Artificial Intelligence (AI) is here to stay. Academics should embrace the excitement around it and explore its potential and many possibilities while incorporating it into the learning and teaching of mathematics.
So said Dr Anita Campbell (left), senior lecturer at the University of Cape Town, specialising in the teaching of first-year mathematics students, at the last 2023 meeting of the Community of Practice for the Teaching and Learning of Mathematics (TLM CoP) on 1 November. The TLM CoP is one of numerous communities of practice of Universities South Africa (USAf).
Speaking to the topic Using AI to enhance your Teaching and Research, Dr Campbell said: “AI has exploded, and it is so exciting. I encourage you all to “dabble” in AI. It can become overwhelming because there’s so much to learn, but try and embrace the excitement, in light of the possibilities.”
She identified ChatGPT as the biggest game changer, accessible by subscription at https://chat.openai.com/. She said she was using version 3.5, adding that “even as we speak, they are developing newer versions that will let you do many more powerful things”.
Wikipedia definition: ChatGPT, which stands for Chat Generative Pre-trained Transformer, is a large language model-based chatbot developed by OpenAI and launched on November 30, 2022. It enables users to refine and steer a conversation towards a desired length, format, style, level of detail, and language.
Admitting that ChatGPT was not good at mathematics, Dr Campbell said it was a matter of time before the AI tool was able to reliably do maths as well. She said even though she had thus far accessed the AI tools completely freely, she would probably soon “succumb and pay for use because of how these things can change my life.”
She then illustrated ChatGPT’s usefulness. “You’re about to teach a course on something you haven’t looked at for a long time. You ask ChatGTP what you need to know to teach this, and how to engage your audience and it will provide options. It’s very good if you already have baseline knowledge. If you already know the content, it’s useful for getting ideas and moving it forward faster. However, if you’re learning something brand new, you have no way to tell if it’s lying.
“If you’re teaching a section, give it a blob of your course handouts, your textbooks, even your notes and ask it for whatever you need – a hook to introduce a section, multiple choice questions to check baseline understanding, a summary of common misconceptions on the topic. Pop your PDF into ChatPDF.com (another tool) and it prompts you, asking what you want to know. You can add your own questions to quickly interrogate the PDF document.”
Dr Campbell said the AI tool was useful for keeping people on track and aligned with their lesson goals.
“If you’re going to teach something and it feels a little bland – like, why do my students need to know how to work out a 3×3 pre determinant – you can get very nice hooks to draw students in. You can also set questions that are specific to your students or to current affairs.”
“It’s useful at the end of a class when you need a quick question, a calculation based on something you did in that class. You can get students to be connected, to engage and give them confidence.”
“Ask ChatGPT how best to use the next 5 hours for maximum effect within your budget constraints. Or get a lesson plan for 180 hours of teaching and learning where you provide information of what it is you need and the AI tool works out optimum timelines.
Dr Campbell said that ChatGPT was not good at maths yet because it has no logical reasoning. This is because it is a large language model scanning probabilistic answers to respond to questions. It draws on existing data – the more the data improves, the better its responses.
For Maths, she named a trustworthy, useful tool, WolframAlpha, adding, however, that it was not good with prompts.
“Combine the two using ChatGPT to translate a prompt into one WolframAlpha can understand. A ChatGPT paid subscription has a plugin for WolframAlpha that does that. Then, to answer a maths question it searches through WolframAlpha and gives a reliable answer.
WolframAlpha is an answer engine developed by Wolfram Research. It answers factual queries by computing answers from externally sourced data. WolframAlpha was released on May 18, 2009, and is based on Wolfram’s earlier product Wolfram Mathematica, a technical computing platform.
Chatbots as tutors
She said studies showed that one-to-one tutoring improves performance by two standard deviations, potentially turning average students into high achievers, and failing students to passing ones. The chatbot is a tutor in your pocket – the Khan Academy are developing one called Khanmigo (not yet available in South Africa). “In response to asking for an answer, it asks questions to help you learn rather than just providing answers. The caveat is until you can trust them, they don’t always give the right answers.”
Khan Academy is an American non-profit educational organisation whose goal is to create online tools that help educate students. The organisation produces short lessons in the form of videos. Its website also includes supplementary practice exercises and materials for educators.
She shared these video links for information
www.youtube.com/watch?v=w-GiUY-DcJY Andy Stapleton EPIC ChatGPT Prompts for Research on Bing in Microsoft Edge
www.youtube.com/watch?v=wBe53TE1EhE Andy Stapleton Researcher App Untools, Flourish, My bib, Paperity, paper pal. Biorender.
www.youtube.com/watch?v=tzx3MGIOwVo Dr Amina Yonis 5 Hottest free AI Tools for Research that are actually useful
“I was complaining about horrible author guidelines in a journal, so I successfully asked ChatGPT to simplify the instructions.
“In my differential calculus class, I needed to work on problems to do with related rates and optimizing. I asked my students to create a question using ChatGPT on optimizing set in Cape Town with a soccer ball using calculus.”
She said the Prompt was crucial, underlining the importance of how to phrase questions.
While ChatGPT might not be good for finding answers, Dr Campbell said it was useful for teaching.
“I’ve set test questions where I ask students if ithe answer from ChatGPT is correct, and if not, what was wrong with it. To be specific I say: Identify what is wrong with it.”
When you get a response from ChatGPT that seems strange, I might reply, “Hmm, are you sure?” Or ask it to explain that answer. You converse with it.”
She said research related tools like Elicit.org “will do a literature review for you and find papers and extract data,” adding that Perplexity.AI – a favourite – included references to a websites as well as journal articles.
Comment by Professor Stanford Shateyi, University of Venda’s Department of Maths and Applied Mathematics: After a discussion in our department, we wondered if, with ChatCPT, we still need to give mathematics students assignments if they can get AI to provide answers.
Dr Campbell: With the Photomath app, you hover your phone over the question and it provides solutions with steps. You know students are using this for assignments when their result is 100% but they fail tests/exams. You have to teach students how to use these tools, but what good is it to them if they don’t understand the principle and can’t adapt when technology adapts? The reason maths is valuable is that it trains you to think. Our job is to convince students to improve themselves.
My view is that these tools exist: you must use them to make ourselves better.
Comment and question by TLM CoP Deputy Chair, Professor Chuene, Senior Lecturer at the University of Limpopo: As maths teachers we shouldn’t shy away from the fact that our students may copy but we should find a way of saying, I will allow your answer, but tell me why you think that answer is correct and explain how you got there.
Also, could you take us through some of the assessments you do. Regarding the formative aspect, what does that mean for your summative assessment?
Dr Campbell: I have a class of less than 100, so my numbers are manageable for me to try out things that would be much harder to do in larger classes. I’ve had students do peer reviews where they have to make a video if they don’t want to talk – using any tools as long as I can be sure that THEY made the video and it had THEIR voice.
But, you can go into ChatGPT to write you a script to explain the question or answer, so you can also fake your knowledge in a video. If the student goes to those lengths, they will be very good at acting or they will pick up a bit of maths along the way. Having multiple ways of assessing is useful: one of my project accounts for 10% of my class record. 50% of the final grade comes from students writing a three-hour exam with pen and paper.
Question by Ms Janet Van Rhyn, USAf Project Manager: Operations and Sector Support: ChatGPT is relatively new. What will happen down the line when more of these are integrated and become easier to use? I don’t know how we are going to manage the use ethically in the learning space. I have a lot of questions! I was recently doing a search on certain authors around a topic for research we were doing and when I went to find a paper, it said it didn’t exist. We have to ask if all the information being received is trustworthy.
Charmain Naidoo is a contract writer for Universities South Africa.