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					Narrative       Charles Koppelman, Lecturer of Mathematics                 Third Year Review


   I began teaching in the Department of Mathematics and Statistics at Kennesaw State

University as an Instructor in 2005. I became a Mathematics Lecturer in August, 2007. This

portfolio is for my third year review. For the five years prior to my coming to Kennesaw State

University I was the Secondary Mathematics Instructional and Curriculum Specialist for the

Howard County Public School System in Maryland (28,000 secondary students in 32

secondary schools). Prior to that, I was a mathematics teacher and department chairman at the

high school level for 33 years, and I also taught mathematics at the college level. My primary

responsibility as the Mathematics Instructional and Curriculum Specialist was to train

secondary mathematics teachers in research-based practices in classroom instruction and

instructional technology. Because of my expertise in teacher training, I have taught both

mathematics and mathematics education courses at Kennesaw State University.

   According to the KSU Department of Mathematics and Statistics Faculty Performance

Guidelines, “Unless otherwise stipulated in an FPA, Lecturers and Senior Lecturers will be

evaluated only on their performance in the area of Teaching and yearly reappointment of these

faculty members will depend heavily on the demonstration of teaching effectiveness.” In

addition to teaching, my FPA specifies that one of my responsibilities is my work with the

Kennesaw State University Mathematics Competition. Therefore, this professional service

initiative will also be addressed in detail in this portfolio narrative.


   At KSU, I have taught Math 1111 (College Algebra), Math 1101 (Mathematical Modeling),

Math 3317 (Geometry and Measurement for Elementary Teachers), Math 3395 (Geometry),

Math 7714 (Geometry from Multiple Perspectives – graduate level), and Math 4475 (Student

Teaching: Mathematics).
  Charles Koppelman                                                                            1
  Third Year Review
   Central to my philosophy of teaching is my belief that I must (1) actively engage my

students in the learning process (2) guide my students to learn through investigation and

discovery, and (3) connect the course content to the lives and experiences of my students.

   In order to actively engage my students in the learning process, I work toward establishing a

supportive environment in which my students feel comfortable asking questions and are

encouraged to participate in class discussions and problem solving activities. This is of

particular importance for Math 1101 students. Math 1101 is the first for-credit mathematics

course taken by our most challenging student population. I have taught this course 21 times at

KSU. The student population in Math 1101 is extremely diverse, with a high percentage of

non-traditional students. Many of these students have been away from mathematics for many

years and enter the course with a great deal of anxiety, significant gaps in their previous

mathematics education, and a lack of confidence. To establish a supportive environment in

Math 1101, I always try to infuse humor, enthusiasm, and a sense of genuine concern for my

students’ success in each class lesson. I want my students to feel free to take risks and to think

on their own. To accomplish this I build my lessons carefully with probing questions

incorporated to continually assess understanding as the lesson unfolds. This helps to ensure

that my students experience success and gain confidence. In this way, I convey to my students

my belief that they can meet and exceed my expectations.

   To encourage my students to learn through investigation and discovery, I structure my

classroom presentations, learning activities, and individual and group assessments around

creative problem-solving situations. My daily PowerPoint presentations (which are posted on

my website) begin with a problem situation and data/information generated from it. This gives

rise to lively discussions, and a genuine interest on the part of the students to analyze the data

and solve the problem presented. It also allows me to assess the students’ prior level of

 Charles Koppelman                                                                             2
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knowledge on the topic, an informal formative assessment. Whenever possible, my students

work in collaborative groups. They share ideas, communicate the mathematics to others, and

reinforce the contributions of their peers in a non-threatening atmosphere.

   Connecting course content to the students’ lives and experiences draws them into rich

discussions about topics with which they are familiar and to which they can relate. The

underlying theme of Math 1101 (Mathematical Modeling) is the analysis of data arising from

problems involving real-world situations. This natural connection to students’ experiences is

why I have requested to teach multiple sections of Math 1101 each semester. I encourage my

students to share their reactions and prior knowledge of the situations under discussion. This

helps motivate the students to want to participate and learn more.

   How do I know whether I have been successful in translating my philosophy of teaching

into student learning? I evaluate my effectiveness through the numerous informal and formal

assessment tools I utilize and through student evaluations. Student evaluations are helpful

because they enable me not only to assess my effectiveness as a teacher, but to incorporate into

my future lessons any insightful comments or suggestions students may have.

   I assess my students using a variety of methods and provide them with multiple

opportunities to receive additional academic support. In addition to periodic graded group

projects, at the conclusion of most class periods students complete an “exit ticket,” which is a

short quiz on the major concepts covered during that class period. Students are encouraged to

ask me and each other questions while they complete the exit ticket, so that misconceptions

about the content can be clarified. Analysis of student errors on the exit tickets helps students

and gives me immediate feedback. As one student stated in their evaluation (Tab 5, page 4)

“The exit tickets were also very helpful. It let me know if I understood everything or not.”

The exit tickets are valuable to me as a teacher because they identify where clarification is

 Charles Koppelman                                                                              3
 Third Year Review
needed before proceeding to the next concept, and what I might need to do to fine tune my

teaching approach on the topic in the future. Students’ questions on the daily homework are

answered at the beginning of each class. Students also receive practice tests with solutions

before each major unit exam, and class time is devoted to reviewing the practice tests. My

office is always open for students to receive individual help and I encourage them to do so. I

have also given my Math 1101 students the opportunity for additional academic support by

participating in the Supplemental Instruction program.

   Student evaluations of my effectiveness as a teacher have been overwhelmingly positive.

Even though many of the students who enroll in Math 1101 begin with a severe lack of

confidence and a weak mathematics background, their qualitative evaluations [see Tab 5

(Student Evaluations), pages 1 – 86] indicate that they feel they have overcome both. The

following two student comments are typical of the evaluations I have received and illustrate

characteristics of my teaching philosophy.

   “Professor Koppelman used very effective, real-life scenarios that made the concepts mean

something and make sense. He was fairly patient in explaining on an individual level. He is

obviously passionate about what he teaches and things make sense.” (Tab 5, page 1)

   “He does a wonderful job with using technology i.e. powerpont, calculator, online

homework, etc. He is very easy to get in touch with and helpful outside class. Does a great job

of getting on a lower level to explain in terms we would understand. Does a good job of

knowing each individual student and helping with their troubled areas.” (Tab 5, page 29)

   My quantitative student evaluations for Math 1101 have been excellent as well. The

following table shows the average scores from Math 1101 students in fall 2008 and spring

2009 on several feedback items. Scale: 0 = strongly disagree, 7 = strongly agree.

 Charles Koppelman                                                                          4
 Third Year Review
                                  Feedback Item                                   Average score
                                                                                    out of 7
The instructor demonstrates good knowledge of the course material.                    6.92

The instructor presents the material in a clear and easy to understand manner.         6.70

The lectures are a valuable part of the learning process.                              6.58

The instructor is enthusiastic about the subject matter.                               6.87

   In addition to Mathematical Modeling, my other area of teaching concentration has been

geometry. My KSU geometry students (Math 3395 taught 2 times, Math 3317 taught 2 times,

and Math 7714 taught 1 time) are primarily mathematics education majors or early childhood

education majors. It is not only important for me to ensure that the students in these courses

demonstrate mastery of the content, it is also essential that I identify, model, and discuss

effective teaching strategies that the students can use when they begin their teaching careers. It

is with these students that my experience as a trainer of teachers has been most valuable.

   The emphasis in the teaching of geometry has undergone dramatic changes since 1990,

primarily because of the integration of powerful geometric software. It has been my goal to

model teaching through investigation and discovery for prospective mathematics teachers by

incorporating Geometer’s Sketchpad software into their KSU coursework. I believe the

integration of technology into instruction is an important vehicle for facilitating student

learning through investigation. Technology enables me to differentiate instruction, providing

opportunities for visual, tactile, and kinesthetic learners to be successful. In geometry,

technology engages and motivates students by allowing students to experiment, make their

own conjectures about geometric relationships, and test those conjectures. The Principles and

Standards for School Mathematics (a publication of the National Council of Teachers of

Mathematics) states “Students learn more and better when they take control of their own

learning…Students can learn more mathematics more deeply with the appropriate and

responsible use of technology.”

 Charles Koppelman                                                                             5
 Third Year Review
   The use of Geometer’s Sketchpad in my geometry lessons motivates students and makes

investigation and discovery possible. The classroom presentations, individual and group

activities, home assignments, and assessment instruments I created made extensive use of

technology driven investigations. Because the students made their own discoveries through

experimentation, and then proved that their conjectures were correct, their understanding of

geometric relationships was strengthened. This approach has increased my students’ level of

enthusiasm for the subject and developed a greater appreciation of how they can effectively use

technology when they teach geometry in the future. The following two student comments

illustrate characteristics of my teaching philosophy, and are typical of the evaluations I have

received from my geometry students.

   “A variety of activities and instruction methods were used throughout this course; not only

did these methods engage me in the learning experience, but it also made it fun. Dr. Koppelman

did an excellent job at providing solid proofs with the help of technology. Group work and

projects also allowed me to learn from my classmates. One of the most important things I have

learned is how to allow students to make discoveries on their own.” (Tab 5, page 58)

   “Utilizing Geometer’s Sketchpad was most helpful because I made my own conjectures and

proved them. I had to understand geometry more in depth to use Geometer’s Sketchpad…”

(Tab 5, page 59)

   Over my long teaching career, many students have told me that I have transmitted my love

of mathematics to them. I am always gratified to receive comments like the following email

message from one of my Math 3395 students after the fall 2008 semester ended.

   “I'd like to take this opportunity to offer my sincerest thanks to you. You see, prior to this

semester, I had not taken a Geometry class since my 10th grade year, 1975, and all I could

recall was not enjoying the class. You've changed my outlook on Geometry. Your enthusiasm

 Charles Koppelman                                                                           6
 Third Year Review
for your students and Geometry is truly infectious, and I'd very much like to teach Geometry

when I begin my teaching career thanks to you. I've become fascinated with the subject and

am looking forward to learning more.” (David Tillison, KSU student)

   I am proud to have been named by at least one student in the spring, 2009 survey of KSU

graduates as a teacher who “was most helpful to them at KSU.”

   Currently, Math 3395 is the only undergraduate geometry course offered for mathematics

majors at KSU. I have been so encouraged by feedback from my geometry students, that I

hope to work in the future to increase the geometry course offerings at Kennesaw State

University to include a course in Non-Euclidean Geometry, which I have taught previously

at the university level.

   Because of my expertise in teaching geometry through investigation and discovery using

technology, I was asked to make a presentation on this topic at a KSU Department of

Mathematics Math Talks in February, 2009. The talk was attended by more than 30

mathematics and mathematics education majors and faculty members. The feedback I received

was excellent, including this brief email message from Dr. Mary Garner, Associate Professor

of Mathematics: “I really enjoyed your talk!!! It was awesome! I was really proud of

you as a math ed person!” Because of the interest generated by my presentation, I presented a

follow-up workshop in April, 2009 which was well attended by math students and faculty.

   Kennesaw State University has an outstanding teacher education program and is the second

largest producer of mathematics teachers in Georgia. Because of my lifelong commitment to

teaching and teacher training, I agreed to supervise mathematics student teachers in spring

2009. As part of my responsibilities in Math 4475, I supervised four mathematics student

teachers in Fulton and Cherokee County schools. The following comment was typical of the

feedback I received from the student teachers at the conclusion of their student teaching

  Charles Koppelman                                                                           7
  Third Year Review
experience. “Mr. K did an excellent job of mentoring me. He gave me some great advice and

good feedback. If it was not for Mr. K I don’t know if I would have made it.”

   My desire to train mathematics teachers and improve the quality of mathematics

education extends beyond the campus. In 2008, I twice represented the Kennesaw State

University mathematics education program by presenting workshops to train secondary

mathematics teachers in Cobb County in using technology-driven investigations to teach

geometry. I also made related presentations to teachers at the Georgia Council of Teachers of

Mathematics State Mathematics Teachers Conference and the National Council of Teachers of

Mathematics Annual Meeting and Exposition, both in 2007.

   In addition to my work with students in the courses I teach and in the workshops I have

presented, I also supervised students as the faculty advisor for the KSU Chapter of Unite for

Sight in fall, 2007. Unite for Sight is a non-profit organization that empowers communities to

improve eye health and eliminate preventable blindness. Student members from the KSU

chapter worked with eye clinics to provide eye care in the community, with the goal of creating

eye disease-free communities. To obtain a KSU charter, student officers were identified,

student volunteers were solicited and trained, and a professional ophthamologist from the

community agreed to act as liaison. Student members of the KSU Unite for Sight chapter

helped at a very successful vision screening event at a Cobb County Elementary School.


   In the 2006-2007 school year, one of the Strategic Goals for the Mathematics Department

was to “increase general public awareness of the quality of Kennesaw State University’s

Science and Mathematics Degree programs.” That same year, Dr. Laurence Peterson, Dean of

the College of Science and Mathematics, stated that “Kennesaw State University is not

generally seen by high school students as a recognized math alternative.” To address these

 Charles Koppelman                                                                           8
 Third Year Review
issues, in fall 2007 I developed and implemented the Kennesaw State University Mathematics

Competition for high school students. The competition, and the awards ceremony and

reception that I also created, have become annual events.

   The Kennesaw State University Mathematics Competition consists of two rounds. The first

round takes place in late October. Each September I prepared and mailed registration packets

to the mathematics department chairs at more than 500 Georgia public and private high

schools. I also advertised the competition by email messages sent to all faculty sponsors in

schools that participated the previous year, by letters sent to principals of all public high

schools, by recruiting in person at regional mathematics competitions, and by advertising at the

Georgia Council of Teachers of Mathematics (GCTM) State Mathematics Teachers

Conference and on the GCTM website. I wrote the questions and solutions for the

competition, and solicited volunteers from the KSU mathematics faculty to proofread and

refine the contest questions. I scored all student papers and sent results to the students’

schools. I also managed the contest website (

   In it’s first year, 1,450 students from 88 high schools representing 42 Georgia counties and

Atlanta City participated in the competition. Those numbers have steadily increased. In 2008-09,

the competition’s third year, 2,153 students from 124 schools representing 55 Georgia counties

and Atlanta City participated. These figures represent a 48% increase in the number of

participating students and a 41% increase in the number of participating schools in just three

years. The KSU Mathematics Competition is the largest high school mathematics competition

in Georgia, and it is making Kennesaw State University’s name well known among high school

mathematics teachers and their best math students. The list of KSU’s incoming freshman in

fall 2009 includes 51 students who participated in the competition in 2008.

   Comments from mathematics teachers in participating high schools have been consistently

 Charles Koppelman                                                                              9
 Third Year Review
positive, indicating an increased awareness in these schools of what KSU has to offer.

Feedback included the following two email messages from math teachers.

   "Thank you for the opportunity to participate in this year’s mathematics competition. It is

the first time my students have ever competed in any math competition and it is absolutely

wonderful that this is a free event to allow high school students to get a taste of college level

mathematics. We look forward to seeing our scores and also entering next year." (Nancy

Walters, South Paulding High School, Paulding County)

   “We are excited about being a part of this competition this year. The students are looking

forward to the challenges that you guys have in store for them. Thank you so much for making

this opportunity available. I have more students than ever looking at Kennesaw for their

college home.” (Bill Jones, Grayson High School, Gwinnett County)

   The second round of the Competition takes place in February. It is open by invitation to the

200 highest scoring students from Round I. Each year, I developed the problems and solutions

for this round and mailed the contest materials to the teachers of qualifying students. I recruited

a volunteer committee of KSU mathematics faculty and mathematics student teachers to score

the high school students’ responses, and worked with the committee to complete the scoring.

   The 35 students in the state with the highest composite scores were invited, along with their

parents, teachers, and principals to the award ceremony and luncheon each April. KSU

Mathematics faculty were invited to the event as well. I coordinated with Dean Peterson’s

office to provide plaques and monetary awards, with the mathematics office to arrange the

luncheon, with the mathematics faculty to arrange mathematics presentations for the event, and

with Dr. Pam Cole of the Bagwell College of Education to secure additional funding.

   Reaction to the awards ceremony and luncheon have been very positive. A parent

 Charles Koppelman                                                                           10
 Third Year Review
who attended with her son sent me the following email message which gives evidence of the

competition’s value to KSU as a tool for increasing awareness of KSU’s mathematics

program and its potential to recruit highly capable mathematics students to attend KSU.

   “The more frequently kids can be on a particular campus, the more likely they can envision

themselves there. I have been very impressed with what you all have shown us at the luncheon,

and I have told a lot of people about KSU. I would never have done that if you had not offered

the exam and luncheon to get us up there!” (Ann Dorminy, Parent)

   The KSU mathematics faculty members support the competition because they recognize the

potential of the competition in helping to achieve our goal of attracting highly qualified

mathematics students. Dr. Josip Derado, Assistant Professor of Mathematics wrote:

   “First, I would like to congratulate you on a superb organization of the competition and the

Award Ceremony. In less than three years, starting from scratch, you established a competition

which is well regarded among teachers and students all over Georgia. The number of schools

and students participating in the competition is impressive. The participating schools are

coming from almost every county in Georgia, and I know that even some schools from other

states were interested and wanted to participate. This is very impressive.

   This competition made KSU and its Math Department a recognizable brand among High

School students. The competition is one of the best recruitment tools for math majors that we

have. The exposure KSU gets from the competition and its award ceremony is the best way to

make students and their parents realize the progress KSU has made in a very short period of

time. This puts KSU on a list of choices where students would like to go to study mathematics.”

   In addition to the specific responsibilities of managing the competition, I have engaged

in other activities related to the competition that are in line with the stated goal of

  Charles Koppelman                                                                          11
  Third Year Review
increasing public awareness of the quality of Kennesaw State University’s Science and

Mathematics Degree programs. I collaborated with Dr. Katherine Kinnick, Director of Pre-

College Programs at KSU, to send letters and brochures to high scoring students from the

competition explaining opportunities for joint enrollment at KSU and inviting the students to

apply. I collaborated with Dale Benham, Director of the CyberTech Program at KSU, to recruit

students from the CyberTech schools. I collaborated with Dr. Ana-Maria Croicu by writing

letters of support for two NSF grants to provide scholarships for competition participants.

After one grant was awarded, I sent letters and brochures to all schools participating in the

competition advertising the Scholarship Program in Science and Mathematics at KSU.


   Throughout my time at Kennesaw State University (and my 38 years as an educator before

that), I have maintained a high level of teaching effectiveness and professional service. As

stated earlier in my narrative, I believe teaching is most meaningful, and learning occurs most

effectively, when students are engaged in activities that require them to learn by investigation

and discovery, and that are relevant to their experiences. “Learning by doing” helps motivate

students and builds their confidence. In line with my teaching philosophy, I have incorporated

my unique skills and expertise with educational technology to engage students and to train our

next generation of mathematics teachers. My professional service, as embodied by the

Kennesaw State University Mathematics Competition, is aligned with mathematics department

and college-wide goals and has made KSU a recognizable alternative for highly capable high

school mathematics students in Georgia.

 Charles Koppelman                                                                         12
 Third Year Review

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