by Robert Black

Sharing the Mathematical Experience

I grew up in a mathematical household. Not only did both of my parents teach high school and middle school math, but my mother was the school’s “math coach”—the faculty advisor for the national, state, and local math competitions that students entered. One competition in particular always posed some strange problems, and we would talk about them at home for days after the event, trying to solve the ones we hadn’t figured out. One year my grandfather, a lifelong engineer, showed up for a Thanksgiving visit, and we shared the problems with him. There was one in particular that he solved in a matter of minutes, after it had stumped all of us—a feat that has become a family legend.

Not everyone has that kind of upbringing, of course, but even a small dose of it can reveal a completely different way of looking at math, a way that is too often left out of the school curriculum. For many people, learning math mostly involved standing in front of a blackboard or whiteboard or sitting at a desk or in front of a computer, working a seemingly endless set of exercise problems. Such drills have their place, in the same way that musicians must play or sing scales and basketball players must practice layups and free throws, but if that’s all students do, they’re missing a big part of what math is about. In fact, they’re missing the most important part: the opportunity to see math as a creative, collaborative experience, full of possibilities for exploration and discovery.

When I started developing my ideas for mathematical fiction, I knew fairly quickly that I didn’t want to take the route of a “minute mystery” type of story, such as the Encyclopedia Brown series. I didn’t want to use a format in which the story presents a math problem and then the reader flips the page or goes to the back of the book to find an impersonal narrator explaining how to get the answer. There are a few books like that available—even some good ones—but I wanted to do more. My goal wasn’t just to present mathematical facts and techniques. I wanted to show as much of the problem-solving experience as I could—all of the twists and turns and dead ends and unexpected realizations that come with it. I wanted to do as much as I could to make my readers feel as though they’re solving the problems along with the characters.

In the Mathematical Nights books (Night of the Paranormal Patterns, Night of the Frightening Fractions, and Night of the Eerie Equations), the heroine Lennie Miller finds herself roped into the role of “Pattern Finder,” solving problems for a group of mathematically challenged monsters. Readers receive all of the information needed to solve the problems at the same time Lennie does, and they can try to solve the problems themselves or follow along as Lennie and her friends find the solution. But the path to those solutions isn’t always the simplest or most direct one. Lennie runs into complications along the way, which not only makes for a more interesting story but also illustrates some often-neglected truths about problem solving:

• It’s okay to be wrong. Sometimes Lennie and her friends make mistakes, or they try an approach to the problem that doesn’t work out. These are completely normal parts of the problem-solving process. In fact, they can be some of the best ways to help students understand the concepts behind a problem. Math classes can sometimes be too focused on finding the right answer. Getting the wrong answer can be useful, too.
• Math is collaborative. Lennie rarely goes off and solves a problem by herself, and even when she does, it’s only after she’s talked through the problem with someone else. I wrote the stories that way because it makes a better narrative, but it also shows readers what math looks like when people work together. In school, math is usually thought of as a solitary activity, but in the real world, mathematicians, scientists, and engineers work together all the time.
• Math is cumulative. Lennie often draws on the experience of past problems to solve new ones. Mathematics is the study of patterns and relationships. Finding a pattern can help solve a problem, but the pattern is rarely confined to that problem. Relationships that exist in one place will show up in other places as well. Every solution can give students another tool to put in their mathematical toolbox, or at least can sharpen the tools that are already there.

The one thing I haven’t covered yet in my books is the more abstract side of mathematics. I’m an engineer by training, so my own interests and experiences favor applied math. I also think that after working through rounds of exercise problems, most students prefer something more grounded in the physical world. But there are some who want to explore the world of patterns for its own sake, to see what new discoveries they can find there. I imagine I’ll venture into that realm in a future book someday.

When people tell me that they hated math in school, I can’t help but wonder what their math classes were like. If they never got to experience math as an adventurous, creative activity, then it’s little wonder they didn’t enjoy it. I also have an interest in music, but I’m sure that wouldn’t have happened if I had only been allowed to sing scales and had never learned any songs. My mathematical fiction books can’t give readers the full math experience, of course, but I try to give them as much of it as I can. If people know what “doing math” is supposed to look like, they might be more inspired to try it for themselves.

Robert Black grew up in Indianapolis, where his parents were both high school math teachers. He attended Park Tudor School in Indianapolis (where his parents taught) from kindergarten through high school. He graduated from Vanderbilt University with a bachelor’s degree in mechanical engineering and mathematics. He has been writing for children since the mid-1980s, when he worked on the Nickelodeon TV series You Can’t Do That on Television. He currently works as quality systems manager in California. In addition to his Mathematical Nights books, he has also written a series of biographies of mathematicians called Mathematical Lives.