Reflections on Learning & Teaching Mathematics
  Jane T. Barnard

  I have committed my professional life to the learning and teaching of mathematics.  My zeal has brought me to teaching/learning situations both inside and outside the “traditional” classroom.  As I reflect on my ideas and experiences and beliefs, I doubt I have the ability to convey to another – with any degree of understanding – what I am about as a teacher, what motivates my interactions with students, what I hold most dear in the learning environment.  So, I will relate a modicum of my feelings and experiences in hopes that a glimmer of my passion for the learning and teaching of mathematics will shine through.

  We are each nourished by serving others.  Thus, my view of teaching is one of service.  I believe I am called into teaching mathematics, because that is my gift.  Whether in the classroom or conducting a workshop or seminar, I try to demonstrate a caring nature, a passion for teaching as well as for the field of mathematics, and a love of the students I teach.  In working with young people in Atlanta, I met a gifted young woman at Grady Hospital ten years ago who had kicked a drug habit but who had AIDS. In conversations with her about how I – as a teacher – could most greatly impact my students, she said: Students don’t really care how much you know; they want to know how much you care.  I find that in many of my mathematics classes even at the University, students will work harder for me because they know I care about them, about how they feel about themselves as learners, and about how they think and reason than because they actually like mathematics or think I am particularly knowledgeable about this subject that so many avoid and often detest. 

  I convey to my students: I am not responsible for what you learn.  I am responsible for providing opportunities and designing the learning environment so that you can construct your own mathematical understandings.  You, individually, are responsible for learning mathematics.  I also want them to realize that I sincerely believe that every student can learn and deserves to learn substantive, meaningful mathematics -- but not necessarily in the same way nor on the same day.  Because of this belief, I seek to find a variety of ways to represent a single mathematical idea and to relate mathematical connections by providing applications from other subject areas.  I also use cartoons and short stories and advertisements or data in magazines and newspapers.  I hold regular out-of-class problem sessions, I give students my home telephone number so they can reach me at home with questions/concerns, and I encourage/motivate them to work in groups and communicate their thinking with others.  I loan out resource materials and manipulatives and calculators; I design projects for right brain or left brain (or total brain) activities. 

  When students leave my classes, I want them to have enjoyed the learning experiences. I regularly share my corny, mathematical humor as well as Rice Krispie treats or homemade soup or the huge jar of chocolates I keep on the desk in my office.  My goal is not to have the students I teach change their majors to mathematics.  I just want them to understand mathematics a little better, to realize its usefulness, to appreciate its place in the history of reasoning and thought, to recognize its relevance in our technological society, to reason and communicate mathematically, to make connections of what we are learning to other areas of mathematics and to other subject areas, and to develop confidence in their own abilities to do mathematics.  I want them to believe that mathematics is more than what is on the pages of their texts – it’s everywhere in the world around them – and it is certainly much, much more than mastering a set of rules or procedures for getting some correct answer.  I want them to believe: The correct answer is not the most important thing.  The most important thing is correct mathematical reasoning which, when followed by careful work, will lead to the correct answer.  This philosophy allows me to permit students to reason as their own brains work and not just arrive at solutions by the way Jane Barnard thinks.  I let them know that what they think and how they reason are of tantamount importance to me. Initially, my assessments can be frustrating to students who have traditionally engaged in the “memorize and regurgitate” way of dealing with mathematics. However, they learn to communicate effectively and demonstrate their thought processes as the course progresses.

  I come to school to learn as well as to teach.  I feel, too, that scholarship is an integral part of teaching.  I have an obligation to model what I ask of my students.  I am constantly learning more mathematics and how to teach it more effectively. I learn from the K-12 students I teach; I learn from my colleagues and from the experiences of my former students; I learn from developing my own activities and modifying ideas of others; I learn from the seminars and conferences I attend; I learn from reading and writing professionally; I learn from seeking grants; I learn from developing and presenting scholarly papers.  What I learn, in turn, gets filtered back into my teaching – and my students are richer for my experiences.

  I believe as Tennyson wrote in Ulysses:  “I am a part of all that I have met.” Each of my students takes a part of me when leaving my classroom.  Likewise, I am a composite of the teaching and learning experiences I share with my students. What I do for students directly benefits me!  It is not uncommon for my students to travel with me out of town to do workshops or make presentations; it is also not uncommon to find some staying in my home if they live out of Savannah and need to save travel time during a summer course or for a local miniconference.  I take graduate and undergraduate students each year to the Georgia Mathematics Conference, assisting them in getting “free” registration and having the lodging fee “waived” or paying for their lodging myself, and helping them select the most appropriate sessions to attend.  I encourage them to be involved in my presentations by assisting with the development and then making  mini-presentations during my talks.  Because of such experiences, I am certain “professional involvement” will be important to each of them; I am equally convinced that they understand more clearly that there is more to my commitment to teaching than just what goes on in the classroom or on the campus of AASU.

  One student I have nurtured in undergraduate and graduate courses chose to teach middle grades mathematics.  She is one whom I “required” to co-present with me at regional or state conferences.  I made arrangements for her to attend the University of Chicago School Mathematics Project National Conference with me in November 1999.  I worked to have her school pay her registration; I invited her to share my hotel room and covered her lodging.  As I was taking pictures in Chicago for the photographic presentation I was making at the conference, I took her with me to help her understand what I “saw” mathematically and assisted her in getting photographs of her own.  Through my encouragement, she submitted a proposal to make a similar photographic presentation at the Core Knowledge Conference in California in March 2000.  It was accepted!  It gives me great joy to know I have mentored a mathematics student and teacher so that she has the confidence and foundation to make the leap into giving professional presentations.  I KNOW I have an impact on the students she teaches because I have supported her as a mentor, as a friend, and as a professional colleague.  My philosophy of “Each one: teach one, reach one” was put into practice through this student.  I may teach just one; however, I ultimately am able to reach many others as this one shares a love and knowledge of mathematics with her own students. 

  In the last year, I assisted six graduates of the Department of Mathematics in writing resumes, coached them for interviews, wrote recommendations and supported them as they decided on the teaching positions they eventually accepted.  Five of them have subsequently enrolled in Armstrong’s graduate program in mathematics education.  The pride I feel in their individual accomplishments is tremendous . . . to me, this is what the teaching, the nurturing, and the encouraging is all about.  When you make a difference in the life of a student (and especially one who want to teach mathematics), you make a difference in the world.

  I believe I have to practice what I preach: be willing to embrace new ideas, seek to find better ways of making sense of mathematics, reflect on what I do and why I do it, not be afraid to make a mistake, and share what I learn with others.  I do what all successful teachers through the years have done.  I am well prepared when I walk into my classroom, and I engage students in the learning environment with a blend of enthusiasm, passion, seriousness, and humor.  Through it all, I enjoy what I do – I wouldn’t do anything else!

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