# Math Lessons in the Age of Social Distancing

Many of us are acting as teachers or teaching assistants for our kids these day. Schools are closed and remote learning is the order of the day. We rely on teachers and teachers rely on us. There is a kind of symbiotic relationship here that is new and different from the past.

And then, there’s math.

I learned math differently from how it is taught today, and I find some of how it is taught today to be confusing. I suppose that research and studies have shown that kids learn math better the way they teach it today, then how it was taught when I was learning it (or for that matter, when Isaac Newton, or Euclid and others learned it). It still often seems nonsensical to me. Thus we hit upon a problem: my kids are taught math in a way that I don’t really get, but I am relied upon to help them learn math in this age of remote learning. I can’t help but fall back on the ways I know.

The Little Man had a math test yesterday involving fraction. The test focused primarily on multiplying and dividing fractions. For one set of questions, the instructions indicated the answers should be given in simplest form. The Little Man was marked off on three of these questions. He gave answers of 7/2, 8/3, and 11/6 respectively. His teacher marked these wrong and said “close” for each one.

The Little Man came to me puzzled as to why these were wrong. “Well,” I said, “let’s look at the definition of ‘simplest form’ in your text book.” We checked and the textbook gave the definition as a fraction in which the numerator and denominator could not be further reduced; that is, they only have a common factor of 1. Well, this was true in all three cases, so I sent the Little Man’s teacher a question, asking for clarification so that I help the Little Man understand his error and avoid it in the future.

His teacher said that his answers were improper fractions and that improper fractions were not in simplest form. I dove into the ancient and dusty parts of my memory to see if I could recall this from my own math classes, but there was nothing there. Maybe she’s right. Still, the definition given in the text book made no mention of improper fractions. It was generalized to “fractions.” I thanked the teacher for the clarification and then said the following to the Little Man:

“Buddy, you basically got these wrong on a technicality–like evidence of crime being tossed because it was come upon improperly. The thing to remember is, if you were an engineer in the real world, and someone asked you to calculate a measurement, and you came up with 7/2 as an answer, that answer is precise and correct, and would have served whatever engineering purpose it was needed for. Your boss would have been happy, and the bridge you were building based upon the calculation would be structurally sound. Sure, the answer was in improper fraction and might not technically be considered simplest form the way 3-1/2 is, but they are mathematically equivalent. You were mathematically correct, and definitionaly wrong.”

This is small potatoes, I know, but it is a frustrating part of being an amateur teacher. It is virtually impossible to unlearn how I learned math and equally difficult to comprehend how it is taught today. For me, math is a tool and I’m not as concerned about the theory. I use all kinds of math every day in my job. 7/2 is just as good as 3-1/2 and in the real world, when we are all trying to be efficient with our time, it also faster to come up with (one less operation to perform). Kelly has been trying to teach the kids how to study–practical advice that will be useful for them in all of their schooling going forward–and something I think was never taught well in my schooling. I am trying to teach practical problem-solving.

Fractions, improper though they may be, are more practical than mixed numbers.

# No Motivation

I woke up this morning feeling completely unmotivated. I’ve got three requirements meetings scheduled for this afternoon. I’ve run 13 of these meetings over the last couple of weeks, with 9 scheduled this week. And three of them are today. I think part of the lack of motivation comes from working ceaselessly for the last 4 months. Normally, by this point in the year, we’d have driven down to Florida for spring break, at which time I would have taken a couple of days off. We may have headed up to New York or out to West Virginia for a weekend family getaway. None of that has happened, of course. The days run together, and the motivation well runs dry without some mental downtime to rejuvenate it.

I’ve often wondered if major league baseball players ever get that feeling. You know, you’re two thirds of the way through the season, there’s still 50 games to play, the team is in the cellar, and you wake up knowing that you’re starting at second base, batting cleanup, far from home, and just feeling like you can’t stay another night in a hotel, can’t bring yourself to swing at another pitch in batting practice. Of course, these are professionals, and are paid to play, so they muscle through somehow. But even those players who are living their dream and love to play ball must have days like this now and then, right?

Baseball is on my mind because it isn’t anywhere else, and I miss it more than I realized. My year is divided into two parts: baseball season, and winter. Baseball provides mental balance for me. The often disturbing news in the morning papers is balanced by the box scores, and sports columns. That’s missing from the papers now and so one place I go each day for a little rejuvenation is gone. Maybe baseball will find a way of coming back this season, but it won’t be quite the same.

These are all small considerations in the face of the larger Pandemic (are we capitalizing this yet?). After all, what is baseball when people are getting sick, people are dying, people are out of work, people are suffering. Maybe it is familiarity during a time of uncertainty that I find comforting. The unknowns pull the levers of anxiety. Because of this, I have to limit myself to thinking about today and not worrying too much about what may happen tomorrow. When I start to think about tomorrow, or the next week, I find that my motivation is sapped just a little bit more.

The show must go on, and so when my first meeting starts early this afternoon, I’ll be ready to go, regardless if the motivation is there or not. I could take a day off at some point, but it seems wasteful to take a day off when all I’ll do is sit at home. Besides, even if I took a day off work, I can’t take a day off from helping the kids get their school work organized, checking their work, answering their questions. If I am doing that, I might as well be getting some work done, too.

Interestingly, my motivation to write has been growing lately and my appetite for reading is as insatiable as ever. This morning I completed my sixth book in six days. It was Frank Deford’s memoir, Over Time. It was, perhaps, the best book I’ve read this year, a complete surprise, and one of those books that I read with absolute delight and dread. The dread came from the certainty that the book would end, and all I wanted was for Deford (who narrates the audiobook version) to keep spinning his tales, making me laugh out loud over and over again. If I ever doubted the value of a book to lift my spirits in troubled times, Deford wiped away those doubts with each delicious anecdote.

# What are you reading back there?

There was an amusing item in the New York Times on what famous people’s bookshelves reveal. Whenever I see someone with a book, I have to know what it is. I almost never ask, since I almost never know the person in question, but I usually try to get a view of what it is they are reading. Sometimes I just wonder if it is something I have read before, sometimes I wonder if it is something that will interest me down the road. This extends to movies and television. I sometimes pause a show to see if I can identify the books on the shelves (who would have thought Isaac Asimov would show up in The Wire?) The Times article refers to the bookshelves behind the famous people in their Zoom, FaceTime, and other video chats that they are doing in this time of physical distancing.

Above is the view people see of me and one corner of my office during Zoom and Team meetings. Like many of the famous people, I have bookshelves in the background. They aren’t designed to be for show, and indeed, the two that appear in the background are 2 of 10 that encircle 3 sides of my office. That said, people may wonder, as I do, what books are on these bookshelves. The two behind me are the first alphabetically in my collection. (I arrange my books alphabetically by author, and then chronologically within a given author.) 9 of the 12 shelves in these bookcases contain books by Isaac Asimov. But there are some other interesting books here as well:

1. A first edition history of the Civil War published in 1865.
2. The official 4-volume chronology of the Apollo spacecraft.
3. Asimov’s Annotated Don Juan
4. A signed copy of Asimov’s Murder at the ABA
5. Several signed copies of Ray Bradbury books (The Martian Chronicles, Something Wicked This Way Comes, and Ahmed and the Oblivion Machine, which he signed for me in December 1998.

I’ve read many, but not all of the books on these shelves.

The remaining 8 bookcases cover the C’s through Z’s. The only book I have within reach while working are Merriam-Webster’s Collegiate Dictionary (Eleventh Edition), Fowler’s Dictionary of Modern Usage, The Concise Columbia Dictionary of Quotations (circa 1993), 2019 World Almanac (I’m due for a new one), and The Elements of Style by Strunk and White.

And what am I reading while stuck at home? Yesterday I finished Camino Island by John Grisham, and today I finished The Black Echo by Michael Connelly. It’s not all light reading though. I’m currently reading The Black Ice (also by Connelly), John Adams by Page Smith, and A New Kind of Science by Stephen Wolfram.

# Vacation in Colonial America

The news lately is unsettling. On some days, I finish the paper hoping the coronavirus pandemic is just a dream that I will wake up from. I know it isn’t, but part of me looks for ways to escape. Thank goodness for books! Opening a book is like opening the lid to an escape hatch. The rest of the world falls away. I become fully immersed in a way that I never reach with movies or television. My current escape hatch has taken me back to colonial America.

I’ve resisted reading Ron Chernow’s biography of Alexander Hamilton since it first came out. After reading David McCullough’s masterful biography of John Adams in 2001, I became a great admirer of Adams. My opinion of Hamilton (and Jefferson, for that matter), distorted through Adams’s lens, was not very high. Because of that, I read other books by Chernow, but not the Hamilton biography.

A few weeks ago, however, I read a great book called The American Story: Conversations with Master Historians by David M. Rubenstein. This was an ideal audiobook because it was Rubenstein interviewing many modern historians, among them, Ron Chernow. That book and Chernow’s interview when he talked about Hamilton was the clincher.

And so, a week ago, I set my reservations about Hamilton aside and started to read Chernow’s biography. It came at a good time. News of the coronavirus was growing increasingly grim, and I needed a mental escape. I found it in America’s colonial past. Even though I didn’t always agree with Hamilton–especially his views of Adams–I looked forward to returning to the book whenever I could, often right after finishing the newspaper.

Hamilton has impressed me in several ways. I mentally divide impressive or outstanding people into two groups: their success is based on extremely hard work; or their success derives from some innate genius. While I admire genius, it is the hard worker that impresses me most–perhaps because that is something achievable without native genius. Rarely do I find people I’d put in both categories, but Hamilton is one. Even among the many hard workers I’ve read about, Hamilton stands out. HIs energy seemed boundless. His prolific output dwarfs Asimov. Then, too, his vision for America’s economic foundation shows genius. So do his ideas on the structure of government as he describes in The Federalist Papers.

Still, McCullough introduced me to Adams and in the two decades since, my admiration for the man, and his thinking has only grown. As I read of Adams and Hamilton’s disputes, this time through a Hamiltonian lens, I kept feeling the need to jump in and defend Adams. If only Hamilton knew… I’d say to myself.

Indeed, I began to wonder how Adams, Hamilton, and Jefferson would react if they all had access to one another’s papers the way we do today. Would their opinions change? Would their feeling for one another differ?

I’m nearly finished with the book, and as I got closer to the end, I worried about my return to the real world. I’ve looked forward to my escapes to colonial America as an anodyne to the uncertainty in present-day America. After all, there is no COVID-19 in colonial America. Instead, they have yellow fever, and their idea of social distancing it to retreat from the cities. I’ve decided, therefore, to extend my vacation in colonial America for now. But I need to turn back to Adams to clear my palate of Hamilton. So I have settled on two books about Adams that I haven’t read before.

The first, just released, is called John Adams Under Fire by Dan Abrams and David Fisher. It is all about Adams’s defense of the British soldiers during the Boston Massacre. The second is Page Smith’s 2-volume biography of John Adams, written in the 1960s not long after access to Adams’s papers was made more widely available. I happened to come across a boxed edition last year at the kids’ school’s annual used book fair.

Our kids, incidentally, will be home from school for the next 5 weeks. All Virginia schools were closed for at least two weeks. Our city’s schools closed down through spring break. They will have virtual classes online. The social distancing can be a real challenge. Last night, I had a virtual happy hour with a bunch of my friends scattered across the country. But with recommendations to avoid large crowds, it makes many of the typical things we’d do out of reach. Fortunately, I am surrounded by books, each one of which is an escape hatch to some other place and time.