has started again for the 2015-2016 year, and it is ripe with
possibilities. Plans for the year include so many meetings that is
seems that one could not possibly fit all of them within one
preplanning calendar. What will this new year bring?
My daughter is a high school mathematics teacher and has just
started her fifth year of teaching. During pre-planning this year,
her school hosted an open house for the students and their parents
to allow them to meet their teachers and to become acquainted with
their new schedules. One particular parent introduced herself to my
daughter and asked her if she is related to the Mrs. Maddox that
used to teach at the school where I served for eighteen years. Sure
enough, that was the case, and the parent divulged that I had been
her mathematics teacher in the eleventh grade. As my daughter
related this story to me, my mind raced back through the all the
years I taught in that school to see if I could spot this student in
my memory. I imagined class after class of students, but,
unfortunately, I couldn’t picture her even now knowing her name. I’m
much better with faces than names, so I then turned to the
consideration of what this parent remembered about her experience in
my class way back then.
I began my career in education with hopes of leading the masses of
students, like the Pied Piper, to the utopia of complete
mathematical understanding. The reality was, however, that I often
underserved my students for shear lack of understanding on my part
about how to help them learn. Teaching is, after all, a craft that
must be molded and shaped and customized to meet the needs of
students with the end goal of empowered student learning. I
completely missed that idea early on and only realized it through
the help and guidance of some key deep-thinkers who invested their
wisdom into my life and faltering career. So I began to wonder if I
needed to draft an apology letter to this parent to ask forgiveness
for the mess I made of her eleventh-grade math class. I hoped she
had come along later in my teaching career when my craft was much
more honed and targeted. I listened carefully as my daughter related
the rest of the story.
This parent, my former student, had a very vivid memory of being in
my class, but it had nothing to do with any of my instructional
strategies or lack thereof. Apparently, the eleventh grade had been
a ruthless year for her that was filled with overwhelming personal
problems. She remembered that I had talked her out of dropping out
of school, and she stated that she went on to graduate from high
school on time. A successful college career came next, followed by a
job and a family. So this turned out to be a very happy memory of
being a student in my class after all.
I have no recollection of such a conversation with any particular
student. Of course, the foundational reason I went into teaching was
to touch the lives of students for the good. I genuinely liked
teenagers and felt a calling to devote my life to their advancement
through the study of mathematics. I often questioned, though, at the
end of one of those really hard days or weeks when nothing seemed to
go right in the classroom if I was helping anyone to advance towards
any goal. What a delight to find out I had helped someone find her
way along life’s journey!
It only stands to reason that the relationships formed with students
are even more important than the academics they are asked to learn
and we are required to teach. I can honestly say that I have never
met a classroom teacher who doesn’t care about students and want the
very best for the group they’ve been assigned. It’s hard to fake a
devoted, compassionate spirit, and students pick up on those who
avidly pour themselves into their lives. I hope you’ll take the time
this new school year to rededicate yourself, whether it’s your fifth
year or your thirty-fifth year, to being poured into the lives of
A teacher affects eternity; he can never tell where his influence
the new editor of Reflections, I sincerely hope that this
publication continues to serve the needs of our readers. You will
likely notice that we have made a few changes to the publication.
For one, we have dropped the “e” from the journal’s title,
streamlining the name to Reflections. Additionally, we’ve
made (or soon will make) several formatting changes throughout.
Mostly, we are striving to come up with ways for this important
conduit of Georgia-specific information to be more accessible to all
our readers. For now, the journal is completely online, and we will
continue to distribute it to our readers via their email accounts.
You may also access Reflections from
after signing into your GCTM account. We are investigating
accessibility options for our readers who have reduced access to the
internet, so please stay tuned.
This year, Reflections will focus on the theme of “Diving
Deeper,” and will highlight topics that our readers have told us are
important to them—hands-on activities, technology, statistics, and
proofs. As always, we are looking for content that describes
innovative, clever, and creative ways to teach mathematics. Do you
have an effective statistics lesson you’d like to share? Are you
using technology in your classroom that mathematically engages and
excites your students to learn mathematics? Have you recently used a
proof that helped your students derive rules and formulas for
themselves? What is your favorite problem-solving activity that
helps students make meaning of the mathematics they learn? If you
are willing, please check out our
Call for Manuscripts page and consider providing content for us.
Do you have ideas, but are not sure where to begin? Feel free to
email me at any time for advice on getting started. I look forward
to hearing from you!
a fraction strictly between 48/97 and 49/99 with the smallest
possible denominator! Play a game like rational tangles or frogs and
toads. Learn about graph theory, transfinite numbers, magic squares,
or codes and ciphers. Tackle games, puzzles, card tricks, or magic.
Use origami to make a stellated octahedron. Any of these
activities could be observed in a meeting of the Metro Atlanta Math
Teachers’ Circle (MAMTC).
The MAMTC is one of a nation-wide network of math teachers’ circles
that have been established over the last ten years with the support
and direction of the American Institute of Mathematics (AIM).
Visit this link to see how the circles are distributed across
the country. The goal of the MAMTC is to bring together middle
school, high school, and university mathematicians to work
collaboratively on interesting mathematics, and enhance
participants’ problem solving skills and enjoyment of mathematics.
Circles for students began in this country in the early 1990’s and
were influenced by those in Eastern European and Asian countries.
The American Institute of Mathematics (AIM) began the first Math
Teachers’ Circle in 2006 at the suggestion of Mary Fay-Zenk, a
middle school teacher and veteran math team coach who regularly
attended meetings of the San Jose Math Circle with her students.
From 2007 to 2014, AIM held a series of workshops on How to Run a
Math Teachers’ Circle. These workshops, sponsored by the
National Security Agency, the National Science Foundation, and the
Mathematical Association of America, helped teams of teachers and
mathematicians start and sustain math teachers’ circles in their
local areas. AIM maintains a support network and website at
MAMTC began with Dr. Virginia Watson of Kennesaw State University (KSU).
At the 2009 Joint Mathematics Meetings in Washington DC, Dr. Watson
attended a talk where she learned about math teachers’ circles. She
returned to Atlanta and assembled a team of KSU faculty, middle
school administrators, and middle school teachers. Dr. Watson, Dr.
Mary Garner of KSU, Ms. Angelique Smith, Principal at Champion Theme
School, Ms. Barbara Johnson, a middle school teacher at Champion
Theme School, and Dr. Brian Davis, Assistant Principal at Pine
Mountain Middle School attended a How to Run a Math Teachers’
Circle Workshop at the American Institute of Mathematics (AIM)
that summer. At this workshop they planned the launching of the
Metro Atlanta Math Teachers’ Circle (MAMTC), the first of its kind
Currently the MAMTC meets the second Monday of the month in
September, October, November, January, February and March. We have
dinner and work on the problem of the day. Our circle membership has
expanded beyond the initial two schools to include middle school and
secondary school teachers in the Metro Atlanta area. We are actively
recruiting in Cobb County and have a Facebook page at
Dr. Watson at
email@example.com and join the MAMTC for some fun
Virginia Watson is a graph theorist with 26 years of teaching
experience at Kennesaw State University. She is a member of NCTM,
MAA and the SIGMAA on Math Circles for Students and Teachers. Dr.
Mary Garner is Professor Emeritus of Mathematics at Kennesaw State
University. Now in retirement, she runs in math circles, and hopes
to start (with Virginia Watson) a non-profit organization called the
Gateway Community Math Center (GCMC). Through GCMC we hope to bring
math circles activities to libraries, museums, schools, the street
Kennesaw State University also offers a Math Circle Summer Camp for
high school mathematics students. More information about their
program may be found at the links below.
Emory Math Circles for Middle and
High School Students
Mathematical circles are a form of outreach that
bring mathematicians into direct contact with pre-college students.
These students, and sometimes their teachers, meet with a
mathematician or graduate student in an informal setting, after
school or on weekends, to work on interesting problems or topics in
mathematics. The goal is to get the students excited about the
mathematics they are learning and to give them an encouraging
setting where they can become passionate about mathematics. Athletes
have sports teams through which to deepen their involvement with
sports; math circles can play a similar role for kids who like to
Emory Math Circle started in the spring of 2014,
after Sarah Trebat-Leder introduced the idea to other Emory math PhD
students. Through her experience in running a math circle and other
math enrichment activities in college, Ms. Trebat-Leder thought that
Atlanta could benefit from similar programs. Thanks to the support
of the Emory Math and Computer Science Department, this program was
given classrooms to use, money for supplies, and a website and email
account on the department servers.
the beginning, two groups met each Saturday at 2:00 pm in the Emory
Mathematics building. Group Euler is intended for students in grades
9 through 12 (and a few younger participants) who are ready for
something significantly more challenging, rigorous, and fast-paced
than a normal math class. The students’ mathematical background
coming to the circle is proficiency with algebra and basic geometry.
Most have done some extra-curricular math before and are already
passionate about mathematics.
Fermat is intended for students in grades 6 through 9 who are
interested in solving puzzles, finding patterns, and figuring out
why and how things work. These students, who have a background in
pre-algebra, probably haven’t done any extra-curricular math before.
They may not necessarily be the top of their mathematics class and
may be unsure as to whether math is something they are passionate
about. However, they generally pick up concepts and make connections
easily compared to their peers.
Neither of the groups focus on competition math. The
focus of the Fermat group is to make math fun by including lots of
Nim, YouTube videos (see Vi Hart examples below), and hands-on
activities such as an origami dodecahedron. In group Euler, sessions
tend to be more traditional and include topics such as the different
types of infinities, complex numbers, and RSA cryptography.
Both groups generally do a different topic each week
so that students may miss a meeting without falling behind. While
some math circles have one primary instructor who teach every week,
the Emory Math Circles have a core group of instructors, Emory
graduate students, and guest speakers who teach regularly and
present mathematical topics and problems.
Math circles work to provide a social context for students who enjoy
learning new, challenging mathematical concepts. If you are
interested in starting a math circle, there are several options from
which to choose in order to get started. The focus of math circles
vary from Olympiad competitions, informal sessions using games and
hands-on activities, and traditional enrichment classes. While some
advertising at the start of a math circle is important, too much
advertising tends to attract students who are looking for remedial
tutoring or who are being forced to attend by their parents. After
our first session, we have mainly relied on word of mouth to attract
more participants. Also, keep in mind that it can be a challenge to
recruit enough instructors. Consider reaching out to students and
professors at nearby universities, and offer some perks for helping
with math circle, such as free lunch.
are some wonderful resources to start up a math circle in your area:
Sarah Trebat-Leder graduated from Princeton
University in 2013. She is currently a third-year mathematics Ph.D.
student at Emory University, and the director of Emory Math Circle.
Her non-math hobbies include board games, hiking, and Doctor Who.
Amanda Clemm graduated from Scripps College in 2012.
She is currently a fourth-year mathematics Ph.D. student at Emory
University, and the co-director of Emory Math Circle. Her non-math
hobbies include volleyball, baking, and playing with her dogs.
Here are some Math Circle problems for you to share
In the number 1234567890, 1 is divisible by 1,
12 is divisible by 2, 123 is divisible by 3, but 1234 is not
divisible by 4. Find a 10 digit number where each digit is used
exactly once and the number formed by the first n digits is
divisible by n for all 1 ≤ n ≤ 10.
Hint: Think of this problem as being like a Sudoku puzzle,
but requiring knowledge of divisibility rules.
How many pieces can you cut a round pizza into
using n straight cuts? The pieces do not need to be the same
size or shape!
Hint: Start with drawing pictures for small values of n, and
try to find a pattern.
Active learning is fundamental to meeting the needs of early
adolescents. The National Council of Teachers of Mathematics (NCTM)
has long promoted pedagogical methods that require students to be
intellectually engaged in constructing new knowledge with conceptual
understanding (NCTM, 2000; NCTM, 2014). Instructional strategies
centered on active learning include problem-solving tasks,
questioning, and inquiry. Additionally, social and physical
activities are also important instructional strategies included in
The purpose of this article is to discuss a framework for thinking
about active learning in middle-grade mathematics classrooms (see
Figure 1). Middle grades students respond well to active learning,
but there are different ways of thinking about activity in the
classroom. Instructional strategies that require students to be
intellectually active should certainly be at the heart of any
mathematics lesson; however, early adolescents need other types of
active learning strategies as well, and mathematical problem solving
promotes this activity. A Venn diagram was purposefully selected to
represent the active learning framework. There are several
instructional methods that simultaneously address multiple
categories of intellectual, social, or physical activity.
Susan Edwards is an assistant professor at Georgia Regents
University in Augusta, Georgia. She teaches middle grades and math
education courses to pre-service and in-service teachers. Her
research interests center around active learning in the middle
school classroom. She is also the author of the book, “Getting Them
to Talk: A Guide to Leading Discussions in the Middle Grades
Classroom” published by the Association for Middle Level Education.
The 2015 Georgia Mathematics Conference promises to
be a great experience. Our conference theme is "Growing Student
Potential in Mathematics" with emphases on the Mindset work of Carol
Dweck and the Eight Effective Teaching Practices for Mathematics as
outlined in the NCTM publication, Principles to Action: Ensuring
Mathematical Success for All.
The conference will be held at the Rock Eagle 4-H
Conference Center, Wednesday October 14 - Friday, October 16, 2015.
On Thursday a special “conference-within-a- conference” will address
leadership in mathematics education and will offer opportunities for
state, district, and school leaders to interact with nationally
known experts in the field and to collaborate with and learn from
their peers. Although these sessions will focus on leadership they
will be open to all conference participants.
Diane Briars - president of the National
Council of Teachers of Mathematics (NCTM), an 80,000-member
international mathematics education organization.
Previously, Briars was a mathematics education consultant,
working primarily to support schools and districts in their
interpretation and implementation of the Common Core State
Standards for Mathematics. She has also been a senior
developer and research associate on the Intensified Algebra
Project, a joint venture of the Learning Science Research
Institute at the University of Illinois at Chicago and the
Dana Center at the University of Texas at Austin. This
project, which is funded by the National Science Foundation,
focuses on developing instructional materials for
underprepared ninth-grade Algebra 1 students. Previously,
Briars was mathematics director for Pittsburgh Public
Schools. Under her leadership, Pittsburgh schools made
significant progress in increasing student achievement
through standards-based curricula, instruction, and
David Dockterman – Dr. Dockterman is the
chief architect of learning sciences at Scholastic Education
where he provides guidance on turning research into practice
and programs. He is an adjunct lecturer on education,
technology, and innovation at the Harvard Graduate School of
Education. Dockterman has dedicated himself to supporting
classroom teaching and the successful integration of
technology into schools.
David Foster – David Foster is the
executive director of the Silicon Valley Mathematics
Initiative (SVMI) comprised of over 160 member districts in
the greater San Francisco Bay Area. He consulted with PARCC
and developed exemplars for SBAC. He is Co-Chair of the
advisory committee of the Mathematics Assessment Resource
Service/Balanced Assessment and is a consultant to the Urban
Math Leadership Network that works with the 25 largest
school districts in America.
Baruti Kafele – Principal Kafele has been a
highly regarded urban public school educator in New Jersey
for over twenty years. As a principal, he led the
transformation of four different schools, including “the
mighty” Newark Tech, which went from a low-performing school
in need of improvement to recognition by U.S. News and World
Report Magazine as one of America's best high schools. He is
the author of seven books which include his national
best-sellers, Motivating Black Males to Achieve in School
and in Life, Closing the Attitude Gap, and his
recently released title, The Principal 50: Critical
Leadership Questions for Inspiring Schoolwide Excellence.
Other featured speakers include:
Sybilla Beckman-Kazez is a Josiah Meigs
Distinguished Teaching Professor in the Mathematics Department
of the Franklin College of Arts and Sciences at the University
of Georgia. Her current research is on the mathematical
education of teachers and mathematics content for children from
prekindergarten through grade eight. She is the author of
Mathematics for Elementary Teachers.
Christine Franklin is a senior lecturer, the
undergraduate coordinator and a Lothar Tresp Honoratus Honors
Professor in the Statistics Department of the Franklin College
of Arts and Sciences at the University of Georgia. She has
served as the lead faculty adviser with Advanced Placement
Statistics and is the author of two statistics textbooks.
Cindy Moss is the director of global STEM
initiatives for Discovery Education, charged with supporting
school districts in their work to develop and deploy student
initiatives to drive science, technology, engineering and math
Sherry Parrish is a national board certified
teacher, a recipient of the 1997 Presidential Award for
Excellence in Mathematics Teaching, and the author of Number
Talks: Helping Children Build Mental Math and Computation
Strategies, Grades K-5.
Pamela Weber-Harris is a former secondary
mathematics teacher, a K-12 mathematics education consultant, a
T^3 National Instructor, and the author of Building Powerful
Numeracy for Middle and High School Students.
James Williams is an Engagement Manager for the
National Center on Education and the Economy. He has years of
experience providing research-based school improvement solutions
in the areas of curriculum, instruction, assessment and learning
for districts and schools.
GMC will also include a conference-within-a-conference on Thursday
from 1:00 pm to 4:00 pm. Sessions are laid out with David Foster and
Phil Daro. Featured speakers also include: Chris Franklin, Sybilla
Beckman (elementary), Cindy Moss, Pamela Weber Harris (secondary),
Sherry Parrish (K-8, Number Talks, and HS), James Williams (all
Keep in mind that registration to the conference will NO
longer include membership. Participants must join GCTM prior
to registering for the conference. For questions about registration,
please contact email
firstname.lastname@example.org. Speaker or session questions may be
forwarded to Nickey Ice
email@example.com. Other general inquiries may be sent to Tammy
It’s Back to School time again. Are you ready? If you teach math,
Matific can help! Matific produces award-winning, online math
activities to supplement K-6 teachers’ lessons, and it’s free for
Engaging, hands-on math activities help reinforce mathematical
concepts, so using Matific is a great idea. To make it even more
enticing, Matific is offering a sweepstakes for anyone who signs up
for a new Matific account between now and September 30th. Prizes
include $25 Amazon gift cards, a Chromebook or even a $500 Amazon
gift card to purchase classroom supplies, and lots of other prizes!
A Matific teacher account includes:
Access to Matific’s library of thousands of
interactive math activities. These engaging games supplement and
reinforce classroom lessons and let children discover math at
their own pace.
The Content is aligned to the Common Core State
Standards and is mapped to popular textbooks.
New episodes are released every week. Students
can complete the activities on desktop computers or mobile
A teacher dashboard that tracks students’
progress in real-time. The dashboard provides student-level and
class-level performance reports allowing for differentiation of
you attend the GCTM 2015 Summer Mathematics Academy? If not, you
missed a treat! This past summer, GCTM held an academy of 2-day
sessions in four different locations. The purpose of this year’s
academy was to: provide information and support for revisions to the
K-8 mathematics curriculum, provide hands-on activities; enhance
questioning; provide support and resources for technology
utilization. Locations for each academy included Freedom Middle
School (Canton), Thomson Middle School (Centerville), Peachtree
Ridge High School (Suwanee), and Brunswick High School (Brunswick).
Participants at each site expressed that the academy was a positive
experience through their session feedback. Participants shared their
‘ah-hah’ moments or things that stood out to them the most about our
summer academy sessions. Some of the participant comments were
things such as:
I wish my entire grade level would have been
able to attend. I just think about all of the collaboration that
could take place if we were all here working together (Grade 5
If I had known about these years ago, I may
have been able to have 100% passing on standardized test instead
of 92% (Grade 3 Teacher).
I am so glad that I was able to attend this
session so that I can have a better understanding of how to more
effectively use my calculator with the students. We learned
about various functions and even about how to use hands on
materials to assist. We rarely work with manipulatives. We
usually think our kids are too big for them, but we had fun so
we know they will (Grade 8 Teacher).
Wow! These are truly Math Interactive
Notebooks. I never liked using them before because they were
never really interactive. They just became a math notes journal.
The ones that we created these past two days are actually those
that students can take home and share with parents about how
they are learning math and have continue hands on practice an
experience away from school (Grade 1 Teacher).
I go to these sessions every year and am so
glad that I came this year as well. I always leave with so much
more. I hope that you all continue so I can go next year (Grade
I have been traveling with you all this
summer. I have been to each location so that I can attend four
different grade levels so that I can go back and share. Plus, I
love to travel so this helps me personally as well as
professionally (Grade 4 Teacher).
We were also pleased that not only were the
participants super excited about attending sessions during the
summer, but the principals who hosted us at the prospective schools
were ecstatic as well. They were very accommodating with technology
needs/concerns and provided us with the best custodial staff members
that we could have asked for in an academy.
Therefore, from the hearts of GCTM, we would like to
thank all of the participants, hosting and supporting principals who
lent their building and sent their teachers, custodial staff,
writers, facilitators, and the Georgia Department of Education for
supporting the life- long learning of all students across the state
Cherokee County Press Release Submitted by Carrie, McGowan
Coordinator CCSD Community Relations and Publications
Summer Academy Involvement Provides Meaningful
Opportunities for Cherokee County Teachers
School may be out for students, but summertime means lots of
Cherokee County School District (CCSD) teachers are back in class
themselves to get up to speed on the latest tools and techniques in
classroom instruction. CCSD offers more than three dozen classes
during post-planning and summer break, covering topics from teaching
strategies to classroom technology. While in the past Georgia
teachers were required to attend courses to keep their teaching
certificates current, state legislation suspended the requirement
during the recent recession as a budget accommodation for school
districts. However, hundreds of CCSD teachers are still attending
classes without the pressure of a state requirement, continuing to
learn out of professional interest and the desire to become better
One opportunity that the teachers took advantage of was
participating in GCTM’s Summer Mathematics Academy. This two-day
program for K-8 teachers had a focus on hands-on activities,
revisions to standards, technology as a learning tool, and more. It
was presented to our teachers by the Georgia Council of Teachers of
Happy New Year! How the summers fly, as well
as the years. Time for celebration, but you probably feel a bit
exhausted today with all the hubbub of a new group of students and
the expectations of your role as a mathematics teacher. But what an
exciting time this is, as you start anew with a clean slate and
exciting new and old ideas to try and use again.
One constant idea is to maintain your membership
in GCTM. It offers continuous opportunities for growth and
support of mathematics teaching and learning in Georgia. So when
that renewal reminder comes your way, please respond and support our
wonderful organization and enrich yourself.
I had a call recently from Brandon, a university
student preparing to teach. He is very interested in being an ACTIVE
GCTM member starting now and into his teaching career. He wanted to
know what we do and what opportunities we offer. It was exciting to
speak with someone already committed to our profession and to being
a volunteer. I imagine there are hundreds more of Brandon that we
can encourage and bring into our fold.
As members we need to encourage the next
generation of teachers. One of the best ways to do that is to
show them the benefits of professional membership in GCTM. So let
your New Year’s resolution be to:
be active yourself
invite a new member or two within your school
share your GCTM experiences with a brand new
Please let us know if there is anything Membership
can do to help you. Have a wonderful new year!
NCTM Annual Meeting & Exposition 2016 “Building a
Bridge to Student Success” will be held in San Francisco, California
April 13-16, 2016. Hotel reservations opened up on August 26th.
NCTM’s conference page to find more information on registration,
programs and presentations, housing and travel, sales opportunities,
and other research conferences.
The Math Forum is Now a Part of NCTM
NCTM is excited to announce that
The Math Forum,
an extensive online resource for the mathematics education community
with nearly 100,000 subscribers, will become a part of NCTM. The
merger will consolidate the resources of the two organizations.
NCTM Accepting Applications From Music Projects
to Teach Pre-K-2 Mathematics - Philanthropy News Digest
The National Council of Teachers of Mathematics is
accepting applications from teachers of pre-K-2 mathematics for
projects that incorporate music into the elementary school classroom
as a way to help young students learn mathematics. With support from
the Esther Mendelsohn Fund, the Using Music to Teach Mathematics
program awards grants of up to $3,000 to individual classroom
teachers or small groups of teachers collaborating on the grade
level or across grade levels. Any acquisition of equipment must
support the proposed plan but may not be the primary focus of the
grant. Proposals must address the combining of mathematics and
music, planning for improving students' learning of mathematics,
and/or the anticipated impact on students' achievement. Find out
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)