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Once, when my daughter first came across the word “chaos” in her readings, she asked me what it meant. I am not quite sure why she knew that I would be able to explain that word, but she must have sensed that there was a mathematical meaning to this new word she had encountered. I explained that in that context, it meant things happening that could not be predicted. However, I added (as she rolled her eyes), things that we call “chaotic” are often very able to be predicted. For example, the movement of a leaf in a stream is often described as “chaotic”, but, if we look hard enough, there are definite equations that would define such motion. A similar idea relates to the word “random.” While we often refer to “random” as unable to be anticipated, random variables are often very able to be predicted. For example, if we flip a coin 100 times, we would expect it to come up heads about fifty times. Once we know a probability distribution, “random” does not mean unpredictable at all. I found myself thinking of this recently when I encountered a former student while out with my family, an encounter that might best be described as “random.”
After a trip to Connecticut to visit my father over the break, my family landed back in Ohio after the long trip and decided to eat dinner at a local casual restaurant that we often frequent. We ordered dinner and spent the time laughing at the fun times we had enjoyed with my father and my sister’s husband and children. As dinner wound down, a woman whom I did not immediately recognize approached our table. She introduced herself, and, I must admit, I did not recognize the name. She said that she had been my student years ago at Ursuline College, when she had decided to return to college as what we often call a “nontraditional student,” since she, possibly close to my mother’s age, was no longer in the typical age range for a college student. She had since graduated and has a career that she enjoys working as a social worker. She had been my student so long ago that she did not know I had a child, and was intrigued at the teenager that occupied our table. However, I was most struck by what she had to tell me, words that have served as inspiration as the chaotic (yes, there is that word again) beginning of the semester unfolds.
She said that she had always had difficulty with math, and was dreading taking her required math course. She was therefore very grateful for the extra time I took to explain things in class, and that I did not rush through the text but made sure that everyone understood the material before moving on. She said that she had often found herself telling others about a math teacher who finally helped her to understand solving systems of linear equations, and recounted the “ah-ha” moment when it finally made sense to her. I was thrilled to hear that she felt that she had gained something from the dreaded math requirement she was forced to take, and reminded myself that this was why such a requirement existed.
Of course, she could have learned math from any of my colleagues, and probably had the same experience. However, I was very happy and proud to have been part of this educational moment for her. The encounter is one that I will recall when the new semester’s schedule begins to feel overwhelming. Even if they never fall in love with math, for some of my students, this may be the last chance they get to finally begin to understand it.
Do any of my readers want to share stories of running into a grateful student years after they have left your class?
