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Vol VII No. 3 Fall 2015 |
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My daughter is a high school mathematics teacher and has just started her fifth year of teaching. During pre-planning this year, her school hosted an open house for the students and their parents to allow them to meet their teachers and to become acquainted with their new schedules. One particular parent introduced herself to my daughter and asked her if she is related to the Mrs. Maddox that used to teach at the school where I served for eighteen years. Sure enough, that was the case, and the parent divulged that I had been her mathematics teacher in the eleventh grade. As my daughter related this story to me, my mind raced back through the all the years I taught in that school to see if I could spot this student in my memory. I imagined class after class of students, but, unfortunately, I couldn’t picture her even now knowing her name. I’m much better with faces than names, so I then turned to the consideration of what this parent remembered about her experience in my class way back then. I began my career in education with hopes of leading the masses of students, like the Pied Piper, to the utopia of complete mathematical understanding. The reality was, however, that I often underserved my students for shear lack of understanding on my part about how to help them learn. Teaching is, after all, a craft that must be molded and shaped and customized to meet the needs of students with the end goal of empowered student learning. I completely missed that idea early on and only realized it through the help and guidance of some key deep-thinkers who invested their wisdom into my life and faltering career. So I began to wonder if I needed to draft an apology letter to this parent to ask forgiveness for the mess I made of her eleventh-grade math class. I hoped she had come along later in my teaching career when my craft was much more honed and targeted. I listened carefully as my daughter related the rest of the story. This parent, my former student, had a very vivid memory of being in my class, but it had nothing to do with any of my instructional strategies or lack thereof. Apparently, the eleventh grade had been a ruthless year for her that was filled with overwhelming personal problems. She remembered that I had talked her out of dropping out of school, and she stated that she went on to graduate from high school on time. A successful college career came next, followed by a job and a family. So this turned out to be a very happy memory of being a student in my class after all. I have no recollection of such a conversation with any particular student. Of course, the foundational reason I went into teaching was to touch the lives of students for the good. I genuinely liked teenagers and felt a calling to devote my life to their advancement through the study of mathematics. I often questioned, though, at the end of one of those really hard days or weeks when nothing seemed to go right in the classroom if I was helping anyone to advance towards any goal. What a delight to find out I had helped someone find her way along life’s journey! It only stands to reason that the relationships formed with students are even more important than the academics they are asked to learn and we are required to teach. I can honestly say that I have never met a classroom teacher who doesn’t care about students and want the very best for the group they’ve been assigned. It’s hard to fake a devoted, compassionate spirit, and students pick up on those who avidly pour themselves into their lives. I hope you’ll take the time this new school year to rededicate yourself, whether it’s your fifth year or your thirty-fifth year, to being poured into the lives of your students.
A teacher affects eternity; he can never tell where his influence
stops. All the best to you for the coming year! Kaycie
This year, Reflections will focus on the theme of “Diving Deeper,” and will highlight topics that our readers have told us are important to them—hands-on activities, technology, statistics, and proofs. As always, we are looking for content that describes innovative, clever, and creative ways to teach mathematics. Do you have an effective statistics lesson you’d like to share? Are you using technology in your classroom that mathematically engages and excites your students to learn mathematics? Have you recently used a proof that helped your students derive rules and formulas for themselves? What is your favorite problem-solving activity that helps students make meaning of the mathematics they learn? If you are willing, please check out our Call for Manuscripts page and consider providing content for us. Do you have ideas, but are not sure where to begin? Feel free to email me at any time for advice on getting started. I look forward to hearing from you!
The MAMTC is one of a nation-wide network of math teachers’ circles that have been established over the last ten years with the support and direction of the American Institute of Mathematics (AIM). Visit this link to see how the circles are distributed across the country. The goal of the MAMTC is to bring together middle school, high school, and university mathematicians to work collaboratively on interesting mathematics, and enhance participants’ problem solving skills and enjoyment of mathematics. Math Circles for students began in this country in the early 1990’s and were influenced by those in Eastern European and Asian countries. The American Institute of Mathematics (AIM) began the first Math Teachers’ Circle in 2006 at the suggestion of Mary Fay-Zenk, a middle school teacher and veteran math team coach who regularly attended meetings of the San Jose Math Circle with her students. From 2007 to 2014, AIM held a series of workshops on How to Run a Math Teachers’ Circle. These workshops, sponsored by the National Security Agency, the National Science Foundation, and the Mathematical Association of America, helped teams of teachers and mathematicians start and sustain math teachers’ circles in their local areas. AIM maintains a support network and website at http://www.mathteacherscircle.org/.
Currently the MAMTC meets the second Monday of the month in September, October, November, January, February and March. We have dinner and work on the problem of the day. Our circle membership has expanded beyond the initial two schools to include middle school and secondary school teachers in the Metro Atlanta area. We are actively recruiting in Cobb County and have a Facebook page at http://www.facebook.com/MetroAtlantaMathTeachersCircle. Contact Dr. Watson at vwatson@kennesaw.edu and join the MAMTC for some fun mathematics! Dr. Virginia Watson is a graph theorist with 26 years of teaching experience at Kennesaw State University. She is a member of NCTM, MAA and the SIGMAA on Math Circles for Students and Teachers. Dr. Mary Garner is Professor Emeritus of Mathematics at Kennesaw State University. Now in retirement, she runs in math circles, and hopes to start (with Virginia Watson) a non-profit organization called the Gateway Community Math Center (GCMC). Through GCMC we hope to bring math circles activities to libraries, museums, schools, the street corner. Editor’s Note: Kennesaw State University also offers a Math Circle Summer Camp for high school mathematics students. More information about their program may be found at the links below. https://math.kennesaw.edu/happening/events/mathcircle_students.html https://www.facebook.com/KennesawStateUniversityMathCircle
Emory Math Circles for Middle and High School Students
Emory Math Circle started in the spring of 2014, after Sarah Trebat-Leder introduced the idea to other Emory math PhD students. Through her experience in running a math circle and other math enrichment activities in college, Ms. Trebat-Leder thought that Atlanta could benefit from similar programs. Thanks to the support of the Emory Math and Computer Science Department, this program was given classrooms to use, money for supplies, and a website and email account on the department servers.
Neither of the groups focus on competition math. The focus of the Fermat group is to make math fun by including lots of games like Nim, YouTube videos (see Vi Hart examples below), and hands-on activities such as an origami dodecahedron. In group Euler, sessions tend to be more traditional and include topics such as the different types of infinities, complex numbers, and RSA cryptography. Both groups generally do a different topic each week so that students may miss a meeting without falling behind. While some math circles have one primary instructor who teach every week, the Emory Math Circles have a core group of instructors, Emory graduate students, and guest speakers who teach regularly and present mathematical topics and problems.
Also see Hexaflexagon Safety Guide Math circles work to provide a social context for students who enjoy learning new, challenging mathematical concepts. If you are interested in starting a math circle, there are several options from which to choose in order to get started. The focus of math circles vary from Olympiad competitions, informal sessions using games and hands-on activities, and traditional enrichment classes. While some advertising at the start of a math circle is important, too much advertising tends to attract students who are looking for remedial tutoring or who are being forced to attend by their parents. After our first session, we have mainly relied on word of mouth to attract more participants. Also, keep in mind that it can be a challenge to recruit enough instructors. Consider reaching out to students and professors at nearby universities, and offer some perks for helping with math circle, such as free lunch.
Author Bios: Sarah Trebat-Leder graduated from Princeton University in 2013. She is currently a third-year mathematics Ph.D. student at Emory University, and the director of Emory Math Circle. Her non-math hobbies include board games, hiking, and Doctor Who. Amanda Clemm graduated from Scripps College in 2012. She is currently a fourth-year mathematics Ph.D. student at Emory University, and the co-director of Emory Math Circle. Her non-math hobbies include volleyball, baking, and playing with her dogs. Editorial Note: Here are some Math Circle problems for you to share or enjoy.
Active learning is fundamental to meeting the needs of early adolescents. The National Council of Teachers of Mathematics (NCTM) has long promoted pedagogical methods that require students to be intellectually engaged in constructing new knowledge with conceptual understanding (NCTM, 2000; NCTM, 2014). Instructional strategies centered on active learning include problem-solving tasks, questioning, and inquiry. Additionally, social and physical activities are also important instructional strategies included in this field. The purpose of this article is to discuss a framework for thinking about active learning in middle-grade mathematics classrooms (see Figure 1). Middle grades students respond well to active learning, but there are different ways of thinking about activity in the classroom. Instructional strategies that require students to be intellectually active should certainly be at the heart of any mathematics lesson; however, early adolescents need other types of active learning strategies as well, and mathematical problem solving promotes this activity. A Venn diagram was purposefully selected to represent the active learning framework. There are several instructional methods that simultaneously address multiple categories of intellectual, social, or physical activity.
Susan Edwards is an assistant professor at Georgia Regents University in Augusta, Georgia. She teaches middle grades and math education courses to pre-service and in-service teachers. Her research interests center around active learning in the middle school classroom. She is also the author of the book, “Getting Them to Talk: A Guide to Leading Discussions in the Middle Grades Classroom” published by the Association for Middle Level Education.
The conference will be held at the Rock Eagle 4-H Conference Center, Wednesday October 14 - Friday, October 16, 2015. On Thursday a special “conference-within-a- conference” will address leadership in mathematics education and will offer opportunities for state, district, and school leaders to interact with nationally known experts in the field and to collaborate with and learn from their peers. Although these sessions will focus on leadership they will be open to all conference participants. Keynote Speakers:
Other featured speakers include:
GMC will also include a conference-within-a-conference on Thursday from 1:00 pm to 4:00 pm. Sessions are laid out with David Foster and Phil Daro. Featured speakers also include: Chris Franklin, Sybilla Beckman (elementary), Cindy Moss, Pamela Weber Harris (secondary), Sherry Parrish (K-8, Number Talks, and HS), James Williams (all levels). Keep in mind that registration to the conference will NO longer include membership. Participants must join GCTM prior to registering for the conference. For questions about registration, please contact email registrar@gctm.org. Speaker or session questions may be forwarded to Nickey Ice atnice@gctm.org. Other general inquiries may be sent to Tammy Donalson at t.donalson@grady.k12.ga.us.
It’s Back to School time again. Are you ready? If you teach math, Matific can help! Matific produces award-winning, online math activities to supplement K-6 teachers’ lessons, and it’s free for educators! Engaging, hands-on math activities help reinforce mathematical concepts, so using Matific is a great idea. To make it even more enticing, Matific is offering a sweepstakes for anyone who signs up for a new Matific account between now and September 30th. Prizes include $25 Amazon gift cards, a Chromebook or even a $500 Amazon gift card to purchase classroom supplies, and lots of other prizes! A Matific teacher account includes:
Educators who want to sign up for a free Matific account and be automatically entered into the sweepstakes can join Matific at https://www.matific.com/us/en-us/join.
We were also pleased that not only were the participants super excited about attending sessions during the summer, but the principals who hosted us at the prospective schools were ecstatic as well. They were very accommodating with technology needs/concerns and provided us with the best custodial staff members that we could have asked for in an academy. Therefore, from the hearts of GCTM, we would like to thank all of the participants, hosting and supporting principals who lent their building and sent their teachers, custodial staff, writers, facilitators, and the Georgia Department of Education for supporting the life- long learning of all students across the state of Georgia.
Cherokee County Press Release Summer Academy Involvement Provides Meaningful Opportunities for Cherokee County Teachers School may be out for students, but summertime means lots of Cherokee County School District (CCSD) teachers are back in class themselves to get up to speed on the latest tools and techniques in classroom instruction. CCSD offers more than three dozen classes during post-planning and summer break, covering topics from teaching strategies to classroom technology. While in the past Georgia teachers were required to attend courses to keep their teaching certificates current, state legislation suspended the requirement during the recent recession as a budget accommodation for school districts. However, hundreds of CCSD teachers are still attending classes without the pressure of a state requirement, continuing to learn out of professional interest and the desire to become better teachers. One opportunity that the teachers took advantage of was participating in GCTM’s Summer Mathematics Academy. This two-day program for K-8 teachers had a focus on hands-on activities, revisions to standards, technology as a learning tool, and more. It was presented to our teachers by the Georgia Council of Teachers of Mathematics.
Happy New Year! How the summers fly, as well as the years. Time for celebration, but you probably feel a bit exhausted today with all the hubbub of a new group of students and the expectations of your role as a mathematics teacher. But what an exciting time this is, as you start anew with a clean slate and exciting new and old ideas to try and use again. One constant idea is to maintain your membership in GCTM. It offers continuous opportunities for growth and support of mathematics teaching and learning in Georgia. So when that renewal reminder comes your way, please respond and support our wonderful organization and enrich yourself. I had a call recently from Brandon, a university student preparing to teach. He is very interested in being an ACTIVE GCTM member starting now and into his teaching career. He wanted to know what we do and what opportunities we offer. It was exciting to speak with someone already committed to our profession and to being a volunteer. I imagine there are hundreds more of Brandon that we can encourage and bring into our fold. As members we need to encourage the next generation of teachers. One of the best ways to do that is to show them the benefits of professional membership in GCTM. So let your New Year’s resolution be to:
Please let us know if there is anything Membership can do to help you. Have a wonderful new year!
Founded in 1920, the National Council of Teachers of Mathematics (NCTM) is the world’s largest mathematics education organization, with 80,000 members and more than 230 Affiliates throughout the United States and Canada. Interested in Membership? Learn more about exclusive member benefits and discounts and join today at NCTM.org, Membership. NCTM Annual Meeting & Exposition 2016 NCTM Annual Meeting & Exposition 2016 “Building a Bridge to Student Success” will be held in San Francisco, California April 13-16, 2016. Hotel reservations opened up on August 26th. Visit NCTM’s conference page to find more information on registration, programs and presentations, housing and travel, sales opportunities, and other research conferences.
The Math Forum is Now a Part of NCTM NCTM is excited to announce that The Math Forum, an extensive online resource for the mathematics education community with nearly 100,000 subscribers, will become a part of NCTM. The merger will consolidate the resources of the two organizations.
NCTM Accepting Applications From Music Projects to Teach Pre-K-2 Mathematics - Philanthropy News Digest The National Council of Teachers of Mathematics is accepting applications from teachers of pre-K-2 mathematics for projects that incorporate music into the elementary school classroom as a way to help young students learn mathematics. With support from the Esther Mendelsohn Fund, the Using Music to Teach Mathematics program awards grants of up to $3,000 to individual classroom teachers or small groups of teachers collaborating on the grade level or across grade levels. Any acquisition of equipment must support the proposed plan but may not be the primary focus of the grant. Proposals must address the combining of mathematics and music, planning for improving students' learning of mathematics, and/or the anticipated impact on students' achievement. Find out more information here.
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Table of Contents President's Message - by Kaycie Maddox Editorial Note - by Rebecca Gammill The Metro Atlanta Math Teachers’ Circle - by Dr. Virginia Watson and Dr. Mary Garner Math Circles Opportunities for Students and Teachers - by Sarah Trebat-Leder and Amanda Clemm Active Learning in Middle School Mathematics - by Susan Edwards GCM Conference Information - by Tammy Donaldson GCMT Report on Summer Academies - by Dr. Valerie Lemon, Summer Academies Co-Director Membership Update - by Susan Craig, Membership Director NCTM News! - by Dottie Whitlow
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Georgia Council of Teachers of Mathematics | PO Box 5865, Augusta, GA 30916 | 1-855-ASK-GCTM |
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School
has started again for the 2015-2016 year, and it is ripe with
possibilities. Plans for the year include so many meetings that is
seems that one could not possibly fit all of them within one
preplanning calendar. What will this new year bring?
As
the new editor of Reflections, I sincerely hope that this
publication continues to serve the needs of our readers. You will
likely notice that we have made a few changes to the publication.
For one, we have dropped the “e” from the journal’s title,
streamlining the name to Reflections. Additionally, we’ve
made (or soon will make) several formatting changes throughout.
Mostly, we are striving to come up with ways for this important
conduit of Georgia-specific information to be more accessible to all
our readers. For now, the journal is completely online, and we will
continue to distribute it to our readers via their email accounts.
You may also access Reflections from
Find
a fraction strictly between 48/97 and 49/99 with the smallest
possible denominator! Play a game like rational tangles or frogs and
toads. Learn about graph theory, transfinite numbers, magic squares,
or codes and ciphers. Tackle games, puzzles, card tricks, or magic.
Use origami to make a stellated octahedron. Any of these
activities could be observed in a meeting of the Metro Atlanta Math
Teachers’ Circle (MAMTC).
The
MAMTC began with Dr. Virginia Watson of Kennesaw State University (KSU).
At the 2009 Joint Mathematics Meetings in Washington DC, Dr. Watson
attended a talk where she learned about math teachers’ circles. She
returned to Atlanta and assembled a team of KSU faculty, middle
school administrators, and middle school teachers. Dr. Watson, Dr.
Mary Garner of KSU, Ms. Angelique Smith, Principal at Champion Theme
School, Ms. Barbara Johnson, a middle school teacher at Champion
Theme School, and Dr. Brian Davis, Assistant Principal at Pine
Mountain Middle School attended a How to Run a Math Teachers’
Circle Workshop at the American Institute of Mathematics (AIM)
that summer. At this workshop they planned the launching of the
Metro Atlanta Math Teachers’ Circle (MAMTC), the first of its kind
in Georgia.
Mathematical circles are a form of outreach that
bring mathematicians into direct contact with pre-college students.
These students, and sometimes their teachers, meet with a
mathematician or graduate student in an informal setting, after
school or on weekends, to work on interesting problems or topics in
mathematics. The goal is to get the students excited about the
mathematics they are learning and to give them an encouraging
setting where they can become passionate about mathematics. Athletes
have sports teams through which to deepen their involvement with
sports; math circles can play a similar role for kids who like to
think.
From
the beginning, two groups met each Saturday at 2:00 pm in the Emory
Mathematics building. Group Euler is intended for students in grades
9 through 12 (and a few younger participants) who are ready for
something significantly more challenging, rigorous, and fast-paced
than a normal math class. The students’ mathematical background
coming to the circle is proficiency with algebra and basic geometry.
Most have done some extra-curricular math before and are already
passionate about mathematics.
Group
Fermat is intended for students in grades 6 through 9 who are
interested in solving puzzles, finding patterns, and figuring out
why and how things work. These students, who have a background in
pre-algebra, probably haven’t done any extra-curricular math before.
They may not necessarily be the top of their mathematics class and
may be unsure as to whether math is something they are passionate
about. However, they generally pick up concepts and make connections
easily compared to their peers.
Here
are some wonderful resources to start up a math circle in your area:
Introduction
Diane Briars - president of the National
Council of Teachers of Mathematics (NCTM), an 80,000-member
international mathematics education organization.
Previously, Briars was a mathematics education consultant,
working primarily to support schools and districts in their
interpretation and implementation of the Common Core State
Standards for Mathematics. She has also been a senior
developer and research associate on the Intensified Algebra
Project, a joint venture of the Learning Science Research
Institute at the University of Illinois at Chicago and the
Dana Center at the University of Texas at Austin. This
project, which is funded by the National Science Foundation,
focuses on developing instructional materials for
underprepared ninth-grade Algebra 1 students. Previously,
Briars was mathematics director for Pittsburgh Public
Schools. Under her leadership, Pittsburgh schools made
significant progress in increasing student achievement
through standards-based curricula, instruction, and
assessment.
David Dockterman – Dr. Dockterman is the
chief architect of learning sciences at Scholastic Education
where he provides guidance on turning research into practice
and programs. He is an adjunct lecturer on education,
technology, and innovation at the Harvard Graduate School of
Education. Dockterman has dedicated himself to supporting
classroom teaching and the successful integration of
technology into schools.
David Foster – David Foster is the
executive director of the Silicon Valley Mathematics
Initiative (SVMI) comprised of over 160 member districts in
the greater San Francisco Bay Area. He consulted with PARCC
and developed exemplars for SBAC. He is Co-Chair of the
advisory committee of the Mathematics Assessment Resource
Service/Balanced Assessment and is a consultant to the Urban
Math Leadership Network that works with the 25 largest
school districts in America.
Baruti Kafele – Principal Kafele has been a
highly regarded urban public school educator in New Jersey
for over twenty years. As a principal, he led the
transformation of four different schools, including “the
mighty” Newark Tech, which went from a low-performing school
in need of improvement to recognition by U.S. News and World
Report Magazine as one of America's best high schools. He is
the author of seven books which include his national
best-sellers, Motivating Black Males to Achieve in School
and in Life, Closing the Attitude Gap, and his
recently released title, The Principal 50: Critical
Leadership Questions for Inspiring Schoolwide Excellence.
Did
you attend the GCTM 2015 Summer Mathematics Academy? If not, you
missed a treat! This past summer, GCTM held an academy of 2-day
sessions in four different locations. The purpose of this year’s
academy was to: provide information and support for revisions to the
K-8 mathematics curriculum, provide hands-on activities; enhance
questioning; provide support and resources for technology
utilization. Locations for each academy included Freedom Middle
School (Canton), Thomson Middle School (Centerville), Peachtree
Ridge High School (Suwanee), and Brunswick High School (Brunswick).
Participants at each site expressed that the academy was a positive
experience through their session feedback. Participants shared their
‘ah-hah’ moments or things that stood out to them the most about our
summer academy sessions. Some of the participant comments were
things such as:
NCTM Vision: The National Council of Teachers of
Mathematics is the global leader and foremost authority in
mathematics education, ensuring that all students have access to the
highest quality mathematics teaching and learning. We envision a
world where everyone is enthused about mathematics, sees the value
and beauty of mathematics, and is empowered by the opportunities
mathematics affords. (Approved by the NCTM Board of Directors,
October 20, 2012)