Math haters, take heed.  One class with Jane Barnard may crack your math-bashing world into a million congruent and precise pieces.  The Armstrong Atlantic State University mathematics professor has for the last 30 years personified the passionate conviction that die-hard math-haters can grasp the difference between pi, probability and Pythagoras—and actually enjoy the process.
      Welcome to Jane’s World.
      “My goal is to effect changes in the way mathematics is taught and learned in all levels,” said Barnard.  Using items from the real world—plants, candy, seashells, basketballs and scarves, to name a few—Barnard emphasizes the concepts that underlie those boring, memorized rules, allowing students to better grasp their meaning and applicability.
      “When you use physical materials and models, it may take longer to teach, but you understand the concept—and the rules follow,” she said.  “Many times we say, ‘use the rule,’ and it doesn’t make any sense—it’s like memorizing a Russian song without knowing the words."
      Math with M&Ms^©?  After this lesson, students understand the concepts of probability, ratio and percentage in much sweeter ways.  Barnard uses the path of a thrown ball or water from a fountain to illustrate the quadratic function, making y = -16x² + 32x + 11 come alive.  To demonstrate Fibonacci  Numbers, Barnard uses dozens of real-world examples: pineapples, artichokes, pinecones, three-by-five cards and art. (See Jane's page on Fibonacci Sequences)
      Many students’ experiences with Math classes are liberally peppered with plaintive “I don’t GET it” or “This is stupid, boring, doesn’t make sense, dumb, unnecessary, (you fill in the blank).”  Barnard understands this frustration and knows she has a gift of “making the light come on” for students, whether they are age 8 or 80.
      “There is a joy in knowing that I make a difference in students’ attitudes about mathematics,” said Barnard.
      Beginning her teaching career in 1972 at Calvary Baptist Day School, Barnard has taught kindergarten through university-level classes and has written and lectured extensively.  With lecture and publication titles such as “Grin and Graph It,” “Playing with Polyhedra” and “As America as Apple (pi),” Barnard infuses complex mathematical concepts with playfulness, delighting audiences and students, enabling them to learn.
      “One of my seventh-grade students asked me, ‘Miss B., is it your goal to teach us all the math you know?’ and my answer was, ‘My goal is to teach you enough so that you can go beyond what I know.’”
      Barnard thrives on the creative interplay between student and teacher.  “I come to school to learn as well as teach.  I’m constantly learning new things from the kids.”
      Barnard finds it gratifying to learn from her students.  Speaking of 2000 Chatham County Teacher ofthe Year Linda Oliver, Barnard said, “When a former student goes beyond what I have done, I end up picking ideas from her.  It’s a true partnership in a professional relationship.”
      “Jane Barnard has had a profound effect on my life,” said Oliver.  “She’s the one who got me started.”
      According to the May Howard Elementary teacher, Barnard “put a thumb in my back, pushed and prodded—forced me to start giving workshops.  From then on, I was on my own.”  Since then, Oliver has served on the Georgia Council of Teachers of Mathematics board for two years and has just been published in their professional journal.
      Pepi Streiff, a teacher at Winsor Forest High School, has also benefited by Barnard's instruction. "She is the most outstanding mathematics teacher I've had in my life—she's extraordinary.”
      Entering the Chatham County Public School System in 1975, Streiff was able to participate in one of Barnard’s popular summer courses through the Eisenhower Grant.  “I was just thrilled,” says Streiff.  “I’ve never had a more enthusiastic teacher.  She makes math come alive for the children.  Her presence in this town elevates the quality of the teaching of math.”
      Although Barnard is heavily involved with hundreds of educational activities, associations and conferences, she was, as a child, opposed to becoming a teacher for that very reason.  Her mother, after having five children in a 10-year span, went back to school, got her masters and became a math teacher.
      “I looked at the hours she spent—she was always working with the students and parents—and I said, ‘I’ll never teach.’”  Later Barnard was offered a teaching assistantship when she went to graduate school.
      “I knew after the first quarter that was what I was called to do, and I haven’t wavered since.”
      Barnard admits that the support and environment for teaching is sometimes lacking.  “Teaching is the most exhausting, demanding, exhilarating, exciting, rewarding, challenging, meaningful job you could ever have,” she said.  But when asked about teachers “burning out,” she quipped, “They’ve never been on fire!”
      Mike Way, a fifth-grade mathematics teacher at Southwest Elementary School, has been ignited by Barnard’s fire.  “It’s not just a special student-teacher relationship—she goes way beyond that—it’s Jane’s World.  A large deal of her success is from her passion,” he said.  “I’ve seen her cry. I’ve seen her get goose bumps because of her excitement.”  Way has learned that if he can infuse all of his curriculum—not just math class—with the same ardor, his students’ classroom experience becomes exponentially richer.
      One of the most memorable experiences for Way was in a teacher workshop in which the participants used fractals—small geometric shapes that when put together by the end of the day made a gigantic shape that mirrored the shape that they started out with.  The participants held the giant paper creation out of the second-story window and it touched the ground below.  “It was astounding,” he said 

Awareness 101

      “There is so much symmetry and balance in the world that we aren’t aware of,” said Barnard.  “We must go  to Awareness 101.
     Take the common pinecone, for example.  Did you know that every pinecone, no matter whether it’s from a snow-covered tree in Denmark or a tall pine in the Georgia mountains, exhibits a certain order of spirals that are called Fibonacci Sequential Numbers.  Every pineapple in the world, every sunflower, every artichoke – all have the same magically patterned numbers.
     “Wherever they go, my students bring back pinecones from all over the world,” said Barnard.  From rabbits multiplying to computers – these numbers are everywhere.
      Next, Barnard asks us to look at a conch shell.  The shell exhibits equiangular spirals.  As the creature grows, the shell gets larger but the angles stay the same.  The horns of wild sheep,  and elephant tusks all form these equiangular spirals and, alas, if you use Fibonacci Sequential Numbers, you may construct a loose approximation of each. 
      Humans have always looked to nature for inspiration in art; we can see the connection using the exact science of mathematics.  The Golden Ratio is actually a proportion of height to width that is present in many of the world’s most famous masterpieces – the same ratio as in the simple seashell.
      From architecture to photography to poetry to patterns of every type – music, crossword puzzles, origami and quilting, hubcaps and manhole covers – mathematics is everywhere, and Jane Barnard is an ambassador to that infinitely interesting world.
     “How many Skittles, if you laid them end to end, would it take to get to the end of this building?”  Barnard asked a recent Saturday afternoon teach/student workshop.  “How about to City Hall?”  After having figured earlier in the day how many (living, squirming) flat-tail worms would it take to weigh five pounds, the students were stone quiet, actually thinking of an answer.  After a challenging pause, she resumed.  “How many Skittles would it take to get to the moon?”
      It is a rare treat indeed to witness such a mind at work, to be profoundly challenged, to enter into Jane’s World, where any mathematics problem can be solved, where rhombuses are a girl’s best friend, and where there is a time each day when you can eat whatever you want and it will have no calories.  “It’s 3:14,” Barnard said with a smile, “pi time.”
      If you would like to become a reformed math-basher, AASU offers a variety of mathematics classes (several for non-math majors including “Mathematical Modeling" and "The Spirit and Structure of Mathematics”).  Call the Mathematics Department at AASU for more information.

The Mathematics of Art and Photography

     Michelangelo's David, along with many famous pieces of art, exhibits The Golden Ratio, explainedJane.  Leonardo da Vinci called this the Divine Proportion. If you divide one of the larger Fibonacci Sequential Numbers by the preceding number in the sequence, you will get approximately 1.618—the Golden Ratio.  From the Parthenon in ancient Greece to the United Nations building, from a Grecian urn to a statue of Buddha to a modern photograph—this ratio appears to be the basic and natural imperative in the human search for beauty and order.