Transitive property

Teachers tell their students all the time that they will one day make use of all the knowledge that they are learning in the classroom, especially when it comes to mathematics. "It is more practical than you realize", including the transitive property.

In its simplest form, the transitive property states that: if a = b, and b = c, then a = c. I can't remember which grade I learned about it, but until this very day, it plays its chorus in my mind as if I learned it yesterday. I have been waiting for its obvious practicality to rise out of its slumber since high school, some 20 years now.This brings me to think about what we wait for.

Immediately I think of Samuel Beckett's Waiting for Godot where the act of waiting is never over, and yet it mysteriously starts up again each day. Each day is the return to the beginning. Nothing is completed because nothing can be completed. I wonder if it is the same in waiting for the practicality of some of our learning to show. Perhaps sometimes it doesn't show because the learning simply isn't practical. It may be an observation of the world, but of little daily use.

The tragedy of Beckett's play is the inability of those who are waiting to achieve any action aside from waiting. This makes me wonder how often I do the same. There is a difference between inactive waiting and active waiting. One assumes that the answers will come and the other sees the necessity to go looking.

A friend of mine in high school became quite verbal about her frustration about the way algebra uses letters. "How can you add and multiply letters...it's so stupid." I could see her point. But letters are used to hypothesize about variables and possibilities. Hypothesis is active waiting. Becoming frustrated and not looking beyond the letters, is inactive waiting.

The transitive property is one of three equivalence properties of equality. They weigh the truth about relationships. When all things are equal, the truth is told and the properties are satisfied.

I think there is a lesson in there somewhere having to do with finding equality, telling the truth, and being satisfied. I guess I'll just keep teaching the content.