Vol IX

No. 2



President's Message
by Bonnie Angel, GCTM President

Another school year is in the books and now is the time for relaxation, recovery, and recreation – at least for most of our students.  Several of my grandchildren have already been on a cruise and spent a week at the beach. I hope all of you are taking the time to enjoy being with family and friends.


As I am writing this, GCTM is preparing to begin the 2017 Summer Academies.  We are starting at Albany High School on June 12th and 13th, then heading to Statesboro High School on June 20th and 21st.  We will finish up the month of June in Cobb County at Allatoona High School on June 27th and 28th.  We are taking the week of the Fourth of July off before finishing the last summer academy on July 11th and 12th at Morgan County High School in Madison, Georgia.  The writers and facilitators have been working hard for several months to plan grade-band sessions that will give participants many tools, ideas, strategies, and activities to take back to their classrooms this Fall.  We are anticipating great crowds and adding a Lunch-N-Learn session at each academy, sponsored by Pearson, that will provide even more opportunities for teachers to learn how to engage their reluctant learners.  Many thanks go to Ms. Kristi Caissie, the Academies Coordinator, and her supporters, who are making this all happen for Georgia’s math educators.


For many of us, this is a time to review this past year and begin preparing for the next school year, which will begin in a few short months.  I remember as a teacher, I enjoyed sleeping in and not having to get dressed up to go to school every day during the summer.  But, I spent many hours working and preparing for the next year’s students.  This summer is no exception. In addition to the Summer Academies, a group of GCTM Executive Committee members will be attending the 2017 NCTM Leaders Affiliate Conference in Baltimore, Maryland at the end of July.  This is a great chance for state affiliates to come together and talk about what is working for their organizations to help support math teachers.  Many of the affiliates are interested in GCTM's ongoing programs or initiatives, such as the Georgia Math Conference, Summer Academies, and how we advocate for mathematics education.  I am proud to say that GCTM continues to lead other state affiliates by example through professional development opportunities and educational advocacy.


In my spare time, I am continually looking for ways to learn how to help the teachers and schools I work with.  This summer, I am participating in several of Jo Boaler’s online courses.  On the youcubed.org website, “How to Learn Math” is a free class for learners of all levels of mathematics.  This is a great course for teachers and students.  Another online course is, “How to Learn Math for Teachers”.  This course is self-paced and includes brain research as well as strategies to help students develop number sense.  Jo Boaler has just released her latest online course, “Mathematical Mindsets”.  These courses include videos of teaching and student interviews as well as activities for reflection and discussion.  I highly recommend these courses as well as her books, Mathematical Mindsets and What’s Math Got To Do With It.



NCTM has many great publications available to use as a book study or individual reading.  NCTM has just recently released the "Taking Action” series for grade bands. These books include ways to incorporate the Principles to Actions’ guiding principles for school mathematics.  The NCTM website, www.nctm.org, provides many outlets stay involved this summer including blogs, webinars, and Author Talks.

So, as we enjoy this much-deserved time off, let’s spend some time reflecting on our teaching practices and our own learning.  Then, as we begin preparing for a new group of students, let’s look for ways to continue to grow as learners and to implement new strategies to help our students enjoy the beauty of mathematics.

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Editor's Note
by Becky Gammill, Ed.D., Publications Editor

This issue’s banner was designed by Rachel Staggs, a student at Kennesaw State University majoring in Early Childhood Education. As part Ms. Staggs learned about how to teach geometry topics to her future students, Ms. Staggs designed this lovely rotational tessellation of doves.  The following pieces were also submitted by Leslie Haynie (top left), Kennedy Gillam (top right), Chelsea Eells (bottom left) and Rachel Staggs (bottom right) all of whom are also pursuing a degree in Early Childhood Education at KSU.


"The Beast"

"Apple of My Eye"

"Cool School of Fish"

"We All Scream for Ice Cream"


Do you have mathematical artwork to share?  Perhaps something that you are working on could become Reflections next banner!  Email submissions to gammillgctm@gmail.com.  Do not forget to include your county’s student work release form if you are sending in student artwork.

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Tournament Updates
by Chuck Garner, VP of Tournaments and Competitions



The GCTM Middle School Math Tournament was held at Thomson Middle School in Centerville GA on April 22, 2017. Middle schools across the state were invited to register up to eight students to compete. The tournament consisted of a 30 question multiple-choice test with a 45-minute time limit; 10 individual ciphering problems, each problem with a two-minute time limit; 3 rounds of four pair ciphering problems (in which students from a school formed teams of two), each round with a four-minute time limit; and a four-person team “power question,” in which the team solves a complex problem with a 10-minute time limit.


The tournament is designed to challenge middle school students and to reinforce classroom skills. However, we also make sure the students have fun! At the conclusion of the tournament, students participate in a fun “Frightnin’ Lightnin’” Round, where students must be quick on the draw to answer math problems posed orally. The winners of this round get candy! Trophies went to the top five teams and the top ten individuals. For the first time in the history of the tournament, there was a two-way tie for first place between Vishaal Ram and Holden Watson of Fulton Science Academy. The top teams are below.



  1. Fulton Science Academy, Alpharetta

  2. River Trail Middle School, Johns Creek

  3. Eureka Scholastic Academy, Atlanta

  4. Stratford Academy, Macon

  5. Tattnall Square Academy, Macon

Fifty-five students from nine schools participated. Sponsors that are members of GCTM only had to pay a $10 registration fee or submit five multiple-choice questions for possible inclusion in a future tournament. The next GCTM middle school tournament is scheduled for April 21, 2018.




The 41st annual GCTM State Math Tournament was held at Middle Georgia State University in Macon, Georgia on April 29, 2017. Schools are invited to the state tournament based on their performance on previous Georgia tournaments throughout the 2016-2017 school year. Thirty-six invited schools attended this year’s state tournament. Four students are selected by their school sponsor to represent each school (one school brought a team of two). Nineteen individuals were also invited to try-out for the state-wide Georgia ARML team, making a total of 161 participants.


The tournament consisted of a very challenging written test of 45 multiple-choice questions and 5 free-response questions with a 90-minute time limit; 10 individual ciphering problems, each problem with a two-minute time limit; and a team round. The team round consisted of 12 problems for each team to solve while working together within eighteen minutes.


The student with the best improvement at the state tournament over the previous year was given the Steve Sigur Award for Most Improved Performance. This award, named in honor of the great mathematician, teacher, and mentor Steve Sigur, went to Matthew York of Rockdale Magnet School. Each participant and their school sponsor were given a 2017 State Tournament T-shirt. The top five teams and the top fifteen individuals are listed below.



  1. Northview High School

  2. Chamblee Charter High School

  3. Fulton Science Academy

  4. Kennesaw Mountain High School

  5. Gwinnett School of Math Science and Technology

The classification winners are the schools which were not in the top 5, but, except for the top 5, placed above all other schools in their classification. We call these “classification champions.” Unfortunately, there was no Class AA Champion this year, as all AA schools that qualified for the State Math Tournament declined to participate.




Class A: Wesleyan School

Class AAA: Westminster

Class 4A: Woodward Academy

Class 5A: McIntosh High School

Class 6A: Johns Creek High School

Class 7A: Walton High School

Non-GHSA Class: Bulloch Academy



  1. Daniel Chu, Kennesaw Mountain High School

  2. Holden Watson, Fulton Science Academy

  3. Joshua Ani, Chamblee Charter High School

  4. Bill Zhang, Northview High School

  5. Shawn Im, Peachtree Ridge High School

  6. Chenthuran Abeyakaran, Chamblee Charter High School

  7. George Hu, Northview High School

  8. Tony Zeng, Brookwood High School

  9. Sean Engelstad, Kennesaw Mountain High School

  10. Harish Kamath, South Forsyth High School

  11. Matthew York, Rockdale Magnet School for Science and Technology

  12. Carson Collins, Woodward Academy

  13. Vishaal Ram, Fulton Science Academy

  14. Irene Zhou, Northview High School

  15. Jason Fan, Gwinnett School of Math Science and Technology

An item analysis of the competition problems was completed at the state tournament. The responses analyzed included the 45 multiple-choice problems on the written test and the 10 problems from the individual ciphering round. Before we discuss what the item analysis revealed, some background information would be useful. The problems on the written test are designed to increase in difficulty. Thus, theoretically, problem 1 is the easiest multiple-choice problem and problem 45 the most difficult multiple-choice problem on the test. Below are those problems.


Test Problem #1: Solve 2/x ≤ 1/(x - 2).

a) [4, ∞)

b) (–∞, 4)

c) (–∞, 4]

d) (–∞, 0) È (2, 4] e) (–∞, 0] È [2, 4]


According to the analysis, problem 1 was not the easiest, as only 112 students out of 161 answered it correctly. It was, in fact, Problem 2 which was the easiest! Of the 161 participants, 145 answered the question correctly.


Test Problem #2: Let A(2, 8), B(6, –4), and C(0, 10) be points in the coordinate plane. Let D be the midpoint of AB, and let E be the midpoint of DC. Compute the length of DE.

a) √2

b) 2√2

c) 2√3

d) 4

e) 2√5


Problem 1 was supposedly a straightforward inequality to solve. By subtracting one of the terms to the other side and combining fractions, one could use a sign chart to determine the signs of the fraction. Since graphing calculators are allowed on the written test, students could also have graphed the inequality. The correct answer is D. The most frequently chosen incorrect answer was C, which indicates that some students forgot that 2 cannot be in the solution set since x = 2 results in an undefined expression.


It is rare that a geometry problem turns out to be the easiest problem on the written test. But Problem 2 was designed to be simple, and, through the midpoint and distance formulas provided by analytic geometry, is easily solved. The correct answer is E.


In contrast, the analysis revealed that Problem 45 – a difficult analytic geometry problem – really was the most difficult since only 5 participants answered it correctly!


Test Problem #45: A parabola has focus F and vertex V, where VF = 7. Points P and Q lie on the parabola so that PQ = 29 and PQ passes through F. Compute the area of triangle VPQ.

a) 7√(203)

b) 58√3

c) 29√(14)

d) 21√(29)

e) 116


Problem 45 requires not only thorough familiarity with the properties of the vertex, focus, and directrix of a parabola but also trigonometry. The area of triangle VPQ can be decomposed into two triangles by the axis of symmetry: triangle VFP and triangle VFQ. The angle of the axis of symmetry makes with the line PQ helps to determine the areas of these two triangles. The correct answer is A.


As for the ciphering, there is no particular order of difficulty for the questions, so it is always interesting to see which problems are answered correctly and quickly. The easiest ciphering problem, judged by the fact that 111 participants gave the correct answer, is the following. (Recall that each of the problems below should be answered in less than two minutes, without a calculator.)


Ciphering Problem #9: The Tile and Board are made up of congruent squares. The 3 × 1 Tile is randomly placed either vertically or horizontally so that it covers exactly three adjacent squares of the 3 × 5 Board. All possible placements are equally likely. What is the probability that the square marked with an X is covered by the Tile?



There are 5 equally likely ways to place the Tile vertically, with one of them covering the X. There are 9 equally likely ways to place the Tile horizontally, with two of them covering the X. Therefore, there are 14 equally likely ways to place the Tile, with three of them covering the X. The answer is therefore 3/14.

The most difficult ciphering problem, judged by the fact that only 10 participants gave the correct answer, is the following.

Ciphering Problem #7: Let g(x) be equal to 2x if x ≤ 7, and be equal to the cube root of x if x > 7. Compute the sum of all four solutions to the equation g(g(g(x))) = x.

One of the four solutions to the equation is x = 0. The other solutions are found by considering the domain of the function, and that one may use different pieces of the piecewise function in succession. For instance, g(g(g(2))) = g(g(4)) = g(8) = 2. Indeed, this gives all the solutions, since we could have started this pattern with 4 or 8 as well. The four solutions are 0, 2, 4, and 8, and the answer is 14.

State Tournament registration is free, but schools must be invited. The next State Mathematics Tournament is scheduled for April 28, 2018.

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Inquiry or Explicit Instruction?
by Rodney Sizemore, Ed. D. Student at Kennesaw State University; Geometry Teacher at Ola High in Henry County

Inquiry or Explicit Instruction?

Developing students’ mathematical thinking is a primary goal of all mathematics teachers. However, how best to develop mathematical thinking has been a subject of heated debates in mathematics education for decades. At the heart of this debate is how students learn. Do they learn better by constructing knowledge through exploration, or do they learn better by being given new information and having its meaning and implications explained to them?

What Does the Research Say?

Inquiry methods are based on theories of learning which stress that students should explore concepts, discover patterns, and integrate new with existing knowledge with little explicit instruction. They encourage collaboration and dialogue as ways to build understanding. Typical inquiry-based classes spend the majority of class time on student-centered activities such as working in groups and giving and listening to presentations by other students, with teachers providing scaffolding through carefully selected problems, giving feedback to students, and providing mini-lessons when needed (Laursen, Hassi, Kogan, Hunter, & Weston, 2011).

For example, the “Patterns of Change” unit in the Core-Plus Mathematics Curriculum begins with students working in groups to create a graph relating a person’s weight to how far he would stretch a cord on a bungee jump. Next, groups perform an experiment to see if their graphs were correct. Then, the teacher asks questions about maximizing profit for a bungee-jump business, which is modeled with a quadratic function. Finally, groups work to answer a series of questions about equations and graphs related to the activity. The strengths of these constructivist methods are that they build conceptual skills and teach students to apply knowledge to unique situations rather than simply recalling knowledge in non-routine problems. Many studies, such as Harold Schoen’s study of the Core-Plus Mathematics Curriculum (2003), argue in support of inquiry methods. Schoen studied three high schools which implemented the Core-Plus curriculum. After three years, Core-Plus students showed a significant improvement over students using traditional curricula. This study as well as others are widely cited by supporters of inquiry methods.

Explicit instruction methods are based on the theories of learning that support the belief the most efficient way for a person to gain knowledge is to be explicitly taught new information. If the topics in the bungee jump example above were taught explicitly, the teacher would begin by explaining linear, quadratic, and exponential functions, showing students what their graphs look like, then demonstrating how to apply that information in scenarios such as profit-maximization.

Supporters of explicit instruction argue that explicit instruction improves learning by freeing up working memory and reducing cognitive load. Conversely, they argue that inquiry learning requires that students process and assimilate more information, and that doing so overloads working memory, causing information to be lost. Advocates of explicit instruction say that instructional design should limit extraneous information so that students can focus on essential elements of what is being taught. Many studies argue that explicit instruction is better. For example, a 2003 study by John Alsup and Mark Springler compared achievement scores for students who used Houghton Mifflin’s traditional curriculum (one characterized by explicit instruction) with students who used the CORD Applied Mathematics curriculum (one characterized by inquiry teaching) . The researchers found no difference in total SAT or SAT problem-solving scores, but students using the traditional curriculum had higher procedure scores.

A Blend

In the last decade, researchers have embraced a consensus view that students learn best using a combination of methods, depending on the standards being taught and on the students’ prior knowledge. The Report of the Task Group on Instructional Practices of the National Mathematics Advisory Council (2008) recommended that teachers “employ instructional approaches and tools that are best suited to the mathematical goals, recognizing that a deliberate and conscious mix of strategies will be needed.”

And that makes sense. According to researchers such as David Klahr, explicit instruction works together with inquiry methods in a couple of ways: (1) it can reduce the cognitive load associated with inquiry learning, and (2) it can help students understand concepts they would not readily grasp using inquiry methods. By combining inquiry and explicit instruction, students can have the best of both: they can be taught new material using explicit instruction, and they can increase their learning using inquiry methods by applying their new knowledge to other problems.

In 2011, Louis Alfieri and colleagues analyzed 164 previous studies that compared inquiry learning with explicit instruction. They found that a combination of inquiry and explicit instruction was more effective than explicit instruction alone. Interestingly, that same study showed that adolescents benefitted more from explicit instruction than adults do.

So What’s a Teacher to Do?

Students who are less knowledgeable about a topic should receive more guided instruction

A study by Tuovinen and Sweller examined students who were taught to use a database program either by studying explicit instruction or through inquiry. The students who had no prior knowledge learned best with explicit instruction, and the students who had prior knowledge learned about equally with both methods. The combination that was least effective was students with no prior knowledge trying to learn through inquiry, which the authors attributed to cognitive overload.

The less knowledge students are about a particular topic, the more guided instruction they should receive. Clark, Kirschner, and Sweller said,

Decades of research clearly demonstrate that for novices (comprising virtually all students), direct, explicit instruction is more effective and more efficient than partial guidance. So, when teaching new content and skills to novices, teachers are more effective when they provide explicit guidance accompanied by practice and feedback, not when they require students to discover many aspects of what they must learn… teachers should provide explicit instruction when introducing a new topic, but gradually fade it out as knowledge and skills increase” (2012, pp. 6-8).

For example, when students learn about trigonometry for the first time, teachers should explicitly demonstrate the meanings of the words opposite, adjacent, sine, cosine, and tangent, and they should explain the difference between the common meaning of opposite and the trigonometry meaning of opposite. They should give students clearly worked examples of how to solve for sides and angles of triangles. As students become more familiar with using trigonometry, teachers should reduce the amount scaffolding.

Keep students engaged

Active learners learn more than passive learners. Graphing calculators and geometry software such as Geometer’s Sketchpad have been shown repeatedly to be useful in promoting conceptual understanding, student engagement and interactivity. Just because learners are active, though, it doesn’t ensure that they are learning. For example, a passive learner is one who watches a teacher use a graphing calculator, an active learner is one who manipulates a graphing calculator himself, a constructive learner is one who uses a graphing calculator to solve a new problem, and an interactive learner is one who uses a graphing calculator with a partner to discuss how to solve a new problem. Aim for students to be constructive or interactive.

Remember the strengths of inquiry methods

With packed curricula and End of Course assessments looming overhead, it is easy to fall into the trap of relying entirely on explicit instruction because it often takes less class time. However, constructivist methods have repeatedly shown important benefits. For example, students who use constructivist methods generally do better on real-life applications and better understand the how topics relate to each other.

When to Use Explicit Instruction

  • When material is new and unfamiliar

  • When connections to prior learning are not readily discoverable by students

  • For topics that are mainly algebraic calculations

When to Use Inquiry Methods

  • To increase the depth of understanding by applying material that has been introduced

  • When connections to prior learning are straightforward for students to discover

  • When it would increase student motivation by increasing student interest


Alfieri, L., Brooks, P. J., Aldrich, N. J., & Tenenbaum, H. R. (2011). Does discovery-based instruction enhance learning? Journal of Educational Psychology, 103(1), 1-18. doi:10.1037/a0021017

Alsup, J. K., & Sprigler, M. J. (2003). A comparison of traditional and reform mathematics curricula in an eighth-grade classroom. Education(4), 689.

Benbow, C., Clements, D. H., Loveless, T., Williams, V., & Arispe, I. (2008). Report of the task group on instructional practices. Washington, DC: US Department of Education.

Clark, R., Kirschner, P. A., & Sweller, J. (2012). Putting students on the path to learning: The case for fully guided instruction.

Klahr, D. (2009). “To every thing there is a season, and a time to every purpose under the heavens”: What about direct instruction? In S. Tobias & T. M. Duffy (Eds.), Constructivist instruction: Success or failure? (pp. 291-310): Routledge.

Laursen, S., Hassi, M.-L., Kogan, M., Hunter, A.-B., & Weston, T. (2011). Evaluation of the IBL mathematics project: Student and instructor outcomes of inquiry-based learning in college mathematics. Colorado University.

Schoen, H. L., & Hirsch, C. R. (2003). The Core-Plus Mathematics Project: Perspectives and student achievement. In H. L. Schoen & C. R. Hirsch (Eds.), Standards-based school mathematics curricula: What are they? What do students learn? (pp. 311-343). Hillsdale, NJ: Lawrence Earlbaum Associates, Inc.

Tuovinen, J. E., & Sweller, J. (1999). A comparison of cognitive load associated with discovery learning and worked examples. Journal of Educational Psychology(2), 334.

Rodney Sizemore is a geometry teacher at Ola High in Henry County and an Ed. D. student at Kennesaw State University. He has been in education for 23 years and has taught both general education and exceptional education high school mathematics, and from eighth grade through college.

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Advocacy Update

The advocacy efforts of GCTM are improved as a result of the consulting services provided by Tyler (TJ) Kaplan of The JL Morgan Company, Inc. For the past three years, TJ has been instrumental in arranging a number of opportunities for officers and members of GCTM to interact with legislators: meetings with legislative leaders in their offices, a luncheon for a discussion about the importance of a sound mathematics education, and a visit by a legislator to a public school in her school district. TJ made contacts and arrangements for a Brian Burdette, a State Board of Education member, to attend the 2016 GA Math Conference. Furthermore, TJ forwards information regarding relevant legislative and State Board of Education considerations. At the conclusion of the 2017 legislative session, TJ submitted the following report.

Georgia General Assembly Summary Report, 2017 Session

Legislative report:

In the early hours of the morning on March 31st, 2017 the Georgia General Assembly completed its 40-day legislative session and adjourned “Sine Die.” After adjournment, the Governor has 40 days to sign or veto bills. If the Governor does not sign or veto a bill, it will automatically become law. The Governor has the power of line-item veto over the budget bills. Below is a comprehensive summary of the most relevant pieces of legislation that were filed and considered in the 2017 session of the legislature.

  • HB 139, sponsored by Rep. Dave Belton (R-Buckhead). This measure is intended to provide for transparency and accuracy of the financial information of local school systems and schools. It would require the Department of Education to make publicly available on its website the budget and expenditure information for each school.

  • Status: The legislation was approved by both chambers and is now on the Governor’s desk.

  • HB 237, sponsored by House Education Chairman Brooks Coleman (R-Duluth). This bill, which has been characterized as a piece of legislation meant to support the intent of HB 338, would authorize the Public Education Innovation Fund to receive private donations that could be used as grants for public schools, and establishes a tax credit for such a donation. The legislation was changed in the Senate to reduce the maximum amount of tax credits available to $5,000,000 and sunset the law on December 31, 2020.

  • Status: The legislation was approved by both chambers and is now on the Governor’s desk.

  • HB 338, sponsored by Rep. Kevin Tanner (R-Dawsonville) is school reform legislation intended to give the State Board of Education more authority to intervene in chronically failing schools. Late in the session the measure was renamed the “First Priority Act” and was amended to include a change that prevents for-profit entities from operating state schools under the terms of the legislation. A change was also made to the formation of the education turnaround advisory council in order to include more representation from the education community and their respective associations. Additionally, the State Board of Education instead of the Superintendent of Schools will appoint the Chief Turnaround Officer who will have substantial authority over the turnaround process. Finally, $1,000,000 in funding for the implementation of the bill was added to the conference committee report on the fiscal year 2018 budget and a provision was included in HB 338 that creates a Joint Study Committee on the potential establishment of an accreditation process for public schools.

  • Status: The legislation was approved by both chambers and is now on the Governor’s desk.

  • HB 425, sponsored by Rep. Joyce Chandler (R-Grayson) would strongly encourage the State Board of Education and local school systems to allow the administration of standardized tests in pencil and paper format. The bill would also ask the State School Superintendent to develop guidelines that would be approved by the State Board of Education to strongly encourage how local school systems should handle students who do not participate in state-wide assessments.

  • Status: The legislation was approved by both chambers and is now on the Governor’s desk.

  • HR 686, sponsored by Rep. Kevin Tanner (R-Dawsonville), creates the House Study Committee on Equitable Local Education Funding to include three members of the House of Representatives. This study committee will present an excellent opportunity for us to engage with key influencers on the local education funding process over the interim period. We will monitor this closely throughout the interim period and report on any relevant developments in real time.

  • Status: This resolution was approved by the House and is awaiting appointments.

  • SB 30, sponsored by Sen. Vincent Fort (D-Atlanta) would create a pilot program for Sustainable Community School Operations Grants and would allow the Department of Education to issue grants to plan, implement, and improve sustainable community schools. In the Senate version of the fiscal year 2018 budget $50,000 was appropriated to allow for grants to be remitted, but the funding was not included in the conference committee report on the budget.

  • Status: This bill was approved by the Senate and was later attached to HB 430 in the House but was removed (deleted) before coming back to the Senate for agreement to the House changes.

  • SB 211, sponsored by Senate Education Chairman Lindsey Tippins (R-Marietta) seeks to clarify many of the provisions of SB 364 that were signed into law in 2016. Specifically, the legislation directs local districts along with the Department of Education to pursue maximum flexibility from the federal government in terms of the tests that are administered and required in public schools. Additionally, the measure instructs the State Board of Education to conduct a study of nationally recognized standardized tests and their alignment with state standards. Included in the conference committee report on the budget is $250,000 in the Department of Education budget to “increase funds for concordant testing models as prescribed by SB 211.”

  • Status: The legislation was approved by both chambers and is now on the Governor’s desk.

Bill Sponsor Status Description
HB 13 Rep. Jeff Jones
Did not pass Creates a school supplies tax credit for teachers
HB 139 Rep. Dave Belton
Approved by both chambers and sent to Governor’s desk Provides transparency of spending for local school systems
HB 237 Rep. Brooks Coleman
Approved by both chambers and sent to Governor’s desk Allow Public Education Innovation Fund to receive private money for grants for public schools
HB 338 Rep. Kevin Tanner
Approved by both chambers and sent to Governor’s desk School reform legislation giving the State Board of Education more authority to step in at chronically failing schools
HB 425 Rep. Joyce Chandler
Approved by both chambers and sent to Governor’s desk Strongly encourages the State Board of Education to allow standardized tests to be administered in pencil and paper format and prohibit “sit and stare” policies for students who do not take the tests
HB 430 Rep. Buzz Brockway
Approved by both chambers and sent to Governor’s desk Implements certain recommendations from the Governor’s Education Reform Commission relating to charter schools
HR 634 Rep. Christian Coomer
Approved by the House, awaiting appointments House Study Committee on Civics Education in Georgia
HR 686 Rep. Kevin Tanner
Approved by the House, awaiting appointments House Study Committee on Equitable Local Education Funding
SB 3 Sen. Lindsey Tippins
Did not pass CONNECT Act – Senate GOP caucus priority that enhances industry credentialing for some programs in high school
SB 211 Sen. Lindsey Tippins
Approved by both chambers and sent to Governor’s desk Sets forth specific instructions to the SBOE around assessment components enacted by SB 364 in 2016

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Awards and Grants
by Peggy Pool, VP Honors and Awards


Do you know a teacher of mathematics that goes above and beyond their job description to assure their students are successful? Now is the perfect time to stop and recommend this person for a well-deserved GCTM honor/award.

The rules for making a nomination make it easier than ever to submit the name of a special educator that truly makes a difference in the lives of their students for a GCTM honor/award. No longer does the person making the nomination need to be a member of GCTM, except in the case of the Gladys M. Thomason Award. This means any teacher, coach, administrator, parent, or student is now eligible to submit a fabulous candidate for any of the other appropriate honors/awards.

The deadline for nominations for the following awards is Labor Day of the current year.

Gladys M. Thomason Award for Distinguished Service
Each year, GCTM selects one outstanding individual as the Gladys M. Thomason Award winner. Selection is based on distinguished service in the field of mathematics education at the local, regional, and state levels. To be eligible for the award, the nominee must be a member of GCTM and NCTM; be fully certified in mathematics, elementary or middle grades education at the fourth year level or beyond -- or if the nominee is a college professor, be at least an assistant professor; and have had at least five years teaching or supervisory experience in mathematics or mathematical education in Georgia.

Dwight Love Award
This award is presented to a teacher in Georgia who models excellence in the profession and in life and gives much to others beyond the classroom as mentor, teacher and leader. The awardee is a master teacher, professionally active, and promotes GCTM and its mission.

John Neff Award
This award is presented to a member of GCTM who demonstrates excellence as a full time post secondary educator and/or district supervisor. The recipient is someone who is an inspirer, a mentor, and an advocate of mathematics and mathematics education.

Awards for Excellence in the Teaching of Mathematics
Three awards, one each for elementary, middle, and secondary levels, are given to excellent teachers who have strong content foundations in mathematics appropriate for their teaching level, show evidence of growth in the teaching of mathematics, and show evidence of professional involvement in GCTM and NCTM.

Teacher of Promise Award
GCTM recognizes one outstanding new teacher/ member in the state each year who has no more than 3 years experience at the time of the nomination and who demonstrates qualities of excellence in the teaching of mathematics.

If you have any questions or comments about any of the above awards, please contact Peggy Pool at awards@gctm.org.


Do you have marvelous ideas for activities and lessons for your students, but just do not have the materials to implement them in your classroom because there is no money available through your school, system, or PTA? GCTM can help!

Be sure to make your rationale simple for those voting on your grant to understand the purpose of your lesson, why you need the items you are requesting, and why you need help with funding. GCTM wants to help YOU! Click here to find out more!

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GMC Update
by David Thacker,
GMC Program Chair

Excitement is building for the 2017 Georgia Mathematics Conference (GMC) to be held October 18-20, 2017, at the Rock Eagle 4-H Center. This year’s theme is “Communicating Mathematics: Creating a Culture for Discourse Fluency.” Conference presenters and attendees will engage in and “facilitate meaningful mathematical discourse” (National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: p. 10.). This year’s Program Planning Committee informed the design and content of the 2017 GMC through numerous collaborative sessions, and the definition of discourse below and the wordle graphic represent two aspects of this design thinking.

What Is Discourse?

Discourse can be messy, and there is no single course of action or step-by-step linear approach that says discourse starts here and finishes over here. Discourse is on-going, circuitous, and reflective. Discourse includes students, mathematics educators, all types of support personnel at the school, district, regional, state, national, and international levels, and the communities/families at-large. Further, discourse can occur through a variety of platforms, including face-to-face, peer-to-peer, student-to-teacher and vice versa, teacher-to-teacher, etc., through digital environments, and others not even realized. Discourse also occurs though spoken ideas, written ideas, reading of text, listening, social media environments, such as blogs, and much more.

Highlights of this year’s GMC are included below:

Keynote Speakers:

October 18, Wednesday evening: Christine (Chris) Franklin, K-12 Statistics Ambassador for the American Statistical Association and retired, a 36-year veteran math educator from the University of Georgia.

October 19, Thursday evening: Sunil Singh, a Lead Ambassador of The Global Math Project and author of Pi of Life: The Hidden Happiness of Mathematics.

October 20, Friday afternoon: Sue O’Connell, an experienced classroom teacher, math coach, district improvement specialist, speaker/consultant, and lead author for Heinemann’s Math in Practice series.

Featured Speakers:

  • Chris Franklin, keynote speaker

  • Sunil Singh, keynote speaker

  • Sue O’Connell, keynote speaker

  • Patricia Baltzley, Montana mathematics educator and experienced pre-K-12 Mathematics Director for Baltimore Public Schools

  • Michelle Mikes, GCSM President, Mathematics Supervisor for Cobb County (and colleagues to include TJ Kaplan, Legislative Representative, State of Georgia; Terry Haney, RESA Math; Vinnie Prasad, Mathematics Coach, Cobb County; Angela Stewart, Principal, Lovinggood MS, Cobb County; Sandi Woodall, Math Program Director, State of Georgia)

  • Melissa Paris, Elementary Instructional Coach, Whitfield County

  • Ge-Anne Bolhuis, Secondary Instructional Technology Coordinator, Whitfield County

EdCamp-Style Discourse Sessions for Wednesday afternoon:

From 3-5 p.m., on October 18, 2017, GCTM will offer its first EdCamp-style discourse sessions at the state math conference. The focus for these sessions will be to engage participants in a discussion on new techniques for teaching mathematics, to enrich their knowledge, and to elevate their understanding of how discourse promotes mathematical literacy and improves academic practice. Sessions occur from 3-5 p.m., in the Wildlife Ecology Building.

Sessions offered are determined organically by the participants during the introductory session (first 20 minutes). In other words, bring your topics and let’s discuss!

For more information on the full EdCamp model, please visit https://www.edcamp.org/ 

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GCTM Membership Report
by Susan Craig, Membership Director

A Membership Worth Millions!

Summertime gives us time to pause and catch our breath before greeting a new class of students. Teaching has many benefits! The ones I always enjoyed were the endings and new beginnings. As hurried as our lives become as the year progresses, we know that the summer will allow us to wrap up our year, close our plan and grade books, head our students out the door and onto new learning experiences. A chance to catch our breath, renew our spirits. Then fall brings newness with blank pages to write upon...in plan and grade books, in children’s minds, in making new memories.

GCTM membership currently stands at 1320. This includes 549 Active members, some 250 student members, 400 Life members, some Retired members and some inactive Life members.

BUT... there are 425 LAPSED members from 2016 and 51 LAPSED in 2017. That is close to another 500 members who have not renewed their participation in this wonderful organization in the last year.

We live in a different world than when I joined GCTM many years ago, but joining was a long term professional commitment - one that enriched ourselves and our students. It cost $15 and was worth millions. That was another century, literally, but today the value is the same and the cost virtually the same, only $20.

PLEASE encourage your colleagues, beginning teachers and yourselves to continue to support GCTM with active, ongoing membership. Our organization and efforts need you!

Please make a point to support GCTM this summer and in the new year which approaches all too quickly! 

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Region Representatives Summer Academy Updates
by Kristi Caissie V.P. Regional Services

Summertime, Summertime, Sum, Sum, Summertime!

Summertime plus math training equals a great time with GCTM!

The Region Representatives are hosting the 2017 Summer Mathematics Academies in four different locations across the state. Participants are learning about the eight most effective teaching strategies for the mathematics classroom as referenced in Principles to Action by NCTM. A large focus on productive struggle had many participants discussing how they would change instruction in the classroom to make learning more meaningful. Engaging, higher-order thinking tasks aligned to GSE are being tackled by teachers so that they may take their learning back to the students in the 2017-2018 school year. Each session has a focus on equity and equality. It is not always appropriate to give every student the same thing in the same way. There are students that need different styles of instruction or different scaffolds, however, every student needs rigorous, demanding tasks. Keeping high expectations in the classroom ensures that the students grow to meet the demands of the instruction.

Participants leave these sessions saying things like:

“This was the first session that was comfortable enough for participation.”

“I loved how one task worked with multiple grade levels”

“I have more learning strategies to implement.”

“I have a greater appreciation for tasks.”

As one school year closes and we begin to move toward another year opening, it is time to increase our teacher knowledge with the Summer Mathematics Academies!  

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NCTM Report
by Dottie Whitlow,
NCTM Representative

National Council of Teachers of Mathematics
NCTM Annual Meeting & Exposition 2017
April 5-8, 2017
San Antonio, Texas


NCTM Mission:
The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for each and every student through vision, leadership, professional development and research.

NCTM Vision:
The National Council of Teachers of Mathematics is the global leader and foremost authority in mathematics education, ensuring that each and every student has 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.

All of the Affiliate groups meet in groups to collaborate with the other Affiliates in their Region. All groups were asked to discuss the questions that follow.

Discussion Questions:

  1. How are you addressing equity, access and empowerment in your region? How could NCTM support you in addressing these issues?

  2. What does your affiliate feel has been a benefit about your relationship with NCTM? What else do you think NCTM & affiliates could do together to make the relationship more productive?

  3. What other recommendation do you have concerning mathematics education issues or NCTM operations issues?

The various Regions of NCTM Affiliates are:

  1. Canada

  2. Central

  3. Eastern

  4. Southern

  5. Western

All of the responses to the questions can be found at http://tinyurl.com/zdbvm3d. It might be beneficial to review them for other ideas and perspectives, even though they originate from other regions.

The Southern Region made two significant suggestions. First, a “parents’ tab” on the NCTM website foster parent buy-om to move mathematics education forward. To increase accessibility, the site should use a common language that is readable for all parents and use video clips to help parents understand. Second, in order to prepare and retain quality new teachers, all stakeholders need to be part of the process of developing new teachers. Therefore, NCTM needs to strengthen relationships between teacher preparation programs, higher education faculty, K-12 mentor teachers, and their school/district administration.

2017 NCTM Affiliate Caucus Discussion

SOUTHERN Caucus Notes

  1. How are you addressing equity, access, and empowerment in your region? How could NCTM support you in addressing these issues?

  2. What does your affiliate feel has been a benefit about your relationship with NCTM? What else do you think NCTM and affiliates could do together to make the relationship more productive?

    • Southern: The focus being more defined for pre-service teachers organizations. Welcome letter for new student members to get to know the organization and how to use the resources. Survey those in Higher Ed who do that work. This population needs a much stronger focus.

    • A better way to network the members and structure, particularly to build community through various mediums. Allow the networking that younger folks use daily.

    • NCTM training or materials for the mentor teacher. Something of high quality; like a mentor teacher toolkit.

    • An advocacy for the classroom teachers who once themselves were a pre-service.

  3. What other recommendations do you have concerning mathematics education issues or NCTM operations issues?

    • Southern: Texas state board removing the process standards from standards based on many parents going to state board. Potentially based on the lots of homework going home, too much. Uninformed parents are basically the issue. NCTM needs to do a better job working with states having issues and the research behind it. Public service announcements, as well as position statements specific to states. Working with affiliates as a need for parents, but maybe not enough support in this manner.

    • Difficult to find math education teachers who mentor student teachers well. All grades teachers and the difficulty to find the excellent teachers who demonstrate these practices. The cost of the NCTM experience would be out of reach, the regional avenue and discounted early career. Quantity discount for bulk conference attendance.

A well-defined role (materials, suggested training, building from other successes) produced by NCTM of the mentor teacher, but addressing leadership’s role in the schools pre-service teachers are placed. The leadership recommendation is extremely important to this issue.

The space for which administrators refer, NCTM documents related to this issue/suggestion needs to be published or presented. The NCTM needs to collaborate with other professional organizations to improve the perception of the profession and advocate because of the decreased enrollments in preparation programs.

Consider the possibility of live streaming sessions from the Annual Meeting for teachers who cannot attend (due to timing, testing, expense of conference, etc.)

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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

Editor's Note - by Becky Gammill, Ed.D., Publications Editor

Tournament  Updates by Chuck Garner, VP of Tournaments and  Competitions

Inquiry or Explicit Instruction? by Rodney Sizemore, Ed. D. Student at Kennesaw State University; Geometry Teacher at Ola High in Henry County

Advocacy Update

Awards and Grants by Peggy Pool, VP Honors and Awards

GMC Update by David Thacker, GMC Program Chair

GCTM Membership Report - by Susan Craig Membership Director

Region Representatives Summer Academy Updates by Kristi Caissie V.P. Regional Services

NCTM Report by Dottie Whitlow, NCTM Representative

GCTM Executive Board


Georgia Council of Teachers of Mathematics | PO Box 683905, Marietta GA 30068