Awakening Wonder through Mathematics
Mathematical play. What a fun concept! How many of us experienced wonder, adventure, and–yes–even play, in our school math classes? For this article, you’ll need a calculator. I promise it’ll be worth it.
Let’s try some math play.
Find the next number in this sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, _____. Many will recognize this as the Fibonacci sequence, which represents the Golden Ratio. The way to find the next number in the line is to add the previous two numbers.
Example: 3 + 5 = 8; 5 + 8 = 13; and so on.
When you take the former number divided by the latter, you get close to 0.618.
When you take the latter number divided by the former, you get close to 1.618.
The further you take these numbers out, the closer they get to the “Golden Ratio,” which is approximately 1.6180339887….
Using a calculator, try dividing 0.618 by 1.618. Keep hitting the equals sign.
Sometime into this pattern, you may start noticing that the numbers get smaller until you start seeing the Fibonacci sequence in reverse inside the decimal. It will include 21, 13, 8, 5, 3, 2, 1…Fascinating!
The idea of searching for patterns through mathematical play can awaken wonder in us as we see God’s handiwork throughout all creation and realize that math is more than just for tests and jobs—it’s a language all its own!
Capstone staff are currently reading The Liberal Arts Tradition: A Philosophy of Christian Classical Education. The authors, Kevin Clark and Ravi Scott Jain, tell us,
“When reminding classes that mathematics is eminently useful, teachers must not fail to tell them the bigger picture. These four liberal arts (of the Quadrivium: arithmetic, geometry, astronomy, and music), when their traditional forms are respected, represent well-worn paths to cultivate virtue in the mind and wisdom in the soul. To accomplish these goals, we should employ a pedagogy of puzzle, proof, and play, and only after providing these should we expect practice and performance.”
Puzzle, proof, and play are so important in the classroom. They instill a sense of wonder to the beauty that God has woven into our universe. When we discover what He has put into motion with our own senses and on our own unique terms, we can’t help but appreciate the marvelous things all around us in more profound ways.
They continue, “When traditional forms of these liberal arts are respected, wonder, wisdom, work, and worship can indeed be woven together.”
By the way, the answer to the initial sequence above is twelve squared. Or two to the fourth times three squared. Or forty-eight multiplied by three. Or… you try!
Mathematical play! Fascinating! Fun!