of Teachers of Mathematics is dedicated to the
promotion of ongoing professional development for mathematics
education as stated in our strategic plan. With this dedication in
mind, the GCTM Summer Academies will offer professional
learning to support teachers as they incorporate these changes into
their instructional planning. Details for the Summer Academies are
posted on our website and will be updated regularly. Additionally,
the GCTM Program Committee for the 2015 Georgia Mathematics
Conference, October 14-16, 2015, is hard at work, planning for
keynote and featured speakers who will bring fresh perspectives on
the implementation of the standards, incorporation of appropriate
resources, and tactical use of high-leverage teaching strategies.
There will also be a Conference-within-the-Conference for Leadership
on Thursday of GMC to address the needs of state educational leaders
and school district superintendents and curriculum leaders.
GCTM also is hosting Math Day at the Capitol on February 24,
2015, to emphasize the importance of mathematics education for the
students in Georgia and to provide our mathematics teachers the
opportunity to meet the legislators who debate and create
educational policies for us. Advocating for mathematics education in
Georgia is another key component of the GCTM Strategic Plan, and
Math Day at the Capitol is one of the ways we use to campaign for
the best opportunities for student learning.
Please contact your GCTM Regional Representative or any member of
the Executive Committee to offer your suggestions or questions as we
continue to serve you and your interests as a mathematics teacher.
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sure to check out the Thinglink at the top of this issue of
eREFLECTIONS for some great Pi-Day activities. This year is an
exceptional Pi-Day with the date being 3/14/15. Check out piday.org to find
some ideas and activities
you can use in your classroom.. You can find more ideas for Pi-Day at teachpi.org.
We would like to hear what YOU did to celebrate. Send us your Pi-Day pictures and comments
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GCTM exhibited at the STEM-Georgia Conference in
Athens, Georgia, on Oct. 20-21 in Athens.
The conference, sponsored by the Georgia Department
of Education, drew teachers and educational leaders in science,
technology, mathematics, and career education from all over the
GCTM’s booth, staffed by Debbie Kohler and Tom
Ottinger, included information about the Georgia Mathematics
Conference, our summer academies, competitions, grants and awards
for teachers, and advocacy for mathematics education. Our
participation in this conference was part of an effort to foster
cooperation with other professional associations and to increase
GCTM’s influence among educational and legislative leaders.
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Biennial Institute for Georgia Legislators is a 3-day
informational event for legislators sponsored every other year by
the Carl Vinson Institute of Government in Athens. Sessions are
designed to inform legislators about a broad range of issues that
the legislature will face during its upcoming session. As part of
GCTM's advocacy initiative, we, in concert with several other
subject area teacher organizations (GCTE (English teachers), GSTA
(Science Teachers), GCSS (Social Studies Teachers, etc.), staffed a
joint exhibit table to present information to legislators about
curriculum and standards. These teacher groups drafted a joint
statement about curriculum (available on the GCTM website) which we
promoted to legislators.
Dan Funsch, right, and Georgia Council of
Social Studies Executive Director Eddie Bennett, center,
talk with Senator Brandon Beach, Chairman of the Science and
Technology Committee (R-Alpharetta), left.
Dan Funsch, left, talks with
Representative Barry Fleming, Vice-Chairman of House
Judiciary and former House Majority Whip (R-Harlem).
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Second Editions of state tournament books (volumes 4
and 5) are now available online.
Order your PDF below!
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Georgia Council of Teachers of Mathematics (GCTM) will host the
second "Math Day at the Capitol" on Tuesday, February 24, 2015. The
event will provide an opportunity for legislators to hear the
importance of a quality mathematics education and to meet math
educators. The purpose of the day is to communicate with legislators
the necessity of having quality mathematics education in order to
support the development of mathematical literacy and proficiency
required for success in careers and in competition in a global
economy. Georgia’s economic growth will be enhanced by the
preparedness of its students, particularly in the STEM (Science,
Technology, Engineering, and Mathematics) areas.
A breakfast for the state legislators will be
provided from 8:30-10:00 AM in room 216 of the State Capitol
Building. If you are interested in attending this event, please
reply to the survey on the GCTM website and
contact your legislator to encourage him/her to attend the
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Georgia Mathematics Conference 2015
“Growing Student Potential in Mathematics”
by Tammy Donalson, 2015 Conference Board Chair
As mathematics educators, this is our motivation for
doing the job we love so much-----teaching! As we strive to help our
students reach their potential, we must continue to fill our “tool
boxes” with effective teaching practices. Once again this year GCTM
is providing one of the best opportunities for professional
development, the 2015 Georgia Mathematics Conference. This
year’s theme: “Growing Student Potential in Mathematics” is
built around the Eight Effective Teaching Practices outlined in
NCTM’s publication, Principals to Action.
The Georgia Mathematics Conference Board is busy
preparing for this great event and we need YOU. Every year, this
conference features many of Georgia’s best educators and we want to
continue to increase that number. There is no better place to show
off the great things that are happening in classrooms across our
state than at Rock Eagle. If you are willing to present or know
someone who would be willing to present, the speaker proposal forms
will be posted at the
GCTM website very soon or
Join us October 14 – 16, 2015 at Rock Eagle!
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seasoned teachers need PLU’s, so that is why I signed up for the
course from Stanford University, “How to Learn Math.” I had never
Jo Boaler, but being acquainted with Stanford, I expected
the class to be good! Little did I know how much I would enjoy it,
and how much I would learn.
I learned about “Growth Mindset” and how to make my classroom a
comfortable environment for making mistakes. Research shows that
when we make mistakes, realize them, and know how to correct them,
Another thing I learned was about Math Talks, or
Simply stated, these are conversations we have with our students
about different ways they understand numbers and problem solving. In
a whole class setting, a Number Talk celebrates that exciting fact
that students think through problems in various ways. Through these
conversations, our hope is that those students who have
misconceptions about how numbers work will be able to see how
numbers can make sense.
The directions on how to conduct Number Talks vary from publication
to publication and between age groups. Actually they can vary from
class to class, because what works for one group of students doesn’t
necessarily work for another. The chemistry of the group must be
factored into the method of delivery.
To begin, you might want to watch this video:
Here is a sample of an elementary class having a Number Talk.
Here are some good Number Talk questions to get the conversation
Math Talk Starters
Why did you choose this method?
How did you get this answer?
How did you know which operation to use?
Why is that the answer?
Prove your answer is correct
Did anyone think of doing this another way?
Have you seen a problem like this before?
How are these problems different?
What is the same about these problems?
So you are saying………
Would you share how to solve this problem?
Solve * Explain * Question * Justify
NCTM has published a PDF that explains the rationale
behind Number Talks. In the next 3 articles you will find the
specifics of how to conduct Number Talks for every grade level.
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Number Talks K-5
by Nicole Anderson and Vinita Prasad
Have you heard the buzz lately about Number Talks?
We are focusing on number sense all around the state of Georgia.
Sherry Parrish’s “NumberTalks” are short, 10-15 minute planned and
purposeful math discussions centering on mental math strategies.
Math instruction today needs to be more efficient
than it has been in the past. Many students have procedures for
solving math problems without determining whether their solutions
are reasonable. Many of us have never explored and manipulated
numbers in the way that our students are having the opportunity to
Here is some advice on implementing Number Talks
into your daily instruction.
How do I get started?
Number Talks should follow the instructional
Opening (Write the problem on the board.)
Work Time (Students are thinking of their
solutions and working on numerous strategies.)
Closing (Students share their answers and strategies
with the class and record them on chart paper/anchor charts. It is a
great time to discuss efficiency.)
Create a classroom environment that allows for
discussion. One suggestion is for all students to be sitting on the
carpet in the front of the room.
The state frameworks for each grade level has a
great graphic organizer to use when planning a Number Talk in your
Watch a variety of Number Talk videos.
Show the videos to your students as a way to introduce
the concept of Number Talks; students are easily motivated by other
students, and this is a perfect way to launch them.
Be prepared for silence the first few days. Your students
don’t know the expectations just yet and don’t have a variety of strategies.
They will go to the procedure immediately and may want the teacher to
re-write the problem differently so they can solve it “more easily.”
Teach number strings, or series of 3 to 4 problems that
build on the previous problem, (5+5; 5+1+5, 6+5).
Certain problems elicit different strategies, but it doesn’t
mean your students will automatically model the strategy that you want them to
Don’t appear to have all of the answers in front of your
students. This is your time to take a step back and be a facilitator and learn
what your students know about numbers and operations.
How do I get the most out of a Number Talks lesson?
Allow enough wait time; turn and talk (students talking to a
partner next to them) is a powerful way to support and engage all students.
Preview/scaffold number strings with struggling students. You
might want to meet with your struggling students the previous day and share with
them the string you will do as a class the next day. This will build their
Review the previous day’s anchor charts (previous day’s number
talks) in order to bridge student knowledge.
What do I do if I’m stuck?
Number Talks might be uncomfortable at times; allow yourself
to make mistakes and be uncomfortable with some of the strategies that the
students are sharing.
It would be beneficial for students to learn some of the
previous grade level strategies. For example, if you are starting out Number
Talks as a fifth grade teacher, your students don’t have all of the strategies
that have been built upon in the book.
Everything needed to implement Number Talks is included in the
Information on Number Talks is readily available all over the
web as well in the state frameworks.
Number Talks support TKES as well as the Standards for
Mathematical Practices. Building number sense is a marathon, not a sprint; it
will take time. For best results, Number Talks should be implemented on a daily
basis. You are already making a difference by just having them look at problems
and discover multiple ways to solve them.
*adapted from Number Talks, Sherry Parrish
Nicole Anderson and Vinita Prasad are currently Title I District
Math Coaches in Cobb County, Georgia. They have both presented Number Talks
sessions at Rock Eagle the past two years. Cobb County is in their fourth year
of Number Talks implementation.
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My Math One class thought they were stupid. They needed something
that was possible for everyone to do, and they needed to feel smart.
Tall task when you have students in the lowest percentile of the
When I heard about Number Talks, I thought they seemed a bit
juvenile. But then I thought about the kind of math problem that ALL
my students could answer correctly, and that kind of problem fit the
So I started with a simple calculation that they had to perform
mentally. (I hoped they wouldn’t think it was too easy.) Actually
they did, but they found the answer anyway. I went around the room
and asked each one HOW they did it, and I wrote their method on the
board with their name beside it. Strangely enough I got 4 or 5
different ways to do the problem before anyone repeated a way. When
the first girl had a repetitive method, she said, “I worked it Tom’s
way!” I looked at Tom and he was just beaming. It was HIS way, now.
That same event happened several different times as they each told
about their way. Everyone had their name on the board, with their
method beside it. You could sense the pride they felt, seeing their
name and their number understanding up there in front for everyone
The next time we had a Number Talk, I followed the same routine.
Thankfully they welcomed the Number Talk because of their positive
first experience. This time, after we had several different methods
of calculation on the board, I asked everyone to try Nathan’s
method. I said something like, “Just try it once, to see if it makes
calculating easier.” They did, and some even liked it. One girl
commented, “Wow, Nathan’s way is so much easier than mine. I’m going
to have to remember that!”
I continued to point out to them that just as we may work a problem
differently, we think differently, and we must celebrate the fact
that we are not all the same, making this world an interesting
There was an instance in the 3rd or 4th Number Talk, where I called
on a student who had an incorrect answer. I still wrote her name on
the board and her method of calculation. As she was telling me how
she arrived at the answer, she realized that her answer was
incorrect, and she self-corrected! In my opinion, that is our goal.
We want our students to realize their mistakes as they review their
work. It was a teachable moment.
In my search of resources for new Number Talks, I have found several
I will share with you. Here are some non-calculating ones I found:
Place the numbers 1 – 9 in the cells, one
number per cell. Be ready to share the reasoning behind your
The area below contains a
set of numbers. All of the numbers belong to the same group, except
for one number. Find the strange number in each set and circle it.
Then explain why you chose that number.
This article was written under a fictitious name for
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I use Number Talks each morning with my 2nd graders. They are part
of our morning routine. We discuss our math journals and then spend
5-10 minutes doing a Math Talk. I use them in a variety of ways: to
review math strategies we have learned, to apply known strategies to
new concepts, to practice finding patterns and to frontload new
My students began the year struggling with number sense. They knew
very few strategies for using mental math to solve problems. By
implementing number talks into our daily routine, I have been very
pleased with their progress. Students are learning to talk about
their ideas about Math in an open way without the fear of being
“wrong”. They consider it a challenge to find a new strategy or
pattern that they can use to solve the problems we are working. Even
those that struggle with new concepts and mental math strategies
have become comfortable enough to ask their neighbors questions
about how they figured out the problem.
Overall, my students have made a remarkable improvement in their
sense of how numbers work and can now implement a variety of
strategies to find the answer to a problem. Their sense of community
has benefitted as a result of these talks as well. Students are both
excited to share and eager to learn new patterns and strategies as
we work through problems together.
Chris Reed teaches at Hannan Academy, Columbus, Georgia.
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Your GCTM Membership matters…and so does that of
your colleagues! Some may think the only benefit of your membership
is our annual conference at Rock Eagle. Certainly it is a wonderful
enhancement of your daily classroom activities!
But GCTM offers much more….
A topnotch journal,
eREFLECTIONS, delivered quarterly!
Awards for teaching and leadership. Nominate worthy
Grant opportunities to bring an innovative idea to your
competitions across grade levels. Support of ARML team
who annually represent Georgia nationally, and always land
in the top 10!
Advocacy, for you and all Georgia teachers,
in keeping our government leaders aware of your concerns and
wishes for Georgia mathematics students.
Math Day at the Capitol is a dynamic vehicle for
face-to-face dialogue with legislators.
Collaboration with other subject area
organizations, such as
Leadership excellence from committed
An organization that is affiliated with
which offers benefits of national experts and successful
pedagogy ideas, so important in this time of national
curriculum renewal and concern.
Publication of practice problems for your
math team, and a resource that can be used throughout the
An outstanding dynamic
to bring you current news and information!
A long list of advantages…well worth $20 a year!
Maybe you can add other benefits from your membership. More
importantly, please share with your colleagues! And let us know what
we can do to make GCTM serve you better. You can reach us through
the website email links.
GCTM depends on you! Our history is rich, but it
needs you and your colleagues to continue to serve you for years to
You Matter to GCTM! We hope GCTM Matters to YOU!
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for up-to-date information about our Summer Academies.
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NCTM Notes is a featured column in each GCTM Reflections
publication. GCTM is an Affiliate of National Council of Teachers of
Mathematics (NCTM) and this column is intended to keep GCTM members
informed of NCTM services & events. All material in this column is
excerpted directly from NCTM e-blasts, updates and newsletters. It
is compiled by NCTM Representative, Dr. Dottie Whitlow.
The results of the NCTM 2014 election are in.
Congratulations to Matthew R. Larson, Nadine Bezuk,
John SanGiovanni, Denise Spangler, and Marilyn Strutchens! Read more
about the members elected to serve on the NCTM Board of Directors.
The NCTM Board sets the direction, establishes policy, and oversees
the activities of the Council. Board Directors serve three-year
terms. All terms begin at the conclusion of the NCTM 2015 Annual
Meeting and Exposition in April.
sadness, we note the death of Carol E. Malloy. Carol received the
NCTM Lifetime Achievement Award in 2013, wrote and edited
numerous NCTM publications, and served on the NCTM Board of
Carol Malloy passed away on January 17, 2015.
Book Your Room in Boston
NCTM's 2015 Annual Meeting & Exposition in Boston, April 15–18,
is now open. Reserve your room early for NCTM's headquarters
hotel—The Westin Boston Waterfront—or the many NCTM official hotels
near the Boston Convention & Exhibition Center to secure the best
possible rate. Guaranteed lowest rates with no booking or service
fees, networking opportunities, and complimentary shuttle service!
Housing is selling quickly–reserve your room today.
From NCTM Mathematics Teacher blog Joy and Inspiration in the
I enjoy student questions. They can be insightful, intriguing, and
stimulating. Questions can reveal a misconception or illuminate a
connection among ideas. But let’s be honest: Although student
questions are often energizing, they can also be enervating. They
can suck the wind right out of your sails.
Raise your hand if you have heard any of the following:
“When am I ever going to use this?” “Will this be on the test?” “Are
we doing anything important in class today?” “I was out yesterday.
Did I miss anything?” “How long will the test be?” “Do we have to do
this?” “Can I work with a different group?” “Can I have the homework
now?” “My assignment is not quite done/at home/in my other notebook.
Can I turn it in later?”
When you hear enough versions of these questions, they can become
numbing. I was becoming annoyed by them. But just as no student
truly wants to fail, no student asks a question just to annoy.
Honoring student voice means believing in good intentions. I
realized that what I was hearing in the questions was different from
what the students were trying to say. I started analyzing some of
these questions, working with students and colleagues to change the
conversation. As a result, I know more about what my students need
and can do a better job of meeting those needs.
Below is a chart that summarizes my research so far.
|The student says...
||The student might mean...
|“When am I ever going to use
“Why are we learning this?”
“How is this used in real life?”
|“Why is your class so boring?”
||“I am feeling overwhelmed.”
|“How long is the test? ”
||“Just tell me exactly what to do. ”
||“I am worried that I am not prepared for
|“Did I miss anything yesterday?
||“Was your planning for yesterday’s class
worthwhile, or did you end up wasting everyone’s time? ”
||“I am nervous that I may have missed
something significant when I was out. ”
|“Are we doing anything
important today? ”
||“I don’t value your class.”
||“I am having trouble following through on
my commitment to our class.”
When I have the presence of mind to reframe a
student’s question, the conversation is more productive and less
tense. Sometimes the rephrasing is only in my head, and sometimes I
ask the student directly, “When you ask [insert question from column
A], do you mean [insert translation from column C]?” Usually the
student will agree or clarify. One student who asked when he would
ever use a certain math procedure replied sincerely, “I was
wondering if this is used anywhere, or if it is just one of those
cool math things.” Priceless.
Uncovering the more revealing, substantial question
behind the demoralizing question is extremely satisfying. I am less
bothered, and the students are more engaged. And student voice is
honored. Students’ feelings are acknowledged, and their
contributions validated. They know that they are an important part
of the learning community.
have only scratched the surface of the topic of student questions.
Please help me expand the chart.
Kathy Erickson teaches
mathematics at Monument Mountain Regional High School in Great
Barrington, Massachusetts. She is chair of the editorial panel for
NCTM’s Student Explorations in Mathematics and is Rock, Paper,
Scissors commissioner for her school. She finds inspiration every
day in the mathematical questions, insights, and joys of her
students and colleagues.
Georgia College Student Receives $10,000
Reston, Va., September 9, 2014— Emily Baum, a rising
junior at Georgia College and State University in Milledgeville,
Georgia, has been awarded the Prospective 7–12 Secondary Teacher
Course Work Scholarship by the Mathematics Education Trust (MET) of
the National Council of Teachers of Mathematics (NCTM). The $10,000
scholarship, which is supported by the Texas Instruments
Demana-Waits Fund, will help Baum continue her undergraduate
studies in mathematics. Baum is from Cumming, Georgia.
The scholarship provides funding for tuition, books,
and other academic expenses to full-time university students who are
rising juniors preparing to become certified teachers of secondary
mathematics. Baum is majoring in secondary education mathematics.
“By providing my future students with an
understanding of math at the most basic level, I want to ensure them
that they have a strong foundation that will lead them to be more
qualified for either more complex mathematics classes in the future
or other aspects of life that require mathematics,” Baum said when
asked about becoming a math teacher. “I want to inspire students to
find a passion for math. Even if math isn’t something they want to
pursue, I want to make sure that no matter what profession they
choose, they will be successful at it because they have the
background knowledge necessary to do so.”
Baum earned the scholarship on the basis of her
academic achievement, extracurricular activities, and volunteer
community projects, all of which demonstrate the leadership,
dedication, and selflessness needed by a successful math teacher.
She is actively involved in two tutoring positions at her school.
Additionally, Baum has volunteered at a church preschool and a Boys
and Girls Club.
“Emily’s desire to help others learn is sincere, her
career goals are well planned, and she is excited about her future
as an educator,” wrote a former supervisor who recommended Baum for
the scholarship. “She has an innate ability to recognize and give
the motivation and encouragement each student needs—a wonderful
asset for an aspiring high school teacher!”
Another letter of support stated, “Emily also
demonstrates her dedication in that she is never satisfied with
taking the easy way by learning only the ‘what’ of a subject, but
she always looks for the ‘why’ and ‘how’—a much more difficult road
to follow in education.”
For more than 35 years, the
Mathematics Education Trust has channeled the generosity of
contributors through the creation and funding of grants, awards,
honors, and other projects that support the improvement of
mathematics teaching and learning. The trust provides funds to
support in-service teachers in improving their classroom practices
and increasing their mathematical knowledge and also provides funds
for prospective teachers.
National Council of Teachers of Mathematics is the public voice
of mathematics education, providing vision, leadership, and
professional development to support teachers in ensuring mathematics
learning of the highest quality for all students. With 80,000
members and more than 200 Affiliates, NCTM is the world’s largest
organization dedicated to improving mathematics education in
prekindergarten through grade 12.
Principles and Standards for School Mathematics includes
guidelines for excellence in mathematics education and issues a call
for all students to engage in more challenging mathematics. Its
Curriculum Focal Points for Prekindergarten through Grade 8
Mathematics identifies the most important mathematical topics
for each grade level.
Focus in High School Mathematics: Reasoning and Sense Making
advocates practical changes to the high school mathematics
curriculum to refocus learning on reasoning and sense making.
Principles to Actions: Ensuring Mathematical Success for All
describes the policies and actions required for a high-quality
mathematics education for all students. NCTM is dedicated to ongoing
dialogue and constructive discussion with all stakeholders about
what is best for our nation’s students.
Cullen, Communications Manager, 703-620-9840, ext. 2189.
The topic for our next issue is Three-Act-Tasks.
Your comments and submissions are welcome.
Cheryl Hughes and Becky
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Past President and
Treasurer – Dan Funsch
– Nickey Ice
Executive Director –
Membership Director –
NCTM Representative –
IT Director –
eREFLECTIONS Editor –
VP for Advocacy –
VP for Constitution and
Policy – Patti Barrett
VP for Honors and Awards –
VP for Regional Services
– Valerie Lemon
VP for Competitions –
Conference Board Chair –
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