Today is the birthday of Juan Caramuel, born 1606 in Madrid, Spain. Caramel was a mathematician and a member of the Cistercians religious order. He developed and explained the general principle of numbers to base
n and the benefits of using bases other than 10.
Today's quote is a joke that I told my father while working with him in his welding shop. I was a 22 year old college graduate and believed that I knew the solutions to all the world's problems.
"The parts of the human body were having an argument about who should be the boss of the body. The legs proposed that they should be the boss because they carried the body from home to work each and every day. The hands retorted, 'We should be the boss because we build homes, hold children's hands, and feed the body.' The brain countered, 'I should be the boss because I coordinate the systems of the body and solve a variety of problems.' Finally, the rectum spoke up and stated, 'I should be the boss because of all the crap I have to deal with every day.' The other body parts just laughed so the rectum stopped working. After a few days, the body parts were in panic and relented and the rectum became the boss. The moral of the story, you don't have to be a genius to be a boss, just an asshole."
My dad chuckled and replied, "Yep, that's about right."
Recently my editor, Maria Burnham, suggested that I reflect about my journey in becoming a mathematics teacher. I was hesitant at first but I was then asked in class if I always wanted to be a math teacher. I teach juniors and seniors and many are exploring their occupational options. This question floated in my mind and I found the answer more complicated than I anticipated. It remained in my thoughts like a sliver working its way through my epidermis, constantly pestering me until I addressed it and removed it. This blog begins my series of reflections that I entitle from
Points A to B. Between two points, there are an infinite number of points which form a
smooth curve that is
continuous and
differentiable. Similarly, the teacher I am today is a result of many mathematical experiences, each forming a link to the beginning. That beginning, that point A, began in my dad's welding shop.
I started working in my dad's welding shop at the age of 9. I earned a quarter an hour and received a $10 bill at the end of each week. The shop was dirty. The walls and floor were covered with a dingy, grayish, brown film that was a mixture of oil, grease, and toxins created by a firework's display of
acetylene torches and
arc welding. One of my duties was to clean the inside of windows to provide additional light into the shop. However, the walls were never cleaned. These blacked walls reduced the chance of receiving
flash burns. Amidst the cacophony of rings provided by a hammer striking an anvil, the sizzle of water cooling iron, and the pop liquid metal exploding on the cement floor, I was introduced to the power of mathematics.
Each day was a lesson in geometry. Terms like square, rectangle, area, volume, height, perpendicular, and plum were added to my vocabulary with an example of what each looked like and how they were to be applied in the task at hand. The
3, 4, 5 rule was introduced early and the
properties of rectangles such as equal diagonals were considered truths long before I was to prove them in my 10th grade geometry class. I was introduce to orientation when I made fifty, 4 foot, cylindrical rods each with a 6 inch,
right handed,
course thread on one end. My jobs weren't complicated but rather repetitive. I was only told once and the repetition was helpful.
The tape measure was my first introduction into fractions. My dad told to halve any fraction, just double the denominator. From that nugget of advice, I was quick to realize that a progression occurs if I kept halving, 1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, ... This sequence, I would later determine was a geometric sequence and when written as a series, 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + ... , ad infinitum, had a sum of 2.
I became quick with fractions because it was a job requirement. I remember I was to cut a 37-inch piece of 4-inch flat iron,
center punch two holes (1/2 inch in diameter) 3 inches from each end, and a hole (3/4 in diameter) centered between the two end holes. I was doing my computation on a piece of paper and my dad asked what I was doing. After I responded, he gruffly remarked that he wasn't paying me to think and proceeded to explain to me how I was to do that in my head. He continued, "One center punch is at 3 inches and another at 34. Their difference is 31. Half of 31 is 15 1/2, added to 3 is 18 1/2. Done. Center punch your holes 3 inches, 18 1/2 inches, and 34 inches. Remember, I'm not paying you to think."
A few weeks later, I had completed a different job and my dad surveyed my work. He shook his head in dismay and asked, "What were you thinking?"
After I had gained some experience. My dad would leave the shop and travel to onsite jobs. The busywork of the shop was in my care, a curious, pre-teen boy. I recall two stories of when I was left unattended.
One day a man entered the shop and wanted a 6-ft. piece of 4-inch flat iron. I retrieved the piece of metal, measured it, and cut it on our band saw. This piece was to have two holes at each end, so I again measured, and centered punch the location for the holes. The piece was heavy for me, and I lugged it to the standing drill press. The bit was large, perhaps, a 3/4-inch bit. I knew that I was to oil the bit, but I was unaware that I also needed to change the ratio of the pulleys that rotated the bit, slowing its rotation. This knowledge would not have been of any use because I was too short. I barely could reach the handles used to lower the spinning bit on to the piece of metal. As I applied pressure, the bit bound, wrenching the 6 ft piece of metal from my hands, and almost decapitating the customer. I dropped to the ground and pushed the foot pedal to off. I stood up, stepped away shaking with tears welling in my eyes. The kind and patient man offered to finish the job and did. My dad anticipated that I might need to assistance in completing a job because I was told to give any customer a 10% discount for helping finish the job.
The other story involves my curiosity. I wondered how everything worked and I investigated everything; the torch, the welder, the grinder, and the forge. Now that I look back, the explosion that never occurred on the north end of Plainview, Minnesota, is in itself, quite remarkable. Leaning in the corner of the shop, my father had an old 22-caliber rifle. I admired it from afar for a few weeks and then had an opportunity to examine it when my dad was again asked to make a "house call". I found a screw driver and took the rifle apart. After scrutinizing each piece, I started to put the gun back together. I was 99% successful. The trigger had fallen to the floor and easily assimilated with the various shards that surrounded me. I scoured the floor, relentlessly looking at each piece of shining metal, praying for a miracle, but none intervened. I shrugged my shoulders and put the gun in the corner. I reassured myself that a missing trigger on an old gold would avoid detection. That evening, a man came to our house and my dad greeted him eagerly and quickly walked to the shop. They were back just as quick and my dad asked if I had "played" with the gun. My face became grim and I nodded. He inquired, "Did the trigger fall to the floor?" I again nodded. "Where did it fall?" he gravely countered. "Among the chains by the door," I whispered, again praying for this last chance of redemption. They never found the trigger and my dad never discussed the topic further.
My dad would always tell me he wasn't a teacher but he held the position in high regard. He was a man of few words. His directions were only given once. I can recall four gems of wisdom. 1) Be smarter than the tool you're using. He told me this right after I hit my finger with a hammer. I have used the quip many times as students try to negotiate the result on their calculator with the mathematics they are trying to learn. Unfortunately, the digital estimator usually wins. 2) The boss may not always be right but he is something you're not, the boss. He told me this when I was disagreeing with some procedure done at the shop. I have carried this into my career. The school district can sometimes create a policy that I disagree with, such as a no-hat policy. My obligation as an employee is to enforce that policy. If all teachers adhere to the policies given by their "bosses" the school system runs much more smoothly. 3) Keep your pecker in your pants. My brothers and I were working together the summer after I graduated from college. A farmer strolled into the shop and announced to dad that he had seen his El Camino parked in the long drive way leading to the farm house. Dad chuckled and told the farmer it must have been one of his boys. After the farmer left, Dad raised his eyebrows and asked which of us were on a date last night. After an awkward amount of silence, he chuckled again, and gave his only sex education talk with that one line. 4) Find a job you love to do and it for the rest of your life. I heard this bit of advise the most often. My dad loved what he did. When I asked him why, he stated that every day there was a new problem to solve and he loved solving problems. I love what I do. Every day is different and every day I have a new problem to solve.
A few days ago, I was interrupted by a colleague as I was tutoring a student. The concept I was reteaching was complex and required a great deal of effort on my part to make the idea attainable. I snapped at the intruder like an old dog focused on a bone and then followed with a confused response to his question. He was taken aback. I have reacted like this before. He accepted my apology but I was left upset with my behavior. At lunch, my confessor (a member of my department) approached me. He had heard the reverberations of the incident. "Your passion," he explained,"is teaching mathematics. You're oblivious to your environment when you enter your passion and you don't transition well. Those people that know you, understand. You are really asking us to enter your passion." My dad had the same reputation. When he was working on a project, you could wait for what seemed like hours before he would acknowledge your presence. He would growl, bark, and snapped as he transitioned from his problem solving to interpersonal communication. The growl, bark, and snap were really invitations to his passion. My final lesson of the shop was a lesson of passion.
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