Proof by Contradiction
Proof by contradiction is a logical mind skill used to reduce a premise or assumption to the absurd, or impossible contradiction. This logical mind game is mastered in logic, but brushed up against in geometry. We play a tug of war game with logic in Geometry. We acknowledge the existence of logic just enough to
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Math History: Euclid
Few modern people can get away with a single name. A few may come to mind, but ancient history are full of those one named wonders. Euclid is one of the most recognizable names in history, and all he did was write a single book. It may have had 13 volumes, but it was a
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Word Problems and Euclid
Euclidian geometry conjures up images of shapes with all of their angles, lines, tick marks, and sides. The most picturesque branch of high school mathematics is geometry. Geometry after all is the science or art of measuring the earth. It started with the images of the created world around us and is often learned using
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Brain Development is Hard
I watch my children struggle. They push themselves physically and mentally. We work hard. That is one of our family values: Hard things are worth doing and worth the struggle. Yet, watching my children learn, grow, and mature through struggle is never easy. Each year, when I start pre algebra with new students I emphasize
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2026 Live Class Updates and Schedule
The beginning of the school year can bring with it bag loads of emotions. Excitement, anticipation, wonder, contentment; these are what we want our children to feel going into a new school year. Fear, worry, stress, anxiety; these are what we may be experiencing. How do we navigate ourselves to the former emotions while also
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Summer Review Challenge!
Augusts come and Augusts go. For some reason, August seems to rush past faster than other months, like April, which drags.. If only August was as slow as April, but I digress. Before we know it, school will be back up and running, math classes will be in full swing, leaves will change, flannel will
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Before Pushing Forward
I’m always thinking ahead, which made me a decent student, helps me travel, and keeps me moving. But thinking ahead has its drawbacks. Most obviously, I don’t always live in the moment. I have to remind myself to enjoy the moment for which I spent month planning. Take the time, smile at my children, tell
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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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