We have access now to chatbot level interfaces that can effectively solve all math homework at practically any level. As a math educator, you may be rethinking the role of homework as an assessment tool. As a parent you may also wonder on many levels the necessity of learning mathematics if there is a tool that will simply do it. And by “it” I mean both the mechanical work and the reasoning work.

We’ve seen the buzz: “Decades old math problem solved by AI”. Here’s one such example from OpenAI.

So what are we to do about these answer-getting machines?

Nothing. There is literally nothing to do. It’s answer-getting. As educators, our constant vigilance is to distinguish between learning and answer-getting. Sometimes they are the same thing, but usually they are separate matters.

Let me digress for a second and I will say a lot. So at the end of this article, is this message to you, dear reader: “If your particular situation as a parent, as an educator, or as a student needs some re-thinking and you want a human sounding board, get in touch.”

Calculators get computational answers, but the button pusher needs to know why they are pressing the buttons they are pressing. A homework exercise asking students to just compute will succumb to the calculator. We know this. We have always known this. Yet, we still have assessments on the times tables and our tens frames and long division and subtraction with carry. But we stop the manual computation requirement once we reach fractional exponentiation. What’s \(2^{0.58}\)? Who knows! Ask the calculator. But why do you need to compute \(2^{0.58}\)? The calculator doesn’t know. You had better.

What’s \(\sin(3.1\pi)\)? Who knows! Ask the calculator. But you had better know if your calculator is in radians or degrees setting. And why did you need to compute this thing?

We can do this all day and separate the utility of the calculator from the utility of the brain. This can extend to other answer-getting machines: Chegg, StackOverflow, Reddit, etc. [and those platforms, while being human-to-human answer-getting platforms, are suffering heavily because of the LLM chatbots ability to give localized, interactive, instantaneous answers]. The same with Wolfram Alpha which can also answer pretty much any computational math question that might show up in homework.

Coming back to AI, we have started to see bans on AI in the classroom. This won’t circumvent students from using AI at home. All policies, no matter how well-intentioned (or poorly-intentioned) will induce a black market of sorts. Answer-getting services have always been present in education, from the online services I mentioned, but also tutoring services that blur the line between paying for additional learning help versus paying for an answer-getting service. Now everyone has access to answer-getting and cheaply.

I invite you to think about this deeply about socio-structural imbalances prior to AI-democratization.

This still doesn’t help with what to do with your classroom, your students, or your own children.

I don’t particularly buy into the AI use = brain rot arguments that float around. I believe that AI use does lead to brain rot (yes, directly contradicting my previous sentence), but this is not the boogeyman. Calculator use leads to brain rot. Answer-getting machines, as a category, lead to brain rot. This phenomenon is not localized to LLMs. Math teachers know this. They have always known this. The brain rot is a personal choice. You can choose to learn the solution provide or pass the solution along [I believe the vernacular du jour is “meat proxy”].

Formal classroom assessments on mechanics have always been a (strong) proxy for whether or not students have learned, not whether or not students have access to answer-getting machines.

For me, when I cut through a lot of this, the reaction to AI and the classroom is first about the challenges to assessment. Some of these assessments, never really measured learning. They measured seat time (some homework, for example). We want our kids to learn. And shocking as it might be, answer-getting is a proper life skill. Both are needed, but answer-getting needs for the recipient to have a strong sense of smell. Does this answer make sense? Does it pass the sniff test? Answer-getting is downstream of learning.

With all this tedious bloviating, what I’m getting at is this: if we want our students to learn mathematics, we need to instill strong foundations in mechanics and in reasoning. This is not some new revelation. This is a basic fact of learning anything, not just mathematics. But what we do in our classroom and how we do it has to change.

Here’s how

• Ungraded homework
• More in-class mechanical practice
• More in-class discussion and discourse
• Formal assessments can have some variety depending on the class. Nothing wrong with quick, weekly assessments nor is there anything wrong with just 3 or 4 exams for the marking period / semester.
• My only twist and long-expressed desire is that learning assessment not be an average of how “on time” a student was with learning, but rather it be a measurement of their latest state. Starting at an F and moving to an A by the end of the course should yield something closer to an A not a C. And moving from an A to an F should yield something closer to an F not a C [many nuances here, so don’t take me literally].

Why ungraded homework? It never should have been graded in the first place! I’m talking about mathematics where a lot of the homework is about answer getting. If we were talking about, say, an Analysis class and the homework assignment is to prove or disprove the irrationality of \(\sqrt{2}\) and a student gets that solution via AI (I mean for this problem you can probably just do the old fashioned internet query via a search engine and get to some math website with a full proof, so it’s not really an AI problem), the assessment is still something that can be done via a pen-paper exam.

I would much prefer that when we have to do mechanical work for our mathematics course, we do a ton of it in the classroom. We should index more heavily on separating the “how” and the “why” in our material. Offload more “why” to at-home thinking. Do more “how” in the classroom.

If your students can get the “why” from AI [and they can], so be it. The in-class assessment of if they understood the why is a conversation. It’s a problem put forth for pen and paper. Do the measurements in the classroom.

Take home exams or any take home assessment at this point is willful stupidity. Don’t do it.

The incentives for students are points. Broadly speaking, learning if it happens is a happy consequence for a student, but they prioritize points. For the teacher, making sure students learn is the goal and we end up in this weird divergence of incentives and behaviors. Quantitative measurement of learning, from the student’s perspective is about point-getting which incentives answer-getting if the assessments are about answer-getting. If the at-home assessments and assignments become informal, then the “threat” of the formal in-class assessment is the alignment between measuring learning (teacher priority) and point-getting (student priority).

So what about the classroom itself? Mechanical stuff is teacher-led with examples and discussion. Then shift to students doing problem sets. Let them work with each other. Let them present their solutions on the board. Let them be confused. Let them figure out how to answer-get from peers and from the teacher. Given them the answer, then give them more problems. Let them self-assess.

Let them raise their hand and say they are ready to be assessed. And yeah, you’re going to yell at me and say, “how? I can’t have 30 students have their own timeline for when they want to take an exam / quiz.” And I’m going to say, it can be done and it doesn’t have to be chaotic nor does it have to be so free that, you, the teacher have lost any semblance of order.

Here’s how.

Have an “exam week”. Everyone is going to take exams that week. Say you meet three times a week. Well, we’re going to take three exams on the same topic. The questions can vary or you can keep them the same. It doesn’t matter. Some will do well on their first try. Some [many] will do poorly. Wake up call! Give them another chance.

Is it more “work”? Maybe? But you, the teacher, are shifting your grading burden to this and removing it from all the prior stuff [no graded homework, no nonsense worksheets that need formal grading or rubrics]. Net-net, it’s probably the same, just a bit more concentrated. But really, you can ask the student if they want that exam graded or if they will take the next one. A student may want all their exams graded. Some will just say, “don’t bother, I’ll try again next time”.

I would use all of this to rethink the math classroom and its practices significantly and you will find that AI’s influence was always about answer-getting and you will impress on your students that only they can think for themselves.

Finally, I have MUCH more to say and I will keep writing on this. If your particular situation as a parent, as an educator, or as a student needs some re-thinking and you want a human sounding board, get in touch.