Another Morning Song

Early in the morning
in the morning
oh so grey

When I should be a sleeping
When I should not be awake
When the last dream of the morning
shows what mood my day may make

Early in the morning
in the morning
oh so bleak

Butterfly (Partner Poem)

You talk about the butterfly:
A tender, fragile thing.
As a caterpillar in a cocoon
It spends its life waiting.

Agog over its innocence,
You stare at it in awe!
Your sane descriptions lose sense
When the butterfly goes hence

You admire its fragility
How it could just disappear
but the better choice is stability
To fly one long life without fear

Still there is a part of you
That wishes it could be
A simple idiot butterfly too
from your duties and worries free

Your Pet Project is Not Essential

Bottom Line: If you find the need to do a supply run for actual essentials, and you realize the store you are going to has hobby materials, get both. Now is not the time to ask an associate for what seeds to plant in April or what tool you can use to patch a hole in the wall.

Algebra and Beyond

I wrote the excerpt (Arithmetic) above quite a few years ago, and although it packages things neatly into a bow it obviously oversimplifies. However, it brushes over the real reason I was able to flip from barely keeping up to the only one pushing ahead. Many of these narratives I have steered away from focusing on the instructors, instead inspecting the environment and my own state of mind as I learned. However, I cannot circumvent the enormous impact an excellent teacher had on my understanding and interest in the field of math.

I met Mr. Helvie in 8th Grade as I and the other smart kids from my grade trekked from the bottom floor of Montesano Jr. High School to the furthest top right corner of Montesano Sr. High School. The shape of his classroom evolved over the years, but one thing that stayed consistent was that in the top left corner of the whiteboard where other teachers might put the date he would put a series of numbers multiplied against each other.

The day I am writing this is 4-20-20. What Mr. Helvie would do is consolidated that date to one number:

42020.

He would then divide into it until he was able to split it into its prime factors. He would do this without ever using a calculator, except to check his work. 42020 is even so it is divisible by two. It’s actually divisble by four so

42020=2²x10505.

10505 ends in 5 so it is divisible by 5 resulting in 2101.

42020=2²x5x2101.

I have a feeling 2101 is also prime, but to double check I add the individual digits to make sure 2+1+1. All numbers divisible by 3 when combined add up to a smaller number divisible by 3. Since 2+1+1=7 I start going down the list of prime numbers in my head or printed. I like to list the prime numbers I had tried in order and cross out the numbers that were not factors. Another way to do this is to say they are factors of 0 since any number except 0 to the 0 power equals 1.

42020=2²x3⁰x5x7⁰x11¹x13⁰… you get the picture.

Basically, I divided that final number 2101 by progressively larger numbers until something breaks it apart or the result is smaller than the next available prime number. The factorialized date is 2²x5x11x191 though admittedly the date 4-20-2020 is cool already.

That is the difference Mr. Helvie made. Not that I know how to prime factor large numbers by hand, which is admittedly rarely useful. The difference this teacher made was that I went from indifferent to numbers to actually enjoying looking critically at mathematical eccentricities. Not that everyone in his tutelage emerged as fascinated and enlightened, but his learning method was absolutely perfect for me.

Up until that 8^th grade class my math teachers had followed a general formula. We read or they lectured on a mathematical topic. The teacher demonstrated how this mathematical concept was used on the whiteboard or a projector screen (yes, I am that old). Then the instructor usually would use an example already written in the book to demonstrate, so that we could later use it as a reference. Briefly, the math teacher would ask if there were any questions, and since no one ever asked, we would move quickly on to complete class or homework assignments.

What Mr. Helvie did, that no other math teacher had done, was force us to critically think about the mathematical concepts we were given. He would explain the materials, but we were expected to read the information in the math book to prepare for certain classes. Mr. Helvie was not a teacher that you could just idly take notes for; when he suspected students had not read the material he would slip in mistakes on the board and watch. If students just copied the errors into his notes, he would raise abruptly raise his volume saying: “Wrong” or “No.” After the class was startled awake, he would then continue at a more reasonable pitch saying, “There’s a mistake” or “I’m not moving on until someone can tell me what I did wrong.” This shocked the new 8th graders, in our first class on the high school side of the building. However, I quickly adapted from passively observing instructions to critically examining the steps he laid out on the white board. The meticulous process of showing my work in homework and the in class math checking laid the essential foundations for later understanding mathematical proofs and programming logic.

Whenever students said that learning math by hand was pointless in the age of calculators Mr. Helvie would say, “What are you going to do when you’re walking down an alley in Seattle and a bum comes at you with a knife and asks [inserts mathematical problem relevant to current lesson] and you don’t have a calculator.” It was a ridiculous question, and we all knew it was ridiculous, but it made me laugh. It’s even stranger now after smartphones have become commonplace; I probably would have a “calculator” in my pocket if a Mathematical Mugger attacked me.

He was a big man, tall and intimidating as hell if he wanted to be. He would walk throughout the classroom speaking at a moderate volume and engaged cadence. Some times he was at the white board in the front of the classroom, the white board at the back of the classroom, or the unit circle white board, Sometimes he lounged back on the corner of his desk grinning widely at the impossible problem he made from numbers students had volunteered. Students took turns offering possible next steps. Instead of telling us yes or no, he had us solve the problem together.

Yet his demeanor changed drastically when he noticed dozing or distracted students. It was like a cheerful jolly man transforming into a controlled, yet angry, giant. Sometimes slightly less controlled. He would walk toward the student in question maintaining his current volume. Then lower his head so that he was closer to the student’s ears at desk level. Suddenly the pitch would raise extremely quickly to “Wake-up” the student. Depending on the student’s potential, offense, or level of distraction to other students this was sometimes followed by speech tailored to the student or situation. This rarely happened and afterwards the students did not doze or pass notes in his class.

Well, I did pass notes some years. I only distracted my best friend, whom I also hounded to make sure his assignments got completed and turned in so he could stay in class with me. I was a bit of a favorite in Helvie’s class. I prime-factored the date and consistently caught his pretend mistakes. When the other math teacher declined to take the Math team to state finals (even though my team with my brother had already qualified) I marched myself out the door across the hallway to ask Mr. Helvie to do it, which he did despite never being involved in the math team before. When I went to college I majored in engineering, because I wanted to do the one type of job that actually used imaginary numbers. I never graduated in electrical engineering, but I did spend four years of coursework in physics, programming, and engineering courses.

Mr. Helvie was one of the teachers who made it to my wedding. I was devastated that I couldn’t make it back for the funeral. Sometimes I wonder if he spent a little time in limbo floating around Seattle demanding passerby answer various math questions. “Boo! What’s the mathematical formula for the quadratic equation!”

Arithmetic

Mathematiques et en Physique est Chouette!

It’s hard to understand what’s being said when someone doesn’t know the language.  It’s the same with any subject taken. There is certain vocabulary in science, dance, and mathematics. Those who understand the language and tools get to see the really cool stuff. A ballerina has to learn the basics before she can do a pirouette. A Mathematician must learn how a derivative is derived before they can use it to approximate how many popcorn kernels are in that container. Once the language and the tools are understood the rest is a blast. The question is what is the most effective way to convey the this information.

Throughout my education I noticed certain methods of teaching were effective on me, while others worked better for my classmates. Students can learn effectively from either lectures, reading, doing, discussion, or some combination of these four methods. Learning math during grade school I was considered slower then my classmates, because I struggled with flashcards and worksheets. It was not because I was unintelligent, it was because those methods are not how I learn most effectively. When I was enrolled in a classroom where I was able to discuss the concepts with the teacher and classmates I was blossomed quickly. I realized I was able to explain concepts to students who had always done the assignments more quickly than me. By determining and tutoring to a student’s learning style it should make it considerably easier for them to understand and enjoy math.

Mathematics and Physics are Awesome!

Once your reading the same language you start to get it.

Had I a Treehouse

Had I money and land and time
I’d build a place and call it mine
All nestled up among the trees
A hideaway to feel the breeze

Had I the skills to make it so
I’d include a garden and help it grow
All thirty feet above the ground
A patch of herbs on my rooftop found

Had I wood and branches and tools
I’d shape a room with certain rules
Walls inside like a hollowed tree
An outside like a nest of a bee

Had I children who could enjoy
I’d hide in hammocks and toys to employ
All beside a kitchenette neat
A place with plenty of snacks to eat

Had I a ladder and platform above
I’d write while resting over all that I love
All alone and yet still connected
To a beautiful tree home once it’s erected.

Hermit

Photo by eberhard grossgasteiger on Pexels.com

I am blind, but am not lost.
I know right where I am.
Although I cannot see the past,
I know where I have been.
I have not the skill to see
what my future may be.
Yet, I am quite confident
My place is right for me.

The World is My Oyster

The world is my Oyster
I’m stuck in this Shell
With a gooey tan creature
And a pearl I can’t sell
While constrained by the bounds
Of these Barnacled walls
Hoping there’s a buyer
Who for this Pearl calls.

Treehouse #2

My home had two tree-houses:
One my father made
The other we hid in the woods
Of branches that we laid.

At first it was a platform
Tied together with twine.
My brother and best friend used to climb
While on the ground I whined

When they left I used it
To climb that tree each day.
It was my favorite pastime
to feel that Cedar sway

My brother told me later
The reason he fears heights
Is the wind in lofty branches
Awaking some pretty strong frights

A Prayer

Dear God, I would ask of you
That nothing but the best
Be what my hands shall give to thee
And all whom you have blessed.

Dear Lord, who made the heavens high
And made the valleys low
I wish to bring you with me
Each avenue I go.

Dear Father, Son, and Holy Ghost,
Who made primordial stew,
I wish that I could worship you
With everything I do.

Divine all present holy one,
Whose name is kept unknown,
You are the center of my strength:
My firm foundation stone.