I am able to communicate with you right now because of one of the oldest and greatest inventions of humanity: Writing.
Prior to writing, humans had to keep their histories alive through spoken stories, which are malleable and unreliable. We had to learn how to do things directly, as apprentices to mentors; if there was nobody in our tribe who know how to do something, we couldn’t learn from others.
Much of our advanced civilization is tied to our use of written language to reach out across space and time to each other.
As a teacher, though, I’ve noticed a disturbing trend: Students put a premium on remembering things, and refuse to write things down. And it’s not just students. In restaurants, servers are expected to take the custom order of a full table without making notes. In meetings, fewer people (including myself) are even bringing something to write with.
I hope it’s just my bubble of reality; I hope the rest of the world is still feverishly jotting down reminders to themselves. But I fear that it’s not.
I teach high school mathematics.
One of the major research paradigms right now is Cognitive Load Theory (CLT). The relevant gist of this theory is that our working (short-term) memory is limited, and so we should avoid overtaxing students with too much new information at once.
Consider this example. If you’re reading this, I assume you can add well enough. What is 52 + 17? That’s probably not very challenging to do without a calculator or a pen and paper. What is 516 + 561 + 912 + 312 + 123? That’s a bit more challenging to do mentally. Imagine having to do it with me reading the numbers aloud instead.
There’s also a bunch of information in CLT about how items pulled from long-term memory into working memory is less costly than absolutely new information, which is why we should memorize our times tables. In this way, CLT is a common rebuttal to Inquiry-Based Learning, since direct instruction is allegedly better at tapping into that long-term memory.
While I accept the basic premise of CLT (although I have a more nuanced opinion on memorizing times tables), one thing I rarely see addressed is that one way of managing our mental limitations is to write things down.
It’s common for mathematics teachers to encourage students to show their work to receive full credit. Students grudgingly do so when they’re going to get points, but when adults demand teens do things they ought to be doing regardless, it’s unclear what the long-term effect on the behavior is.
Furthermore, in my experience, teachers often expect work to be shown even when it’s obvious. In practice, competent mathematicians do not write down everything. Competent mathematicians write things down when a problem is too complex to hold everything in working memory.
My own notebooks are filled with equations, false steps, scratch outs, circled bits, arrows, and so on. I agree with CLT that teachers should be mindful of the memory limitations of students. But the crucial strategy of writing things down is often sidelined. One article, for instance, refers to the strategy of “the use of vertical nonpermanent surfaces.” This sort of distancing obscures what ought to be a very basic concept.
Another emerging concept in mathematics education is the Number Talk. The purpose of the number talk is to encourage students to see how to strategize problems, and to see that there are different paths to the same solution. Consider, for instance, doing 18 x 5. You could recompose this as (10 x 5) + (8 x 5), or as 2 x 9 x 5, or as (20 x 5) – (2 x 5), among others.
I like Number Talks, but I’m concerned that they also push the notion of doing mathematics exclusively mentally. Number Talks are supposed to involve problems simple enough to do without aids, but there’s already a major industry devoted to mental math.
Writing things down is not a sign of weakness. It’s an acknowledgement that our brains have a limited capacity. One of the eight standard principles of Common Core is that students should “use appropriate tools strategically.” Pen and paper is one of our oldest technologies, and yet it increasingly feels as if we’re discouraging students from using it.
The examples in this article are about mathematics education, but it seems to be part of a larger societal pattern. As individuals, we write texts and social media posts; some of us write longer pieces, like this one. But what of daily notes?
Our technology makes written texts easier to archive, but it comes with its own challenges. In college, many students take notes on computer instead of on paper, a process which might be more harmful than good. And, according to the encoding hypothesis, even the process of actively filtering information through writing it down is a major aid to retaining that information.
I have been to meetings where nobody has written anything down, on the defense that “I’ll remember it.” Then things get forgotten, and the next week, at the next meeting, we’re not just discussing the same strategies, we’re arguing about what we agreed to at the previous meeting.
And it’s become a major trend over my lifetime that servers never write down orders at the table. I understand that this is often at the directive of management; somewhere, we’ve decided as a culture that it’s part of the dining experience to have the server not break eye contact in order to write things down (even as we’ve embraced cell phones, and as a result often ignore the server’s gaze regardless).
I’m fine with my server writing things down; I’m not fine with my server bringing the wrong food because their short-term memory couldn’t hold all the details of my table’s order.
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