# William L. Culbertson

# Odds & Ends & Thoughts

## Calculus in Middle School

Calculus for Middle School? Why Not? Right at the start, I’d like to stipulate that there is a difference between explaining Calculus and teaching Calculus to students. A twelve-year-old would have to be quite precocious indeed to have mastered the skills of algebra, as well as learned about the various other functional relations, needed toContinue reading “Calculus in Middle School”

## How to Tell If Your Writing Has Value

February 9, 2017. Answering a question on quora.com: How Can You Value Your Writings? I’m assuming you have written something, and are now questioning if what you have written has value? First of all, does it have value to you? Are you proud of what you have written? It’s not always easy to answer this question,Continue reading “How to Tell If Your Writing Has Value”

## Recreational Mathematics

April 17, 2018. Answering a question on quora.com: Can I do math as a hobby? Yes, by all means! While you may think that doing math means boring computations, nothing could be farther from the truth. There is a whole field called recreational mathematics—no, that is not an oxymoron. True, higher mathematics usually requires yearsContinue reading “Recreational Mathematics”

## Contradicting Euclid?

Answering a question on quora.com August, 2019: Why do high levels of maths contradict lower level maths? Why do ground rules of math get broken when you get to higher levels of maths? Unless you had a bad teacher, what was true remains true. There are times when things might seem to change, but ifContinue reading “Contradicting Euclid?”

## Writing the King’s Series

February, 2016: Despite good intentions, it has been too long since my last post. So, what is my justification for the wait? What excuse do I offer? Well, I have been publishing. (Bows, and waits for the swell of applause . . . and waits . . .) Last summer I finally put two ofContinue reading “Writing the King’s Series”

## Becoming a Writer

December 2015: How did I become a writer? I’ve always been a reader, and, for as long as I can remember, I’ve had the urge to write something others could read. Note that word “urge.” It was an urge, not a passion. I thought I had to make a living, and I could not conceiveContinue reading “Becoming a Writer”

## “Fantastical” Science Fiction

November, 2015: Fantasy, Science Fiction, and “Fantastical” Science I’ve read lots of science fiction and lots of fantasy over the years. Most times the line between the two is pretty clear. Magic and dragons? Fantasy. Rocket ships and ray guns? Science fiction. However, some writers blur the genres. The best writers can create hybrid genresContinue reading ““Fantastical” Science Fiction”

## Home Life

August, 2015: Want to cut your writing production? Get a puppy. We are the newly adoptive parents of lab named Bindle. Bindle is not quite four months old, and is quite a handful. Right now she is dozing peacefully on the hearth, but this will change within the half hour. While I have the timeContinue reading “Home Life”

## Home Life

July, 2015 Update: Now that I’m retired, I have all the time in the world. That’s a lie. I have been incredibly busy, and most of it is self inflicted. I have finally gotten my Starship series out the door and up for sale on Kindle. It is two related, novelette-length stories about the distant futureContinue reading “Home Life”

## Where Are the Math Students? Part 2

April 13, 2020: Introducing the Harry Potter School of Mathematics. Intrigued by the idea of a Hogwarts Academy for algebraic wizardry? Unfortunately, not only is this a bad idea, it’s an all too common feature of current mathematical education. Math requires an interesting combination of high level abstract reasoning skills linked with basic rote learningContinue reading “Where Are the Math Students? Part 2”

## Where are the math students? Part 1

May 11, 2015: I’ve been teaching mathematics for some forty years. That entitles me to make a few observations about mathematics students—at least mathematics students in the United States. Actually, this essay is based on anecdotal observations of my own northwest Ohio classrooms over the years. But! I have had a lot of students, andContinue reading “Where are the math students? Part 1”

## Where do I get my ideas?

April 24, 2015: Where do I get my ideas? I often use a sort of “bedtime-wandering” technique. While I’m trying to fall asleep, my mind wanders off in all sorts of directions. How do I keep from dwelling on the past day’s failures or tomorrow’s challenges? I wander off down the road to fantasy orContinue reading “Where do I get my ideas?”

## Leonard Nimoy

March 1, 2015: Leonard Nimoy’s passing reminds us that we are all mortal. Unlike most of us who live in quiet anonymity, Nimoy had the rare chance to create a character who will be known and loved for ages. I was already a fan of science fiction when the original series ran for the firstContinue reading “Leonard Nimoy”

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