They say “a picture is worth a thousand words”… and they’re not wrong.
But can you imagine a story without words? Purely a visual experience? It could be enchanting, but no two people would ever see the same thing. Words clarify, explain, interpret, inspire, instruct… and they can do all this clearly and concisely. Imagine the world before books!
Words are the building blocks of story. They are how we explain and instruct, the basis of human communication. Even sign language uses symbols for what we call words. I suppose it might be more accurate to say “words” are the symbols or labels for the concepts we wish to communicate. The better our vocabulary, the more beautifully we can craft our stories and communication.
Language is a system of words we use to express our thoughts and ideas. Language is built of words and rules – structure if you will. Nouns have a different role than adjectives, verbs, prepositions, and adverbs. Conjunctions like “and” combine, while “except” excludes. Each language has different ways of expressing the same concept, and reflects slightly different ways of thinking.
So what has any of this got to do with math?
Math is the language and art of STEM – science, technology, engineering, and math. If a picture is worth a thousand words, math is worth a million pictures. It’s that powerful.
As a student in junior high, I struggled with algebra at first – I just couldn’t crack the word problems and got a rare C. That C shocked me into action. I did something way out of my comfort zone… I went to the teacher and asked for help. It meant staying after school several days, but I did it. Once I cracked the code, it became fun. I loved algebra. Good thing, too, because (in my opinion) algebra is the fundamental backbone of 90% of engineering math.
Yes, there’s geometry, trigonometry, calculus, and differential equations. They’re all relevant and extremely important. But on a day-to-day basis as an engineer, I didn’t solve differential equations. I had computer programs and finite element models to do that. But manipulating variables in a formula to solve for a desired answer – think math recipe – that I did frequently.
I even use it in my hobbies – to calculate how much fabric I need for a quilt design, or how to best optimize the use of 60-inch wide fabric for making a sit-upon or tote, or 54-inch wide mesh for making protective screens for sea turtle nests (see the sea turtle project for more details).
Math is used for modeling, to describe, explain, and predict how our universe behaves. If we can model behavior accurately, we can anticipate problems, like hurricanes. We can build cars, trains, airplanes, satellites and spaceships. We can design machines that do useful work.
There are many types of models, all are wrong, but many are useful.
Physical models, or prototypes, are often simplified versions or scaled-down versions of the final product. Their goal is to simplify the product to test, evaluate, and refine elements of the final design with minimal cost. Rapid prototyping is a strategy for quickly developing and evaluating a Minimum Viable Product (MVP) to get feedback, refine and incorporate improvements into your design early in the design process.
Math models are the most powerful models in our universe because they allow us to design, evaluate, and optimize our designs without cutting a single piece of metal, wood, fabric, or… well you get it. The only cost of a math model is your time, paper and pencil, and today, most likely a computer or tablet of some sort… which you probably already have on hand. Compare that to the cost of making a billion dollar prototype aircraft engine to test, and you can begin to see the leverage that math brings to solving real problems in real time.
Math doesn’t replace physical models and prototypes… it allows us to build the right prototypes more efficiently, at lower total cost.
So why should you care?
The number one barrier for many students interested in STEM fields is lack of confidence in their own math skills.
When members of the Greater Cincinnati Stem Collaborative (GCSC) talked with seniors at Walnut Hills High School – a college prep high school in Cincinnati – asking if they saw themselves in STEM fields, thinking it a softball question to get the dialog going, they were surprised when all the students answered no. When they asked why, they were stunned at the answer: the students lacked confidence in their own math skills.
How could that be? Research shared at the NEXT Lives Here STEM conference held at the University of Cincinnati in 2017 revealed that parent attitudes shaped student attitudes about math. Many parents don’t understand the relevance of math, or think their kids are smart enough for STEM fields. Attitudes affect motivation which is directly linked to success in learning. Change your attitude, and you’re halfway there.
In retrospect, I was very lucky growing up. My mother was extremely proactive about encouraging good grades, particularly math. How proactive? When my sister was in high school, and kept getting a different substitute math teacher every week, my parents actually put our house up for sale and moved to a better school district. My mother would not tolerate anyone messing with our math education.
Why the extreme reaction? I didn’t realize it at the time (I’m six years younger than my sister, so the move was made between fourth and fifth grade for me), but my mother attributed my dad’s lack of confidence in his own math skills as the reason he didn’t pursue a degree in aerospace engineering – his passion – which limited his career opportunities and income.
My father was a World War II veteran. When he returned from service, he could have gone to college on the GI bill. But he didn’t. The high school he went to kept dropping him from the math classes he signed up for, and he ended up with extra English classes instead.
For most of his married life, my father worked as a non-degreed industrial engineer. Big promotions were given to people with college degrees. My father was brilliant, inventive, and a creative problem-solver, but he had limited advancement opportunities. He actually wrote most of the reports for the Vice President of the company he worked for… those extra English classes paid off there! But he was limited in his career options just like many students today because he lacked confidence in his own math skills and didn’t pursue the degree he wanted.
So what can you do about it? Learn about the relevance of math today and share that with your children, your grandchildren, your students. Be proactive. Find fun ways to engage students in STEM activities that also show the relevance of math. You can start with the experiments on my website, under the STEM menu.
In fact, I started writing STEM adventure books because stories change attitudes, and I wanted to show the magic and power of math (and problem-solving skills) through story.
I worked hard to dodge the math bullet in my first book, Putney and the Magic eyePad, a 2021 Readers’ Favorite Gold Medal winner in the Children – Adventure category. I wanted to hook kids on problem-solving, a sort of a Nancy Drew meets MacGyver premise. I skated very close to but dodged a big math bullet – explaining how air can hold up a column of water in a straw – with a scuba diving fact reference instead. Air pressure at sea level is equal to the weight or pressure of 33 feet of water. But I redesigned my website to support my new book and added an experiment, “The Straw Trick Explained” on the STEM page for anyone interested in the details. So, I found a way to entice without overwhelming in my book, providing more resources for learning through my website.
Like Madeleine L’Engle, A Wrinkle In Time, I believe kids are capable of understanding complex concepts. They are natural problem-solvers – they just need the motivation and insight to see things in a different way.
I knew the kids could grasp the concept of algebra if they already knew how to multiply and divide numbers. It’s just playing secret agents, using letters for variables instead the real number itself.
In 2015, I was helping to lead after school STEM experiments as part of a GE Volunteers partnership with Girl Scouts of Western Ohio. I was the leader for the last experiment and was supposed to give some advice on what subjects to take for STEM. I had the experiment all prepped, but read that last bit at lunch the day of the experiment! Thinking quickly, I grabbed a plastic knife and a reference book and sketched out a couple pages on beam bending. I demonstrated how a simple “Math Recipe” can predict whether a beam (or plastic knife) will behave like a diving board (bendy), or an I-beam (stiff), and how simply turning the knife on its side can result in more than times the deflection. Curious? Check out the beam bending experiment on my STEM page.
In my second book, I took the scary plunge of getting into some real math… but I channeled Douglas Adams’ Hitchhiker’s Guide to the Galaxy with my chapter, “Don’t Panic, Math is Magical,” and I give the students (and readers) permission to daydream or doodle. I don’t care if they can do the math… I just want them to get a glimpse of what math can do for you. Which in this case, allows them to size a boat and come up with some very different designs than they might otherwise have dreamed of.
In fact, much of the main plot in The Cardboard Boat Race is based on an actual cardboard boat race which was a real blast! I had so much fun that I designed other surfboats to take my dogs surfing in the ocean. It was the basis for a buoyancy experiment I lead at the Girl Scouts Year of the Girl Summer Camp for two years, receiving awards from GE Volunteers and Girl Scouts. Splashing in water is fun. But the real kicker for many girls was seeing pictures of my golden retriever, Harry, standing on a surfboat in the ocean, and realizing that they could design and make something like that right now. They had all the skills and tools they needed.
So, I hope I’ve convinced you about the magic and power of math. My wish is that you spark curiosity about math in the children around you, and kindle that spark into something that ignites their imaginations and sets their feet on the path of discovery and innovation.
Not everyone is going to become an engineer. If you’re like me, you probably won’t figure out what you want to do until high school… maybe even college. The most important thing you can learn in school, is learning how to learn, learning to solve problems, building confidence in yourself, and believing that you can do hard things because you’ve succeeded time and again. If you take small steps, build on the power of small wins, you can accomplish almost anything with time. Your attitude, the words others say to you, and the words you tell yourself – your inner dialog – shape your reality and your limitations.
No matter whether your dreams are to invent or create something new, help people live better lives, or win a gold medal at the Olympics, learning to solve problems can help you achieve your goals. Succeeding in math can be challenging, but it can also be life-changing and open doors for you that you never imagined.
Have you seen the movie or read the book Hidden Figures? It’s the inspiring story of three black women whose math skills helped land a man on the moon. That’s the magic and the power of math in a nutshell.
It takes hard work to accomplish big things… what you do today matters! What you say to others matters. Seeing the relevance of math can shape attitudes that change lives for the better. Maybe even your life!
Marsha Tufft, aka MK Tufft, award-winning author of Putney and the Magic eyePad, a Mystery STEM Adventure
