My grandfather could fix anything. If you had a problem with your electric food mixer, he would take it completely apart. He would lay out every screw, every washer and every wire, neatly and in order on the workbench, to study them. He would write away to the manufacturer to get the schematic and study that as well. He would clean every part so that there was not a spec of dust. He would oil every moving part carefully and then put it all back together. The whole process would take a long time, but when he finished, your mixer would work even better than when it had first been purchased from the Sears Roebuck Catalog. It might have been his first time tinkering with that particular type of device, but once he was through with it, he could not only explain its theory of operation but he had six ideas on how to design a better one. He was an engineering supervisor at “The Western” (The Western Electric Company, the manufacturing arm of AT&T in those days). He had little opportunity for formal education, but he had lived through two World Wars, Prohibition, and the Great Depression, had thought deeply about many things and seemed very wise.
So when I obtained my first slide rule, I asked my grandfather how to use it. He was pleased by my interest, but agreed to teach me on one condition: I must first learn to do “figuring” by hand, including an understanding of the principles that enable the slide rule to work. One of his benchmarks was that I must be able to compute cube roots using a procedure similar to long division. Once I had accomplished this goal, I could then also get a circular slide rule. Now, one day I would join Texas Instruments, but long before that day I realized that being able to take a cube root by hand might no longer be an important life skill, since we lived in an era of transistor radios and handheld calculators. My deeper lessons from this experience, however, went to how much my grandfather loved knowledge and wanted to share it, and, especially, how he experienced the importance of mathematics on a personal level in his everyday life. Students tend to be more astute than we give them credit for; if their teacher “hates math” or considers themselves “bad at math,” the main takeaway from math class will be that mathematics is something to be avoided, that even “smart people like our teacher” will get a stomach ache should they ever find themselves in a dark alley face to face with an integral sign. Surely it matters more that students sense our love of learning than that they can name the capitals of all fifty states or recite the value of π to N places?
Meanwhile, the modern version of my grandfather’s slide rule debate rages on. Is it bad to give students calculators before they have learned their multiplication tables? Should students be allowed to use Mathematica before they can derive the quadratic formula by completing the square? Should we provide access to Geometer’s Sketchpad before students can prove congruency of triangles using side-angle-side? Should students be required to use a hard bound Encyclopædia Britannica before they are given access to Wikipedia? Perhaps we are asking the wrong questions! It was not learning to take a cube root before learning to use a slide rule that stimulated my own intellectual growth; my inspiration came much more from my grandfather’s evident passion for a deeper understanding of how things work, all the way down to the individual nuts, bolts, and wires.
When my grandfather retired, my mother and father bought him an electronic musical keyboard, since he loved music but had never had the opportunity for music lessons. It was not the sort of keyboard one might buy for a professional musician: you played the melody with your right hand, by following a color coded system, superimposed over the simplified sheet music; and you added harmony by pressing a single button to select the chords with your left hand. Still, that first night, when he managed after a relatively short time reading the manual to bang out My Wild Irish Rose (in honor of my grandmother, Rose McCloskey), we all sang along and clapped. And I saw a sparkle in my grandfather’s eyes that night the likes of which I had not seen since that day when I first took a cube root by hand and then was allowed to learn all about the slide rule.
So I was completely perplexed, the next morning, when I heard that the keyboard was being returned to the store. What my grandparents really needed, since we lived in New Jersey, was a new set of snow tires. Someone — I doubt this was entirely my grandfather’s thinking — had reminded him that “you can’t teach an old dog new tricks.” Shortly after that, our extended family packed up and moved to the San Diego area; the snow tires were sold in a garage sale. And it was not very many years later that my grandfather was diagnosed with cancer and died.
Sadly, some of our most experienced, senior educators are apparently advocates of the “old dog” canard. “I’ve been teaching for 40 years and I never needed more technology than a chalk board and a red pen. Why should I change now?” “There just isn’t enough room in my classroom for that thing; take it out of here.” “Besides, you can’t each an old dog new tricks.” Meanwhile, we live in a world where most people will change careers two to three times in their lifetime, each time learning new skills and completely reinventing themselves. We all pay lip service to the importance of developing students who will become lifelong learners. Why do we forget that our students always learn more from our actions than from our words?
One senior educator I knew — one who had used all of the familiar excuses to avoid integrating technology into their own teaching despite all the pleading and cajoling I could muster — called me a few months after retiring. “I just bought a computer. I have time to learn it, now that I am retired. I want you to show me.” Of course, I was — mostly — genuinely delighted. Still, I have some human faults, so a part of me could not help but thinking, “Why, then, did you deprive your students of this wonderful opportunity to see you finally acting as a lifelong learner? Take the cursed computer back to the store and get the snow tires!”