Vol IX

No. 3

Fall
2017

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The additional fallout will occur within the House and Senate Majority Caucuses as retirements lead to open chairmanships. The data show that there will likely be more than 40 percent turnover in the legislature between 2015 and 2018. The anticipated retirement of longtime committee chairmen will leave large gaps in institutional knowledge and present a plethora of opportunities to cultivate new key influencers as allies.
Although we do not support particular candidates for office, your GCTM team will continue to monitor these key elections and make regular reports on relevant developments.
 

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The Executive Committee is pleased to report that The Georgia Council of Teachers of Mathematics, Inc. is now designated a public charity exempt from federal income tax under Internal Revenue Code Section 501(c)(3) effective January 1, 2017.

Donors to GCTM can now deduct contributions made under IRC Section 170, and GCTM is qualified to receive tax deductible bequests, devices, transfers, or gifts under Section 2055, 2106, or 2522.

GCTM will maintain a list of its donors and grantors and the amount of cash contributions or grants (or a description of the noncash contributions) received from each. For tax deduction purposes, each donor will receive written acknowledgment from GCTM of the contribution including the date and amount of any cash contribution, and description of any non-cash contributions and whether any goods or services were provided in return for the contribution.

Please address any questions to:
Nicole Ice, Ph.D.
Treasurer
The Georgia Council of Teachers of Mathematics, Inc.
P.O. Box 683905
Marietta, GA 30068

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Summertime: A time for relaxation, a time for fun, a time for family, and a time for growth...growth of your personal and professional self!

Over 550 teachers participated in professional growth with the 2017 Summer Mathematics Academies with GCTM. The teachers learned many things throughout the two-day academy. A heavy focus was placed on the eight effective teaching practices from the book, "Principles to Action: Ensuring Mathematical Success for All". Teachers learned how to establish goals within lessons in order to focus the students learning and to guide instructional decisions. Tasks for each grade level and goals associated with these tasks were used to develop the conversation amongst teachers and to facilitate mathematical discourse about the math and about the classroom. Teachers practiced using purposeful questions to guide the lessons and to help students reason about the math and to make sense of the important ideas and relationships. Teachers used productive struggle to increase their knowledge of classroom strategies and mathematical ideas. In the words of a participant, "It is Ok and appropriate to let our students struggle and that they learn more from that." Video about Productive Struggle

During the Summer Academies teachers participated in grade level activities focused on standards for that grade band. They were able to walk away from the academy and immediately use the tasks with students. Many teachers experienced new manipulatives, new activities, and new games to support student learning. A Lunch-N-Learn was provided at each academy where teachers received a free lunch and the opportunity to learn about 3 Act Tasks. Teachers walked away from the one-hour lunch with free resources to fully engage their students in real-life problem-solving activities. Other teachers learned more from the tasks within the class where they not only learned the strategies for implementing problems in the classroom but also played along with each other while enjoying the numbers! Video of Teachers Playing a Game

During the summer of 2017, these teachers focused on professional growth! They grew their mathematical mindset, their toolbelt of strategies, and their knowledge of math. They grew their circle of collaborators until they had friends from other districts and schools. The knowledge and experiences they gained during these two days are invaluable to them and their students. Grow your math mind! Video about Collaborating

Join us for mathematical fun during the summer of 2018...more information about times and locations available at GMC!

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Abstract: To deepen students' understanding of fractions a variety of representations, methods, explanations, and justifications should be presented. When asking students to visually represent a given fraction, we likely get different yet equivalent representations. However, for a given visual representation, there may be several correct answers, depending on our "whole."

Fractions: Not Always a Two-Way Street

Students need a strong understanding of fractions as a launching pad for further progress in mathematics, particularly in algebra, which is a foundation for higher-level mathematics (Wu 2002, Fennell 2007, NMAP 2008, Wu 2014). However, the subject of fractions continues to be difficult for many students (Hecht, Vagi, & Torgeson 2007; Mazzocco & Devlin 2008; NMAP 2008), leading to further implications for their mathematical studies or careers. An effective way to help students understand fractions more deeply is to present a variety of representations, methods, explanations, and justifications (Harvey, 2012; Pantziara & Philippou, 2012, Cramer & Henry, 2002; Siebert & Gaskin, 2006). By using this approach, several different yet equivalent visual representations of a single fraction can be explored in order to help students better understand its value. With this technique in mind, we must examine the opposite direction--that is, for one given visual representation, are there several correct fractions, or is there only one correct fraction (or an equivalent one) that represents the visual? In this article, the authors include tasks and student responses designed to help teachers uncover some common misconceptions so that they are better prepared when introducing fractions to their own students.

Read more.

Dr. Heidi Eisenreich is an Assistant Professor of Mathematics Education at Georgia Southern University and a 2017 STaR (Service, Teaching, and Research) fellow through AMTE (Association of Mathematics Teacher Educators). Her interests lie in finding meaningful tasks that push beliefs about mathematics teaching and learning through discourse and reflecting on those tasks with preservice teachers, inservice teachers, and parents. She earned her Ph.D. in Mathematics Education from the University of Central Florida in Orlando.
Currently an Assistant Professor of Mathematics Education at Georgia Southern University, Dr. Ha Nguyen has taught mathematics courses and mathematics content courses for pre-service teachers as well as providing professional development for K-12 in-service teachers in Georgia. She was a Project NExT (New Experiences in Teaching) Blue'10 Fellow through the professional development program of the Mathematical Association of America. She is interested in students' understanding and thinking of mathematics and how to make mathematics relevant to students.
Dr. Joy Darley currently has the title of Associate Professor of Mathematics Emerita at Georgia Southern University and serves on the executive board for GCTM. Prior to her retirement in 2016, she taught mathematics content courses for pre-service teachers at Georgia Southern University. She is interested in both students' and pre-service teachers; conceptual understanding of mathematics, especially fractions and the arithmetic to algebra connection.

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I have recently incorporated the Showme app into my instructional practices. This interactive whiteboard application allows me to develop mathematical literacy to my students. Before I get into how I use the application in my classroom, let's first take a look at the application itself and why I choose to use this interactive whiteboard.

While searching for a way to better communicate mathematics to my students outside of the classroom I came across the idea of using an interactive whiteboard on my tablet. I knew I needed an interactive whiteboard that will record my annotations and my voice. This is why I chose the ShowMe app.  The app is available for purchase in the iTunes store and Google play for a small fee. The app lets the user record their annotation and their voice simultaneously; it also has the option to upload pictures that you may annotate, such as the Cartesian plane. Once finished recording the user has the option to email the recording or upload the video onto a website. There is a quick learning curve for using the program, and I found the program simple and easy to learn. I have found the use in the ShowMe app through answering emails from students by sending a video, one on one discussions with students where we use the app to discuss the proposed topic, and creating videos that review the solutions to assessments.

When answering emails from students I am able to use the ShowMe app to answer the questions and, more importantly, to show a visual representation of the answer. The Showme app allows me to dive deeper into the content remotely. Positive feedback from my students indicates that they seem to enjoy the recordings and understand the material better than a simple written out solution. The app is able to capture the real-life explanation to the student's question; it is as if the student is attending a private lecture that covers their question. It takes very minimum time to record and I have found that I spend more time discussing the topic instead of answering the question; hence, the student is obtaining the answer and is also developing a deeper understanding of the material. As an example, imagine if a student asked you to solve a basic quadratic equation. Consider the following exchange between student and teacher.

Email from student: Good afternoon Professor, I have a quick question. How do I solve the following equation x²-4=0? Thanks!

Email to student: Hello, we are dealing with a quadratic equation. Therefore, we must be sure that the equation is set equal to 0. We see that the equation is set equal to zero. We will now see if x²-4 is factorable; if we are able to factor the expression then we can apply the Zero-Product Theorem. Observe, x²-4=(x+2)(x-2). Thus, we have the following (x+2)(x-2)=0. Which implies that x+2=0 or x-2=0.
Consequently, x=-2 or x=2. Be sure to check the solutions!

It is an easy task to write a solution using a document writer, as illustrated above. However, with the use of the app, you are able to answer the question by showing and explaining the steps in solving the equation. Furthermore, you are able to show the visual representation of the equation and the solutions. This process helps the student to better understand how to solve the equation but, more importantly, they understand the meaning behind the solution.

I also use the app to answer questions in my office. When I meet with students in my office we use the app to discuss the proposed subject matter. Once the meeting is finished, I send the recording of the discussion to the student. This gives the students the pleasure of not taking notes during the meeting, to give all attention to the discussion, and to review the discussion at later times.

Another great use of the ShowMe  app is for covering the solutions for test. Instead of having a class set aside for the specific task, I record the solutions and explanations using the app. Then, I send the recording to the students once the test is finished. I have found that students who do poorly on the test are able to see the mistakes that they have made, and they are also learning from the mistakes that they have made in hopes to develop the understanding of the content. For the students who did well on the exam, the recording will be a great way for students to review for a comprehensive exam. In both situations, we are able to move to new material without getting bogged down in the previous work. For college instructors, this can be a vital tool to stay on your pacing guide. For secondary instructors, this can be a great way to use differentiation. The app also has the capability of creating videos that can be remotely assigned through email or class blogs. After giving the assigned videos, students are better prepared to work on in-class assignments related to the video content--much like in a flipped classroom.

The ShowMe app has been a blessing in my classes. I am not only able to send answers to the students' questions but also recordings to explain mathematical content. This process affords me the ability to stay on pace with the subject matter and while developing the confidence that my students have the opportunity to review material that has already been assessed. Although sending recordings to students is a great way to communicate the material, there is no substitution for written explanations. Students need to develop the skills to mathematically communicate through reading and writing in a mathematical language. Just keep in mind that this app is a great tool for developing mathematical literacy, but it is the responsibility of the instructor to not let it replace or take away from the beauty of reading and writing in mathematics.

A native of Southern Georgia, Andrew Shealy serves as a Lecturer of Mathematics at Mercer University. He earned his B.S. and M.S. in Mathematics, and has successfully completed the GaTapp program. Before Mercer University, he served as an Instructor of Mathematics at a State College and a Teacher of Mathematics at a High-School, both of which in Georgia. Although trained in Combinatorial Design Theory, his current research interests are found in mathematics education.

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This past summer, I had the opportunity to facilitate the Geometry (Analytic Geometry) class at the GCTM Summer Academies. Not only did I enjoy meeting teachers from areas all over the state of Georgia, I was able to both share and receive great ideas for my personal teaching practice, especially in the area of Geometry.

After the first day's sessions, I gave the participants an opportunity to ask questions anonymously to make sure we covered as many topics as possible on the second day. A common question was "could we go over strategies to cover the standards most effectively for the EOC Milestone?" Although our seminar focus was not to do "teaching to the test" strategies, the question is a legitimate concern in this era of high stakes testing. In response to this question, I thought about some of the practices I use in the classroom to teach material as it would naturally develop or make sense in the learning process. When I look at a curriculum map, such as the one developed for Geometry, I try to consider why we teach the topics in that particular order or whether there is a better logical way to approach the standards that would make sense to my students.

For example, in my earlier years of teaching the standards on Geometric Constructions, I would take a few days with a class set of compasses in tow and cover every construction that could possibly be asked on the EOC Milestone. We might pause to enjoy a few extraneous constructions such as the 6 petal "flower" (which leads to the hexagon). When we had more time for projects (before Milestones), I would even assign students to construct their own snowflake using geometric constructions. Yet overall, constructions was a unit of its own with little connection to the other geometric topics.

More recently, I've reconsidered the purpose of teaching constructions. By design, constructions are a way to reinforce the properties and relationships that are being discussed in other geometric topics. So why not spread out the constructions to when they are needed in other parts of the curriculum? I propose some of the following times to use a construction in context:

Bisect a Segment: when exploring properties of a perpendicular bisector to the base of an isosceles triangle

Constructing a Line Parallel to a Given Line Through a Point Not on the Line: when exploring properties of parallel lines and corresponding angles.
 

Construct an Equilateral Triangle: go ahead and drop an altitude (through construction) and introduce trigonometric ratios with a 30-60-90 triangle.
 

Construct a Square or Hexagon Inscribed in a Circle: discuss rotational symmetry or inscribed angle properties.
 

Almost every geometric construction can be used within the context of the curriculum. This approach makes constructions a teaching tool instead of a separate two to three-day unit. Since constructions are active based learning, students tend to be more engaged in the learning process and are using the compass throughout the semester instead of one week. I have even found that staggering the constructions within the curriculum tends to save a day or two of instruction in the overall picture of the semester or year. This instructional revelation would not have been possible if not for the shared dialogue that took place at the Summer Academies. Continue the discussion with us Georgia Mathematics Conference this year. We hope to see you there.

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The 2017 Georgia Mathematics Conference will be held on Oct 18-20th at the Rock Eagle 4-H Center

This year's theme is "Communicating Mathematics: Creating a Culture for Discourse Fluency."

What is this "discourse" of which we speak? 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 through spoken ideas, written ideas, reading of text, listening, social media environments, such as blogs, and much more. Keynote speakers include:

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. Oct 18 (Wednesday Evening)
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.   Oct 19 (Thursday Evening)
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. Oct 20 (Friday Afternoon)

Featured Speakers

left to right, and top to bottom
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)

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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HONORS & AWARDS

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.

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

GRANTS
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!

Mini-Grants
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.

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!

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Membership Matters!

Your GCTM Executive Board and Georgia Mathematics Conference Board are very busy preparing for a banner year ahead!

Now do your part and renew your membership!  Encourage a colleague!  Welcome a new teacher! Volunteer

Membership stands at about 1400.  We were 3000 strong just a few years ago!

YOU ARE GCTM. Without YOU we are nothing!  Renew today!

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Table of Contents

President's Message - by Bonnie Angel, GCTM President

Advocacy Report 2017 - by Denise Huddlestun, VP for Advocacy

Treasury Update - by Nicole Ice, Treasurer

Summer Academies - by Kristi Caisse

Fractions: Not Always a Two-Way Street - by Heidi Eisenreich, Ph.D., Ha Nguyen, Ph.D., Joy Darley, Ph.D.

Interactive Whiteboard use Outside the Classroom - by Andrew Shealy

Balancing the Equation - by Michelle Mikes, GCTM Secretary

A Special Geometry Note from the Summer Academies -
by Jeff McCammon, East Metro Region Representative

GMC Update - by Dr. David W. Thacker, GMC Program Chairperson

NCTM Affiliate Conference (Summer 2017) - by Brian Lack, Advocacy VP Intern

Awards and Grants - by Peggy Pool, VP Honors and Awards

GCTM Membership Report - by Susan Craig Membership Director

NCTM Report - by Dottie Whitlow, NCTM Representative

GCTM Executive Board

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