There is much to learn and much wisdom to gain, and every day offers the opportunity to increase in both. Sometimes, it depends on the student and sometimes it depends on the teacher. A memory about the “dot function” (also called “dot product” in math) reminds me of those truths.

Fr. Leininger was an incredible teacher. Phenomenal, actually. How he was able to reach such a wide variety of high school students in the early 1970s in a variety of subjects could be a case study in teaching – it occurs in the classroom, on the grounds, in the cafeteria, on walks and in one-on-one conversations. Teaching/learning happens all the time and must adapt to people and conditions. Mathematics was among his many expert fields.

Mathematics was not among my limited areas of interest in high school. Geometry clicked for me, thanks to Mr. Hendry’s approach during sophomore year. I actually enjoyed it, which shocked both me and my parents. Fr. Leininger caught my attention in pre-calculus. It was during one of his chalkboard sessions that his explanation of the “dot function” became a master class in teaching and in being taught.

My mind doesn’t do math, but his approach made the function understandable. Compare that to my teacher at the University of Houston, a math graduate student.

I took pre-calculus my freshman year in college. The instructor was, in a word, terrible. I got a 9 (out of 100) on my final exam. With the curve, a 9 counted as a B. When students grumbled after receiving the exam, he told us to quit complaining and that we should try tackling what he was having to deal with as a graduate student, which, of course, we were not. I digress.

There was a time during the semester that the dot function was the subject. I forced myself to quit listening because the instructor muddied my understanding that was quite clear, thanks to Fr. Leininger’s teaching. When I hit my “enough is enough” moment, I raised my hand and asked if I could take a shot at explaining it to the class. He agreed.

I stood at the chalkboard, chalk in hand. I began replaying Fr. Leininger’s explanation in my head and shared it with the students as I wrote. I didn’t think, I just replayed and relayed. I didn’t look at the class, I just wrote and shared. Then, I stopped, turned to the class and asked, “Does that help? Does that make sense?” Their response reflected a resounding success. The instructor was not pleased.

That was 50 years ago. Don’t ask me to explain today anything that involves math. Like much knowledge gained over time, it is easily forgotten. While I did not hold onto dot function knowledge, I did retain the wisdom about teaching and about being taught, and that is more valuable to me.