Algebra Redux

Basic Algebra Review (by StarbuckGuy)

When I entered the 9th grade, age 14, I left behind the boring world of arithmetic and entered the new world of algebra. I was transfixed. It switched on something in my brain that validated all my thoughts about studying math and science. I felt I had arrived.

The experience was heightened by lucking into a great teacher at just the right time. My algebra teacher, Roger Buikema, was fresh out of university on his first teaching assignment. He was late-50’s, early-60’s cool, sporting a crew cut, black-rimmed glasses, and a fondness for the Kingston Trio. His enthusiasm for math and science was infectious.

Algebra was the most elegant thing I had yet encountered in school, and even now, fifty years later, the study of algebra, then advanced algebra, remains as one of the highlights of my education. I was never a math wizard or math precocious, but I liked math and did moderately well at it.

I later studied plane and solid geometry, and trig, which I also loved. I dipped my toe into calculus, but by the time I reached that point in my study of math, my primary interests had shifted to folk music, girls, and literature. I always regretted I hadn’t taken math a little further.

A few weeks ago it occurred to me (I’m a slow thinker) that there was nothing preventing me from restudying math. I was already doing puzzles — crosswords and sudokus — and math exercises are the same: puzzles to be solved. I thought I’d start with trig, but when I looked at the subject anew, I realized my math infrastructure had rusted out with age and disuse. I needed to rebuild the scaffolding in my brain by backing up and starting with algebra.

In my brief one-year stint as an engineering student, I had discovered the Schaum’s Outlines series of publications on math and engineering topics. They were excellent as supplementary material to the main textbooks, and served as inexpensive tutors. I liked them because they were clear, but terse. They didn’t muck about with long explanations of things. They gave the essential information then presented a bunch of exercises and review exercises. They also provided the answers so you could check your work as you went.

Just the thing, I thought. I checked and the Schaum’s Outlines are still going strong, so I sent for Elementary Algebra. The covers are much slicker than they were in the mid-60’s, but the content is much the same.

As I started my review, I’ll admit outright that my brain hurt from working on the exercises. I could no longer “think math” the way I once did. I kept mucking up signed number operations and even simple arithmetic. But I’ve kept at it, relying on brain plasticity to work up some new neurons or perhaps reassign some old ones to get me back into math think. (Note to brain: I really don’t need the complete lyrics of all those 50’s rock songs in my head. Perhaps you could reassign them?)

Slowly, it’s beginning to work. Each lesson becomes a little less strained. I picked up a nice Texas Instruments scientific calculator for $20 to use to check my work, as well as to learn its higher functions. Back in the day I used a Post Versalog slide rule. Calculators hadn’t yet been invented.

As of today I’m working on the review exercises for chapter five, “First Degree Equations.” Chapter six, “Formulas,” appears to be a review of plane and perhaps solid geometry.

I won’t say it’s been easy, but it’s been worthwhile. Some of the excitement of a long-ago fourteen year old is returning. Each exercise is another puzzle to solve. They feel good when I get them right with no errors. They make me think hard when I get them wrong and have to backtrack through my work to see where I went off the rails. That’s good exercise too.

My brain’s capacity for math is improving daily. Not that it’ll help me tie my shoelaces in the morning, but I’ve recovered a lost love. I have no idea where this might lead, if anywhere, but the journey is stimulating.

Basic Algebra Review (by StarbuckGuy)

7 thoughts on “Algebra Redux

  1. Good for you, Gene.

    I’m in total agreement with your ideas on neuroplasticity. Gotta keep challenging those brain cells.

    That is why, a couple of weeks ago, I purchased a banjo. For a couple of years, I have been saying “I think it would be neat to play the banjo”. I’ve loved Alison Krauss for years and love listening to local live bluegrass. While in the music store to have my son’s trombone appraised, I fell into the abyss. I doubt they sell many banjos as “impulse items”.

    I have a rudimentary guitar background, having taken lessons as a student, but never learned to read music. The chords carry over simply enough. The picking is where it gets interesting. As with your algebra, I’m finding a new challenge that also gives me a sense of satisfaction.

    I’m still not quite ready to admit to many that I am a 45-year old mom and speech pathologist who is learning the banjo. But I’ll work on it.


  2. Amy, I’m impressed! Banjo is a neat instrument (I dabble at it occasionally). Are you learning to play bluegrass style or frailing, clawhammer style?

    In Peanuts Guide to Life cartoonist Charles Schultz said that, in order to get a good start in life, “as soon as a child is born, he or she should be issued a new dog and a banjo.”

    Yes, new challenges. They keep us from getting into a mental rut.


  3. Gene,

    What a coincidence that you also play banjo! I am trying to learn the bluegrass style with the rolls and pinches. There are a lot of resources on the web and I’ve picked up some books too. In fact today’s mail delivered, from Amazon, “The Complete Ignoramus’ Guide to Bluegrass Banjo” as well as “Banjo for Dummies”. Not quite sure what is the “best” all around bluegrass roll yet, and maybe I’m muddying the waters with too many instruction sources, but I figure it will all sort itself out. The clawhammer method looks really neat too but I’m hopeful that once I master the picking I can transition to frailing.

    I love the Peanuts quote! My dad’s friend grew up in St. Paul and this man’s father used to go to a certain barbershop. The barber there used to complain all the time about his kid that just wanted to draw cartoons and would never amount to anything. You know the rest of that story.

    All the best,

  4. Hi Gene,
    We continue to have much in common. I’ve just started dipping into a recent translation of Euclid’s Elements by T.L.Heath. I’ve always liked the IDEA of geometry, but missed out on a lot of what he had to say during my formal education years. So I’m attempting to find my way through his amazing proofs. The new book, published in 2002, assumes the reader would like to attempt the proofs… most of which are done with ruler and compass. So they’ve left room on the pages for my scribbling. Great for the end-of-the-day contemplation or for a relaxed sit in the garden on a lovely spring morning.
    Jamie Pillers

  5. Jamie, for sure.

    What a great way to present Euclid, with the opportunity to study along and work the proofs. Euclidean geometry was one of the most significant contributions of the Greeks. A way to study math, logic, and history all in one.

    Coincidentally I was working on geometry today, learning to cast solutions to perimeters and areas into algebraic notation when one or two variables is known. My daily puzzles. I stop when my brain gets too fatigued to carry on 🙂


  6. “I always regretted I hadn’t taken math a little further.”

    The important thing was taking the girls a little further!

    I’ve had the 4×5 out a few times recently, and noted how rusty I am, especially setting up the tripod. But it does feel good to work with that big neg in a deliberate, methodical way.

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