
Submitted by
Nancy Ricciardi of Clayton County School District.
Each school year seems to pass by
more quickly than the previous year. I understand that is what
happens as you get older. I think we attempt to accomplish more and
more, and this keeps us busy throughout the year. At GCTM, we are
continually planning for the next year's events before the current
one ends.
As
posted on our website, the objectives of the Georgia Council of
Teachers of Mathematics are to encourage an active interest in
mathematics and to act as an advocate for the improvement of
mathematics education at all levels. To help GCTM meet these
objectives, several activities are on the calendar for 2018 and
plans are already in place. The GCTM Program Committee for the 2018
Georgia Math Conference scheduled for October 1719, 2018, has
already confirmed several keynote and featured speakers. This
year's conference theme will continue the emphasis on the Effective
Teaching Practices outlined in NCTM's Principles to Actions (2014).
Attendance at the 2017 Georgia Math Conference was about 1,100 and
we are looking for even more this year. We had perfect weather,
great enthusiasm from participants and special guests, time to
recharge and opportunities to reconnect and make new "math" friends.
Make plans now to be with us at Rock Eagle in the Fall. We are
planning something very special for the Wednesday afternoon
"preconference" session.
GCTM will be hosting the annual
Math Day at the Capitol on Tuesday, February 13, 2018. This is a
great platform 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. GCTM has also sponsored several visits
to Georgia classrooms by legislators and we plan to continue this in
2018. Thank you, Advocacy committee and TJ Kaplan, for making this
happen. We love to show off the great things happening in our
schools!
Plans
for the 2018 GCTM
Summer Academies have been made. We will be hosting three
academies this year. We will be in Coffee County and Pickens County
in June and in the Warner Robins area in July. This professional
learning is provided to help support math teachers as they continue
to create more opportunities for students to explore the beauty of
mathematics and make connections with the math they are learning.
Details for the Summer Academies will be posted on our website and
registration will open in February.
The GCTM Executive Committee has
a retreat scheduled for the beginning of 2018 to streamline our
responsibilities, brainstorm ideas to better support Georgia math
educators and to continue to improve communication between GCTM
members. Be looking for updates on our website to stay informed
about upcoming events. 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.
GMC 2017 Photographs
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Please
join us on Tuesday, February 13 at 9AM for the Fifth Annual Math Day
at the Capitol. For the second consecutive year, Senator Chuck
Hufstetler (District 52) will sponsor a resolution in support of a
highquality mathematics education for all. GCTM members are invited
to sit in the Senate gallery and will be recognized after the
reading of the resolution.
To better plan your trip to the Capitol building,
click here or see the information below:

To enter the Capitol building, visitors may use
the Washington Street or Mitchell Street (ground floor)
entrances of the Capitol.

When the state legislature is in session
(JanuaryApril), the closest public parking lot is located one
block from the Capitol at
65 Martin Luther King, Jr. Drive (at the former World of
CocaCola building). Parking fees apply. Please call
4048728868 for additional information about this lot.

Metered parking is available on city streets.

Additional information about parking can be
found
here

All adults aged 18 and older must show a photo
I.D. upon entering the Capitol. In compliance with security
regulations, visitors must enter the Capitol through a metal
detector; the Xray machine must examine handcarried items. No
weapons, including pocket knives, are allowed in the Capitol.

Pictures are allowed throughout the Capitol,
with the exception of the House and Senate Galleries when the
General Assembly is in session (January  April). Here is a
photograph from Math Day at the Capitol 2017.
Front Row (L to R): Senator Mike Dugan, Nikita Patterson, Joy
Darley, Bonnie Angel, Senator Chuck Hufstetler
Back Row (L to R): Denise Huddlestun, Brian Lack, Lieutenant
Governor Casey Cagle
Additionally, GCTM appreciates the support of the
Senator Matt Brass and
Senator Tonya Anderson, who attended GMC this year. Both
legislators were able to attend sessions and came away highly
impressed with what they observed. Senator Anderson added that she
"cannot wait to attend the conference again next year."
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A highquality mathematics
curriculum, taught by wellqualified teachers, must be offered to
all pupils. Learners need challenging experiences to be more
successful. With scaffolding, the mathematics teacher might motivate
pupils to attain more complex objectives of instruction. Vital
knowledge and skills objectives arranged sequentially may positively
influence students' attitudes toward mathematics.
Teachers should emphasize
important soft skills along with subject matter content; such soft
skills will assist pupils to do well in acquiring mathematics
content. Which soft skills might then be incorporated into teaching
and learning strategies?
Strategic Teaching of Soft Skills
Objectives need careful scrutiny
that pinpoints social and emotional learning known as soft skills.
Soft skills might be imparted within the framework of learners
achieving poignant knowledge and skills objectives of instruction.
Teachers should be cognizant of the factors involved in teaching and
learning, such as resilience and persistence. Too frequently, pupils
give up on solving a word problem in mathematics out of frustration.
Rather, the learner must be encouraged to pursue the solution(s) in
spite of setbacks.
As adults, individuals are
hesitant in facing dilemmas due to a lack of knowledge as to what is
inherent in solving personal and social problems. "Don't give up the
ship," might well be a useful slogan to follow in these situations.
In the school setting, the teacher needs to scaffold knowledge and
skills in guiding pupils in identifying and solving problems. In
mathematics problem solving, the pupil needs to analyze, synthesize,
and evaluate each involved sequential inherent step.
Then too, lost opportunities in
life accrue when individuals do not take advantage of what is good,
excellent, and has considerable merit, in decisionmaking
situations. Decision making from among hard choices is difficult
with its complexities. It takes motivation and time to pursue
selected alternatives. Thus in the mathematics curriculum,
problemsolving requires resilience in achieving solutions to
problemsolving experiences. Frustrations do occur.
Maintenance, as a soft skill, is
also poignant in that continuous effort must be put forth to achieve
in oncoming learning opportunities. Frequently, a pupil might become
hesitant in completing an assignment, and here is where maintenance
of effort put forth is important. A very brief pep talk to motivate
the learner might do the job in assisting a pupil to complete a
task. Motivation is a salient skill for pupils to develop in wanting
to grow and learn. Much time might be wasted when pupils stop to
pause, for one or another, when continuous achievement is desired.
Time wasted is time taken away from learning. This does not mean
that pupils are like large containers whereby a liquid can be poured
in continually. Learners do need time for stretching and exercising.
Recess time is excellent for
pupils to run, jump, skip, and do other of rigorous types of
exercise. The body requires movement and motion for it to function
well, mentally and physically in school and in society. Following
wholesome exercise, the pupil is ready for cognitive activities in
ongoing mathematics lessons and units of study.
Learning Opportunities and Soft Skills in
Mathematics
The mathematics teacher must
continue to stress soft skills within the framework of teaching and
learning. Thus within each activity, the teacher of mathematics
might emphasize empathy with the following:

assisting others to
participate in the collaborative efforts of problemsolving.

helping a learner to master
basic operations

guiding a child who is
struggling to use manipulatives

assisting another teacher by
providing materials he or she needs for a particular lesson

working toward success for
all in mathematics.
The feeling dimension is involved
in the concept of empathy; thus there are emotions inherent in
empathizing with others. Social and emotional learnings are poignant
in school and in society. There are a plethora of situations whereby
individuals need encouragement and help to attain objectives of
instruction, and here is where learners might well develop feelings
of empathy. To languish by the roadside when an individual has been
wounded should definitely be unthinkable. Rather aid must be
provided to remedy the injury and take the wounded person to a
hospital for treatment and care. So it is with more minor cases
whereby needs must be met in time and place. Pupils in the classroom
need assistance in mathematical problemsolving. Effort must be put
forth by the learner, but there is a point of no return in feeling
frustrated. Assistance must then be provided with bridging the gap.
Feelings to help others and follow the Golden Rule is still very
important.
Mathematics teachers may struggle
to know when to step in when pupil frustrations occur and when is it
good to come to the aid of learner within an ongoing learning
opportunity. The answer, many times, might well be to bridge the
gap. This involves the pupil in being guided to find a solution to
the mathematical problem faced. Mathematics needs to be challenging
and invite engagement in activities and experiences.
Interest in mathematics is a key
factor in teaching and learning situations. With pupils involved in
learning due to interest factors, the chances for achievement
improve. Mathematics teachers should select learning activities that
capture the attention and interest of their students. Pupils who are
turned off will not do well in ongoing activities. Teachers need to
find ways for students to see the relevance of what they are
learning. Pupils must perceive that each learning is vital and is
worthwhile  not only in school but also in the societal arena.
Mathematics then is perceived as possessing practical implications.
Relevancy resonates throughout the curriculum. Students should be
encouraged to see that we live in a mathematics world such as in

noticing the day of the month
and the present time

time limits of an experience
as well as time for an appointment

being on time for school or
for the workplace

coming to a meeting on time

paying for utilities and
other necessary expenses, and the list goes on.
The utilitarian values of
mathematics are endless. Mathematics, too, should be fascinating
with its many enjoyable ongoing experiences in the curriculum!
References
Ediger, Marlow, and D. Bhaskara
Rao (2014), Essays in Teaching Mathematics. New Delhi, India:
Discovery Publishing House.
Ediger, Marlow (2008), Modern
School Mathematics, College Students Journal, 42 (2), 986989.
Resources on Soft Skills
Teaching Soft Math Skills that Prepare Students for Any Career
Teachers' hard and soft skills in innovative teaching of mathematics
Top Five Soft Skills College Students Need
Hard Skills Verses Soft Skills
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The Logarithmic Chicken or the Exponential Egg: Which Comes
First?
by Marshall
Ransom, Senior Lecturer, Department of Mathematical
Sciences, Georgia Southern University; Dr. Charles Garner,
Mathematics Instructor, Department of Mathematics, Rockdale
Magnet School; Laurel Holmes, 2017 Graduate of Rockdale
Magnet School, Current Student at University of Alabama 
Background:
This article arose from
conversations between the first two authors. In discussing the
functions ln(x) and in introductory calculus, one of us made good
use of the inverse function properties and the other had a desire to
introduce the natural logarithm without the classic definition of
same as an integral. It is important to introduce mathematical
topics using a minimal number of definitions and postulates/axioms
when results can be derived from existing definitions and
postulates/axioms. These are two of the ideas motivating the
article. Thus motivated, the authors compared manners with which to
begin discussion of the natural logarithm and exponential functions
in a calculus class.
Logarithms Before Calculus
Existed:
Values of trigonometric functions, to many decimal places,
were calculated and available hundreds of years ago. Although these
were not necessarily in a form we would recognize in the modern era,
precision in calculations was becoming more and more important
during the 16th and 17th centuries. This was due in no small part to
observations made by astronomers. Using this data in ways that
required further calculations was tedious, laborious and
timeconsuming. Enter John Napier and Henry Briggs. Napier's work
involved the use of a base and an exponent, and then using the
exponents to aid in calculations. The basis for this early work with
what we know today as logarithms was closely related to 1/e in one
case and was 10 the other case. Today, we would not recognize the
approaches taken by these earlier mathematicians. More on the
history of logarithms is presented in the next section, due to the
work of Dr. Garner's student, Laurel Holmes.
Read more.

Marshall Ransom is a Senior Lecturer in the Department of
Mathematical Sciences at Georgia Southern University where
he has taught for 15 years. His primary interests are the
teaching and learning of calculus and the Advanced Placement
Calculus program. Prior to teaching at Georgia Southern, he
was a secondary math teacher and administrator for 30 years
in Volusia County Schools, Florida. 

Chuck Garner teaches single variable and multivariable
calculus, advanced finite mathematics, history of math, math
of industry and government, and coaches the math team at
Rockdale Magnet School for Science and Technology in
Conyers, where Laurel was his student for two years. He
loves teaching and doing mathematics, but his first love is
comic books. Whereas he used to add to his collection of
23,500 comic books exponentially, he now only adds to them
logarithmically. 

Laurel Holmes graduated from the Rockdale Magnet School for
Science and Technology in 2017. She is now attending the
University of Alabama where she is majoring in Nursing. In
her free time, Laurel enjoys reading, traveling, and getting
coffee with her friends. Her best friend is her twin sister. 
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A classroom of fourth graders is
presented with the following problem: Alex has 4 times as many
marbles as Lucas. If Lucas has 7 marbles, how many marbles does Alex
have? What might be happening as students try to make sense of
the problem? Their background knowledge from third grade has helped
them understand multiplication as equal groups of items and
multiplication as the area of a rectangle. But how can they apply
this understanding to the idea of 4 times as much? Will the
tools and strategies they know, like equal groups, arrays, and area
models, help them model this problem? Let's explore these issues as
we consider interpreting multiplication as a comparison.
After students have developed a
robust understanding of multiplication as groups of and as
area in third grade, they are ready to consider a new type of
multiplicative relationship in fourth grade. The Georgia Mathematics
Standards of Excellence introduce the concept of comparative
multiplication through standard 4.MGSE.OA.1, which states:
Understand that a
multiplicative comparison is a situation in which one quantity
is multiplied by a specified number to get another quantity; (a)
Interpret a multiplication equation as a comparison e.g.,
interpret 35 = 5 x 7 as a statement that 35 is
5 times as many as 7 and 7 times as many as 5; and (b) Represent
verbal statements of multiplicative comparisons as
multiplication equations. (GA DOE, 2016, p. 32)
Thus, students are comparing the
multiplicative relationship between two sets of quantities in
4.MGSE.OA.1. Gojak and Miles (2015) describe it as thinking about
one set of a "certain amount of items" as compared to "multiple
copies of the first set" (p. 33). If we were to apply this
interpretation to the opening problem, we could think of it as one
set is the 7 marbles Lucas has as compared to Alex's four copies of
those 7 marbles. We could represent the equation for that problem as
4 x 7 = 28; therefore, Alex has 28 marbles.
In order for students to become
proficient in interpreting comparative multiplication problems and
modeling those situations as equations, they must first develop a
conceptual understanding of this special multiplicative
relationship. To support conceptual understanding, teachers should
focus on two main instructional strategies: (1) present comparative
multiplication problems in context; and (2) use handson and visual
tools to represent the comparative relationship. As Lannin, Chval,
and Jones (2013) note, "contextual situations provide a starting
point for introducing and extending student understanding of
multiplication" (p. 36). Context is powerful because students can
visualize the situation, which will support them in making sense of
the mathematics. Likewise, providing opportunities to physically
model and draw visual representations of mathematics requires that
students make sense of the relationships among quantities. It is
important that this work takes place prior to introducing symbolic
representations like equations, which are more abstract. In fact,
"effective teaching of mathematics engages students in making
connections among mathematical representations to deepen
understanding of mathematics concepts" (NCTM, 2014, p. 24). Thus,
teachers should support students in connecting how their
interpretation of comparative multiplication situations is reflected
in the physical models they build and/or the visual representations
they draw, as well as connecting how those representations relate to
the corresponding equation.
Because comparative
multiplication marks a departure from conceptualizing multiplication
as groups of or as area (rows and columns or length
and width), it is especially important to select appropriate tools
in order to accurately represent the multiplicative relationship in
comparative multiplication problems. In fact, "us[ing] appropriate
tools strategically" is one of the Standards for Mathematical
Practice (GA DOE, 2016, p. 6). Teachers must facilitate experiences
to help students realize that particular tools or strategies may
lend themselves well to represent certain mathematics concepts, just
as they must realize some tools and strategies have limited
usefulness. Specific to tools and strategies for multiplication,
"each representation provides different insight into the
multiplicative structure" (Lannin, et al., 2013, p. 40), which is
certainly the case when introducing comparative multiplication.
Based on the thirdgrade
multiplication standards, fourth graders should have an
understanding of multiplication as both equal groups and area. Thus,
they have experience with physically and visually representing
multiplication as groups of using tools such as
building/drawing equal groups or jumping on a number line. They also
have experience with representing multiplication as an area
by building/drawing rectangular arrangements using arrays and area
models. These tools, however, cannot accurately represent the
comparative relationship in multiplication problems because there
must be a visual representation of a comparison. In order to
compare, each factor must be represented so that the difference (n
times as many) is illuminated. That is the number of items and
the copies of those items both must be represented in order to see
the comparison. When representing multiplication with equal groups,
the number line, arrays, and area models, only the groups of/rows
and how many in each group/columns are represented as
demonstrated in Figure 1.
Figure 1. Multiplication
strategies for 4 x 7
There is no representation of two
sets of quantities in any of these models. Therefore, the tools used
in the initial conceptualization of multiplication in third grade
are not effective in representing the mathematics of comparative
multiplication. As a result, fourthgrade teachers must look to
other tools when introducing multiplicative comparisons.
One of the best tools to
illuminate the comparative relationship in a multiplicative
comparison problem is the bar model, which is also known as a tape
diagram (Common Core Standards Writing Team, 2011; Gojak & Miles,
2015; Van de Walle, et al., 2014). Bar models or tape diagrams
capture the comparative relationships between the two sets of
quantities as reflected in Figure 2.
Alex has 4 times as many
marbles as Lucas. If Lucas has 7 marbles, how many marbles does Alex
have?
Figure 2. Initial model of
opening problem
Here we can see that Lucas has a
certain amount and Alex has four copies of that same amount. We know
the amounts are the same because equalsized bars represent them.
Also, notice how the four copies of the initial amount should be
counted using the as many as language to reinforce the idea
of copies (or multiples). To support students in using the bar model
or tape diagram, it is recommended that they physically build the
model first. Cuisenaire rods are an excellent manipulative for
building bar models or tape diagrams because they do not represent a
specific amount. Therefore, the emphasis can be placed on making
sense of the situation and matching the comparison in a contextual
situation with the model. Once students have physically modeled the
multiplicative comparison, they can represent their model as a
drawing and add more details as shown in Figure 3.
Alex has 4 times as many
marbles as Lucas. If Lucas has 7 marbles, how many marbles does Alex
have?
Skip Counting: 7, 14, 21, 28; Alex has 28
marbles
Equation: 4 x 7 = 28; Alex has 28 marbles
Figure 3. Drawing of
opening problem with details and possible solution strategies
Once the bar model or tape
diagram has been drawn and labeled, then students can use strategies
such as skip counting or writing an equation to solve the problem.
It is important that students refer back to the question to ensure
that they only multiply the seven marbles four times, since the
problem is asking about how many marbles Alex has, which is
four times as many (or four copies of) the amount Lucas has.
It is also important that the equation match the contextual
situation, so the first factor should represent the as many times
as (or copies of) amount and the second factor should represent
the certain amount of items. In the case of the opening problem, the
equation should be 4 x 7 = 28. As you can see, the bar model or tape
diagram is a very effective tool for representing the comparison in
comparative multiplication problems. Not only does it visually
reflect the comparative relationship, it also supports students in
making connections to more symbolic representations like equations.
It is for these many reasons that fourth graders should use bar
models or tape diagrams as the primary means for engaging in work
with the 4.MGSE.OA.1 standard.
Comparative multiplication is a
new and challenging way for fourthgrade students to conceptualize
multiplication. They must move beyond thinking about multiplication
as groups of or as area (rows and columns) to consider
the relationship between a set of a certain amount and a set of
copies of that amount. Likewise, they must move beyond the
multiplication tools and strategies they used in third grade to
consider a more appropriate tool, specifically the bar model or tape
diagram, to represent that comparison in comparative multiplication
situations. When teachers help their fourth graders make connections
among comparative multiplication situations, physical models and
visual representations of bar models or tape diagrams, and
equations, it is only then that the comparison is illuminated in
comparative multiplication problems.
References
Common Core Standards Writing
Team. (2011). Progressions for the common core state standards in
mathematics: K, counting and cardinality; K5, operations and
algebraic thinking. Retrieved from
https://commoncoretools.files.wordpress.com/2011/05/ccss_progression_cc_oa_k5_2011_05_302.pdf
Georgia Department of Education [GA DOE]. (2016).
Georgia's standards of excellence: Mathematics: Kindergartenfifth
grade. Retrieved from
https://www.georgiastandards.org/GeorgiaStandards/Documents/GradeK5MathematicsStandards.pdf
Gojack, L. M. & Miles, R. H. (2015). The common
core mathematics companion: The standards decoded, grades 35.
Thousand Oaks, CA: Corwin Mathematics and National Council of
Teachers of Mathematics [NCTM].
Lannin, J., Chval, K., & Jones, D. (2013).
Putting essential understanding of multiplication and division into
practice in grades 35. K. Chval & B. J. Dougherty (Eds.).
Reston, VA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics [NCTM].
(2014). Principles to actions: Ensuring mathematical success for
all. Reston, VA: Author.
Van de Walle, J. A., Karp, K. S., Lovin, L. H., &
BayWilliams, J. M. (2014). Teaching studentcentered
mathematics: Developmentally appropriate instruction for grades 35
(2nd ed.). Boston, MA: Pearson.
Dr. Andria Disney is an Assistant Professor of Elementary
Mathematics Education in the College of Education at Georgia
Southern University. Prior to receiving her Ed.D. from the
University of Montana in 2016, she worked in public schools as an
elementary teacher, a middle school math teacher, and a mathematics
curriculum and instructional specialist. Dr. Disney's research
interests include supporting preservice and inservice teachers in
making mathematics instructional change and using sensemaking tools
with their students.
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The banner for this issue was
submitted by Nancy Ricciardi of Clayton County School District. What
an
interesting example of mathematics in the real world. An
image like this could be used to jumpstart
discussion of conversions, unit prices, or even other foods that are
sold by the yard or foot. Nancy
submitted this image after a request for banner
submissions was posted to GCTM's facebook page.
Have you found GCTM on facebook yet? Members post
fascinating articles and topics and create
mathematical discussion boards often as a way to
connect to other mathematics teachers from all over
the state to network. You should consider checking us out
on Facebook.
While you are at it, you should
also consider contributing your own mathematical content to
Reflections. Send
in your ideas for banners, lessons, or mathematical research for
publication to get your ideas out to our readers.
Among the many benefits of being published in our journal, you will
also have your annual membership waived for one
year. A publication in Reflections is also a great TKES example of
your professional knowledge via reading and contributing
to mathematical journals.
Do you see mathematics in the
world around you? Are you taking chances in your classroom by trying
more adventurous lesson plans? Have you tried new
collaborative techniques that have lent themselves
to increasing student achievement? We
would love to hear your story. If so compelled, check out our
publications page,
send me an email of your
submission. Don't forget to include a short bio and a picture of
yourself! We at GCTM cannot wait
to hear from you. The Spring Issue is right
around the corner.
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Membership Musings
Happy New Year! Welcome back for
the second half of your academic year!
What are your new year's
resolutions for your teaching? For your students? For your
professional life? Whatever they are, I am sure they include wishes
for making all of these things better and more beneficial.
Make someone else's professional
life more beneficial by encouraging a colleague to join or renew
membership in GCTM. We have so many benefits to offer them and you
can be the catalyst to encourage their professional growth.
Our membership stands at 1292
today. If everyone of you brought another member, we would be near
2500.
Now go out there and do your
teacher encourager thing! And make 2018 the best year ever...for
you AND for me!
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Join thousands of your
mathematics education peers at the premier math education event
of the year! Network and exchange ideas, engage with innovation
in the field, and discover new learning practices that will
drive student success.
The latest teaching trends
and topics will include:

Tools and Technology:
Using Technology to Effectively Teach and Learn
Mathematics

Access, Equity, and
Empowerment: Teaching Mathematics with an Equity Stance

Purposeful Curriculum:
Cultivating Coherence and Connections

Teaching, Learning,
and Curriculum: Best Practices for Engaging Students

Assessment: A Tool
for Purposeful Planning and Instruction

Professionalism:
Learning Together as Teachers

Mathematical Modeling:
Interpreting the World through Mathematics

Emerging Issues and
Hot Topics
Back to Top
President 
Bonnie Angel
President Elect 
Denise Huddleston
Past President 
Kaycie Maddox
Treasurer
 Nickey Ice
Executive Director 
Tom Ottinger
Membership Director

Susan Craig
NCTM Representative

Michelle Mikes
Secretary 
Kim Conley
IT Director 
Paul Oser
REFLECTIONS Editor 
Becky Gammill
VP for Advocacy 
Brian Lack
VP for Constitution
and Policy  Joy Darley
VP for Honors and
Awards 
David Thacker
VP for Regional
Services  Kristi Caissie
VP for Competitions

Chuck Garner
Conference Board
Chair  Nikita Patterson
2018 GMC Program Chair 
Martha Eaves

Back to Top 
Table of Contents
President's Message  by Bonnie
Angel, GCTM President
Advocacy
Update  by Brian Lack, VP for Advocacy
Soft Skills
and the Mathematics Curriculum
 by Dr. Marlow Ediger,
Professor Emeritus, Truman State University
The Logarithmic Chicken or the Exponential Egg: Which Comes First?
 by Marshall Ransom, Senior Lecturer, Department of Mathematical
Sciences, Georgia Southern University; Dr. Charles Garner,
Mathematics Instructor, Department of Mathematics, Rockdale Magnet
School; Laurel Holmes, 2017 Graduate of Rockdale Magnet School,
Current Student at University of Alabama
Illuminating the Comparison in Comparative Multiplication by
Andria Disney, Ed.D. Georgia Southern University
Editor's
Note  by Becky Gammill, Editor
GCTM Membership Report  by
Susan Craig, Membership Director
NCTM
Report  by Michelle Mikes
GCTM Executive Board
