One of the strangest features of contemporary higher education is its false egalitarianism. Teachers and students, by definition, are not equals with respect to the practice in which they are engaged, though of course they may be equals in other respects. If the student were on the same level as the teacher, he wouldn’t need her to teach him. The practice of education is essentially hierarchical. This hierarchy is built into our institutions, but it sits uncomfortably with our rhetoric.
In the academy, “hierarchy” is always a word of opprobrium, and faculty are very fond of emphasizing “how much our students have to teach us.” The irony of professors teaching students that all hierarchies are bad is not much acknowledged, except by some who prefer the equally wrongheaded view that all hierarchies are good.
While some militantly traditionalist institutions may lean toward that other extreme, most Christian universities today are no less susceptible than their secular counterparts to the rhetoric of false egalitarianism. We may even be especially vulnerable to it; since we have faith that in Christ there is neither Jew nor Greek, we might be tempted to imagine that in Christ-centered institutions there ought to be neither teacher nor student.
None of this is about classroom style, by the way; my own is casual and friendly. I’m not strict, I don’t dress up, and I don’t require my students to address me as “Doctor.” It’s about how we understand what it is we’re doing when we’re teaching, regardless of how we teach.
Nor is it a political statement. I happen to oppose many of the hierarchies that structure our current world, including the one that ruthlessly sorts society into college-educated winners and uncredentialed losers while the people who do the sorting talk incessantly about toppling hierarchies. And I’m not interested in returning to the explicit hierarchies of race or gender that attract certain reactionaries.
But that’s beside the point, which is about explicitly acknowledging the necessity of this hierarchy. My purpose in making this point, however, is not to insist on the general principle that education depends on the inequality between teacher and student. It is to suggest that if we recovered that principle, we might be able to grapple more confidently with the particular challenges to education posed by the new digital technologies misleadingly known as “AI.”
Consider first a humbler piece of technology. Boosters love to compare LLMs to the calculator, which in its day provoked similar outcries about cheating and brain-rot, but was quickly accepted and incorporated into daily life, and is now ubiquitous. The booster argues that programs like ChatGPT and Claude are no different, and that if we learn from the calculator’s history, we can move more past these wasteful phases of shock, anger, and grief toward those of acceptance and celebration.
The problem for the boosters is that their analogy is too accurate. The concern about calculators was and is that, because they make it possible for anyone to get the right answer without going through the process that delivers it, these devices can prevent students from building an actual understanding of mathematics, which is not a collection of answers to be possessed, but a structure of logical relations to be grasped and further developed.
This concern was valid from the start and still is today. Calculators do have this effect,1 and there is a long-running debate about when, whether, and how they should be used in classrooms. Opinions vary, but almost no one thinks they should be used willy-nilly, without regard for stages of development. One math professor at my institution still does not allow them in her classroom.
The real lesson of the calculator is not that tools are good when they speed up the process of producing results, full stop. It is that such tools are good for some people and not for others. A mathematician can use a calculator without harming her mind because she has already developed a mind that understands what the calculator is doing. She can safely offload the work of calculating to the machine, which enables her to do other work.
That is precisely what a beginning math student should not do. If at this stage the student offloads his work to a machine, he will not develop the kind of mind that is capable of using the machine without being harmed by it. If we aim to become capable of using the machine without being diminished by it, we must not use the machine until we are ready.
Call this the Calculator Principle. The Calculator Principle suggests that the question is not what machine I use, or whether or not I use it, but when I use it, which is to say, who I am when I use it. Whether its use aids or hinders my development depends on how far I have already developed. Teachers and students are at different stages in a process. There are certainly exceptions, and real education attends to individual differences that may well escape institutional roles. Some students are further along intellectually than some professors. But that only bolsters the point that the teacher-student relation is not one of equality and must not be mistaken for one.
The Calculator Principle should help us as we try to discern use-cases for LLMs in higher education. What is permissible for professors may well not be permissible for students, and we should be able to state this plainly. The Calculator Principle won’t resolve every disagreement, but it can promote more nuanced arguments. For example, I think it’s obviously bad for a student if they use an LLM to summarize a course text instead of reading the text itself. Would it also be bad for a professor who’s read that text multiple times to use such a summary while preparing her lecture? Regardless of your answer, it certainly wouldn’t be the same as when the student does it. That difference should make a difference in our conversation.
It might not be so difficult to think through the promises and perils of these tools if we were not so beholden, consciously or unconsciously, to the rhetoric of false egalitarianism. If we started by acknowledging that teachers and students stand at different points on a developmental path (which is the relevant distinction between them – not “intelligence”), it would become much easier to say frankly that what’s ok for one is not ok for another. And in many cases, that is exactly what needs to be said.
I agree that recapturing the explicit differences in the teacher/student role is important in any serious discussion about academics. The Calculator Principle, however, is a bit misleading when it comes to writing. The challenge of producing and structuring language is fundamentally different from the use of a calculator to add, subtract, multiply, and divide. The primary difference is the much greater degree of nuance and difference adhering to and within language and its rhetorical contexts vs. the more stable “meanings” numbers have in most mathematical contexts. I would also add that as someone who is a very experienced writer, writing continues to be very hard, challenging work for me. I can’t imagine that math problems are so challenging for a math professor who has learned all the functions; but a writing professor, with years of experience, still grapples with all the nuance of language, context, audience each time she/he sits down to write.
Thanks for the piece, Adam. Rescuing the value of good hierarchy is a noble task inside and outside of the classroom, not to mention being honest about its omnipresence. Great line: “I happen to oppose many of the hierarchies that structure our current world, including the one that ruthlessly sorts society into college-educated winners and uncredentialed losers while the people who do the sorting talk incessantly about toppling hierarchies.”
I also agree with the previous comment, however, that a calculator is not ultimately analogous to LLM AI. Your point is salutary – Wikipedia is another good example of something that is very helpful if you know enough to recognize mistakes (which are very rare on straightforward facts) – but calculators or Excel basically do objective calculations 1000x faster than humans. The answer to the calculation is simply right full stop. But generative AI produces “original” content (scraped from others) from a mindless program with no conception of truth, goodness, or beauty. There is a difference in kind with calculators, Excel, and anything published by a human. And the industry incentives not to ask the fundamental “whether” question are a major problem, in my mind. As educators it seems like we have lead our students and ourselves to question whether outsourcing our thought and speech – what makes us human – to unaccountable tech lords and mindless market-driven bots has basic problems. You can see where I stand 🙂
Thanks again!
Thanks to you both for your comments. I certainly (and strongly!) agree that numbers are different from words, and that calculators are different from generative AI. But the analogy that leads to the “Calculator Principle” is about the use of the tool, not what the tool does when it is used. Just because there are objective answers to the kinds of questions that a calculator answers (as opposed to the kinds of questions that an LLM answers) doesn’t mean that it’s less damaging for a beginning math student to use a calculator than for a beginning writer to use an LLM. I think the damage is the same in both cases, because in both cases we are supposed to be learning a process — even if the processes of working with numbers and working with words are very different. The point here is that if you use the tool too early, you fail to learn the process, whatever the process may be.