My last math class was 25 years ago. I earned a “B” in precalculus. I’ve always liked math and have been pretty good at it. I’ve enjoyed using it in the line of duty when I was an estimator for a construction company and had to calculate a lot of volumes such as cuts and fills for site work projects, areas, quantities and unit costs, etc. As a machinist I used trigonometry to set up machines to make parts for the construction of submarines. For some of those parts I even used what I learned in pre-calculus and applied it to a special NC milling machine job that no one else in the shop could do. I also used a lot of financial and accounting math when I was a mortgage consultant and owner of my own construction business.
I’ve liked math for a long time. But I distinctly remember when I fell in love with math. I sat in on my stepson’s high school math class one day. The lesson involved calculating the area of a circle. Simple: Square the radius then multiply by pi. I mastered that little piece of geometry about 15 years prior to that day. Back then, math in high school, the Navy, and a couple of semesters in college, the teaching and learning methods were different; what is termed “parrot math.” My stepson and myself that day, were having the subject presented to us in a way that’s been termed “fuzzy math.”
His teacher had the kids cut squares out of graph paper with each side of the square equal to the radius of the circle they were calculating the area of. Then the kids were instructed to put those four squares back together to form a big square. Next they took a compass, spanned it open to the size of one of the sides of one of the squares, set the point in the center of the four squares, and scribed a circle. Lastly they cut the circle out of the squares. So when they counted all the little quarter inch squares on the graph paper that remained in the four pieces that made the circle and compared it to the total number of quarter inch squares in the large square that the circle was drawn within, they came up with the ratio of roughly 3 : 4 …
Good Lord! All these years working with areas of circles and perimeters of circles and I never realized that pi is a ratio of a circle drawn inside a square; in other words: A circle with a diameter that is equal in length to a side of a square that the circle tightly fits in. I just never saw it that way! It got me wondering why the perimeter worked out the same way based on the diameter. I started pondering that, fuzzy-math style, and then that made sense to me too –a new kind of sense!
This new-fangled method was less about memorizing formulas and applying them to get the right answer to problems. It was more about the reasoning behind those formulas and explaining how to come about the right answer which in turn explained what was going on behind the scenes of those formulas that churned out solutions. I still feel like I’m a strong proponent of parrot math. In the age of computers and calculators I still believe it’s important for a child to memorize multiplication tables and basic geometric formulas. But that day, my first math lesson –fuzzy style– opened my eyes, amazed me, and turned me on. It got my wheels turning about math in a whole new way. I put “learn calculus” on my bucket list… Last night was my first class in the subject, Calculus 1.
I hope I don’t suck at this!
The first homework assignment involves solving about 222 problems. I completed the first four problems, matching up equations with their graphs, without any difficulty (see below) Then I got to problems 24, 25 and 26 and realized…
I suck at this!
My algebra is weak. I’ve heard from reliable sources that doing well in Calculus 1 is all about strong Algebra skills. My professor, Melinda Duquette –who was just learning to use her opposable thumb to pick up Cheerios off the tray of her high chair while I was just learning how to graph functions– is going to have her hands full with this student. I hope she has patience. I think I’m destined to be her problem child. She set up a Facebook Group (with my hero, Sir Isaac Newton –with whom I share an incredible eschatological idea– in the headline spot) so the class can help each other out. I think that was a great idea, and maybe even the key to my success. She even gives us credit, equally, for our participation in the group, whether we are the helpers or the helpees.
This is going to be a lot of work, but I’m committed to success!
Here are those first four problems below, along with some of those new-fangled fuzzy math explanations to go along with the correct answers: