It is with cold, hard, unfeeling logic that all things will be made better… said nobody ever. Well, maybe Spock or Sheldon from The Big Bang Theory. Those of us who live in reality know better. Human beings don’t actually work this way. We sense, feel, and intuit our way through the world and through daily life. So if that is how we really work, if cold logic doesn’t actually motivate people to better solutions, what good is all this data collection, visualization, and analysis? This isn’t a paradox. Collecting and analyzing facts does a lot of good. The trouble lies in how we understand mathematics. That’s what I plan to explore over the next several articles. I hope you’ll join me on this thought journey.
Let’s begin with where this trouble with math starts. I’ll explain it through my own relationship with the subject. At some point in elementary school, I remember my parents telling me I might enjoy engineering as a profession. The reason? I would take everything apart to see how it worked… my toys, my desk, my bicycle, etc. Typically, I would put these things back together, though sometimes I tried to change them or add something new. By high school, my parents’ message had shifted slightly: “Matt, you should try to become an engineer… if you can figure out how to get through the math.” My math grades were typically poor. On standardized tests, I was average, at best. And average isn’t good enough to get through an engineering program. My first year of college was a disaster. I ended freshman year on academic probation with a 1.6 GPA. I’ll never forget getting my first calculus test back with a big fat F and a note from the professor suggesting I consider dropping the class before it was too late. I dropped the class.
Clearly, I lacked the “math gene,” that supposed bit of DNA that makes one person good at math and another hopelessly lost. Still, I was undeterred. I decided to give it another try.
For my sophomore year, my parents advised me that if I couldn’t improve after the first semester, I should drop engineering and explore a different career path. I had to retake calculus and physics. I wasn’t exactly sure what I would do differently. I was just going to “try harder.”
One thing did help. This time, I had a calculus professor who cared about our learning. He drew pictures, made himself available, and would look at us and say, “This is as easy as barbecue pork!” I don’t know why barbecue pork was easy, but he made the class fun. But something more important happened. As I started to understand what calculus did, then things began to click. I’ll never forget sitting in physics class when my brain connected a formula from calculus with the arc of a thrown object we were studying. It was a tremendous sensation and the turning point of my college career.
I progressed from there, though the struggle never disappeared. At one point, I told one of my professors, Dr. Richard Marcellus (another great teacher), that my problem was that I’m a visual person and math is all numbers. He looked at me, confused, and said, “All of math is visual; it’s imagination and visualization.” I returned an equally confused look.
“Math is the science of imagination.” I later read these words in the book, “Mathematica: A Secret World of Intuition and Curiosity” by David Bessis. As I explore this topic over the coming months, I’ll be leaning heavily on his work. I highly recommend the book, as my articles won’t do it full justice.
That statement, “Math is the science of imagination,” caused me to reflect on my years of struggle. My breakthrough in college came when I was able to imagine a ball moving through the air and connect it to a mathematical model describing the area under a curve with precision. Unlike everyday language, which is loose and open to interpretation, math is exact. It can only mean one thing.
This is what Dr. Marcellus was trying to show me. Math is about taking real life, abstracting it through imagination, and then verifying it using the rigorous language of numbers. The numbers, models, and computations I struggled with were simply tools to solidify imagination. I began to appreciate this when I taught statistics as part of Green and Black Belt classes, but I didn’t have the words for it until I read Bessis’ book.
So what is the trouble with math, and what does this have to do with Continuous Improvement? The trouble is that we teach math as an arithmetic exercise rather than focusing on its true purpose, which is abstracting reality into imagination and then using arithmetic to test whether that imagination reflects reality or is just fantasy. The connection to continuous improvement is that when solving problems, we are always using our imagination. We imagine processes, people doing the work, machines, and future states. Math is how we test those ideas against reality and align people around the future we want to create. Improving our problem-solving outcomes requires improving our math skills. Improving our math skills requires resolving the trouble with math.
Over the next several newsletters, I’ll explore these topics in hopes that you’ll be inspired to strengthen your math skills and become a better problem solver.
- Learning begins when we confront confusion rather than avoid it.
- Good problem solvers are not born—they train their intuition.
- Humans reason about systems through mental images.
- Operational ideas aren’t counterintuitive—they’re just unfamiliar.
- Avoiding math is avoiding disciplined thinking.
In closing, there is no “math gene.” It’s an excuse we use to avoid the focus and concentration required to test our imagination using the rigorous language of math. My turning point in my sophomore year had several causes, but one was certainly time… time spent working problems, being okay with not understanding, and waiting or even searching for those moments when everything clicks. We are all capable of imagining, and we are all capable of testing our ideas against mathematical reality.