Summer Reading For Math Teachers

My school had graduation yesterday, so I can look forward to having some extended periods of time to do some reading. Here are three books I’ve enjoyed recently and you might find interesting (clicking on the titles will take you to their Amazon pages):

Love and MathLove and Math: The Heart of Hidden Reality, by Edward Frenkel. This is a terrific book about Frenkel’s struggles to overcome institutional anti-Semitism in his native Russia and become a world-class mathematician. He is currently a professor of mathematics at UC Berkeley. He intersperses autobiographical details with explanations of how his mathematical research helped physicists develop their theories of quantum mechanics, as well as unite seeming unconnected branches of math. Along the way, he shares his love of the Platonic world of mathematics: “Nothing can stop us from delving deeper into this Platonic reality and integrating it into our lives. What’s truly remarkable is mathematics’ inherent democracy: while some parts of the physical and mental worlds may be perceived or interpreted differently by different people or may not even by accessible to some of us, mathematical concepts and equations are perceived in the same way and belong to all of us equally. No one can have a monopoly on mathematical knowledge; no one can claim a mathematical formula or idea as his or her invention; no one can patent a formula!” (pp. 235-236) Frenkel delves into some very deep and advanced mathematics, but he manages to explain it terms most everyone can understand.

Program or Be ProgrammedProgram Or Be Programmed: Ten Commands For A Digital Age, by Douglas Rushkoff. My daughter gave me this book after she read it for a coding class in college. It is in the vein of Neil Postman, asking users of social media to be aware of digital technologies’ inherent biases. It’s relatively short, but very powerful. Rushkoff’s main point is that unless users understand basic coding principles, they will be at the mercy of an élite who create the social media platforms that can manipulate them. The ten commands are:

  1. Time: Do Not Be Always On
  2. Place: Live In Person
  3. Choice: You May Always Choose None of the Above
  4. Complexity: You Are Never Completely Right
  5. Scale: One Size Does Not Fit All
  6. Identity: Be Yourself
  7. Social: Do Not Sell Your Friends
  8. Fact: Tell The Truth
  9. Openness: Share, Don’t Steal
  10. Purpose: Program or Be Programmed

Favorite quote: “In a digital culture that values data points over context, everyone comes to believe they have the real answer and that the other side is crazy or evil.” (p. 65)

Brain on Music

This Is Your Brain On Music: The Science of a Human Obsession, by Daniel Levitin.

This technically isn’t a book about math, but if you’ve ever wondered why humans are the only animals to create and appreciate music, then you will enjoy this. Levitin knows what he’s talking about: he’s been a record producer of very successful rock artists, and he is now a neuroscientist at McGill University, where he runs the Laboratory for Musical Perception, Cognition, and Expertise.

Levitin spends the first few chapters explaining what music is, and what terms like pitch, timbre, rhythm, and tempo mean. He also discusses the mathematical relationships in tones and octaves.

Levitin spends the rest of the book explaining the latest research in how the brain processes music, and what is involved in creating, performing, and enjoying it. No other activity involves as many parts of the brain as performing music does. He laments the separation between performer and audience that has happened in western cultures. In earlier times, everyone played some sort of instrument or sang. The easy availability of recorded music has caused a decline in music performance, however, to the detriment of us all.

So, three books with three very different foci, but I believe teachers of mathematics will find all of them interesting and enjoyable. Have a great summer!


Visualizing Punctuation

At, Adam J. Calhoun has come up with a fascinating way to look at famous literary works: take away all the words and only look at the punctuation. Don’t believe punctuation matters that much? Compare Cormac McCarthy’s Blood Meridian (on the left, below) to William Faulkner’s Absalom, Absalom (on the right):


I shared his findings with all the English teachers at my school, and they were really interested in the information one can glean from this analysis.

Check out Calhoun’s post to see some beautiful “heatmaps” of famous novels. They look like Rothko paintings.

A Couple of Reading Recommendations

I’ve been on Spring Break this week, and we’ve stayed home this year, which has been nice. I’ve had a chance to catch up on some reading, and I really enjoyed two books in particular – one nonfiction, and one fiction. Both will appeal to teachers and lovers of mathematics.

First, the nonfiction book: Amanda Ripley’s The Smartest Kids in The World and How They Got That Way. I’ve read many books about education, and how American schools are failing our students, but this one is the most eye-opening and refreshing take on that subject I’ve seen. Ms. Ripley shares her data and conclusions through the personal stories of three American high school students who participate in foreign exchange programs. Kim leaves Oklahoma to spend a year in Finland, which has been in the news lately because of its students’ extraordinary performance on the PISA (Program for International Student Assessment). Eric travels from Minnesota to Korea, and Tom goes from Gettysburg, PA to Poland. Among the trials and tribulations Kim, Eric, and Tom undergo are lots of hard data on their host countries educational systems.

Finland’s secret boils down to recruiting the best and brightest college students to be teachers, and making an education degree as demanding as a medical one. The Finns drastically cut the supply of teachers, which increased their value. My favorite quote is from a sixth-grade teacher in the course of a conversation with Ms. Ripley:

Vourinen was visibly uncomfortable labeling his students. “I don’t want to have too much empathy for them,” he explained, “because I have to teach. If I thought about all of this too much, I would give better marks to them for worse work. I’d think, ‘Oh you poor kid. Oh well, what can I do?’ That would make my job too easy.”

Poland is interesting, because they put into place a radical change to the way they tracked their students; they waited an extra year until they were 16 before deciding if they went to vocational school or a university. They had almost immediate improvement in their PISA scores, but it looks like they may slide backwards. The party of reform was voted out in recent elections.

Korea is simply a nightmare. Students attend public school during the day, then attend a private “tutoring” hagwon every evening to prep for the big exam that determines if they will get into one of three elite universities. Basically, every student attends two days’ worth of school every day! The government has enacted a ban on hagwons staying open past ten p.m., but it hasn’t been effective.

Over and over again throughout the book the message is, students will rise to meet high expectations. The fact that almost all of our students in America are bored and not challenged is an indictment of our educational system. Also, technology appears to have no effect on students’ academic achievement; it may even be counterproductive. And speaking of counterproductive, our culture’s obsession with sports comes in for a lot of criticism. Ms. Ripley also has some concrete things parents can do to help their children succeed in today’s competitive environment. They are surprisingly simple and don’t cost a thing.

The fiction work is Yoko Ogawa’s The Housekeeper and the Professor. I’ve enjoyed this twice now; it is one of the most moving and beautiful stories I’ve ever read. It is set in contemporary Japan, and I’m not giving anything away when I explain the premise: a young, single mother has a job with a housekeeping agency, and she is hired to care for a professor of mathematics. He has suffered head trauma, and his memory only lasts for eighty minutes at a time. Her remembers everything he did before the accident, but nothing since. Every eighty minutes he forgets what he has just experienced.

The  housekeeper, the professor, and her son struggle to develop some sort of relationship, and Ogawa makes the reader question what constitutes a family; is it possible to deeply care for someone when there are no shared memories? Along the way, Ogawa uses the professor’s love of mathematics to share her wonder at the beauty of numbers. Here are some of my favorite quotes:

He had a special feeling for what he called the “correct miscalculation,” for he believed that mistakes were often as revealing as the right answers.

“The truly correct proof is one that strikes a harmonious balance between strength and flexibility. There are plenty of proofs that are technically correct but are messy and inelegant or counterintuitive. But it’s not something you can put into words – explaining why a formula is beautiful is like trying to explain why the stars are beautiful.”

“The square root sign is a generous symbol, it gives shelter to all the numbers.”

When he is helping the housekeeper’s son with a word problem, he says this:

“You’re right. This is the trickiest one in your homework today, but you read it well. The problem consists of three sentences. The handkerchiefs and socks appear three times each, and you had the rhythm just right: so many handkerchiefs…so many socks…so many yen; handkerchiefs…socks…yen. You made a boring problem sound just like a poem.”

And finally, as the Housekeeper goes to the library to try to understand a simple formula the Professor has written down:

In my imagination, I saw the creator of the universe sitting in some distant corner of the sky, weaving a pattern of delicate lace so fine that even the faintest light would shine through it. The lace stretches out infinitely in every direction, billowing gently in the cosmic breeze. You want desperately to touch it, hold it up to the light, rub it against your cheek. And all we ask is to be able to recreate the pattern, weave it again with numbers, somehow, in our own language, to make even the tiniest fragment our own, to bring it back to earth.

Ogawa’s prose is delicate and understated, which makes the story even more powerful as it unfolds.

Every summer, my school has an “All School Read”, where each upper school student and faculty member reads the same book, and we discuss it in small groups. Last year, the history department sponsored Ruta Sepetys’ Between the Shades of Gray, the story of the Soviet genocide of the Lithuanian people. This year, it’s the math department’s turn, and we will be reading The Housekeeper and the Professor.

Kindles In The Classroom

This post isn’t particularly math-related, but I wanted to shine a spotlight on some amazing things a colleague of mine is doing with technology in her classroom. Meg Griswold teaches high school English, and at yesterday’s faculty meeting she made an outstanding presentation of all the ways she is taking advantage of the Kindle.

She uses the Kindle app on her tablet computer to quickly locate and display important passages from whatever book her class is discussing. She also has her students highlight their own passages and add notes that can be referenced later during discussion. Meg also uses Twitter to send out to her students study tips, helpful notes about book passages, or questions to be thinking about while reading.

Since so much classic literature is public domain, many titles that English courses cover are free or incredibly inexpensive. When I got my own Kindle, the first purchase I made was the complete works of Charles Dickens. Total cost: $2.99! With the free Kindle app, students can access thousands of classic works on their smartphones or computers at little or no cost.

It is such a privilege to work with creative and pioneering educators like Meg. Check out her blog where she is chronicling her efforts to incorporate Kindles into her classes. It’s fascinating.