Books about mathematics and human flourishing

This collaborative piece first appeared in the Early Family Math December 2023 newsletter. 

Alex Box and Chris Wright decided to embrace the holiday spirit by coauthoring this newsletter with personal reflections about the teaching and learning of mathematics. We highlight three authors who have affected us deeply with their descriptions of the richer aspects of mathematics. 

Francis Su writes about mathematics as “a vitally human endeavor, grounded in basic desires that we all share, and elevated by virtues to which we can all aspire.” Paul Lockhart describes how to unlock wonderful mathematical explorations through playfully following one's natural curiosity. Yoko Ogawa weaves a charming story illustrating how gentle mentoring can lead students to discover for themselves the richness of what mathematics has to offer.

These three authors talk about the joys and values inherent in teaching and learning mathematics. This contrasts strongly with folks who would advocate for teaching mathematics because of its practical uses. This practical lens focuses on how math education is important because it leads to better results in school, more access to STEM careers, and improved social equity. Of course, all these things are true. However, it is like suggesting that a walk through a beautiful park is important because you arrive at a place you need to get to on the other side of the park.

It is the beautiful park that has drawn the two of us to be teachers and learners of mathematics, and it is that topic that we would like to explore together in this holiday newsletter.

Francis Su – Mathematics for Human Flourishing

Chris: The problem with discussing this book is that there is too much good material to choose from. It is the best book I have seen in capturing what mathematics really has to offer in a humanistic way. Su’s writing comes from the heart and is filled with interesting anecdotes and examples that help his ideas come to life.

Su writes: “A society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without an opportunity to play with beautiful ideas and see the world in a new light. To grasp mathematical beauty is a unique and sublime experience that everyone should demand.”

In response to the question “Why do mathematics?” Su answers: “Mathematics helps people flourish.” He goes on: “... the movement toward virtue is aroused by basic human desires – universal longings that we all have … When some people ask, ‘When am I ever going to use this?’ what they are really asking is ‘When am I ever going to value this?’ … each of the following chapters is devoted to one basic human desire whose fulfillment is a sign of human flourishing. In each, I illustrate how the pursuit of mathematics can meet this desire, and I illuminate the virtues that are cultivated by engaging in math in this way.”

Alex: This book captures mathematics in an enlightening and complete way, and is a welcome invitation and set of provocations for reimagining mathematics.

Su’s intention is not to make mathematics the hero; its goal is not meant to focus on how great it is and what it can do (it humbly does this regardless). Rather, the book “grounds mathematics in what it means to be a human being and to live a more fully human life.”

To do this, Su describes a set of thirteen desires and subsequent building of virtues through the pursuit of mathematics. He illustrates, for instance, how:

• The desire for EXPLORATION fosters imagination, creativity and an expectation of enchantment.

• The desire for STRUGGLE can develop endurance, unflappable character, competence to solve new problems, self-confidence, and mastery.

• The desire for PLAY builds hopefulness, curiosity, concentration, confidence in struggle, patiences, perseverance, ability to change perspectives, and an openness of spirit.

I am grateful to have accessed this wonderful set of ideas.

Here is a video recording of Francis Su giving a talk about many of the ideas in his book.

 

Paul Lockhart – A Mathematician’s Lament, Measurement, and Arithmetic
 

Arithmetic
Alex: As someone who had not seen or enjoyed mathematics for its own sake until well beyond the school years, and who was long crippled by painful arithmetic practices, I have found Arithmetic to offer many refreshing facts and viewpoints, and playful number computation ideas.

Lockhart begins by describing counting and arithmetic as an art, and by offering ownership to the reader:

“Arithmetic is just like any other craft; you can get good at it if you want to, but it is no big deal either way. My hope is that by reading this book you will be inspired to try it out for yourself and to experience firsthand the simple pleasure and satisfaction that comes with numerical fluency. Have fun!”

There is important food for thought for educators in this book. He says, for instance:

“There’s no point counting something you don’t care about. Don’t ever do that. It’s boring, and it will make you hate counting. There are actually a lot of people who hate arithmetic (far too many to count!), and it makes me sad. Usually it’s because they were made to do something they weren’t interested in doing. Let’s not have that be you."

Measurement

Chris: I was teaching high school Geometry when I read this book for the first time. I immediately felt how right it was to teach by simply drawing a diagram on the board without any prompt, having students create questions about it, and follow those questions wherever they led. It is so much healthier, when it can be done, to have a student follow their interests and curiosity, rather than being told what they must learn.

Try some of these, or make some up yourself. 

• Draw two or three differently shaped quadrilaterals (4-sided figures) and in each one connect the midpoints of the sides to create new quadrilaterals. What do you see and what questions do you ask? This is one of the most beautiful and satisfying geometric results I know.

• Draw a square and one of its diagonals (a line joining opposite corners). Next, draw a circle inside one of the two triangles you just created so that this circle just touches each of the three sides of the triangle. What do you see and what do you ask?

• Draw a square around the outside of a circle so that the circle just touches each of the four sides of the square. Next draw a little circle in one corner that touches two sides of the square and the outside of the circle. What do you see and what do you ask?

I had one Geometry class that always tried to finish early so there would be time to dig into one of Lockhart’s diagrams. They didn’t care that the subject of the diagram had little to do with anything they needed to know for their assessments - they loved the experience of exploring and playing with these diagrams. Those were deeply satisfying times for all of us in the room. 

A Mathematician’s Lament

Alex: This must be one of the most important papers written about mathematics education. Lockhart opens by crafting a vivid dystopia where music and painting are taught in ways that stifle creativity and make these vibrant and expressive art forms mechanical and meaningless. This allegory sets the scene to argue that, in reality, an overly narrow and rigid approach is robbing learners of the innate creativity and joy inherent in mathematics.

Chris: One of the things I love about this essay is how down to earth and relatable his arguments are. You don’t need to have had extraordinary experiences with mathematics to understand the truths he puts forward. It is the rare piece of writing that hits every reader with a thunderbolt of understanding about something they had somehow missed for so many years.

Yoko Ogawa – The Housekeeper and the Professor

Alex: In this novel, a brilliant mathematician (the Professor) lives with a short-term memory of only 80 minutes due to a traumatic accident. A young housekeeper, who comes to work for him and who narrates the story, discovers joy in mathematics through their interactions and through the mathematical lessons he provides her son.

The Professor reminds me of mathematicians and other maths enthusiasts I have met who are also excellent teachers. He is an encouraging and patient mentor and there are many scenes in this book that model a gentle pedagogy that fosters a desire to learn in his students.

This book illustrates the power of impromptu and meaningful conversations that quickly bring in mathematics and, through these, we get to enjoy many of the untold stories of numbers and the beautiful relationships that exist among them.

I count in the reading of this novel many lessons relevant to my role as a mathematics educator and learner. It is also a simply beautiful story.

Wrap Up

We love mathematics and we are very grateful for these three authors and the other influences that have helped us see the beauty of mathematics. If you have books, people, or events that moved you to gain a deeper appreciation for mathematics, we encourage you to share them with us. 

Alex Box
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and/or
Chris Wright
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