by Mr. Andrew Gass
High school is a time of starting to understand. Working with the students, therefore, is like mining for gold: long periods of labor, punctuated by great sparks of joy as different students grasp a concept or make a connection. As with mining, however, it’s only those best parts you share.
My first highlight was actually one of my first days teaching. I was showing the students “if…then…” statements from a logical and grammatical perspective, and one of them chimed in: “Is this like cause and effect?” He had leapt ahead to where I was going next, which is the division of conditional statements into causal and non-causal. He engaged with the material and thought ahead to possible connections and consequences of the idea he had before him.
Another highlight was when I made a diagram on the board, documenting my steps in what we call a “Two Column Proof.” In the end, there were only two lengths of straight lines on the board, spread out as different radii or triangle sides. I then asked them to find which lines were the same length. A variety of students found different pairs or triplets of lines, but they couldn’t place one line that extended beyond a radius: the only one of its kind on the board. Then one of the students chimed in that it was the same as the radii of a different circle, and went on the explain why. And she didn’t just say “it looked like it!” She had begun to employ deductive reasoning in a concrete way, proceeding from the principles we had learned and that she already knew to deduce concrete conclusions.
The final highlight I will share is more of a theme. Our primary goal in geometry is to train the students in reasoning. All day long different arguments assail us: political, commercial, social, personal, and more. These are difficult to consider and recognize, and so we can be overcome by a bad argument without realizing it. By studying reasoning in an area where we can agree on every definition and step, we hone our minds to be sharp tools that can cut to the heart of arguments and offer agreement or rebuttal. To encourage the students, we have looked at a few of these arguments: statements like St. Augustine’s “If I am deceived, I am,” which came long before Descartes’ “I think, therefore I am,” or the chain or reasoning that relates the study of philosophy to the love of God in only a few steps, or the few simple arguments that form the basis of pro-life. The last in particular has been an area of interest for the students, who before now may have doubted they could bring together their reason and their faith. Supporting them in doing so is a definite highlight of my time teaching.
Mr. Andrew Gass teaches math at St. John Paul II High School. Read his full bio here