Teaching Advice from a Tree

By Julie Barnes, Western Carolina University

When I first bought my house, the view from one window included a plum tree with crisp burgundy leaves and little plums on which squirrels enjoyed snacking. My cats loved the show, and I enjoyed the beautiful fractal. At that time, though, I had no idea how much that little tree would teach me about life and teaching.

Several years later when the pandemic hit, I found myself spending significant amounts of time at home near that window overlooking the plum tree. One day, a small wind picked up, and I watched in amazement as the tree slowly toppled over. This exposed many of the tree’s inner secrets, including the concentric rings in the trunk representing each year of its life. Looking at those rings reminded me of the collection of experiences that have become my core and have affected my teaching.

One of my central rings, for example, goes back to early childhood memories of playing with Lincoln Logs. After building a variety of cabins, I would take the broken pieces and create imaginative playground equipment from them. It was both a challenge to find unconventional uses for those pieces and a sense of not wanting any of the broken pieces to feel left out. This, no doubt, framed my later desire to find unconventional props to explain mathematics, and at the same time, strive to be inclusive of all my students.

Multiple rings create the core of a tree. Reflecting on my life, some of my core rings connect to my years of involvement with 4-H, which is a club somewhat like scouting. The 4-H motto is “Learn by Doing,” and they mean it literally. I spent hours as a teenager in activities such as leading hands-on cooking and sewing workshops for kids or sorting through piles of leaves to learn how to accurately identify different trees for a forestry competition. Now, as I strive to get students physically involved with the material, I think back to my 4-H days. We didn’t read about trees; we walked in the woods and experienced them. In my life now as a professor of mathematics, I have students walk out function transformations or physically act out the formal definition of continuity with yarn and feather boas. I’m hoping this will provide them with fun and memorable mathematical experiences like those 4-H events did for me.

Just as each broader ring in the tree reflects new growth, so too did my college summers as a camp counselor at a Christian outdoor adventure camp. We did a variety of noncompetitive activities, like hiking, zip-lining, and rappelling off of cliffs. We explored nature and encouraged each other in everything that we did. I remember seeing the wonder in kids’ eyes when they saw something unusual, like one day when the wind was blowing upward by a cliff so that you could position a leaf under your finger and the wind would hold it in place. I still look for those moments of wonder in my students, trying to detect mathematical learning opportunities. I have also noticed that when students are afraid to try difficult math problems, I draw upon techniques I used to encourage campers who were afraid to take the first step when rappelling off of a cliff. The scenario is different, but the fear is the same. In addition, thinking of my camp experience reawakens my desire to engage students both outside of class and in noncompetitive settings. Some of my favorite moments reflect this, such as hiking with students and comparing the mountain topography to surfaces we could study in multivariable calculus or traveling with students to a version of math camp at our section MAA meeting.

One thing I find interesting about playing with Lincoln Logs, 4-H, and camp is that nobody who knew me in those settings expected me to become a mathematician. Yet, those early experiences produced skills that appear to be dormant in later years, hidden like the tree’s inner rings, while providing us with abilities that feel almost instinctual. I think we all have unique experiences at our disposal that we can use to enhance our teaching. We navigate successes and challenges and are enriched by our experiences, allowing us to do some unrelated things almost effortlessly.

Looking back at the tree, my arborist noticed something unusual in the ring structure. There was a dark line coming in from the bark towards the center, indicating that the tree had had lawnmower damage many years before. It struggled to heal, but never quite succeeded. Fungus then seeped in and damaged the root system, leaving the tree with nothing to support it. This brought back memories of some of my own deep scars from middle school. I was dealing with fairly intense bullying at that time which included kids stepping on my lunch, putting glue in my hair, and placing a maxi pad in my desk with lipstick on it, then standing by to watch for my reaction. I tried to be strong, to hide any emotions, and to focus on my schoolwork. I kept covering it up. But if I am honest about it, even today, sometimes I notice fungus getting in, triggering that old sense of being rejected.

Reflecting on the tree’s rings and its scars again brought me back to thoughts of my classroom. I’m not the only tree in the room. My students have their own rings of life experiences and hidden scars that I don’t know about. All I see is the bark. Yet, we are going to be more impactful as teachers if we can find ways to connect to each student’s rings of experience. This is why we teachers talk so much about various forms of active learning and having classrooms where everyone feels welcome and accepted. We will never know the whole story behind any of our students, but we can be authentic with them and share our joys and struggles with learning mathematics. We can engage students in class. We can help deepen their foundations, grounding them for the future.

Happily, my plum tree lives on. A colleague of mine does woodworking as a hobby and collected some pieces from the trunk. Once the wood cures, he will hand-craft it into new pieces of art that will have a life of their own. Likewise, our students will grow into their own works of art, adding new rings of life and memories influenced by their time with us. It reminds me that we do make a difference, even if we never see the final product that our students become.