Given the amount of time we spent on it in class in high school, I’m assuming the quadratic equation is one of the more important concepts in math, but the only thing I remember is “plug and chug,” which sounds more like something you’d do at a football tailgate than in a classroom.
Okay, I remember a numerator and a denominator, maybe three variables and there’s a square root in there somewhere, but despite all that plugging and chugging, I could not tell you what one might want to use the quadratic equation to do.
To me, the purpose of learning to use the quadratic equation was so I could pass trigonometry (or was it pre-calculus?) so I could get to a point where I never had to think about the quadratic equation ever again. If I’d been told what the quadratic equation was for, I forgot it instantly, this context overwhelmed by all that plugging and chugging.
My experience is reflective of what I believe to have been the predominant mode of teaching schoolkids math at the time (mid-80’s), a kind of purely prescriptive methodology, filled with hacks and tricks to get the “right” answer. I’m assuming that some of my classmates understood what the heck we were up to, but I know I wasn’t alone in my ignorance.
Those prescriptions were sufficient to get me to a level where I could do well enough on the SAT and ACT – though I’m not certain they even tested the quadratic equation – but when it came to truly understanding math, I left high school largely illiterate.
In contrast, the instruction I received on writing, particularly in grade school and junior high was largely not prescriptive. We spent much more time exploring a wide variety of genres, less worried about demonstrating specific proficiencies than ranging through experiences which would hopefully lead to a broad conception of what it means to write and communicate.
I’m almost certain it wasn’t until high school that I first wrote the kind of academic essays that seem to be somewhere between a predominant and exclusive part of the diet for the students I would see in my first-year writing course.
Prior to high school, while I always knew my teacher would be grading the assignment, almost never was the teacher the audience, and if we were given “standards” to aim for, they didn’t leave any real impression on me.
Instead, we were given problems, real problems, and asked to solve them with words to the benefit of the audience.
Over the years, however, “accountability” pressures often – but not exclusively - in the form of standardized testing has made prescriptive instruction for writing much more commonplace and crammed it down to some of the earliest grades.
The five-paragraph essay is a form without a genre, a template divorced from larger purpose, except as a tool to prove a surface-level competence with moves that may resemble effective writing, but in my view are simulacra, Potemkin essays masquerading as something real and meaningful.
And then to succeed on the five-paragraph essay, additional prescriptions are doled out, like the ideal number of sentences per paragraph, putting the thesis at the end of the first paragraph, and signaling the conclusion (in which the thesis is restated) with “in conclusion.”
I have seen even more levels of prescriptive detail inside the five-paragraph form, start with a hook, include the subject of the essay, give a brief outline, and then end with another hook that transitions to paragraph two. Each more detailed set of prescriptions is meant to bring the artifact closer in line with what we believe good writing to be, but it never seems to work out.
The final product may pass muster, but the process for creating that product prevents students from engaging with the kid of thinking which underpins all writing, a concern for the rhetorical situation, genre, and audience.
When writing instruction is merely a series of prescriptions, what happens when the writing-related problem shows up without any prescriptions? Not much that’s good.
I’ve fallen prey to prescriptive thinking many times during my teaching career. When you are in the midst of the semester, and you are confronted with reading 60 (or 80 or 120) pieces of student writing times six assignments, the incentive to make those assignments as good as possible is strong.
And so I would give students prescriptions. Use this structure, start this way, make sure to do this, or do that. Once you have a few years of teaching writing under your belt, the errors students are going to make become entirely predictable and so you can often head them off at the pass.
I thought I was shortening my students’ learning curve, doing them a service, but over time, I began to see that I wasn’t shortening the learning curve, I was short-circuiting their chances to have learning experiences which involved the kind of struggles they’d face when someone wasn’t around to give them the prescriptions.
I realized that when it comes to learning, going over some of the potholes on the way was more important than a smooth ride. https://www.insidehighered.com/blogs/just-visiting/against-shortcuts-and... In the short term, particularly early in the semester, this would result in inferior student products, as they made those mistakes I knew were coming, but didn’t want to prevent because they were truly shifting their mindsets about how writing was going to work now that prescriptions had been left behind.
To assuage my own worries and frustrations with their sometimes substandard product, I would ask myself if what I was doing in class was designed to help them in the days, months, years after our class, when the would be confronted with unfamiliar writing challenges.
If the choice was between a good grade on an single assignment, or having the chance to experience a failure which may cement a permanent lesson about writing on their psyches, I would do my best to choose the permanent lesson.
Unfortunately, this is not always possible. There are many structural impediments to privileging student learning (messy, unpredictable, time-consuming) over student performance (standardizable, scalable, efficient).
My attraction to prescription was significantly tied to my overwork. If I could narrow the field of what students could, or should do, it meant less work for me. When I realized that I was primarily focused on students replicating writing, rather than using writing as a tool for discovery and advancing and uncovering knowledge, I knew I needed to rethink my approach.
It now strikes me that replication of existing forms and knowledge is the equivalent of me being given the quadratic equation and told to “plug and chug.”
I may survive long enough to move up a class, but what have I learned?
 After graduate school, when I went to work for a survey research company, very quickly I had to become comfortable reasoning with numbers, which did involve some math, such as probabilities, standard deviations, and confidence intervals. I often wished I wasn’t starting from scratch on those concepts.
 The exception was sentence diagramming, which I’m not sure was prescriptive when it comes to writing, so much as just being its own thing. It was neither here nor there in my development as a writer and thinker.
 I used my third grade teacher Mrs. Goldman as my model