Construction vs. recognition
Want attention? Just incorporate pictures of cute animals into your content at regular intervals. (Library of Congress photo)
Kids do a lot of work to memorize their times tables, which is important.
Often, though, they get lost in the computation. If they’re not quick at addition yet, they sit there painfully adding sevens in their head until they get six of them. (It’s easier to add seven sixes, but we’ll get into that another time.)
What’s arguably even more important than multiplication when it comes to succeeding in math in school, however, is recognizing multiples and spotting their factors.
In other words, when you can see instantly that 42 is a familiar, friendly number that has shown up in your times tables (as opposed to, say, 43), you are most of the way toward solving whatever problem you’ve been called to solve, from simplifying a fraction to factoring a quadratic expression.
Unfortunately, many students get so bound up in performing arithmetic operations that they don’t get a chance to develop this number sense. They never have a chance to play with the numbers and take shortcuts based on their understanding of how numbers work. Faced a simple task like simplifying 132/144 or finding 25% of 48, they freeze.
That’s why it’s so helpful to practice stuff like finding all of the numbers in a short list that are multiples of a given number in order to “make friends” with the multiples they will see over and over. Even if they don’t have all of their times tables memorized yet, this kind of work will trick them into it if they approach it in that spirit.
It’s just slightly easier to recognize that 56 is a multiple of 7 than to multiply 7 x 8. You can recall that 56 is some multiple of 7, and then figure out which one if that info is needed. It’s not cheating to approach it that way — it’s a related and useful skill.
The perspective I’ve just given you might be useful if you happen to be in grade school or the parent of a grade schooler. But let’s broaden this a little bit. Where else do we do the extra work to construct or compute an answer when we could just recognize one?
My assertion is that this pattern shows up in the way a lot of us approach making things, from the sketches we draw to the emails we send. Taught from a young age that copying others gets us in trouble, we make things from scratch that we could have borrowed and adapted without stealing anyone else’s intellectual property. This is often exhausting and time-consuming — and then demoralizing when we see how easily others do it.
Perhaps the reason others are creating so easily is because, like the savvy student who observes that 36 and 45 are both multiples of 9, they are recognizing patterns and taking advantage of them.
The amazing Regina Anaejionu fills her instructional materials with templates to adapt, like the one where she offers a staggering 156 different content ideas that can be tailored to any business. Her students have a serious head start when it comes to coming up with videos, articles, and social media posts — and if they build the outline for the actual content by copying what their favorite blogger or YouTuber does, they’re practically done.
The early songs of just about any songwriter tend to be a pastiche of the music they’ve been listening to. Singers and instrumentalists faithfully reproduce the stylings of their favorite artists, just the way Ray Charles did with Nat King Cole. Heck, Liz Phair made an entire album that was a song-by-song response to the Rolling Stones’ Exile on Main Street. It was completely new and original — but also a great example of recognizing and making use of patterns.
Building a meal is easy — and it’s pretty much the same the world over. You combine protein, starch, and veggies. You serve something sweet for dessert. To ignore these patterns and try to come up with something else on your own would be silly, and yet so many of us do it all the time in non-food scenarios.
Instead of recognizing the moves that have already been made and using them as a jumping off point — for instance, by starting with a recipe — they try to invent the thing from scratch. This is not only takes a long time, it might not fit what others recognize — and therefore, is less likely to be embraced enthusiastically. No one wants to eat our weird corn-rice-potato sandwich or listen to our song that has no familiar form.
Everyone knows that answering multiple choice questions is easier than writing essays. While the deeper thinking of constructing an answer has its value, sometimes the result is more important than the way we got there. When the easy way is the best way, honing our ability to see the structure that underpins the work of others will allow us to make use of such frameworks for our own endeavors. We’ll still have to do the work to put flesh on the bones, but we will find additional patterns that we can use to add these layers. Much of the hard work has been done for us — we just have to take it the rest of the way there and make it our own.
