“‘Show the work’ as a key exhortation
In instructions for chem calculations:
Denoting the process
Will optimize progress
As one seeks unknowns in equations.”
The 5 April 2023 Twitter limerick again drew inspiration from a common saying encountered in my own STEM coursework.
Interestingly, years before I wrote the poem, I had written about this particular phrase in an online creative writing class, via the prompt: “What is your one ironclad rule?” Today’s essay will adapt that previous response in translating the limerick, so I’ll allot more space than the 280 words that I normally give myself in these posts.
“‘Show the work’ as a key exhortation /
In instructions for chem calculations…”
My one ironclad rule is that I show the work. It’s an exhortation from my eighth-grade algebra teacher that I’ve never forgotten. She would add “STW!” as an abbreviation on my homework and exams when I would take a step of the solution for granted. Her advice served me well through the many years since, as I proceeded through an academic path to a teaching job of my own, from college through grad school through post-doctoral training, and ultimately to teaching my own classes. I succeeded in many aspects of my chemistry coursework thanks to dimensional analysis: showing the work (!) and– via a tenet only marginally less important– including and understanding the units.
“Denoting the process /
Will optimize progress /
As one seeks unknowns in equations.”
As I teach classes of my own, I try to “STW” as a model for my students. In my first few years of teaching, I worried often about the prospect of student questions to which I would not know the answer. Now, I recognize the value of showing to students that scientific understanding is very much a process, that while I might not know “A,” I do know “B” and “C,” and that makes me suspect “D” about the original question. (“And it’s a great question! Let me know what you find out when you look into it.”)
I tell students at the start of every exam to show me their thought processes even if they aren’t sure of the final answer: “Show me the set-up even if you know your answer is wrong.” In other words, “denoting the process will optimize progress,” regardless of setting.
***
Right around the time I had received that essay prompt, several years ago, I read an article in The Washington Post, in which Professor Alan Levinovitz commented in part on the importance of science educators’ discussing the work and identity of scientists: the processes and individuals via which our introductory textbooks and curricula come to be: “When I was a child, scientific knowledge was presented to me as though it came from a big book of Important Truths,” Levinowitz wrote. “We discussed the scientific method, yes, but the scientists tasked with executing it and the communities tasked with underwriting their work were rendered invisible.”
It’s the need to “STW,” writ large: the processes are the stories of science, and they are fascinating. Two major reasons that I pursued science were an interest in those underlying stories and some inherent sense that I wasn’t yet nearly fluent in the notation and vocabulary necessary to appreciate them. It should be easier to access these stories, to show the work that leads to the principles that we expect students to readily memorize.
In many of the courses I teach, and in several of the essays I’ve posted here, I reference state functions and path functions, which are different from a mathematical perspective.
State functions are those that can be defined via only the initial and final states of a system. Altitude is my go-to example. “Imagine a group of mountain-climbers, each climbing a mountain via a different path,” I say. “When they reach the peak, they are at the same final altitude regardless of the path they took. Altitude is a state function.” Path functions are those that require a consideration of the path between the beginning and ending states. “Remember the mountain climbers? The distance they traveled will be very different depending on whether they took a scenic route that wound around the mountain, all the way up to the top, or forged ahead straight up the mountain.”
All this to say: science is presented in textbooks as a state function, but it’s very much a path function, dependent on human constructs, individual triumphs and setbacks, necessary course corrections. Far, far too often, textbooks present the final state as the whole story. It has been fun and rewarding on this site to appreciate more of the paths.
Likewise, to return to my ironclad rule, I find it immensely helpful to “STW!” in writing as well: to grapple with drafts and word choice and talk to other writers, to remember the value of the process. It’s been a great revelation in the past few years to remember how rewarding it can be to treat writing as a path function, too: taking advantage of existing structures, but ultimately seeking the unknown in this field, as well.
Chemphasis 