I am trying to think about use of LLMs in education as similar to calculators. This post reflects how I was taught: students couldn’t use calculators to solve problems initially. For example, no calculators to do addition and subtraction when you’re learning to add or subtract. But also, probably not when learning to multiply or divide. Doing addition and subtraction builds skills and intuition for what multiplication and division are. The same is true with understanding fractions.
Moving up the math hierarchy to algebra, though, this changes. Algebra is at first about the concept of solving equations, and the core idea is that “to solve the equation, you can do whatever you want to one side, as long as you do it to the other.” The mechanics of addition or subtraction, for the most part, no longer matter. Go ahead and use a calculator to solve obscure divisions and multiplications so you can better understand algebra (though it feels appropriate to note that a student who is good at arithmetic can still outpace a calculator for problems that are likely to be used pedagogically, since the numbers are easy).
In this example, algebra is to calculus what arithmetic is to algebra. A calculus teacher cares little if his students can solve equations; he expects they can. They’re instead learning integrals and derivatives and series, and I doubt a calculus teacher would begrudge their students using a calculator to solve a difficult equation.
The problems with treating LLMs this way are many. They are not calculators. You cannot (trivially, or maybe at all) understand how an LLM works. You cannot (trivially) fact check it if it spits out an absurd-sounding answer. You cannot limit the LLM to what your own, personal abilities to trivially do are. We need AI that cites sources, so we can debug when it’s wrong. We need understandable AI for the same reason, not the obscure black boxes we have today. We need AIs that not only can solve our problems, but that can also help us to solve our own problems. When we have those things, AI will be much more useful for education and for widespread use.
Moving up the math hierarchy to algebra, though, this changes. Algebra is at first about the concept of solving equations, and the core idea is that “to solve the equation, you can do whatever you want to one side, as long as you do it to the other.” The mechanics of addition or subtraction, for the most part, no longer matter. Go ahead and use a calculator to solve obscure divisions and multiplications so you can better understand algebra (though it feels appropriate to note that a student who is good at arithmetic can still outpace a calculator for problems that are likely to be used pedagogically, since the numbers are easy).
In this example, algebra is to calculus what arithmetic is to algebra. A calculus teacher cares little if his students can solve equations; he expects they can. They’re instead learning integrals and derivatives and series, and I doubt a calculus teacher would begrudge their students using a calculator to solve a difficult equation.
The problems with treating LLMs this way are many. They are not calculators. You cannot (trivially, or maybe at all) understand how an LLM works. You cannot (trivially) fact check it if it spits out an absurd-sounding answer. You cannot limit the LLM to what your own, personal abilities to trivially do are. We need AI that cites sources, so we can debug when it’s wrong. We need understandable AI for the same reason, not the obscure black boxes we have today. We need AIs that not only can solve our problems, but that can also help us to solve our own problems. When we have those things, AI will be much more useful for education and for widespread use.