Technology and Math Education: ChatGPT is here—now what?
Dr. Carrie Diaz Eaton
ChatGPT can be a valuable tool for mathematics teachers, particularly when it comes to generating practice problems and examples for students. By training ChatGPT on a set of math problems or concepts, teachers can quickly and easily generate new and similar problems for students to work on or explanations and examples to enhance their understanding. This can be especially beneficial for teachers looking to provide their students with additional practice opportunities or create engaging and effective lesson plans.
However, it's important to note that ChatGPT is a language model and not a subject matter expert. Therefore, teachers should always review and fact-check the information generated by the model and students should not consider the information generated by ChatGPT to be authoritative. Additionally, while ChatGPT can generate practice problems and examples, it cannot provide the human interaction and feedback that is necessary for true understanding of mathematical concepts. As a teacher, it's always important to keep in mind that the information provided by ChatGPT is a tool and should be used in conjunction with other methods such as classroom instruction, textbooks, or personal interaction with a teacher.
Are you convinced? If you are even slightly intrigued, I submit the above to you as the possibility of ChatGPT, a chatbot built on language models trained from billions of texts through documents and interactions. OpenAI released ChatGPT as a prototype for public use and training in November 2022. The first two paragraphs in this blog were written by Chat GPT in response to the following prompt:
“Write me one paragraph for teachers about how ChatGPT can be used in helpful ways in mathematics courses and one paragraph about what caveats students and teachers should be aware of. Write it in the style of Carrie Diaz Eaton.”
I have been involved in conversations about ChatGPT because of my position in a digital and computational studies department and in the context of the data science research groups I am working with during my sabbatical. To be honest, my first feelings about ChatGPT are actually shared well by the OpenAI CEO. Math education has been challenged by calculators, by Google, by homework and notes sharing platforms, by WolframAlpha, and more. This is another moment for us to think about how we want to adapt our instruction in light of an ever-changing landscape.
My challenge to you is to consider whether your response to ChatGPT is reflective of your core educational philosophies. I reject a binary that suggests all or nothing, and suggest that there may be times for each. There is a time to teach arithmetic without calculators. There is also a time to assume that calculators exist and use them to help students focus on higher level thinking. I worry that the emphasis of some conversations on ChatGPT in education is on the policing of students instead of how to help students scaffold their work. Artificial intelligence detection algorithms have false positives and false negatives which suggests we refrain from overdependence. As we continue to test the system for vulnerabilities, we are now in a potential arms race between chatbots and AI detectors.
One early example of a failure of ChatGPT to do math was in a prompt to provide a proof for the irrationality of the square root of 2. I gave ChatGPT the same prompt, and it created a similarly flawed proof. However, I responded by telling ChatGPT where the proof was wrong. Each time, it responded with an apology and a corrected proof. After three corrections, it produced the following:
A correct way to prove the irrationality of the square root of 2 is by proof by contradiction. Assume that the square root of 2 is a rational number and can be expressed as a ratio of two integers, a/b. Then, squaring both sides of this equation, we get:
(sqrt(2))^2 = a^2 / b^2
Which simplifies to:
2 = a^2 / b^2
This implies that a^2 = 2b^2, which means that a^2 is an even number. However, by assumption, a and b have no common factors other than 1, which means that b is an odd number. Since the product of two integers with no common factors other than 1 is always odd, it follows that a must also be odd.
However, we know that a is the square root of an even number, a^2. This means that a is the square root of an even number but it is also an odd number which is a contradiction. Therefore, the assumption that the square root of 2 is a rational number must be false, and we can conclude that the square root of 2 is an irrational number.
I suggest that this is an excellent assignment for a student who is learning to critique proofs. Here is an example where interacting with ChatGPT could be a meaningful and fun learning experience for students.
Which leads me to my most important point: what are we teaching in our classrooms, in our colleges and universities? When ChatGPT can write a few paragraphs, can suggest incorrect proofs and correct them into proper proofs, and more, are we teaching students how to imitate, how to do rote computation, or are we teaching students to analyze, question, and critique? Is ChatGPT an opportunity for us to remember the liberal arts traditions of mathematics?
A colleague of mine asked ChatGPT to write a poem about a mathematician. It was an excellent poem—all referencing the mathematician as “he.” I suggest here is another point at which we should be ready to critique. If we embrace the tools that AI is delivering, we need to make sure we are preparing the next generation of students to critique these tools. The conversation I started with my colleague prompted others to re-add Weapons of Math Destruction to their reading list. Already publishers are chiming in with their own professional guidelines for use.
Our mathematics communities should also have ongoing conversations about our professional values, ethics, and responsibilities in this rapidly changing landscape.
I close with this message, also authored by ChatGPT, as queried by my colleague, Sam Hansen, a mathematics librarian, and podcaster. They asked Chat GPT to write about the intersections of mathematics and humanity in the style of themself.
Mathematics is often thought of as a cold and abstract field, disconnected from the messy complexities of human experience. But the truth is that mathematics is deeply intertwined with our humanity. From the earliest counting systems of ancient civilizations to the cutting-edge theories of modern physics, mathematics has been a tool that humans have used to make sense of the world around us. It is a way for us to find patterns, to understand relationships, and to make predictions about the future. But perhaps most importantly, mathematics is a way for us to connect with one another, to share our understanding of the universe and to build on the knowledge of those who have come before us. In this sense, mathematics is not just a subject to be studied, but a reflection of our humanity itself.
Carrie Diaz Eaton is an Associate Professor of Digital and Computation Studies at Bates College and a visiting researcher at the Institute for Mathematical and Statistical Innovation at the University of Chicago.