Welcome to the winter edition of Reflections,
the Georgia Council of Teachers of Mathematics quarterly
publication. So much has transpired since the last edition of
Reflections was released!
The final results of the 2014 Winter and 2015 Spring
Georgia Milestone Assessments were released in October, providing a
wealth of much-anticipated data through which to sift and decipher.
Some of you who teach high school have already given the 2015 Winter
Milestone in December. Hopefully, these assessment results will
provide opportunities for conversations centered on authentic ways
to affect student achievement. I would recommend Visible Learning
for Teachers: Maximizing Impact on Learning by John Hattie as a
book that can frame these discussions for highly effective
strategies for the facilitation of learning as well as NCTM's
Principles to Actions.
The Georgia Mathematics Conference 2015 was a
jam-packed event on October 14th, 15th, and 16th. The theme of this
year's conference, Growing Student Potential in Mathematics, was
evident in the presentations, workshops, and sessions provided by
keynote, featured, and volunteer speakers. The theme allowed us to
focus on two major areas of research: motivating our students to
grow their minds and classroom implementation of the eight Effective
Mathematics Teaching Practices as outlined in the NCTM publication
Principles to Action. Each conference participant received a
copy of Principles to Actions, enabling each one to open to
exact passages as various speakers made references. We also held our
very first "conference-within-a-conference" for leadership on
Thursday afternoon, targeting state, district, and school-level
leaders to make all stakeholders aware of the latest findings on how
people learn and of the challenges facing mathematics teachers in
today's classrooms. The beautiful weather served as a backdrop as
GCTM members were provided with opportunities to grapple with new
mathematical concepts and explore resources to incorporate into
their own teaching practices. With another successful GMC completed
(see the GMC collage below), GCTM looks forward to new events on the
horizon, such as Math Day at the Capitol 2016 on February 8th and
the NCTM Summer Academies on July 11-16, 2016. More information on
these events will be forthcoming
As we move into the New Year, we also welcome our
newly elected GCTM officers: Michelle Mikes as Secretary and Joy
Darley as Vice-President for Constitution and Policy. Michelle is
the Mathematics Supervisor for the Division of Instruction and
Innovation Practice for Cobb County Schools, and Joy is an associate
professor in the Department of Mathematical Sciences at Georgia
Southern University. We are excited about the leadership that these
new officers will bring to the GCTM Executive Committee.
Sometimes the winter months can seem dark and gloomy
and long. Keep fighting the good fight with your eyes on the prize
of fostering student learning! The warmer days of Spring are right
around the corner.
Mini-Grants are awarded in any amount up to $300 and
are awarded on the criteria that the proposals highlight creative
innovations, provide potential to impact student learning or for
replication by and dissemination to other teachers, and advance
NCTM's Principals and Standard for School Mathematics. This year's
mini-grant recipients include:
Chris Brown
iPAD Mini Creations (K-5)
Rocky Creek Elementary School
Hampton, GA
Marian Dingle
Exploring Volume
Ashford Park Elementary School
Norcross, GA
Melanie Helms
Touching Mathematics (6 - 8) Waycross Middle School
Waycross, GA
Tami Sigman
Padding Along! (9-12) Coosa High School
Silver Creek, GA
For more information about Mini-Grants or Funds for
Special Projects, please visit
GCTM's Grants page.
Other award recipients were also recognized for
their expertise, passion, and leadership in teaching mathematics at
this year’s Georgia Mathematics Conference at Rock Eagle.
Congratulations to the following awardees.
Teacher of Promise Award
Middle School Teacher of Excellence
Dwight Love Award
Jennifer Donalson
Washington Middle School
Grady County
Ashley Clody
Awtry Middle School
Cobb County
Brian Stone
Northview High School
Fulton County
About the Awards
GCTM recognizes one outstanding new
teacher/ member in the state each year who has no more than
three years of experience at the time of the nomination and
who demonstrates qualities of excellence in the teaching of
mathematics.
GCTM honors 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.
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.
The Gladys M. Thomason Award for
Distinguished Service
Cheryl Hughes
Landmark Christian School
Fairburn, GA
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. For more information
about how to apply or nominate outstanding teachers for one
of the several awards GCTM offers, please visit
GCTM's Awards page.
The Presidential Award for Excellence
in Mathematics and Science Teaching
Valerie Camille Jones
Ron Clark Academy
Hapeville, GA
Presidential Award – This is the nation’s
highest honor for teachers of mathematics. Awardees serve as
models for their colleagues, inspiration to their
communities, and leaders in the improvement of mathematics
and science education. Awardees receive a citation from the
President of the United States and a $10,000 award from the
National Science Foundation On July 1st, 2015, the White
house announced the winners of the Presidential Awards for
Excellence, and Georgia’s own Valerie Jones included in this
group of elite educators! For more information about the
Presidential Awards for Excellence in Mathematics and
Science Teaching, please visit:
https://www.paemst.org/
The
2015 Georgia STEM Leadership Forum was held at the Classic Center in
Athens, Georgia, on October 25th. This joint effort was sponsored
by:
Georgia Association for Career & Technical
Education
Georgia Council of Supervisors of Mathematics
Georgia Council of Teachers of Mathematics
Georgia Science Supervisors Association
Georgia Science Teachers Association
Georgia STEAM Alliance Network
The
purpose of the forum was outlined as: “Bringing excellent STEM
education to all students requires STEM leaders who not only
understand good teaching but also have the ability to advocate for
students at local and state levels. This special workshop provided
an excellent lead-in to the Georgia STEM Forum by giving STEM
leaders the tools they need to promote STEM education across the
state.”
Speakers at this event included Dr. Gilda Lyon, from
the Georgia Department of Education STEM Office, Georgia Senator
John Wilkinson (pictured to the right), and Matthew Gambill,
President of the Georgia Association for Career & Technical
Education. Each speaker provided insights and updates into the
current state of STEM education in Georgia as well as ways to
advocate for the teachers and students here in our state. Kaycie
Maddox, President, Denise Huddlestun, Vice-President for Advocacy,
and Chuck Garner, Vice-President for Competitions, represented GCTM
at the STEM Leadership Forum.
GCTM President-Elect Bonnie Angel, GCTM V.P of
Advocacy Denise Huddlestun and GCTM Secretary Debbie Kohler attended
the 2015 NCTM Affiliate Leadership Institute in Phoenix, AZ July 14
– 16. Three main focuses for the conference included networking with
other affiliate leaders across the United States, continuing to work
on the strategic plan for GCTM, and studying change with discussions
from Switch: How to Change Things When Change is Hard (Chip & Dan
Heath). This book involved looking at problems in schools and
classrooms with a desire to change. There are three main ideas
involved with “Switch” – the Rider, the Elephant and the Path. Each
of these ideas was developed in a method that the leaders involved
learned ways to effect change.
The Rider is our rational side. It is important to
direct the rider by following the bright spots in the classroom,
script the critical moves and point to the destination. Directing
the rider might include studying what has worked in the past, or
looking for bright spots in the classroom. One might also look at
other situations that are similar but had positive outcomes. For a
difficult student, this could mean greeting them in a positive way
as they come in the door or giving them problems to solve that they
had access to. Scripting critical moves means that one has to be
specific instead of looking at the big picture. In order to “switch”
and create change, the behavior must be scripted and done so in a
way that eliminates ambiguity. Laddering down to a specific
behavioral goal is also a possibility. Finally, the rider needs to
have a destination. It is critical to point to that destination as
well as ensure that it is a rich destination – one that is
important.
Picture from left to right: Denise Huddlestun,
Debbie Kohler,
Diane Briar, and Bonnie Angel
The Elephant is the second part of the “Switch”
process. The elephant represents our emotional and instinctive side.
Its strengths are love, compassion, sympathy and loyalty. To make
progress toward a goal requires the energy and drive of an elephant,
but the elephant must also be motivated. Motivating factors include
using pictures or graphs to track progress. Breaking down the change
until it no longer spooks the elephant is helpful. Also, limit the
investment you are asking for and set small goals. The elephant must
be kept moving forward, given motivation and helped to feel
confident and needed. Cultivating a sense of identity and instilling
a growth mindset allow the elephant to move forward and shrink the
change.
The Path is the final component of the “Switch”
mindset. Shaping the path includes tweaking the environment and
building a habit. Tweaking the environment means recognizing that
what looks like a person problem may be a situation problem. When
the situation changes, the behavior will change. If the right
behaviors are made a little easier and the wrong behaviors are made
harder, then the path is changed. When the path is changed, the
behavior changes also. Building a habit that involves autopilot
opportunities with action triggers can create an ‘instant’ habit.
Action triggers are better than harder goals. Leaders who instill
them reinforce their team’s goals and make “free progress.” A good
change leader thinks “How can I set up a situation that brings out
the good in these people?” Good habits should advance the mission
and be easy to embrace. Thus, the “Switch” mentality involves three
main ideas --- 1) Speak to the Riders by pointing to the
destination, 2) Appeal to the identity of the group (elephant) and
3) Rally the herd by establishing a group norm.
Affiliates from each state also worked on the
Strategic Plan for their state. Since Georgia has a strategic plan,
action steps were developed for the strategic plan for three
specific goals. The Georgia leaders worked on strategic steps for
promoting a high quality mathematics education for all students,
promoting ongoing professional development for mathematics education
and for effective internal organization and execution in order to
meet objectives. Breakout sessions allowed for Georgia
representatives to meet with representatives from other states and
learn what each state was doing for Mathematics Education. Grant
availability, future NCTM Annual meeting dates, and best practices
in mathematics were also discussed. Leaders also met with Diane
Briars, President of NCTM, to discuss what NCTM is doing and how it
operates. Georgia’s goals and standards are very close to the goals
and standards of NCTM, so many of the other states’ leaders wanted
Georgia to share information. We presented information about the
Georgia Summer Academies, and individually spoke with other groups
about many things that Georgia’s GCTM does well including our
conference, advocacy and the use of our website. The Georgia leaders
left with more knowledge as well as positive goals to help improve
and sustain the state organization.
In
an effort to raise awareness of GCTM and its mission, GCTM had a
table at the 2015 Georgia Education Leadership Institute: Supporting
Student Success!The annual event, sponsored by the Georgia
Department of Education and the National Center for Youth Issues,
provides an opportunity to bring together leaders from many fields
interested in promoting and improving education in Georgia and was
held at the Marriott Marquis in Atlanta September 9 - 11. GCTM
representatives had access to speak to district, state, and building
leaders to inform them of GCTM’s mission and purpose and to extend
an invitation to attend the Leadership Strand of the Georgia
Mathematics Conference. Dottie Whitlow, NCTM Representative, spoke
with Superintendent Richard Woods during one of the breaks at the
conference. (See photograph below.) Other GCTM Executive Committee
members who helped with the table were Kaycie Maddox, GCTM
President; Bonnie Angel, GCTM President Elect; and Denise Huddlestun,
VP for Advocacy.
Advocacy
With the assistance of Tyler Kaplan, the legislative consultant
assisting GCTM in advocacy efforts, GCTM representatives met with a
leader from both the House and the Senate to promote the importance
of a quality mathematics education in Georgia. Kaycie Maddox and
Denise Huddlestun met with Senator Lindsey Tippins, Senate Education
Chairman, and Representative Brooks Coleman, Chairman of the House
Education Committee, to make them aware of GCTM’s mission and
purpose. The Education Reform Commission expressed their
appreciation for our discussion of the adoption of 1)a regular
curricula adoption cycle and 2) the importance of professional
learning for teachers. As the President of GCTM, Kaycie made a
public comment at the end of the Education Reform Commission meeting
on October 22, 2015 to communicate our support of these two items
being considered by the Commission. Find out more information about
the
Education Reform Commission.
NCTM Representative Dottie Whitlow and Superintendent
Richard Woods
Math Day at the Capitol
The
third annual Math Day at the Capitol is tentatively scheduled for
Monday, February 8, 2016 pending confirmation of the legislative
calendar. Representative Mike Dudgeon will sponsor a resolution to
be read in the House that day. When the resolution is read,
representatives from GCTM will be recognized on the floor of the
House and other GCTM members in the gallery will be recognized.
Rather than sponsoring a breakfast with limited time to engage in
conversations with legislators about the importance of a quality
mathematics education program in the state, a lunch and learn is
tentatively scheduled for key leaders in the education committees of
both the House and the Senate. A few GCTM representatives will
present information and offer an opportunity for discussion while
providing the lunch.
As I reflect over the last 24 years in math
education, I realize how much better I have become as a teacher. I
think back to those first few years teaching middle school. Yours is
not to reason why, just invert and multiply was how I taught
division of fractions! I am embarrassed to admit that I resorted to
short cuts and silly songs but I was doing the best I knew to do at
the time. Students would ask me why a certain procedure was used,
and I didn’t always know the answer. I was troubled when students
would mix up procedures or apply mnemonics to incorrect situations.
I knew that I needed to do something different. I was teaching at a
very superficial layer. My journey into improving my teaching
happened very early in my career and continues to this day. I had to
teach myself conceptual understanding to accompany the procedural
skills that I already had.
I quickly learned the power of having students use
manipulatives to discover mathematics. Manipulatives provide a
kinesthetic way to represent what could be very abstract concepts to
students. I began slowly by using two-color counters to teach
addition and subtraction of integers, algebra tiles to model solving
equations, and Cuisenaire rods to teach ratios and fractions.
Students can see, feel, move, and talk about mathematics by using
manipulatives. Their eyes light up when the mathematics was revealed
through the use of manipulatives. Finally, concepts were beginning
to make sense to students!
It hasn’t always been easy. Sometimes the
manipulatives backfire. If the problems are not carefully planned
out, the manipulatives may not reveal the mathematics, or they may
be too troublesome to use. I still struggle with using manipulatives
to demonstrate division of integers. I refuse to use geoboards in my
middle school classroom because arming middle school students with
rubber bands scares me. However, I continue to seek out new ways to
help students discover concepts with manipulatives.
This year, I planned a series of lessons to
introduce the Pythagorean Theorem to students. I wanted students to
have a solid grasp of the relationships of the sides in a right
triangle before introducing them to the formula. This lesson
addressed the standard, MGSE8.G.6, where students are to be able to
explain a proof of the Pythagorean Theorem and its converse. There
are multiple resources available for students to discover this
relationship. The state teacher edition (https://www.georgiastandards.org/Georgia-Standards/Pages/Math-6-8.aspx)
contains a Spotlight Task, The Pythagorean Relationship, which leads
students through a discovery activity. Students draw a right
triangle on grid paper, form squares on each side, find the areas of
the squares and look for the relationship. In my class, we performed
more of a hands-on approach by cutting out the two smaller squares
and reassembling them to fit on top of the square formed on the
hypotenuse. In particular, I used an activity from AIMS Education
Foundation, A Pythagorean Puzzle, from Looking at Geometry.
The physical movement of the pieces reinforced the concept of area
and the relationships between the areas on each side. As we
progressed through then unit, I frequently heard students
distinguish between areas and side lengths as they discussed
problems and helped each other. “You forgot to find the area – you
were just using the side length.”
We spent one class day discovering the relationship.
I closed the lesson by reviewing the relationship using the model.
At this point, I still had not formally introduced the Pythagorean
Theorem.
I asked questions such as:
If square A has an area of 81 square units, what
is the length of side a?
If the length of side b is 12 units, what
is the area of B?
If square A has an area of 15 square units and
square B has an area of 25 square units, what is the area of
square C?
If side a has a length of 6 units, and
side b has a length of 8 units, what is the area of
square C?
Students were able to successfully answer each of
the questions and truly had a good grasp of the concept.
On the second day, we discovered the converse of the
Pythagorean Theorem using the Triangle Discovery activity. Students
cut out squares from grid paper and used them to create triangles.
Using the manipulatives, students discovered how to determine if a
triangle was an acute, right, or obtuse triangle given the side
lengths. This activity connected nicely to a previously learned
concept from seventh grade (MGSE7.G.2) where students are to
“explore various geometric shapes with given conditions. Focus on
creating triangles from three measures of angles and/or sides,
noticing when the conditions determine a unique triangle, more than
one triangle, or no triangle.” Students remembered that the sums of
any two sides of a triangle must be greater than the third side in
order for a triangle to be formed. This activity allowed them to
delve further into the concept to determine the type of triangle
formed based on the side lengths. Students referred to the grid
paper manipulatives as they made generalizations. I heard comments
such as, “When c2 is larger than the a2
and b2, the a2 and b2
squares have to stretch out to make the triangle. That is why an
obtuse triangle is formed.” I recommend using fairly large grids
such as centimeter grid paper or larger. For some of the triangles,
if they are not carefully lined up, could appear to be a right
triangle. If this happens, address it during the lesson debrief and
reach class consensus on the type of triangle.
I debriefed the lesson using questions such as:
Name three side lengths that would make an acute
(right, obtuse) triangle. How do you know?
Name three side lengths that wouldn’t make a
triangle at all. How do you know?
If a right triangle had a hypotenuse of 10
centimeters and a leg of 8 centimeters, what would be the length
of the other leg?
Up until this point, I still had not officially
introduced the theorem to the students in its traditional form, a2
+ b2 = c2. Students were able to
successfully answer all of the questions based on the experience
they had with the manipulatives. On day three of this mini-unit, I
introduced the traditional form of the Pythagorean Theorem to
students. Because of the activities we had completed, expressions
such as a2, b2, and c2
had meaning to them. As we continued through the unit, they
constantly referenced these introductory activities. The initial two
days I spent with discovery activities at the beginning of the unit
not only were engaging and meaningful to students, but they “bought”
me extra time as we progressed through problems and applications. I
did not have to spend additional time reteaching the theorem, the
relationships, or vocabulary. The conceptual development had laid a
firm foundation for procedural fluency.
Resources: Looking at Geometry. (2009). AIMS
Education Foundation, Fresno, CA.
Dina Sherwood teaches math at Barber Middle
School in Cobb County. Prior to Barber, Dina served as Cobb County's
secondary math coach for their Title I schools. Dina's career began
in Texas where she taught middle school and high school math, served
as a district math coach, and was the senior math consultant for
Region 4 Education Service Center.
Interactive Notebooks were a hot topic this summer
at the GCTM Summer Math Academies. During the summer sessions,
teachers who teach kindergarten through 2nd grade students learned
how to support classroom tasks and learning activities through
various independent notebook ideas. Initially, participants set up a
notebook and added several activities to it as they participated in
tasks throughout the two-day academy.
It is important to note that Interactive Notebooks
are a tool to support instruction; they do not replace instruction
or tasks in the classroom. Students desire creativity and a way to
express their ideas, and teaching students how to create notebooks
encourages this process. The activities highlighted in the summer
academies illustrated how to accomplish this in kindergarten through
second grade settings. Session activities embedded writing
opportunities for participants that demonstrate how students can
process the information they had learned from a given task. All of
the activities shared during the two days showed how students can
use their notebooks to review and practice skills and concepts over
and over again.
When setting up interactive notebooks in your
classroom, consider getting parent volunteers to help out. This will
save class time, keep the notebooks uniform, and include parents in
the students’ learning. A volunteer could number the pages, glue in
the beginning organizers, and even help label the notebooks with
student names for kindergarteners. However, students should still be
encouraged to decorate the front cover of the notebook. Doing so
helps students understand that the notebook is theirs and will give
them ownership over the care of the notebook.
A special thanks to
Jennifer
Smith for sharing her resources and ideas with GCTM Academy
organizers. Jennifer allowed the academy participants to use her
ideas and several of her Interactive Notebook tasks for free.
Summer academy participants learned a few tips and
techniques for setting up their notebooks to support the frenzied
pace of a primary classroom. On the inside front cover of the
notebooks, they glued 6 x 9 inch manila envelopes and labeled them
“My Safe Place.” This envelope can be a student and teacher
lifesaver during those times in class when a student did not get
completely finish with a task but has some of the pieces that need a
safe place to stay until they complete the task. For example, when a
student has several pieces left to glue into place, but it is time
to leave for lunch, the remaining pieces can be placed in the
envelope until the student has time to finish the activity. This
idea was a favorite of the academy participants and was used several
times throughout the two-days to keep small pieces or work that
needed to be finished later.
Figure 1: My Safe Place
As all K-2nd grade students are required to learn
about informational text, the Interactive Notebook is a great place
to make setting up a booklet a real-life learning experience. The
numbered pages of the notebook help K-2nd graders apply the idea of
a book’s not skipping pages and moving in the direction of left to
right. The very first page of our summer notebooks was numbered as
page 1 and became our “Title Page.” On the title page, participants
wrote their first and last names, as well as their instructors’
names, just as students do in the regular classroom.
Figure 2: Title Page
The second page of the notebook became a place to
add a rubric for scoring activities, and page three was saved for
gluing the rules for the proper care and use of the notebook in the
classroom. It is important to remember that establishing rituals and
routines for the use of the notebook with the students is an
important classroom management requirement. It is better to set the
learning stage in the beginning so that students know what is
expected at all times. For more specific instructions on setting up
an Interactive Notebook, please see the video below.
Once the notebook skeleton has been created, I
provide copies of the
rubric and a copy of the
rules to my students. (See the resources below.) After setting
up the notebooks, the academy participants began to add different
activities that mimicked the tasks done in class. An academy
favorite was the number line activity. Participants wrote addition
and subtraction problems to represent the different common addition
and subtraction situations. The
different problem types are helpful in building an in-depth
understanding of these operations, and it is important to include
all the types of these problems in the math classroom. The written
math problems were then used to act out the problems on a huge
number line which really made the participants think about the
unknown part of the problem. Participants used hats with symbols
such as a square to represent the “start,” a triangle to represent
the “result,” and a frog to represent the “change,” while acting out
the word problem on the number line.
Figure 3: Summer Academy participants created
and used a real number line activity.
These same representations were then recorded in the
Interactive Notebook. The idea is for the students to experience the
interactive number line as an activity in math class and to transfer
the information into the notebook as an independent review.
Figure 4: Number line
activity for Kindergarten, 1st, and 2nd grade students.
Interactive Notebooks can be a great tool to support
instruction in the primary classroom, but there should be a strong
connection between the math class and the interactive activity so
that students develop an in-depth understanding of the big ideas for
a strong mathematical foundation. Are you interested in implementing
Interactive Notebooks into your instruction? I’ve included some
links below to help you get started.
Kristi has 19 years of teaching experience, and
has taught Kindergarten, 2nd grade and 5th grade as a homeroom
teacher. For the last 6 years, she worked as an Academic Coach
helping teachers from Pre-K through 5th grade in all academic
subjects, but her favorite is mathematics. She holds a Specialist
degree in Leadership and Administration as well as a certificate as
a Teacher Support Specialist.
Pringles, car tires, cosmetics, ice cream, Levi
jeans, explosives and Laffy Taffy. What do all of these things have
in common? Cotton! Cotton is Georgia’s only food and fiber crop, as
well as the leading crop in the state. The United States has the
purest and most desired cotton in the world. What does this have to
do with math? The list is long, but there are ways to engage
students in applicable, relevant mathematical activities, and one
such way is with the Cotton Boll task developed by Carrie Pierce of
Lee County Schools.
Students really enjoy this a differentiated 8th
grade State Performance Task which could easily adapted for other
grade levels. Through the activity, students discover whether there
is a relationship between the weight of cotton lint and the number
of seeds that it contains, and students also develop possible
related equations that they could give to a farmer to predict their
profit.
To begin this task, I put in front of the students
samples of cotton products and have them brainstorm what all of them
have in common. Next, they get to pick their own cotton boll from a
cotton plant. Students get to take a virtual tour with a cotton
farmer to see the harvesting of cotton and ask their questions
through face time. I was able to set this up with a neighbor that
knew a cotton farmer. If you don’t have access to a farmer, I would
suggest contacting your local county extension office to make a
contact. Then, they get to experience picking the cotton lint out of
the boll followed by picking the seeds out of the cotton lint [This
is the part that the GMC participants discussed about the
presentation].
Students realize that it takes about 10 minutes to
pick the seeds from the lint, and we discuss what this would be like
to do for 8-10 hours every day. This leads to the discussion on the
pros and cons of industrialization. While they are picking the
seeds, they listen to the history, economics and science of cotton
farming through a video created by The University of Tennessee AG
Research.
Real world data: This information can be accessed from the
NCCA website.
To wrap up the activity, we celebrate by snacking on
cotton products such as Chips Ahoy, Ritz Crackers and Mary Janes,
and the students take a museum walk with the artifacts of the Cotton
Kit provided by the Georgia Cotton Commission while they are
snacking. The Cotton Kit contains lesson plans and three brief
articles. I gave these to the Georgia History teacher to use in her
class where students collaborated and summarized each article in
groups. They presented their findings back in my math class the next
day. I asked the class math related questions to their findings
during each presentation. Then, I revealed who had the most accurate
line of best fit based upon the linear regression found on the TI84.
The task took two math/history class periods of 50 minutes each.
If
you are interested in implementing this task in your classroom, keep
in mind that Georgia typically harvests cotton in October/November.
So, check with your local extension agent to connect with a cotton
farmer and the Georgia Cotton Commission (see link below) to obtain
a “cotton kit.”
The cotton kit contains lesson plans with
information on the history and economics of cotton, as well as
sample artifacts. The materials needed for this task include cotton
bolls, measuring devices, stop watch/smart phone, and a cotton kit.
Additionally, students will need computer access for
video/statistics, cotton snack products, and baggies so that
students can take their organic cotton home with them.
This
is a great integrated, interesting task for students that actively
engages them. Performance tasks may be brought to life with a few
materials, videos and collaborative settings. This activity
incorporates 3-Act Tasks by using cotton related videos online,
STEM/Interdisciplinary lessons which are found in the cotton kit,
and Problem Based Learning through discussions of the eradication of
the Boll Weevil and issues of cotton farmers today that need
resolving-which could extend this task. It is through the
intersection of these three instructional tools – 3-Act Tasks,
STEM/Interdisciplinary lessons, and PBL - where students create
memorable, relevant experiences from real world scenarios that
students would not typically have access to. This is authentic
learning. Take a given task and bring it to life by creating a
hands-on experience for students. This will most likely require some
revision, and is enhanced with a real life problems or situations
for students to find possible solutions. Your students will thank
you for it. Keep Calm and Cotton On!
Michelle’s resource tool kit for this task may
be found
here.
Images to use with this activity or with your
students:
Cotton Plant
Cotton Boll
Michelle has over 20 years of teaching in middle and
high school mathematics. She was recipient of the John Neff Award in
in 2012. She is currently the Mathematics Supervisor for the
Division of Instruction and Innovation Practice for Cobb County
Schools.
The
Reflections staff would love to feature student artwork
upcoming issues of our journal. Do you know a budding artist? Have
you thought of collaborating with your school’s art department to
create something mathematically beautiful? Do your students create
mathematical artwork in your classroom? Please consider submitting
this work to Reflections! This would be a wonderful way to
highlight your school’s talent, creativity, and love of mathematics
within a public forum. In order to have Reflections showcase
your student’s work, please submit the following:
A clear digital photograph of the artwork.
Artist’s name
Artist’s school and school district
A copy of the student work release form (from
your school district’s website) so that we can publish the work
of a minor.
Any additional information you would like to
include with the piece.
We are excited to offer this new feature of
Reflections. Email all inquiries to the Reflections
editor, Becky Gammill.
Winter’s Featured Artwork:Archimedes
Abraham Diakite, Kennesaw Mountain High School, Marietta, Georgia
If you attended the Georgia Mathematics
Conference at Rock Eagle in October, did you join GCTM before
you registered?
If the answer was NO, did you find
the conference fruitful and exciting enough to join GCTM
now? Do you know of the other benefits of membership – our
journal, Reflections, summer academies, regional events,
GCTM’s work with lawmakers, and more?
If the answer was YES, thank you! We
hope you will be an active member and encourage your
colleagues to join you as a member!
If you did not attend GMC at Rock Eagle this
year, and your membership has lapsed, won’t you consider
renewing and again being an active member? $20 is a small price
to pay for the benefits of membership and to support the work of
GCTM!
Are you willing to write an article for our
Reflections journal/newsletter? We are willing to offer a year’s
membership for articles accepted for printing in Reflections!
Contact our editor, Becky Gammill
for more publishing information!
GCTM has a long and effective history for helping
shape and support the teachers and students of Georgia, with the
most effective mathematics instruction. It needs YOU and your
colleagues to exist and thrive.
GCTM has had such a significant effect on my
classroom for decades. I hope that once you reflect on the positive
outcomes you have seen from GCTM events and membership, you will
press that RENEW button on the website and be an active member! GCTM
needs you!
This issue of Reflections comes filled with
lessons that focus on student activities which are both hands-on and
engaging. The three articles respectively presented by Kristi
Caissie, Dina Sherwood, and Michelle Mikes offer tasks and
strategies that can be useful at all grade levels. Kristi discusses
Interactive Notebooks and how they were used during the 2015 Summer
Academies. Dina suggests a hands-on method for presenting the
Pythagorean Theorem in a conceptual way, and Michelle explains the
novel adaptation of the Cotton Boll task that she presented at this
year’s GMC. So whether you want to try an interdisciplinary task,
learn strategies for helping students discover and record their
notes interactively, or extend your knowledge about old topics in
new and interesting ways, these articles undoubtedly have something
for you!
And don’t pass up our new Reflections
contributor incentive! Each of the three authors above will have her
annual GCTM membership renewed at no cost as a reward for
contributing. Do you have something to share that might benefit
others? Don’t hesitate to email me your lessons, articles, and
reflections for possible publication in this journal and have your
membership renewed for free.
I’m happy to report that your Georgia Council of
Teachers of Mathematics has done a great job of representing Georgia
math teachers by attending numerous state and national conferences
this Fall. Please check out our updates of GCTM’s involvement at the
2015 NCTM Affiliate Leadership Conference, the 2015 Georgia STEM
Leadership Forum, the Georgia Education Leadership Institute, and
our communication with the Education Reform Commission. We also have
another Math Day at the Capital scheduled for this coming spring
which will allow GCTM even more opportunities to interact with state
legislators while positively advocating for mathematics teachers in
Georgia.
Finally, a few additional math circle resources have
come to our attention since we went to press with the Fall issue of
Reflections. As you may know, math circles are an interesting
way to get students to discuss mathematics and solve problems for
recreational purposes. Chuck Garner, GCTM’s Vice President for
Competitions, has provided some great additional resources for
creating math circles within different settings. He suggests that
the best math circle books are found at the
American Mathematical Society Bookstore website. However, he
also notes that “this series published by the American Mathematical
Society is great, but the ones I strongly recommend are the first
two volumes, A Decade of the Berkley Math Circle, and Math
Circle in a Box. Additional references Chuck points to are the
math-circle-specific
Special
Interest Group of the Mathematical Association of America, the
National
Association of Math Circles, and the
Math
Teachers’ Circle Network.
Of course, our favorite math circle is the one that
includes you, and from all of us here at Reflections,
we wish a happy, safe, and most of all relaxing holiday break to all
our wonderful GCTM family. We look forward to lots of good things in
2016 and we’re excited you’re with us!
NCTM News!
Excerpted from NCTM
Affiliates News & NCTM e-blast August 2015 Dr. Dottie
Whitlow
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 ANCTM 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)