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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