My 8th graders are finishing up a unit on geometric proofs. This material has even my live-and-breathe-math kids questioning, “When will we ever have to use this?”
And I’m honest with them. I confess that they will never be asked to write a two-column proof justifying why two triangles are congruent in order to clinch a job interview. No romantic interest will ever look over their paragraph constructed to show that a quadrilateral is, in fact, a rectangle and criticize the fact that they failed to correctly use the slopes to show right angles. In fact, the only time that this exact skill will come in handy is if they happen to become math teachers. (In fact, I’m kicking myself now for making my way through 9th grade geometry in a zombie-like haze.)
But I don’t stop there.
“Forget the content for a moment,” I advise them. “What does this process, as painful as it may be, actually teach you?”
There are confused looks. A few random and half-hearted attempts to answer my question. And then I hear it from the back corner –
“It teaches us how to think. How to move from one fact to another and not jump to conclusions.”
When I was four, I had not yet had the benefit of geometric proofs to teach me how to think. At my grandmother’s house, I would spend hours sitting by her side as she narrated her way through countless family photos. Photos, that were for the most part, in black and white.
So I reached the obvious (well, to a four-year-old at least), conclusion: the world used to be in black and white.
That made sense. But I still struggled to understand how my grandmother, who sat next to me in full color, could have become pigmented as a young adult. I wrestled with this dilemma for a time until I finally solved the problem (and felt quite proud of myself for my powers of deduction) – Rainbow Brite was responsible for bringing color to the world.
Well, it sure seemed reasonable then.
I had leaped from one fact – photos had transitioned from black and white to color over time – to a completely arbitrary conclusion that was based solely on the information generated within my own mind.
That particular assumption was harmless (and humorous). But that’s not always the case.
Once we believe something, even if we leapt recklessly to that opinion, we then proceed to ignore that which doesn’t support our conclusion.
We become willfully blind. Feeding on an information diet filtered through confirmation bias. Conclusions, like habits, are much more difficult to shape once they’ve hardened into place. The time to be careful is when you’re laying down the initial layers. Jumping to conclusions has a tendency to keep you in one place.
And that’s what my students are learning. Just like you can’t claim that an angle is right because it “looks” like 90º, you can’t assume things in life just because it “feels” a certain way.
It’s harder in life than in the classroom. After all, the stakes are higher when you’re you’re talking about real life instead of a poorly drawn polygon. Yet the lesson is still the same as we learn how to not carelessly jump to conclusions:
Base everything on the facts.
Move from one fact to another. No jumping.
Accept that there may be more than one correct way to link these facts and don’t be afraid to explore these options.
Ask for another person’s opinion. Sometimes a fresh set of eyes will see something you do not.
When you have enough facts, make a conclusion.
If you find other facts that refute your conclusion, be ready with the eraser.
In fact, actively look for ways that your reasoning may be wrong. That’s how you test its strength.
It’s okay to make temporary assumptions to test a theory, but refrain from putting it in writing until you can prove it using facts.
Here’s an example of how I put this into practice in my own life as it pertains to learning to trust again after betrayal.