(I Got) 99 Problems

But at least it ain’t one.

Unpaired problems don’t exist – they are always a 2-for-1 special. When my students recognize a problem – whether in writing, math, or their overall thinking – we look for its pair. There is never only one thing wrong because that’s not how systems work. A disturbance in the force *over here* will always have some sort of effect somewhere else. The worst possible state is to see only one problem, because that means there’s at least one more somewhere and you don’t know about it yet. 

Off the bat we should clarify that “problem” here means both an actual mistake and the symptom of that mistake, and the mistake and the symptom are usually pairs. I don’t separate symptoms versus mistakes with most of my students because it feels cumbersome and a little preachy, so we just think about all of them as problems. The “wrong answer” is a problem (technically a symptom), as is the sloppy decimal work — the mistake that created that problem. This is the real benefit to showing work mathematically: so that if a problem arises, finding its pair is easy and quick. 

Finding the second problem comes up a lot in writing. Here’s a typical sentence I’ll see: “When camping in lake tahoe one of the biggest dangers is bears there’s a list of things that you should and shouldn’t do.” Clearly there’s more than one problem happening here. The student told me that it felt “long”. Okay, that’s a symptom. We went back to our writing checklist and he discovered a few additional problems: 

• Capitalization needed
• “Things” (vague)
• No actual subject (who’s camping in Lake Tahoe?)
• Run-on sentence (and likely the pair to “long”)

After some iterations, he settled on a much improved, “Bears are dangerous, however there are some precautions you can do to keep you safe.” Perfect? No. But so much better! 

Problems often coexist on the same tier, however they can also be hierarchical, and this takes some bigger thinking. I steal from Eisenhower’s “enlarge the problem” principle here, and we zoom out until we find the other problem. A simple example, and one that shows up waaaaaaay more than you want to believe: a student gets a math question wrong and just cannot figure out why. He shows me all of his steps, which are perfect. He’s entered the answer correctly on the digital platform. He’s included units. What’s the (other) problem? He answered the wrong question. 

For myriad reasons (problems), this sort of analysis isn’t often taught in school. I wish it were. For me, this is one of the actual take-aways for complex math and a decent answer to the famous and fair question, “When will I ever use this?” Finding the roots of a quadratic w/out a calculator? Probably never. Applying a systematic approach to discovering flawed work? All the time. I use paired problems when I examine inefficiencies in my business, when my wife and I face behavioral challenges with our kids, and when I fly. 

It’s terrifying to be 5000 feet up in a small plane and discover only one problem. Yesterday my instructor and I were coming in to land when we heard a rightfully distressed pilot radio in that he needed to immediately return to the field because he had a blown oil cap and was purging oil. Two problems right there! My instructor, without missing a beat, looked at me and said, “That means a seized engine isn’t far behind.” We were happy when the distressed plane touched down a couple of minutes behind us, mostly because it meant that the pilot and passengers would be ok, but also because it meant one less problem. And that really meant two.