Vol IX

No. 1



President's Message
by Bonnie Angel, GCTM President

Spring is always a time for renewal. This season is a great time to reflect on the accomplishments and struggles of this school year and look forward to the planning and freshness of the upcoming year. I believe teaching is a unique profession because teachers get the chance to reboot every Fall. As teachers, we have the opportunity to try again and continually improve ourselves and our instruction.

We thought that Spring was in the air, but I woke up to snow on the ground this morning in North Georgia. This school year has already turned the corner, and we are heading for the home stretch, with one major hurdle - Georgia Milestones - still on the horizon. While teachers and students prepare for end of the year testing, GCTM is also busy preparing for Summer Academies and the Georgia Math Conference at Rock Eagle in October.

Registration is now open for the 2017 Summer Math Academies, which are headed to four locations across Georgia in June and July. Sessions offered during the institutes will include the following grade bands: Kindergarten – 1st grade, 2nd-3rd grade, 4th–5th grade, 6th–8th grade, Algebra, Geometry, and Algebra II/Pre-Calculus with the TI-84. The Academies will focus on Principles to Actions and participants will learn all about:

  • Effective teaching strategies for the mathematics classroom \

  • Engaging, higher order thinking tasks aligned to grade band GSE standards, and

  • Classroom strategies to meet the needs of ALL students

For more information about the Summer Math Academies, visit the GCTM website and click on the Academies tab or use the following link: https://new.gctm-resources.org/gctm/dv7/?q=academies. We are very excited about providing the opportunity for teachers to collaborate and learn together to make all of us better instructors for each of our students.

Preparations for the 2017 GCTM Georgia Math Conference have been going on since October 2016. The dates for the conference are October 18 through 20 at Rock Eagle 4-H Center. We have our keynote speakers lined up and are finalizing the logo. The theme for the conference is “Communicating Mathematics: Creating a Culture for Discourse Fluency.” We are currently accepting speaker proposals for breakout sessions. Please consider presenting on what you are passionate about. You can find the speaker proposal form on the GCTM website (www.gctm.org) under the GMC at Rock Eagle tab.

In other news, GCTM was recognized by the Georgia Senate on February 21, 2017 at the State Capitol in Atlanta. This was our annual “Math Day at the Capitol.” Five GCTM members were present on the Senate floor while the resolution was read by Senator Chuck Hufstetler, who sponsored the resolution. Nikita Patterson from Gordon State College, Denise Huddleston from Metro RESA, Joy Darley from Georgia Southern, and Brian Lack from Forsyth County accompanied me during the event. Several other GCTM members were seated in the gallery and offered their support. We had the privilege of having lunch and speaking with several members of the Finance Committee. I would like to express my appreciation to T. J. Kaplan and Denise Huddleston for their hard work in coordinating Math Day at the Capitol and setting up the opportunity for us to meet with the Senators to express our goals and concerns. I would also like to thank all of the members who took time from their busy schedules to represent GCTM.

Finally, as Spring Break is upon us, I’d like to recommend the movie Hidden Figures as a “must-see” movie for all math educators and students. This inspirational movie emphasizes the importance of students understanding and being able to apply mathematics to problem-solving. Your opportunities are unlimited if you have a strong foundation in math. The movie also stresses the importance of equity among all learners by focusing attention on the contributions of these female mathematicians to The Space Race and other missions. “Hidden Figures” has been regarded as relevant to the cause of improving youth awareness in education and careers in the Science, Technology, Engineering, and Mathematics (STEM) field. It was designed to help encourage a new generation of women to consider STEM careers. Research indicates that by the year 2020, there will be 2.4-million unfilled STEM jobs. The challenge for Georgia’s math educators is to find ways to use the lessons learned from this historical event to springboard today’s classroom instruction and encourage our students to problem-solve and be inspired by mathematics. That being said, I hope each of you enjoy a fun, relaxing Spring Break and has a strong finish to this school year.

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by Denise Huddlestun, VP for Advocacy

School Visit

Rep. Beth Beskin, a member of the House Education Committee, visited Fickett Elementary School in the Atlanta Public School System on Thursday, Oct. 13. She visited a 2nd, 3rd, and 5th grade classroom accompanied by the math coach at the school, the district elementary math coordinator, TJ, and Denise. In each of the classrooms she engaged with students and asked them questions about what they were doing and was impressed with what the students were doing as well as how they could explain what they were doing. In the 3rd grade classroom she saw students working in different centers and observed how the students working in the small group with the teacher were making sense of problems, representing the problems with manipulatives, and determining the solution.

State Board Member visit to GMC

Brian Burdette, the State Board of Education member from the 10th congressional district, attended the Thursday evening session at the GMC and heard Jenny Bay-Williams. Prior to the meeting, several members had the opportunity to talk with him about the need for rigorous standards for students.

Lunch with the Lieutenant Governor

I was invited to have lunch with Lieutenant Casey Cagle. Jeremy Peacock, President of GSTA and I were the only educators in the room. Other agencies/interests represented were the Hotel Association, transportation, Piedmont Hospital, Medicare/Medicaid, vendor for rehabilitation facilities, DeVita Dialysis, energy (Southern Company, Oconee Energy) and a few others. Each shared their interest. I shared the continued support of the GSE, a rigorous curriculum appropriate for all students.

Math Day at the Capitol

The resolution was written and declared Monday, February 13 as Math Day at the Capitol. The Senate Finance Committee (15 members) were invited, and I asked if the Chairman of the Senate and House Education Committees could be invited as well. There were about five GCTM members who attended the luncheon and chat with the senators. Below is the Math Day is highlighted in Michael William’s Capitol update.

“This past Wednesday, we had the privilege of recognizing the Georgia Council of Teachers of Mathematics for their work promoting mathematics education as part of Math Day at the Capitol. Math and all STEM education are vital because they influence every part of our lives.”

WWW.SUPPORTWILLIAMS.COM; michael.williams@senate.ga.gov  COMMITTEES:  Appropriations Subcommittee on Fiscal Management and General Government (Chair), Banking and Financial Institutions (Secretary), Financial and Public Safety, Ethics, and Appropriations Committees.

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2017 GCTM's Elections

The 2017 GCTM Elections Are Upon Us!

Online voting instructions and unique ballot codes will be emailed* to members very soon (by April 15th). Online voting begins a day or two later, with the last day to vote being April 29th. In the meantime, become familiar with the candidates running for President, Vice President for Awards and Honors, Vice President for Advocacy, and Secretary by following the links below:

Chuck Garner
Denise Huddlestun

Vice President for Advocacy
Joy Darley
Brian Lack

Vice President for Awards and Honors
David Thacker
Michael Wiernicki

Kimberly Conley
Jennifer Donalson

*Members with no email address listed in our database will be sent a paper ballot via US Mail

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End-of-the-Year Student Engagement Strategies
by Wendy Sanchez, Professor of Mathematics Education, Kennesaw State University

Well, Georgia mathematics teachers—spring break is upon us and another year is almost over. We know that students tend to check out on us after spring break. How can we keep them “checked in”? In this article, I will share three student engagement strategies that might help you make it to the end of the school year with some level of sanity! Even students who are good at sitting still, listening, and taking notes are antsy this time of year! They need movement and something interesting to figure out. My 13-year old son said that the problem with math is that the teachers always want to tell him how to solve problems, but he wants to figure out how to solve them himself. My 9-year old, who is very rigid, thinks that he’s only allowed to think about and do problems using the method his teachers have taught him. I know you have students like both of my boys. Working challenging problems that lend themselves to multiple strategies in small groups is a great way to engage students. The three strategies shared below assume this kind of task and structure.

Strategy 1: Discourse and Talk Moves

Discourse is a hot topic right now in mathematics education. In fact, it’s the theme of this year’s Georgia Math Conference! Thinking about your own classroom on a typical day, who does most of the talking? Is it the teacher? Is it students? What kind of talking is going on? Is it an IRE (Initiation, response, evaluation) pattern of discourse (Moschkovich, 2007)? In this pattern, teachers initiate a question and one or more student(s) respond. Finally, the teacher evaluates the answer(s) as correct or incorrect . This discourse pattern can also be characterized as vertical discourse (teacher-student-teacher-student…). A more engaging pattern is horizontal discourse (Nathan & Knuth, 2003) in which there is student-to-student discourse. There are some “Talk Moves” (Kazemi & Hintz, 2014) that a teacher that can use to promote classroom discourse.

Talk Moves to Support Classroom Discussion (Kazemi & Hintz, 2014)

Revoicing: “So you’re saying”—
  • Repeat some or all of what the student has said, then ask the student to respond and verify whether or not the revoicing is correct. Revoicing can be used to clarify, amplify, or highlight an idea.
Repeating: Can you repeat what she said in your own words?—
  • Ask a student to repeat or rephrase what another student said. Restate important parts of complex idea in order to slow the conversation down and dwell on important ideas.
Reasoning: “Do you agree or disagree, and why?” “Why does that make sense?
  • After students have had time to process a classmate’s claim, ask students to compare their own reasoning to someone else’s reasoning.
  • Allow students to engage with each other’s ideas.
  • Student: “I respectfully disagree with that idea because…”; “This idea makes sense to me because…”
Adding On: “Would someone like to add on to this?”
  • Prompt students, inviting them to participate in the conversation or to clarify their own thinking.
  • Student: “I’d like to add on…”
Wait time: “Take your time…”
  • Wait after asking a question before calling on a student.
  • Wait after a student has been called on to give the student time to organize his or her thoughts.
  • Student: “I’d like some more time.”
Turn-and-Talk: “Turn and talk to your neighbor…”
  • Circulate and listen to partner talk. Use this information to choose whom to call on.
  • Allow students to clarify and share ideas.
  • Allow students to orient themselves to each other’s thinking.
Revise: “Has anyone’s thinking changed?” “Would you like to revise your thinking?”
  • Allow students to revise their thinking as they have new insights.
  • Student: I thought….But now I think… because…. I’d like to revise my thinking.

These Talk Moves can help you get students talking about mathematics. Some of them, such as wait time, are likely familiar, but you might try some of them that are not already part of your regular practice. 

Strategy 2: Technology

Technology has come a long way! There are so many apps and open-resource materials that you can access easily and without cost. My favorites are Geogebra and Desmos. Did you know Desmos has a new feature called Desmos Teacher? You can pull up all your students’ screens on your computer and see what they are working on. And if you don’t have graphing calculators—not a problem. Desmos has an app and students can use it right on their phones. Geogebra has tons of shared investigations that other teachers have designed. If you don’t know how to use the software yourself, you can find things other teachers have created and students can investigate mathematics by clicking and dragging (and, of course, they are ALL experts at that!) objects to notice patterns and relationships.

Like Desmos, Geogebra is free, and is available as a phone app as well. There are also many websites that provide exciting problems and activities for you to use. I really like engageny (engage New York) at https://www.engageny.org. They have resources for all grade levels.

Another great site is the Math Assessment Project at http://map.mathshell.org/lessons.ph. They have full investigations tied to standards for grades 6-12, with all of the student materials already created. Another nice trick is that our GSE standards have the similar codes as Common Core standards. For example, the GSE standard MGSE9-12.G.GMD.1 matches the Common Core Standard CCSS.MATH.CONTENT.HSG.GMD.A.1. If you find the Common Core standard code, you can search by code to find many online resources for any GSE Standard.

And if you don’t know about Dan Meyers’ 3-Act tasks, check him out at http://blog.mrmeyer.com/category/3acts/. My younger son (4th grade) loves to use the Hands-on-Equations app. He’s solving 2-step linear equations in 4th grade! Kids always amaze me with what they can do.

Strategy 3: Open-ended questions

Open-ended questions are a great way to engage students in a different kind of thinking other than what they are used to using. One of my favorite types of open-ended questions is asking a question backwards (kind of like Jeopardy—you give the answer and let students come up with the question). In 8th grade, students are studying systems of linear equations. My older son is in 8th grade, and I asked him to write me a system of linear equations that has a solution of (2,3). He struggled at first, but he figured it out. He was very proficient at using the methods, but this question stumped him a bit. You could give students a graph of a function with no numbers on the axes and ask them to write an equation that would produce such a graph, or a story that would fit the graph. In the early grades, you could ask them to write a story problem that would match an equation like 10 – 4 = 6. In geometry, you could ask students to come up with the dimensions of two different cylinders that have the same volume. These questions are often at a higher level of cognitive demand because the students don’t have a step-by-step procedure to solve them. Give them a try!

We at GCTM wish you a wonderful and relaxing spring break—we know you deserve it! I hope you will find some of these ideas helpful as you prepare yourself for the home stretch. Thank you for all you do for children in mathematics classrooms across Georgia!


Kazemi, E. & Hintz, A. (2014). Intentional talk: How to structure and lead productive mathematical discussions. Portland, MA: Stenhouse.

Moschkovich, J. (2007). Examining mathematical discourse practices. For the Learning of Mathematics, 27 (1), 24-30.

Nathan, M. J. & Knuth, E. J. (2003). A study of whole classroom mathematical discourse and teacher change. Cognition and Instruction, 21 (2), 175-207.

Wendy Sanchez is a mathematics teacher educator at Kennesaw State University. She teaches undergraduate and graduate content and methods courses for preservice and inservice mathematics teachers. Her research is related to mathematics methods courses for preservice teachers.

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Teacher Talk
by Becky Gammill, Publication Editor

Teacher Talk is a new section for Reflections. This section will be used to showcase the perspectives of teachers in the informal setting of an interview. This Teacher Talk showcases the experiences of Diana Lossner, a retired mathematics teacher from Cobb County and a part-time lecturer at Kennesaw State University. In this interview, she discusses her struggles with learning how to teach mathematics nearly four decades ago, and imparts some advice for those who continue to teach mathematics today.

Becky: When did you start teaching mathematics?

Diana: I started teaching math in 1970 in Knox County, Tennessee. I taught 7th and 8th grade math in an elementary school. In Tennessee at that time, it was K-8 and 9-12. I had six classes a day. Students were tracked. Twelve students were in my low-level classes and around 25 were in my on-level and advanced classes. I taught three years, took a three year break, and then taught another 33 years straight. I taught four years in three different private schools and the rest public [schools].

Becky: What resources did you find most helpful when you first started teaching?

Diana: We were given the textbook, told to start on page 1 and get as far as you could. I had no other math teachers at my disposal. I made up all my own worksheets and tests. The biggest challenge was that I had to teach my low level kids to add, subtract, multiply and divide. I had no background in that so I made up my own manipulatives and hoped that was right. It seemed to work okay. The math I taught was much harder than now. My 7th grades learned base 5 arithmetic. Teaching that showed me that the kids really know the base 10 system, so I went back and showed them that. My unofficial mentor was an English teacher. Her favorite saying was "The kids will learn in spite of us." Our principal wanted to try different approaches to teaching but never fully understood how to implement any of them. I had no resources except teacher's edition of textbook.

Becky: When you went from one school to another, did you have a difficult time adapting to the new school culture or going from private to public? What challenges did you face?

Diana: Each change was so different that it was like starting over. But they all had one thing in common - no resources. I started working with my first real mentor…when I taught Physics at Baylor School for Boys (now coed). My department head helped me tremendously. I really had no help until I came to Cobb County in 1984. I was in a department of fifteen at Walton High School. We worked together just like they do today. (Walton teaches "lock step" with all teachers teaching the same thing on the same day with the same test and a lead teacher in charge. They formed professional learning communities before they were called PLCs. I know a lot of schools still have them, but it doesn't seem mandatory now.) The biggest challenge was always a lack of material. I relied totally on the textbook.

Becky: What was your favorite subject to teach and why?

Diana: My favorite class to teach was Analysis. Our department head at Pope, Cherlyn Sheperd, left and said, “Here it is, but there's a chapter zero that we teach also.” She and Debbie Poss had developed the curriculum, and it had set theory with rings and fields that I knew nothing about. It was an interesting summer, but I loved the class and learned a lot. I taught it for about 10 years and actually incorporated some of those topics in Accelerated Math 3. This class was all over the map and showed the real beauty of math. It also allowed me to stretch the kids. I gave them topics that were not in the curriculum and had them research and present them to the class.

Becky: As you look back on your career, what stands out the most, and what words of wisdom do you have to share with our readers.

Diana: The school may assign you a mentor. Use him or her. Also find an unofficial mentor that has your values and hopefully teaches what you teach. Collaborate, collaborate, collaborate!!! I loved being on the cutting edge of technology. Students learn much better visually (mostly anyway) and I loved the graphing calculators and the programs on computers that show the students what the algebra really means. I know we have had a lot of complaints about the "new math", but what I see coming through the elementary schools now is fantastic!! We are teaching the real meaning of the math and then showing them the algorithms. That's the way it should be done. If they see that with numbers I think they will have a better handle on algebra. Now I want to finish my other thought about mentors. Always find the most positive people around. There is nothing that will bring you down faster than a negative person. Unfortunately they are in every school. Use the internet. There are so many sites that can give a different approach that may help you present the topic better. But once again remember there are sites that aren't that good.

Becky: I appreciate you taking your evening to answer some of these questions and sharing your insights on teaching mathematics. Thank you!


Who would you like us to interview for the next Teacher Talk? A coworker? An author of your favorite mathematical article? A special presenter from GMC? Email us with your request, and we will be happy to reach out to them. Be sure to sure to include any questions that you want us to ask during the next interview. Thank you for being part of Reflections.

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GMC Update
by David Thacker,
GMC Program Chair

Before you know it, it will be that special time of the year when mathematics teachers from across the state come together to learn, discuss, and be inspired about teaching mathematics. The 2017 Georgia Mathematics Conference at Rock Eagle will be filled with engaging sessions and insightful keynote speakers, so please save the dates of October 18th through 20th. This year’s theme will be “Communicating Mathematics: Creating a Culture of Discourse Fluency.”



The keynote speakers will include Sunil Singh, Chris Franklin, and Sue O’Donnell.

Sunil Singh is the author of Pi of Life: The Hidden Happiness of Mathematics and a Lead Ambassador of The Global Math Project. He is also a Regular Contributor to the New York Times Numberplay Blog and spends much of his time doing Family Math Nights all over his home province of Ontario. Currently, he works with Scolab (a partner with The Global Math Project) as a math consultant to the development and promotion of interactive and integrative digital resources for K to 12 schools in the US and Canada. He has given over 50 presentations and workshops on creative mathematics to principals, teachers and students in Ontario.
Christine (Chris) Franklin is the K-12 Statistics Ambassador for the American Statistical Association and elected Fellow. She is retired from the University of Georgia after 36 years as the Lothar Tresp Honoratus Honors Professor and Senior Lecturer Emeritus in Statistics. She is the co-author of two Introductory Statistics textbooks and has published more than 50 journal articles and book chapters. Chris was the lead writer for the American Statistical Association Pre-K-12 Guidelines for the Assessment and Instruction in Statistics Education (GAISE) Framework and chaired the writing team of the ASA Statistical Education of Teachers (SET) report. Chris completed her term serving as the Advanced Placement Statistics Chief Reader in July 2009. She has been honored nationally by her peers with the Mu Sigma Rho National Statistical Education Award, the United States Conference on Teaching Statistics (USCOTS) biennial lifetime achievement award, and the ASA prestigious Founders Award. She was a 2014-15 Fulbright Scholar, spending six months at the University of Auckland, New Zealand working with statistics educators on the project, “Implementing K-12 Statistics Standards: Comparing Practices in New Zealand and the United States”. She also spent time with mathematics and statistics educators at the University of Tasmania.
Sue O’Connell has years of experience as an elementary classroom teacher, math coach, district school improvement specialist, and math speaker/consultant. She is the lead author for Heinemann’s Math in Practice series and is the coauthor of Putting the Practices Into Action, Mastering the Basic Math Facts in Addition and Subtraction, and Mastering the Basic Math Facts in Multiplication and Division. She has authored numerous other books that support the teaching of K-5 mathematics and is particularly focused on instructional practices that support the development of mathematical thinking. She is a frequent speaker at math conferences and is Director of Quality Teacher Development, providing on-site professional development for schools and school districts across the country.

Would you like to be part of this wonderful conference? Consider using your expertise and present your own ideas in a session! For more information, please visit this GMC page located on GCMT’s website found at https://new.gctm-resources.org/gctm/dv7/?q=gmc.

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2017 GCTM Summer Math Academies
by Kristie Caissie,
VP Regional Services

Email questions to academies@gctm.org.

Cost: $120 for non-member and $90 for member

Registration Opened February 14th at

GCTM Summer Academies

Locations and Dates:

  • Albany High School in Dougherty County—June 13th-14th

  • Statesboro High School in Bulloch County—June 20th-21st

  • Allatoona High School in Cobb County—June 27th-28th

  • Morgan County High School in Morgan County—July 11th-12th

Don’t miss out on this wonderful opportunity. Sign up today!

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Competitions Update
by Chuck Garner, VP Competitions

Middle School Math Tournament
Would you like to challenge your middle school students? Get them excited about mathematics by encouraging them to compete in the GCTM Middle School Math Tournament! The competition will be on Saturday, April 22 at Thomson Middle School in Centerville. The registration fee is $20 if the teacher is not a member of GCTM, and only $10 for members. More information and a registration form can be found on the Competitions page of the GCTM website. Don’t forget to check out GCTM’s Middle School Tournament text to help your students prepare for the event. This book is filled with example problems and solutions to surely get your math team talking and problem-solving.

State Math Tournament
The State Math Tournament are by invitation only, but registration is free. This year’s State Math Tournament will be Saturday, April 29 at Middle State University in Macon. Competition materials from 1998 to present can be found a collection of three texts mentioned below. The texts include problems that model the style, scope, and topics found in the State Math Tournament! Check them out!

Full solutions, and sometimes multiple solutions, are provided along with a topic index so that students may find any problem by topic. (Note: All sale proceeds go directly to GCTM and fund the State Math Tournament and ARML team.)

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Funding Opportunities
by Peggy Pool, VP Honors and Awards

There are plenty of opportunities to receive funding for new teaching endeavors. Check out the following grants and contact Peggy Pool at awards@gctm.org.

The Mini-Grant program has been implemented to provide funding for creative teaching projects. Proposals will be judged anonymously, and grants will be awarded in any amount up to $300.00. Each winner should be willing to either write an article for Reflections, the GCTM publication, or participate on a panel with other Mini-Grant winners at the following Georgia Math Conference. The criteria upon which applications will be evaluated are:

  • Creativity, innovation

  • Potential impact upon student achievement

  • Potential for replication by and dissemination to other teachers

  • Advancement of NCTM's Principles and Standards for School Mathematics

  • Unavailability of funding from local sources

Special Projects
GCTM is now offering its members an opportunity to apply for funds to support large projects that promote the improvement of mathematics teaching in Georgia. These projects can be focused on staff development activities, conferences, curriculum development, task forces, research projects, or other initiatives with similar impact.

Emerging Teacher-Leaders in Elementary School Mathematics Grants for Grades PreK–5 Teachers
The purpose of these grants is to increase the breadth and depth of the mathematics content knowledge of one elementary school teacher who has a demonstrated commitment to mathematics teaching and learning. The applicant must have the support of the school principal in becoming a mathematics teacher-leader within her or his school or district. For the 2013–2014 school year, grants with a maximum of $6,000 each will be awarded. Only one teacher per school may receive the award. The desired outcome of the funded project is the development of an elementary school mathematics teacher with mathematics content expertise.

Teacher Professional Development Grants for Grades PreK–5 Teachers
The purpose of these grants is to support professional development to improve the competence in the teaching of mathematics of one or more classroom teachers*. For 2013–2014, grants of a maximum of $3,000 will be awarded to person(s) currently teaching at the grades PreK–5 level. The proposal must delineate the professional development plan and address how the proposed project will improve the teacher(s)’ competence and affect students’ learning. Any acquisition of equipment must support the proposed plan but not be the primary focus of the grant. Recipients must have three or more years of teaching experience in grades PreK–5. Proposals must address the following: the professional development plan, how it will enhance the applicant(s)’ mathematical knowledge, and its anticipated impact on students’ learning. (*The definition of a classroom teacher is an individual who spends half or more of his/her work time teaching in the classroom.)

Improving Students’ Understanding of Geometry Grants for Grades PreK–8 Teachers
The purpose of these grants is to develop activities that will enable students to better appreciate and understand some aspect of geometry that is consistent with the Principles and Standards for School Mathematics of NCTM. For 2013–2014, grants with a maximum of $4,000 each will be awarded to persons currently teaching at the grades PreK–8 level. The project should include applications of geometry to, for example, art, literature, music, architecture, nature, or some other relevant area and may integrate the use of technology into the teaching of geometry. The activities may use published materials. Any published sources must be documented. Any acquisition of equipment or payment of personal stipends must be critical to the grant proposal and may not be a major portion of the proposed budget. Proposals must address the following: geometry content, the appropriateness of the application, the link between the Geometry Standard and the project’s activities, and the anticipated impact on students’ learning.

Summer Mathematics Study Grants for Grades 6-8 Teachers
The purpose of these grants is to provide financial support for teachers seeking to improve their understanding of mathematics by completing course work in mathematics content. For 2016–2017, grants with a maximum of $6,000 each will be awarded to persons currently teaching at the grades 6-8 level. Primary emphasis is placed on enrollment and completion of appropriate courses on mathematics content and the relevance of the course content to enhancing the teaching of mathematics in Grades 6-8. Proposals must address the following: rationale for the coursework, anticipated instructional improvements, and the expected impact on student learning. The grant will advance funds to cover tuition, and books. The balance of the funds will be issued as a stipend upon receipt of an official transcript that demonstrates completion of the proposed mathematics course work with a grade of C or better.

Connecting Mathematics to Other Subject Areas Grants for Grades 9-12 Teachers
The purpose of this grant is to create senior high classroom materials or lessons connecting mathematics to other fields. For 2016–2017, grants with a maximum of $4,000 each will be awarded to persons currently teaching mathematics in grades 9–12. Materials may be in the form of books, visual displays, computer programs or displays, slide shows, videotapes, or other appropriate medium. The focus of these materials should be on showing the connectivity of mathematics to other fields or to the world around us. Any acquisition of equipment or payment of personal stipends must be critical to the grant proposal and may not be a major portion of the proposed budget. Any published sources must be documented. Proposals must address the following: the plan for developing and evaluating materials, the connectivity to other fields or disciplines, and anticipated impact on students’ learning.

Grants and other Funding Opportunities compiled by Texas Instruments
Texas Instruments has collected a freely-available, and very long list of federal and private funding opportunities in math, science, and technology for grades K-12 and higher ed; teacher professional development; and university-level research and fellowship programs. They also offer guidelines and tips that will help you become a grant writing expert. The grant information is updated quarterly, so interested individuals may want to check their site frequently.

ING Unsung Heroes Grants
The ING Unsung Heroes awards program annually recognizes K-12 educators in the United States for their innovative teaching methods, creative educational projects, and ability to positively influence the children they teach. Educators are invited to submit grant applications describing class projects they have initiated or would like to pursue. Each year, one hundred educators are selected to receive awards of $$2,000 each to help fund their projects. At least one award will be granted in each of the fifty United States, provided one or more qualified applications are received from each state. Of the hundred finalists, three will be selected for additional financial awards. First place will receive $$25,000; second place will receive $$10,000; and the third-place winner will receive $$5,000. All awards must be used to further the projects within the school or school system. All K-12 education professionals are eligible to apply. Applicants must be employed by an accredited K-12 public or private school located in the U.S. and be a full-time educator, teacher, principal, paraprofessional, or classified staff member working on a project with demonstrated effectiveness in improving student learning. Previous recipients of ING Unsung Heroes awards are not eligible to apply for another award.

Advanced Technological Education (ATE)
With an emphasis on two-year colleges, the Advanced Technological Education (ATE) program focuses on the education of technicians for the high-technology fields that drive our nation's economy. The program involves partnerships between academic institutions and employers to promote improvement in the education of science and engineering technicians at the undergraduate and secondary school levels. The ATE program supports curriculum development; professional development of college faculty and secondary school teachers; career pathways to two-year colleges from secondary schools and from two-year colleges to four-year institutions; and other activities. Another goal is articulation between two-year and four-year programs for K-12 prospective teachers that focus on technological education. The program also invites proposals focusing on research to advance the knowledge base related to technician education.

The Toshiba American Foundation (TAF)
Toshiba America Foundation (TAF) grants fund the projects ideas and materials teachers need to innovate in their math and science classrooms. TAF is interested in funding projects designed by teachers or small teams of teachers for use in their own schools. Toshiba America Foundation believes science and mathematics are exciting fields in which all students can succeed with the proper tools and instruction. They offer grants up to $$1,000 to K-5 teachers with Application due on October 1st each year, and grants up to and beyond $$5,000 for teachers of grades 6-12. Grade 6-12 applications for $$5,000 or less are accepted on a rolling basis, throughout the calendar year. Grants requests of more than $$5,000 are reviewed twice a year. Applications for grants of more than $$5,000 are due August 1st and February 1st each year.

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Call for Manuscripts
by Becky Gammill, Ed.D., Publications Editor

Do you have something to share with other mathematics teachers or mathematics teacher educators? Do you have a favorite mathematical lesson that invites your students to dive into mathematics? Have you discovered a new technology tool that you cannot wait to share with your colleagues? If so, please consider submitting your manuscript to Reflections, a publication of the Georgia Council of Teachers of Mathematics. How do you dive deeper into problem-solving, collaboration, mathematics, or instructional practices?

The next four issues of Reflections will focus on the following priority topics:

  • Technologies for teaching and learning mathematics

  • Activities for teaching mathematics (hands-on and/or collaborative)

  • Statistics for each grade level and beyond

  • Mathematical proofs

  • Differentiated Instruction

  • Assessments

  • Favorite “ah-ha” lessons

  • Teacher Talk – Interview Style

  • Student mathematical art-work

As Georgia’s leading platform for the exchange of ideas among mathematics educators, contributors vary in subject areas, levels of expertise, and target audiences. Additionally, we welcome first-time contributors, writing collaborators, mathematicians, new and preservice teachers, and retired teachers and professors. One of the perks for submitting an article is that your membership fee for GCTM will be waived for one year. How great is that? If you wish to discuss your ideas for a topic prior to submission, please contact Dr. Becky Gammill at gammillgctm@gmail.com.

Guidelines for Submissions

  • Manuscript Format: Manuscripts are blind reviewed by members of the editorial review board. For this reason, each manuscript should include a cover sheet containing: title of manuscript, author’s name, position and email address. Identifying information should not appear elsewhere in the manuscript in order to ensure an impartial review. Manuscripts should be double-spaced, with 1-inch margins on all sides, typed in 12-point font and follow the APA 6th Edition style guide. Manuscripts should be submitted in MS Word. If you have a picture or graphic in the text, please include the original picture(s) in a separate file.

  • Manuscript Submission: Manuscripts should be submitted to Rebecca Gammill (gammillgctm@gmail.com). Receipt of manuscripts will be acknowledged. Manuscripts are accepted for consideration with the understanding that they have not been published previously and are not being considered simultaneously for publication elsewhere.

  • Manuscript Publication: When a manuscript is accepted for publication, the editor/journal reviewers may make suggestions or revisions in consultation with the principal author. However, because of publication deadlines the editor reserves the right to make minor revisions without seeking prior approval from the author. Release statements for all copyrighted materials must be received prior to publication.

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NCTM Report
by Dottie Whitlow,
NCTM Representative

Below I am sharing an important article of the history and swinging pendulum of the different foci of the approach to teaching mathematics since 1788 to today! Matt Larson, President of NCTM, shares this history and some advice for coping with changes and challenges in mathematics teaching and learning in most all educational settings and times.

For more excellent articles and perspectives from the Matt Larson, check out the following website:


Matt Larson, NCTM President
February 20, 2017

The Elusive Search for Balance

In a recent President’s blog post on the need to make homework comprehensible, I referred to the Fordham Institute Report, Common Core Math in the K–8 Classroom: Results from a National Survey. The report offers another interesting finding: “The math wars aren’t over.” 

The authors of the report observe, “The Common Core math standards seek to bring a peaceful end to the ‘math wars’ of recent years by requiring equal attention to conceptual understanding, procedural fluency, and application (applying math to real-world problems). Yet striking that balance has not been easy. We see in these results several examples of teachers over- or underemphasizing one component to the detriment of another” (p. 6).

I found this statement particularly striking. This over- or underemphasis may be less a function of independent teacher actions in the classroom than a result of teachers doing their best to interpret and implement what they find in their curricular materials, which, as the Fordham report indicates, are aligned (or not) with the Common Core State Standards to varying degrees. The over- or underemphasis of a particular component may also reflect teachers’ trying hard to comply with mandates at the district or school level. 

It is critical to appreciate that the over- or underemphasis phenomenon is not a new one. Mathematics teachers in the United States today are just the latest generation of U.S. educators to be caught in a 200 plus–year pendulum swing between an overemphasis of rote practice of isolated skills and procedures and an overemphasis of conceptual understanding, with their respective overreliance on either teacher-directed or student-centered instruction.

It all began in 1788 (the same year that the U.S. Constitution was ratified), when Nicolas Pike published the first major U.S. mathematics textbook, entitled Arithmetic. The process that Pike recommended for teachers was to state a rule, provide an example, and then have students complete a series of practice exercises very similar to the example. If that teaching process sounds familiar, it is probably because that was the way you experienced math instruction as a student yourself. This process became the U.S. script for teaching mathematics and is deeply embedded in our culture—expected by the vast majority of students and parents alike.

In the 1820s the pendulum swung for the first time when Warren Colburn published a series of texts, including Colburn’s First Lessons: Intellectual Arithmetic, Upon the Inductive Method (1826). Colburn recommended that teachers use a series of carefully sequenced questions and concrete materials so that students could discover mathematical rules for themselves. By the 1830s the pendulum was swinging back with the publication of the Southern and Western Calculator (1831) and The Common School Arithmetic (1832), which once again emphasized direct instruction of rules and procedures, taught the “good old fashioned way.”

The late 1950s and 1960s were the era of “New Math.” Proponents of new math worked to make the pendulum swing from rote learning to discovery teaching approaches that emphasized developing students’ understanding of the structure of mathematics, how mathematical ideas fit together, and the reasoning (or habits of mind) of mathematicians. The 1970s and 1980s saw the pendulum swing in the opposite direction yet again as these two decades became known as the “back to the basics” era, with a focus again on procedural skills and direct instruction.

In 1989 NCTM gave birth to the standards-based education reform effort with the release of Curriculum and Evaluation Standards for School Mathematics, and subsequently NCTM followed up this transformative publication with a series of other standards publications, culminating in Principles and Standards for School Mathematics (2000). By the mid-1990s over 40 states had created state math standards or curriculum frameworks consistent with the NCTM standards. But by the late 1990s the pendulum began to swing back to the basics when the “math wars” erupted in California and then spread across the country as parents and others demanded a renewed emphasis on procedural skills and direct instruction.

And that brings us to the latest perceived pendulum swing: the Common Core State Standards and the associated myriad of misinformation and misinterpretations surrounding them, as well as the historic and seemingly inevitable pushback that now benefits from and is fueled by social media. So what should a mathematics teacher caught up in these historic and continual pendulum swings do? My advice: Seek balance.

In many ways it seems as though we live in a world that is out of balance—pushed to extremes—that has “lost the middle” in various ways. To move mathematics teaching and learning forward, we have to resist the urge to be pushed to extremes. We have to do our part to break the historic cycle of pendulum swings. As Hung-Hsi Wu, professor emeritus of mathematics at the University of California–Berkeley, wrote nearly two decades ago, “Let us teach our children mathematics the honest way by teaching both skills and understanding.” This is essentially what the Common Core authors argue when they state, “[M]athematical understanding and procedural skill are equally important” (National Governors Association and Council of Chief State School Officers 2010, p. 4). 

Over a decade ago the National Research Council (NCR) published Adding It Up (2001), which promoted a multifaceted and interwoven definition of mathematical literacy:

Procedural fluency and conceptual understanding are often seen as competing for attention in school mathematics. But pitting skill against understanding creates a false dichotomy … Understanding makes learning skills easier, less susceptible to common errors, and less prone to forgetting. By the same token, a certain level of skill is required to learn many mathematical concepts with understanding, and using procedures can help strengthen and develop that understanding. (p. 122).

We need to return to, promote, and implement in our classrooms the NRC definition of mathematical literacy. The goal of mathematics education is not complicated. We want students to know how to solve problems (procedures), know why procedures work (conceptual understanding), and know when to use mathematics (problem solving and application) while building a positive mathematics identity and sense of agency. How? Why? And when? These questions are the very essence of rigor in the Common Core. We can ask ourselves simple reflective questions at the end of each lesson and over the course of a unit:

  1. Are my students learning how to solve a problem (or problems)?

  2. Are my students developing an understanding of why certain solution strategies work?

  3. Are my students learning when and where they might apply particular solution strategies?

  4. Did the experiences in my class help my students see themselves as capable doers and users of mathematics?

If the answer to all four questions is yes, that is more than likely a good sign. If we stay focused on all four learning goals, and resist (or dodge) the pendulum swings in any one direction while steadily building students’ positive mathematics identity, perhaps the constant criticism that moves the pendulum will stop. When we stay the course and let students engage, learn, and develop their understanding, skills, and abilities to use mathematics, our students will be the beneficiaries of our efforts to find and maintain that balance.

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GCTM Membership Report
by Susan Craig, Membership Director

Spread the Good News of GCTM Membership

I have been working on my Lenten resolution. I took a nudge from a Facebook post and am doing a bag-a-day purge. It means I use time I might waste on other things to fill a bag to go to recycling, a charity or even the trash. The bags are things that I can remove from my life to share with the needy or to clear the clutter that complicates my life and allow me to focus on helping others. As teachers, I think you can relate to the idea of clutter. Even if organized, our materials accumulate.

There is one thing I would never remove though, and that is my GCTM and NCTM memberships. They have been the cornerstone of my career and have never been a sacrifice in any way. Rather they have enriched my life and teaching in more ways than I can list.

As members, reflect on the good aspects of your GCTM membership. Has it been worth the cost of a couple of movies, a meal out, a magazine subscription per year? $20 is all it takes to be and remain an active GCTM member.

So when your membership comes up for renewal, please don’t hesitate to renew. And while you are at it, encourage a new teacher to join, or even a veteran colleague. Each year at the conference, I am amazed that teachers approach me to say that they have been teaching over 20 years and had never heard of GCTM. These teachers are saddened by they and their students had missed over those years. As members, we have to be our own advocates. Spread the good news! Let’s fill our membership roles with as many teachers as possible to bring our numbers to the levels we have had in the past! We are counting on you!

Please visit your membership page on the website and volunteer for GCTM projects and update a new entry regarding your NCTM membership! 

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GCTM Executive Board

President – Bonnie Angel

Past President – Kaycie Maddox

TreasurerNickey Ice

Executive Director – Tom Ottinger

Membership Director – Susan Craig

NCTM Representative – Dottie Whitlow

Secretary – Michelle Mikes

IT Director – Paul Oser

REFLECTIONS Editor – Becky Gammill

VP for Advocacy – Denise Huddlestun

VP for Constitution and Policy – Joy Darley

VP for Honors and Awards – Peggy Pool

VP for Regional Services – Kristi Caissie

VP for Competitions – Chuck Garner

Conference Board Chair – Tammy Donalson

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Table of Contents

President's Message - by Bonnie Angel, GCTM President

Advocacy - by Denise Huddlestun, VP for Advocacy

2017 GCTM's Elections

End-of-the-Year Student Engagement Strategies by Wendy Sanchez, Professor of Mathematics Education, Kennesaw State University

Teacher Talk by Becky Gammill, Publication Editor

GMC Update by David Thacker, GMC Program Chair

2017 GCTM Summer Math Academies by Kristie Caissie, VP Regional Services

Competitions Update by Chuck Garner, VP Competitions

Funding Opportunities by Peggy Pool, VP Honors and Awards

Call for Manuscripts by Becky Gammill, Ed.D., Publications Editor

NCTM Report by Dottie Whitlow, NCTM Representative

GCTM Membership Report - by Susan Craig Membership Director

GCTM Executive Board


Georgia Council of Teachers of Mathematics | PO Box 5865, Augusta, GA 30916 | 1-855-ASK-GCTM