I had a conversation the other day with one of our math tutors, Alex, about connections among all the different subjects we tutor and study. Yes, we tutors are still studying in one way or another.
In fact, for the year 2015 I have embarked on a personal project to study in depth the Scientific Revolution and the Enlightenment periods of history. My students learn about these eras to varying degrees in all of the history and government subjects I tutor, and part of what I like about tutoring history is discussing context. I have decided to explore the details surrounding these particular periods of history because they are responsible for a plethora of revolutions, movements, new ways of thinking, and for the creation of entirely new education systems.
What an incredible opportunity to connect the Enlightenment movement in the 1600s to the reason we promote liberal education today: essentially, the reason this particular student in front of me has the right, the obligation, to attend a school wherein she learns a little bit about all the subjects she can possibly imagine, for free.
So there we sat, our Spanish tutor Nichole, Alex, and me.
“I love that in our Humanities program I get to help kids think critically, think about ways of understanding things, ways of thinking, and not just address basic skills or answers,” I said.
“Well, but I’m sure that those same opportunities are not as often available in, say, Math,” Nichole responded, motioning to Alex.
“On the contrary,” he said, “It is so much more important for me to teach my students how to find their own answers, how to think about math in an abstract way, why math matters, than it is for me to teach them equations. If I can give them the tools to first think about the problem in different ways, then I can help them think about how they might go about finding their own answers to those problems. Unlike most other subjects, math is derided by many students as unnecessary in the real world. It’s the one area about which students always ask, ‘when will I ever use this?’”
I remembered then having a similar discussion with a tutor from our Berkeley center, Jennifer. I asked her, after hearing yet another student complain, yet again, that geometry is “useless in the real world” since she had no intention of going into architecture. I knew I was putting Jennifer in the spotlight, but, like a lawyer in the courtroom who knows to ask her star witness only questions for which she already has the answer, I knew Jennifer would shine.
“How about when you need to parallel park? How about when you think about fitting all of your items in a bag? How about when you load your car? When you go rock climbing and need to make the next precarious move? All of these things are spatial concerns. Geometry helps you think about spatial relationships.”
Yea, she’s pretty brilliant. The student knew she had no
I relayed this conversation to Alex and Nichole, and Alex exclaimed, “exactly!”
You know those perfect moments, when you’re having a really good conversation, and you feel like you are all on the same page; everyone just “gets” everyone else? This was like that.
“Math is about relationships, spatial and otherwise. Ways of understanding the world, making connections, from addition and subtraction to geometry and even physics,” Alex said.
“Right,” I nodded, “math will help my daughter think about the planets someday. Because when she understands basic geometry, she will be able to imagine herself on this sphere, Earth, and imagine the planets around us. Without math we cannot see the world in all its wonder.”
I described the current book I am listening to for my Scientific Revolution project, called The Jewel House, by Deborah Harkness, about the birth of the Revolution on the streets of Elizabethan London. In this book, math, mathematical function, and even thinking mathematically are new and exciting phenomena in the world. Harkness describes the interactions between Queen Elizabeth and the everyday members of society who are trying to get letters of patent to practice teaching math, to sell books about math, to create and sell mathematical instruments. People at all levels of society are coming to realize how crucial math is to life, both personally and in business.
At this point, Alex jumped up and ran out of the break room, only to come running back in with a book in his hand.
This book, Thinking In Numbers: On Life, Love, Meaning, and Math, by Daniel Tammet, which Alex had apparently been carrying around in his backpack and reading at his leisure is made up of different math stories; Tammet highlights points in history when math has played a crucial role.
“So this particular story,” he explained, flipping through the pages to find the right chapter, “is about the adoption of the Arabic number system in Elizabethan London.” Apparently, the author makes the point that Shakespeare waxes philosophic on the zero several times in his works. “The author asks us to imagine what it must have been like. For Shakespeare’s father, basic math involved X as 10, V as 5, I as 1. Imagine trying to do math with those symbols. X and I can be seen as entirely different numbers, so that the meaning of numbers, of mathematical thinking is forever changed when all of a sudden, those same numbers are exactly a zero apart, 1 and 10. More than just the arithmetic, it is the expressions themselves that alter, or illuminate, meaning. What a revelation, what a wonder, to be able to simply line numbers up and multiply, divide, add, subtract. The beauty of simplicity.”
The beauty of information, of knowledge. The beauty of curiosity, of the joy of learning.
I tutor Shakespeare. My students and I pick apart lines, we examine words, we search for meaning, but many of the conversations we have are about why this matters now. Why should I care about Julius Caesar? Othello?
Alex tutors math. He helps students start from zero and understand its relationship to the vast infinity of numbers beyond. But he also shows them why that infinity matters. And why the relationships within infinity are important. Why math is cool.
At the Bay Area Tutoring Centers, yes, we tutor most high school, middle school, and even college subjects; we help you get through an upcoming test; we support the learning you’re experiencing at school.
But at our best (and in my not-so-humble opinion, our best is, if not constant, consistent) we are excited, and we get our students, if not quite as excited as us, engaged. Because we are engaged. As Alex, Nichole, and I sat that day discussing interconnectedness we found a new connection among our subjects. Why? Because we live and breathe our subjects; we are curious, and we enjoy creating and feeding curiosity.
The beauty of curiosity, of connections.
Shanna Mendez
Humanities Tutor