Nicomachus Ratios & Harmony
Ancient mathematicians are a unique tribe. Exploring the works of Nicomachus in Algebra shows us that he and his comrades were thinking deeply, discussing thoroughly, and contributing consistently. Take the simple mean. Most students learn the calculation of the mean of a group of numbers as the sum of the group divided by the quantity
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Nicomachus Revisited
Although we may want to pursue the wonder of the world and open the beauty of creation with mathematics, we often find ourselves in the weeds. We teach our children to identify numbers, patterns, and symbols. We teach them to compute sums and products as though the calculator didn’t exist. In short, we teach arithmetic.
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A Note on Admissions Tests
Admissions tests like the SAT, CLT, and ACT have been historically required for students wanting to enter college. Not only did the tests give the colleges an idea of a student’s abilities, but they also helped colleges find students and students find scholarships. In the past 10 years, there have been multiple studies showing the
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Infinity Glimpsed
My algebra 2 class started rubbing elbows with Calculus this past month. Do the students know how close they got to the infinite God? Do they see that their discovery of an asymptote of a rational function is the beginning of the study of calculus? No. Except that I told them. I cannot let an
Ecclesiastical Joy
“Of making many books there is no end; and much study is a weariness of flesh,” (Ecclesiastes 12:12 KJV). It is true. You know it, I know it, and our teenagers in the deep-end of Omnibus know it. If we are not careful, we can interpret this with the same sentiment that runs wild in
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The Road We Walk
Pragmatism is not the enemy of a classical education. And yet… Somedays I bounce from practical to theoretical faster than a ping pong ball. I relish the delight and wonder of pondering the “deeper magic” and the beauty of the mathematics of calculus or even exponential functions. I want my children and students to glory
Do You Compute?
We have a love/hate relationship with math in our house. Much like our fickleness about the weather, we love math when it is fine, and hate it when it is gray and cold. Recently, I have discovered the joy of the order of mathematics and how it is reflected in my daily life. When a
Math Class Ramblings
Mathematics spreads like wildfire. The more you understand numbers, the more you see them everywhere, and the more you wonder why it took us hundreds of years to create numbers. I jest, of course. For the concepts of mathematics and numbers were being used by humans many years before anyone wrote it down. That is
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The Problem of Change
Change is everywhere. Beyond the sudden change of children’s growth and maturity, there is the slow change of aging. Everything seems to be in a constant state of flux. As Heraclitus famously said, “you can never step into the same river twice.” because the water is always changing. This concept of change has pondered and
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Hardly Working
It has become an occasion in my life to hold drywall over my head. Not voluntarily, out of context (I’m not a weirdo), but having consistently lived in a house-in-progress, or rather, house[s]-in progress, I have found myself, more times than I can count, on a ladder, assisting with a ceiling. It is odd, how