“Mathematics reveals its secrets only to those who approach it with pure love,
for its own beauty.” Archimedes
I think most people who are reading this article have at one point or another made the following comment, “I don’t understand this ‘new-fangled’ (Common Core) math. This is not how I learned math when I was in school.” I know that I have repeated this comment more times than I care to admit. As a teacher of mathematics, I have had to learn math from a whole new perspective in order to teach it to my students. As a bibliophile, lover of books, I have never quite felt the same love for math that I feel for literacy. Even though I may not love math the same way I love literacy, I have grown to appreciate its beauty. I have come to understand math is also about storytelling with a language that is both universal and unique.
Literacy expert Louise Rosenblatt (1978) distinguishes between two types of reading: efferent and aesthetic. The stances represent opposite ends of a continuum. I believe the same is true for mathematics. When a student is viewing math from an efferent stance, he or she is engaging in math for pragmatic reasons. For example, completing a calculation using a traditional algorithm to efficiently solve a problem like 12 x 5 = 60. At the opposite end of the continuum, a student who is viewing math from an aesthetic stance finds joy, pure love, in curiously exploring the beauty of math.
What is beauty? Merriam-Webster defines beauty as, “the quality or aggregate of qualities in a person or thing that gives pleasure to the senses or pleasurably exalts the mind or spirit.” Beauty is in the eye of the beholder. Not sure who first said that famous quote, but I do know that sometimes we pass by beautiful people, or things, because we don’t take the time to stop, notice, reflect, and wonder. I have come to learn that “mathematics is not about numbers, equations, computations, or algorithms: it is about understanding”—William Paul Thurston. Math is orderly, sublimely pure, and perfect. The simplicity of math can be found everywhere (see pictures below). The University College London has used brain scans to show that complex mathematical equations, or formulas, can evoke the same sense of “beauty” as an artistic masterpiece or music from a great composer. My job as an educator is to help my students efficiently and accurately calculate numbers, equations, computations, or algorithms, as well as look for the universal beauty in math. My job as an educator is to help my students understand and appreciate that beauty, because mathematics is not just a worksheet, it inhabits the world all around us.
According to Stahl and Nagy (2007), “Language is a key component in the learning process. People’s perceptions of the world are largely shaped by their vocabulary knowledge. Indeed, words are the tools we use to access our background knowledge, express ideas, and learn new concepts” (p. 4). Students can solve equations with little effort, or vocabulary knowledge, using a calculator (efferent stance). I need to also help my students develop the language they need to communicate their mathematical thinking beyond that of calculating a simple equation (aesthetic stance).
This “new-fangled” math is definitely not the math I learned in school. This “new-fangled” math reveals secrets that open a world of possibilities and opportunities far exceeding any numbers, equations, computations, or algorithms. It requires language, storytelling, processing skills, critical thinking, creativity, perseverance, and teamwork. All skills necessary for success in the global society we live in today. What a gift students have been given that I rarely had access to when I learned math. After being cooped up all winter due to the weather and COVID-19, take a moment to go outside with your child and explore the beauty of math in all its forms. What mathematical beauty do you notice? What do you wonder? What words can you use to tell the story of math? The real-world applications of math are endless!
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