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# X, Y, and Z…

…are common variables denoting points on a system of mutually perpendicular Cartesian axes (pronounced ax-ees) in three-dimensional space. Why is a writer penning this information?

As a teacher, I often hear from a room full of whining students, “Why do we have to learn algebra?”

I hear from disgruntled parents, “My child will never use this.”

Frustrated, I have asked, “Wouldn’t a life-skill math course be more valuable?”

Algebra is a life-skill math course. It is a problem solving game. It is an exercise in creating more information from a set of parameters that may or may not offer a fixed solution. It is a way of thinking about our increasingly complex world.

Last semester, I sent home an assignment concerning measurement. The activity seemed simple. The student’s hands were a unit of measure to determine width and length of a table. Children are literal. If you tell them to measure a table with their hands, they will eagerly look for a table and start measuring. But what if there is no table to measure? He or she has a vision of ‘table’ implanted in the mind. It seems like an easy task until there is no table, and therefore no way he or she can measure one. Assignment aborted.

Was I so literal in my thinking processes as a child? If I had an assignment to measure a table with my hands and had no table, would I suddenly have no direction in which to proceed? Though I was considered gifted, I was also a child, so my answer is…yes, probably. “No table? No can do. I’m supposed to measure a table.”

Fortunately, my father was well versed in mathematics. I can imagine his glee as he jumped up. “We need a table,” he’d exclaim. “Let’s see if we can create one!”

This ability to create, to conceptualize that which isn’t, comes from an ability to generalize. My father had facts. He knew what a table was. He knew the assignment wasn’t about a table, but about measuring a plane by counting hands from edge to edge. I can imagine him patiently explaining a table was nothing more than a flat surface – a rectangular plane that one can measure from side to side. I may not have understood his words, but I would have followed him around as he took on the task of replicating a table for me so I could complete my assigned schoolwork.

How many of us, now parents, were lost when algebra was offered? How many followed the steps in class when a teacher explained the process, but never grasped the reasons behind them? As parents, many of us may not make the conceptual leap to creation because we did not understand the mechanics of x, y, z.  Algebra was a nightmare with no connection to life or its future.

In this particular case, where were the parents in this endeavor? Were they as stymied by the lack of a table as their child was? Some, like my father, came up with alternatives. Others did not. Sometimes, as teachers, we take for granted that parents have the knowledge they need to help their children with schoolwork. Often, that is not the case.

Adults, like children, have a mental picture dictionary of ‘table’, a fixed iconic image of what it looks like. They can probably draw one. However, having that picture does not guarantee they know what a table is, a flat plane with given points in space connected by line segments that form edges. If they knew this, anything with those attributes could become a table. However, this takes a level of thinking that most of them had to learn, an ability to generalize in order to conceptualize alternatives.

We teach algebra not to become math experts, but to learn this way of thinking. We learn to start with unknown and mysterious variables, and experiment to create solutions. We learn to understand the mechanics of the world, with axes x, y, and z so that we can recreate a replacement structure for our kids when they get a silly homework assignment about measuring a table using their hands as a unit of measure. If one cannot conceptualize this way, when there is no table, one uses the only answer available. “We have no table so we can’t do it. Go ask your teacher.”

A basic knowledge of algebraic concepts is the language of our world. It is how we speak of its structure and its function. It is how one creates a table out of a space on…well…anything that is flat.

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# Rest in Peace, Sweet Jack.

(Author’s Note: This is a personal story.)

November 21, 2019 – 6:27 pm PST

“Blog finished, Jackie.” I hit the enter button to send the notice to my newsletter recipients. “Jackie?”

He stretched out and chuffed. I turned to look at him as he chuffed a second time.

“Hey, buddy. Are you alright?”

There was no response. He’d been sleeping a lot lately, but his eyes were open. Were they unfocused?

“Jackie?” I said, suddenly fearing and realizing the worst. “Jack?”

I called my neighbor. “I think my dog just died.”

He told me to cover him with a blanket, since no one was available in the vet community to help.

I did, but I didn’t cover his nose, because I kept imagining that he was still breathing. After a few minutes of feeling for movement, checking for breath sounds or puffs of air, and imagining that damned blanket moving up and down with a breath, I called my son.

“I think Jack died.”

“What? You think?”

“He’s not moving or responding. I even shook him. Nothing. I can’t tell if he’s breathing or not. I don’t think he is.”

There was shuffling and murmuring in the background and then my son was back on the phone. “I’ll be there in thirty-five minutes, forty tops.”

I watched Jack not breathe for a while. I now know what “deathly quiet” means. I opened the front door to wait for my son. Children were laughing and playing around the corner. Across the street, men discussed man things in gruff, mirthful tones. I stepped out. Behind me, the house was a sudden tomb.

November 24, 2019 – 10:46 am PST

As I sit here, contemplating memories of a life shared with an extra-large cream-colored standard poodle, I see my two house cats, a brother and a sister, curled up on the bed in a previously forbidden room. My bedroom was Jack’s sanctuary, no cats allowed. But, there’s a hole in the house, a poodle-sized hole that none of us can fill, so I let them stay there. Somehow it fills my heart a little.

God, I need to be writing “U is for…” today. I don’t think I can. I wonder how everyone will feel if I skip another week?

November 27, 8:01 am PST

I stare at the binder paper, covered front and back, with a collection of thoughts that I could use for a blog, but my eyes are swimming in tears and I can’t focus. This is a good idea though – to write down all the random thoughts about eleven years and five months with a witty character who was a best friend when I became a single mom empty nester. Even if I never use it for a blog, it’s helping me cope. Yeah, it’s helping.

I need some more coffee. I need to put ice on my foot. A cat wants in. Tomorrow is Thanksgiving. I feel empty rather than thankful, and I’m worried my daughter will face her grief here when she comes. So much for writing….

December 3, 2019 8:14 pm PST

I received a card from Dr. Matt, Jack’s vet. I made the mistake of opening it at work. Inside was a note about how well I had taken care of Jack, and three cards, one for each of us who loved him. On each, someone had taken the time to make a print of a paw. That means they took him out of the shroud my son so lovingly wrapped him in. I shouldn’t have opened this at work.

When I arrived home, there was a message on my phone machine. “ Jack’s ashes came in today. You can pick them up anytime.” I am not driving yet!

My daughter says, “Don’t worry. We’ll figure it out.”

I am probably too emotional to write well tonight, but a blog is due tomorrow. This dog lived through so much change in this family. Eleven years, five months is a long time for a dog. Even with all the familial upheavals it was not long enough for the owner.

Five stages of grief do not follow in a specific order. Sometimes all the stages hit me at once, and I dissolve into a puddle of tears until there’s nothing left of me. Like tonight. Again. Surely he’s not gone, yet, here is the card from the vet, and the saved message on the answering machine. Dammit. He didn’t even finish chuffing, before he left. Gone, just gone. Really? Was it something I said? “Jack, do you have to go now?” This house is so empty. Cats are small and so very quiet. Acceptance? Brief glimpses that look more like denial. You were supposed to stay for eighteen years. That was our plan. You didn’t even make it for twelve. Was it something I said? Something I did? Something I didn’t do? There should be six stages. Someone should add guilt to the list.

One of my notes says, “I don’t want to remember just the “good things.” I want to remember all the things…good, bad, silly, ridiculous, infuriating, beautiful, ugly…all of it. Jack was arrogant, bossy, and intuitive. He was born to police, a mix of hunters and gatherers. Poodles are a working breed. One side of his pedigree was a line of herding dogs, the other hunting dogs. He was intelligent and curious. he nipped people’s heels when he first met them, trying to teach them where to go. He beat up the male partner of the brother and sister house cat team. He was an alpha dog, which required me to be a boss dog. I am not good at being a boss dog, so our relationship had to be well balanced. My children got the fun dog, the dog that liked to play…and prance…and hike and dance, the dog that jumped in puddles and piles of leaves.

He was a dog that was afraid of things with wheels, a dog that walked ahead, though he learned to match the walker’s speed. He changed directions as if reading the mind of the person handling him. I often thought he’d make a good cart pony. He was big enough. I wonder if he would have found that demeaning?

He wore a red collar. The red warned people with other dogs, “Hey, this dog is an alpha, approach with caution or better yet, don’t approach.” That was true for strangers as well. Poodles are the fiercest of protectors. Even law officers don’t want to enter a house with a standard poodle inside. He wasn’t a mean dog, but he was tall and this intimidated everyone. Taking him places was an ordeal because of it. I hated leaving him at home.

He was sensitive. He didn’t respond to harsh voices or loud noises. He learned hand signals. He was controlling, but when it was imperative that we work as a team, he was quiet, attentive and immediately responsive. He was amazing.

I miss him. I will miss his exuberant, tail high and wagging prance into the house after a jaunt outdoors. I will not miss the muddy trail of paw prints on my blonde floor.

There are a few other things I won’t miss. I won’t miss having to place a brick and a flower pot in front of the gate because we taught him how to do obstacles, which included knowing how to crawl under things. I won’t miss cleaning the yard daily, although he and I worked it into our empty nester routine after the kids moved out. We cleaned every morning before I went off to work. He liked to be clean, though with a white coat he was clean only a few days after his grooming sessions. He hated his nails being touched, and had to be restrained for that chore.

I won’t miss the guilt I felt over leaving him home alone all day in the house, because if I left him outside he barked at other dogs, or people, or leaves, or birds or strange cats, or whatever, and we received a noise ticket. Well, only a warning…it was enough. I don’t have to keep my couch covered with a blanket because he jumped onto it after I left for work. I knew he did it, though he was always off by the time I opened the door. The blanket allowed us to keep our little secret. It kept the peace between us.

I started to worry about him dying in March sometime and asked the vet what I would do. I’m older, he’s a big dog. What are the steps? Where can I get help? I think I was noticing changes even then. He slept more, he didn’t want to play with his toys. He struggled with health after contracting Leptospirosis, but this was different. He was restless at night, his routines became irregular, he ignored commands, and refused to eat. Oh my god, that bothered me the most. How could he expect to stay alive and healthy if he refused to eat? Dr. Matt said I was a pushover. I should just wait him out. It worked for about two weeks, but then he really just wasn’t hungry. It pushed all my buttons. We fought about it daily. “I can’t take this anymore,” I exclaimed, as he walked from the food I had lovingly prepared. He could tell I was at my wit’s end. He turned and ate a few bites, maybe a half cup. An hour later, he was gone. Was it easier for both of us to end the fight this way?

Christmas is coming. Jack loved Christmas and always looked for his gift under the tree as soon as we put it up. If it wasn’t there, he hunted for it. We would hurry to wrap up gifts. Once he saw his under the tree, he relaxed. Once he opened his gifts, he’d help the rest of us open ours. He loved his pretties. He needed a new collar. He would have found it under the tree this year with a new yellow rain jacket.

I know I will find his collar adorned with jingle bells and I will fall apart again. It’s probably with the Christmas decorations. I also know I will save it. It will go with the string of bells my childhood friend wore when he was alive, a prancing, arrogant, dancing horse, who also thought he was boss of everything.

This house is too quiet. There is a poodle-sized hole in my heart.

Rest in peace, sweet Jack.

Baker’s Frosted Jack Roddy

b.3/13/2008 d.11/21/2019

Some news: My novel, Blood On His Hands, is live on Amazon. Here is the link: https://www.amazon.com/Blood-His-Hands-AV-Singer-ebook/dp/B081ZK1DGK/ref=sr_1_1?keywords=AV+Singer+BLood+On+His+Hands&qid=1575471844&sr=8-1