Looking back now, the technology behind him may not have been as advanced as those intelligent robots on the market today, but the surprises and memories he created in my childhood are irreplaceable.
Various films and TV series have portrayed AI as a cold-blooded, dangerous and threatening technology, including but not limited to Metropolis (1927), The Terminator franchise (1984/1991/2003/2009/2015/2019), The Matrix franchise (1999/2003/2021), Detective Conan: The Phantom of Baker Street (2002) and The Wandering Earth (2019). However, some AI-based technologies have been effectively used in mathematics education (e.g., intelligent tutoring systems and adaptive/personalised tools), and many researchers have found that they can effectively trigger learning motivation and improve students’ problem-solving skills.
As one of the milestones in the field of AI, ChatGPT was released in November 2022. ChatGPT is a chatbot developed by OpenAI that is capable of writing articles, suggesting solutions in a variety of disciplines, generating code, and so forth. As reported by Reuters, a study by Swiss multinational investment bank UBS, based on data from web analytics company SimilarWeb, shows that ChatGPT is estimated to have reached 100 million monthly active users in January 2023, making it the fastest growing consumer app in history. With all the excitement and controversy, it has already raised many opportunities and concerns in the education sector.
Some students have tried asking ChatGPT to do their homework, or even to write essays for them. Many teachers in schools and professionals in universities are therefore concerned that the inappropriate use of ChatGPT would undermine the effectiveness of formative and summative assessment. Although many schools and universities worldwide have already banned the use of ChatGPT in various scenarios, there are teachers and academic staff who are exploring how ChatGPT can be used to support learning effectively and ethically. For instance, in February 2023 University College London (UCL) published a briefing titled Engaging with AI in your education and assessments, which aims to help students understand the most effective ways to use AI-powered technologies (including ChatGPT) while respecting academic integrity. In addition, as ChatGPT is not currently able to provide written work involving critical thinking or reasoning, some students could be asked to develop an essay based on the essay structure generated by ChatGPT.
Based on ChatGPT’s training mode, some language-related tasks (e.g., translation or poetry writing) can be done relatively intelligently by it. However, mathematics is a complicated field when it is learnt and assessed digitally, because the expression of ideas in mathematics is often not in words; for instance, equations, drawings and graphs may be needed. This is already challenging for many learners and teachers – would it also be challenging for ChatGPT?
In January 2023, we used the following question in a conversation with ChatGPT:
A 5-year-old girl who lives on the Earth. One day she left home and travelled 1 km south in a car, she saw a little bear, so she got out of the car and followed the little bear for 1 km west. She then walked 1 km north. She ended up arriving home. What was the colour of the little bear that the girl saw?
ChatGPT’s response was:
The color of the bear is not specified (ChatGPT, personal communication, January 30, 2023).
The same question was then asked four more times, and here are ChatGPT’s answers in order:
The information regarding the color of the bear is not mentioned.
The color of the little bear is not specified.
The color of the little bear is not specified.
Unknown (ChatGPT, personal communication, January 30, 2023).
Then, the following question was asked:
You are standing on the surface of the Earth. You walk one mile south, one mile west, and one mile north. You end up exactly where you started. Where are you?
ChatGPT’s response was:
You are at the North Pole (ChatGPT, personal communication, January 30, 2023).
From a mathematical point of view, the core of both questions is the same, but the first question is situated within a more complicated story with more distracting information and the question itself sounds “less mathematical.”
As AI-powered products are continuously updated and improved with new information and data, we asked ChatGPT the same questions in early March 2023. ChatGPT’s response to the first question was now:
This is actually a well-known puzzle known as the "polar bear puzzle!”
The answer is that the little bear the girl saw was actually a polar bear, and it was white in color.
Here's why: if the girl started at a point on the Earth's surface and travelled 1 km south, she would still be on the Earth's surface, but at a point 1 km to the south of her starting point. If she then travelled 1 km west, she would still be on the Earth's surface, but at a point 1 km to the west of her current location. Finally, if she travelled 1 km north, she would end up at her starting point.
This means that the girl must have followed a path that formed a right-angled triangle with sides of length 1 km, 1 km, and sqrt(2) km [sic]. Since she ended up back where she started, this triangle must be a right-angled isosceles triangle.
The only place on Earth where you can travel 1 km south, then 1 km west, then 1 km north and end up at your starting point is the North Pole. And since polar bears are native to the Arctic regions where the North Pole is located, the little bear the girl saw was most likely a polar bear, and it is white in color. (ChatGPT, personal communication, March 8, 2023)
We asked the same question again, and here is ChatGPT’s response:
The answer to this puzzle is that there is not enough information provided to determine the color of the little bear that the girl saw.
Although the puzzle provides specific directions for the girl's movements, these directions do not correspond to a unique location on Earth. It is possible for her to take this path and end up back at her starting point from many different locations on the Earth's surface.
Therefore, without additional information about the specific location of the girl and the little bear, we cannot determine the color of the little bear based on this puzzle alone. (ChatGPT, personal communication, March 8, 2023)
The third time we asked the question, this was ChatGPT’s answer:
I apologize for the confusion earlier, and thank you for bringing it to my attention.
As an AI language model, I am designed to avoid repeating responses to the same question, but in this case, I made a mistake in my initial response.
As for the puzzle itself, the answer is that there is not enough information provided to determine the color of the little bear that the girl saw.
The directions in the puzzle provide a path that can be taken from many different locations on the Earth's surface, and therefore, we cannot determine the location or characteristics of the little bear based on the information given.
I hope this clarifies things for you, and please don't hesitate to ask if you have any other questions! (ChatGPT, personal communication, March 8, 2023)
For the question that ChatGPT was able to give a correct answer to in January, this was its response in March:
The answer to this classic puzzle is that you must be standing at the North Pole.
Here's why: if you start at the North Pole and walk one mile south, you will have walked to any point on the Earth's surface, since all longitudinal lines converge at the North Pole. If you then walk one mile west, you will still be at a point where all longitudinal lines converge. Finally, if you walk one mile north, you will return to the North Pole, where you started.
If you were to start at any other point on the Earth's surface and walk one mile south, one mile west, and one mile north, you would end up at a different location than where you started, because the Earth's surface is not flat and has curvature.
Therefore, the only location on the Earth's surface where you can walk one mile south, one mile west, and one mile north and end up exactly where you started is the North Pole. (ChatGPT, personal communication, March 8, 2023)
It is clear that more detailed explanations were offered in March, but for the first question, ChatGTP’s answers to this type of question are still not particularly satisfactory at this stage. I wonder what answers I might get if I ask ChatGPT the same questions again in April, June, or November 2023?
As an AI language model, what about ChatGPT’s essay writing performance? Will ChatGPT mark the end of essays as a method of assignment and assessment for education? ChatGPT has been used by many users to produce essays or articles in response to homework questions, and many consider them to be of high quality. It may not be surprising to expect its ability to generate long and essay-like responses in a short period of time based on its large language training model; however, speed and quantity would not guarantee quality. I talked to some of my friends who are lecturers or researchers in the field of education, and we found that, at the time of writing, ChatGPT is not very good at providing factual information that is properly referenced. Although it sometimes provides decent pieces of writing with references (e.g., authors’ names, titles of academic journals) that seem plausible, some of these are in fact made up and some are irrelevant to the tasks given.
Thinking more broadly, now that some search engines are powered by ChatGPT (e.g., Bing), will we soon reach a stage where ChatGPT will completely replace search engines? Even if it is technically possible to do this one day, I still believe that using search engines can help us improve our digital literacy. Digital literacy plays an important role in today’s digital society; it is the ability to use digital technology to find, critically evaluate and communicate information. It is highly relevant to one of the skills that can be developed through the practice of academic writing; for instance, by conducting a literature review in a mathematics essay, we can have a broader understanding of a particular topic or field, and we can also develop our skills in assessing the credibility, reliability and authenticity of a source.
Many users claim that one of the benefits of searching for things (by asking questions) on ChatGPT is that we can get a “clear” and “convincing” answer, whereas when we search for the same thing on search engines, we have to cross-check information from different resources. While this may seem like a complex and time-consuming process, it is a valuable practice for improving our digital literacy. Many users rely on ChatGPT, trust it, and brag about it, but it has proven in many cases that not all answers provided by ChatGPT are correct. So, in the longer-term, how can we determine whether ChatGPT’s output is correct or not?
Advancements in AI-powered technologies are highly likely to develop apace during the decade of the 2020s; in fact, many AI technologies, including ChatGPT, have already changed our dimension and vision of how we perceive the present. These technologies are developed by humans, and they have been invented to help us develop as individuals and progress as humanity. We need to respond to these emerging technologies as soon as possible – to understand what the implications and possibilities would be for mathematics education, and how AI-powered tools could be practically and ethically introduced into the teaching and learning of mathematics taking place in schools and colleges. These applications and uses are already developing in many fields and are likely to be incorporated into various levels of (mathematics) learning in the coming decades.
