The Transitive Property: Not Just for Math Facts, Anymore

Lynne 150If A equals B, and B equals C, then A equals C.

Remember this? If the name escapes you, that’s called the transitive property, and we all learned it. Lately, I’ve been noticing that the transitive property applies to our thinking about ourselves — or more specifically, to adolescent girls’ thinking about themselves.

It’s no secret that the judgments and conclusions derived by ten- to twelve-year-olds — particularly when judgments and conclusions about themselves are involved — can be more emotional than logical. But as they grow just a little bit older, and have just a little bit more experience with life under their belts, the logical portion of their brains does begin to take hold. That is when the transitive property can kick in, for better or for worse.

It’s no secret that the judgments and conclusions derived by ten- to twelve-year-olds … can be more emotional than logical.

An example of “for worse” might go something like this:

“I enjoy my friend Delilah, and think she is the coolest person I know, and I work hard to be just like her. Delilah enjoys pretending to be sick to get out of stuff. Therefore, I should pretend to be sick to get out of stuff, too, because I will enjoy it and be as cool as Delilah.”

Simplistic? Sure. Realistic? Unfortunately, this type of “negative peer pressure” and logical thinking gone awry is far too common in middle schools everywhere. It is why Oprah Winfrey, a guru of positive thinking, says, “Only surround yourself with people who will lift you higher.” In this example, Delilah is definitely not lifting her friend higher!

Adolescent girls change so much, and so rapidly, it’s not always easy for them to find, much less surround themselves with, others who will lift them higher. They themselves may not be doing much lifting of others, truth be told! Additionally, the orchestrating of friendships, appropriately, falls less and less to parents as girls grow up — not that we parents ever were infallible in this regard anyway.

That is why the climate and expectations prevailing in her school environment are so critical: An adolescent girl will spend nearly 1500 of her waking hours each academic year in the framework of that school culture. The peers with whom she shares that enormity of time will certainly figure into the transitive property logic she applies in thinking about herself.

Not long ago, I asked my advisory group to decide, as a group, what one word they would use to describe “an Irwin’s girl,” a moniker often used in referring to girls who attend our school. They each started with a few words of their own, winnowed, and then discussed/debated their final choice.

My advisees arrived at the conclusion of leader to denote an Irwin’s girl, and the success of the exercise prompted me to encourage all advisors, fifth through eighth grade, to try it out with their own groups. It pleases me to tell you that each advisory settled on a positive word, and that the list included independent, creative, talented, powerful, confident, intelligent, well-rounded, happy, opinionated, loyal, and ambitious… as well as erudite.

Let’s apply the transitive property to these self-declared assumptions about what girls in our school are like. Whether consciously or not, a student operating within a culture of these assumptions and expectations is far less likely to emulate Delilah, the malingerer, and far more likely to conclude:

“I am an Irwin’s girl. Irwin’s girls are leaders/powerful/well-rounded (pick an adjective from above). Therefore, I, too, am a leader/powerful/well-rounded (pick same adjective).

By applying the transitive property, she is actually doing her own “lifting up,” creating a cycle whereby she is both responding to positive influence and creating it for others.

Whether this thinking simply frames how a girl thinks of herself, or eventually becomes a self-fulfilling prophecy, the impact is compelling. In fact, by applying the transitive property, she is actually doing her own “lifting up,” creating a cycle whereby she is both responding to positive influence and creating it for others — surely a happy cycle in which to navigate these pivotal years.

e.e. cummings wrote, “It takes courage to grow up and become who you really are.” And while he never wrote about Irwin’s girls specifically, it is gratifying to consider that being one, in a culture that communicates growth and confidence, supports our students as they become who they “really are.”

Certainly, we have the luxury of small class size and small advisory groups, in addition to a program specifically focused on being healthy and empowering for girls, and those factors do a great deal to create and maintain that culture.

Parents of girls in larger schools and co-ed schools, however, can assess — through observation, questions directed to teachers and administrators, engagement in school events, and so on — the expectations, opportunities, and unwritten messages conveyed to their daughters. Should the climate prove lacking in its attention to developing outstanding young women, it may be helpful to bring the transitive property to light in those environments, too!

Lynne Myavec, Middle School Director

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