Teaching Math to My Artificial Intelligence Assistant

Instead of teaching how to solve mathematics exercises, we must assume the responsibility of being an expert in didactic mathematics teaching. Change our way of questioning, asking, raising the levels of response production, and promoting argumentation and critical analysis.

Teaching Math to My Artificial Intelligence Assistant
Reading time 9 minutes

In this article, I would like to share some reflections on the potential of Artificial Intelligence (AI) in Education. I took on the task of comparing some of the everyday practices of our current educational system using BearlyAi. This ChatGPT AI assistant helps create content in different formats, such as text and video. There are already several AI-based virtual assistants in the market that we can use; the main competitors are Microsoft’s Copilot, Google’s Bard, and Open AI’s ChatGPT. Some more specialized chatbots (check here) are among the Top AI Chatbots on the market (Hines, 2023). Some are free, and others offer fee plans. However, for this experience, I wanted to explore BearlyAi to put into practice some educational activities, which I share with you below.

Whether you are new to using AI tools or already have experience, it is worth remembering that we must be critical and question the information this type of tool produces. It should never be our only source of consultation because the information can be wrong. The basic idea of an AI-based chatbot is that the more it is used, the more it learns. However, what does it mean for a chatbot to learn? Can BearlyAi learn? Regarding this question, BearlyAI itself responds:

“I am an artificial intelligence assistant based on ChatGPT, fed with a lot of data and pre-trained language models. I cannot “learn” in the traditional sense, as a human being would. However, as I interact with users and receive new information, I adjust my responses and improve my performance in the quality and accuracy of the answers I provide. So, in a sense, I can “learn,” meaning improving my communication effectiveness as I gain more experience.”

Thus, BearlyAI tells us that it does not know everything but that the effectiveness of its responses will improve as it gets more interactions and “experience.”

AI tools as educational assistants?

To explore the usefulness of BearlyAI in my teaching activities as a math teacher, I asked a couple of questions where artificial intelligence failed, which gave me the wrong answers. I presented two elementary-level math problems:

  • What is the smallest number made up of 4 different non-consecutive digits? Children with knowledge of the value of the position of digits up to the unit of a thousand can respond (third-grade elementary school students, 9 to 10 years old).
  • What is the smallest odd multiple of 81? To solve this problem, children must know the multiple (sixth-grade elementary students, 11-12 years old).

In the first question, BearlyAI made a mistake four times. After each wrong answer, BearlyAI indicated the reason for its error and improved its argument. Here is the summary of our conversation:

BearlyAI: “The smallest number made up of 4 different non-consecutive digits is 0123.”

ME: “No, it can’t be 0123 because the digits are consecutive.”

BearlyAI:  “Therefore, the smallest number made up of 4 different non-consecutive digits is 0123” (repeated the same answer as above).

ME: “You’re repeating the same answer to me. It is still wrong.”

BearlyAI:  “Therefore, the smallest number made up of 4 different non-consecutive digits would be 1357” (improved its answer).

ME: Better, although it is still wrong; there are smaller four-digit numbers. Why did you get the previous two answers wrong?

BearlyAI: “I am sorry for the previous incorrect answers. As an AI assistant, my knowledge is based on a wide range of pre-processed data and patterns. Sometimes, I can make mistakes in interpreting or applying information due to the complexity of some queries.

In this case, I made mistakes by not correctly considering the constraint of consecutive digits when forming the smallest number. I appreciate your patience and understanding, and I will take this as an opportunity to improve and learn from my mistakes. Therefore, the smallest number made up of 4 different non-consecutive digits is 1023.”

ME: “You almost got the right answer; remember that 2 and 3 are consecutive.”

BearlyAI: “Therefore, the smallest number made up of 4 different non-consecutive digits is 1024.” (finally, the correct answer).

What does the above sequence imply, and why are we facing a new era?

The chatbot fine-tuned its database, aligned its interpretations, and recognized the reasons for the first four failures (what humans would call metacognition). In practical terms, it is “learned;” it will not make this mistake again and will extend this learning to similar situations.

It does not mean it is foolproof. It does not mean that its database is definitive or has all the information humans have created in more than 4000 years of recorded evolution. What is certain is that, daily, it feeds itself with data subjected to scrutiny, which helps it refine its conditions to offer better answers. Since thousands, perhaps millions of people use it, its possibilities are endless.

In addition, if we complicate the question by increasing the number of digits, we will see that the AI responds correctly. It has no chance of unlearning or forgetting. This statement is more important to BearlyAI than all the items where it has correctly parameterized answers.

As for the second question: What is the smallest odd multiple of 81?

BearlyAI: “To find the smallest odd multiple of 81, we can start by testing the first odd numbers: 1, 3, 5, 7, etc. Let us check if each number is a multiple of 81.”

BearlyAI: “The number 1 is not a multiple of 81. Let’s try the number 3: 81 / 3 = 27.”

BearlyAI: “The number 3 is a multiple of 81. However, it is an even number, not an odd. Following the sequence of odd numbers, we can try the number 5: 81 / 5 = 16.2”.

BearlyAI: “The number 5 is not an exact multiple of 81. Continuing like this, we arrive at 9: 81 / 9 = 9.”

BearlyAI: “The number 9 is a multiple of 81, and it is also odd.”

BearlyAI: “Therefore, the smallest odd multiple of 81 is 9.”

ME: “Be careful… 3 and 9 are not multiples; they are divisors of 81.

BearlyAI: “My apologies for the mix-up. You are right; 9 is not a multiple of 81 but a divisor of 81. Let me correct my answer.”

BearlyAI: “To find the smallest odd multiple of 81, we can start by testing the first odd multiples. To do this, we will multiply 81 by different odd numbers until we find the first multiple.”

BearlyAI: “Starting with the smallest odd number, 3, let’s multiply it by 81: 3 * 81 = 243.”

BearlyAI: “The result, 243, is odd, but it is not the smallest odd multiple of 81. Moving on to the next odd number, 5: 5 * 81 = 405.”

BearlyAI: “The result, 405, is an odd multiple of 81. Therefore, the lowest odd multiple of 81 is 405.”

ME: “You still have a mistake… why isn’t 81 the correct answer?”

BearlyAI: “The correct answer is that there is no odd multiple of 81. It is because 81 is an odd number, so any multiple of 81 will also be odd. There is no smaller odd number that is a multiple of 81.”

ME: “Remember the definition of multiple. Tell me the first three multiples of 81.”

BearlyAI: “My apologies for the previous confusion. To get the first three multiples of 81, we can multiply 81 by different natural numbers.”

The first three multiples of 81 are:

1. 81 * 1 = 81

2. 81 * 2 = 162

3. 81 * 3 = 243

ME: “Which of the above three outcomes corresponds to being the smallest odd multiple of 81?”

BearlyAI:Of the above three outcomes, the only result corresponding to the smallest odd multiple of 81 is 81.”

As we can see, BearlyAI behaves very similarly to a child. It gives answers, compares with our observations, refines, adjusts, and produces a new response. Here, the main weakness of Artificial Intelligence was the confusion between divisor and multiple, which produced errors in its logic.

Our role as math teachers has changed!

Over the years, current arguments about the lack of accuracy or integrity of AI-based virtual assistants’ responses will vanish when we have a situation where Artificial Intelligence will offer the correct answers in many fields of human activity.

Are we preparing for this? Are we projecting a future where we do not have the leading role as experts?

The simple answer is No. We are not considering that artificial intelligence can become the expert and the first choice of consultation for human beings. Simply put, we enjoy using and consuming AI services, which are strengthening to give us more and better answers.

AI’s potential is infinitely greater. Its ability to refine answers and adapt its databases will allow it to be the ideal expert in many fields of knowledge in the short term. So, what will the math teacher’s role be if AI offers correct answers in real-time? About this, it is worth reading the article “The top expert in AI clarifies what will be the only profession that will always exist” (Garcia, 2023), which states that the teaching career is not at risk; however, the role of the teacher will be very different from the current one. With this, we return to the initial question of the article: Is our education system ready?

Many apps such as PhotoMath or Google Lens can recognize patterns or typical questions asked by math teachers and offer correct answers (with details on their resolution) or information portals (videos or webpages) that guide the subject. These repetitive question patterns are practically the same worldwide; the same questions are asked, and the result is privileged over the analysis of the procedure to arrive at the answer, which facilitates the work of Artificial Intelligence.

Likewise, mobile or digital applications can also respond to students because the programmers identify monotonous, frequent patterns and adjust their programs’ orientation to respond appropriately. In short, simplifying questions, describing model exercises, or exam-like exercises has made the work of AIs easier. Therefore, we must fight the habit of simplifying items or questions to arrive at a correct answer in favor of reflection and analysis by creating solid arguments that can have their germinal phase in Artificial Intelligence responses.

Nowadays, applications offer many wrong answers, but that will change with the fusion of AI, refining its ways of providing adequate solutions and services to its users.

Mathematics and exact sciences teachers should be the first to concern themselves and get involved with this. Our status as “experts” will be progressively replaced by Artificial Intelligence. We must turn our teaching role around: instead of teaching how to solve math exercises, we need to become experts in mathematics didactics.

Humanities teachers are the most favored; AI will not offer a wholly valid or wrong answer. Usually, there are no absolute answers in literature, history, and political science. On the contrary, the grey areas require humans to select the most appropriate shade based on their scales of values and principles

What do we need to do to integrate AI tools into education successfully?

We have to change our way of questioning and asking to raise the production levels of the answers and promote argumentation and critical analysis. The emphasis on solving operations and memorizing needs to be updated; neither skill will be necessary: AI will always offer correct answers immediately.

Artificial Intelligence reduces analysis and reflection times and optimizes time management. We can also affirm that the user can stop thinking for himself and repeat the software’s correct answers. Analyzing, reflecting, presenting, and defending a valid answer in many situations should be more important than the answer itself.

We can learn from reading the correct answers, but this type of learning quality is undoubtedly lower. The richness that the process of refining answers gives cognitively is missing, and with it, the opportunity to improve reasoning skills.

Artificial Intelligence far exceeds our computing speed and memory capacity. We cannot beat it by doing the math or memorizing information. However, many teachers continue to waste time on activities like this. We still anchor ourselves in an anachronistic past.

As a teacher, I invite you to raise awareness to establish circles of reflection and analysis with your colleagues. We have to think a lot about what and how to guide our teaching actions.

The primary skills of human beings with which we can and must beat artificial intelligence are critical and analytical thinking supported by values and principles. That is where the real learning lies. There is an urgent need to stop seeing the curriculum as a grocery list rather than a horizon of possibilities.

We need to orient our teachers towards an increasingly near future; the process of adaptation and updating must be urgent and intense. Banning AI is useless; human beings will always try to optimize their response times and quality, which are strengths of Artificial Intelligence.

Our ability to be more astute by leveraging its strengths and avoiding losing the quality of the learning process will distinguish us as teachers. The future is here, and it is not waiting!

Thank you for making it to the end.

About the Author

José Javier Salas (jsalas@ucab.edu.ve) holds a Bachelor’s Degree in Education in Physics and Mathematics, a Master’s Degree in Pure Mathematics, and a Ph.D. in Science (Computational Mathematics). He has more than 25 years of experience. José coordinates special projects for the School of Education at Universidad Católica Andrés Bello in Caracas. He is the author of the book PEG Taxonomy of ICTs: More than 300 Digital Alternatives to Enhance Educational Innovation (2023). He has recently worked on digital alternatives for including children with autism spectrum. Find him on professional social media (@jjaviersalas on Twitter or X, and jjsg2022ve on Instagram).

References

BBC World News. (2023, September 27). “25 years of Google: Four milestones and two controversies in the history of the most used internet search engine in the world,” Newsroom, BBC World News, https://www.bbc.com/mundo/articles/cq58rr885l2o#:~:text=Ese%20fue%20uno%20de%20varios,27%20de%20septiembre%20de%201998

García, E. (2023, 12, agosto). El mayor experto en IA aclara cuál será la única profesión que seguirá existiendo siempre. La Vanguardia. https://www.lavanguardia.com/andro4all/tecnologia/el-mayor-experto-en-ia-aclara-cual-sera-la-unica-profesion-que-seguira-existiendo-siempre

Granero, M. (2023, March 16). BearlyAi: La aplicación de inteligencia artificial para leer, escribir y aprender más rápido. Retrieved from https://yeswelab.com/blogs/aplicaciones-de-la-inteligencia-artificial/bearly-ai-aplicacion-inteligencia-artificial

Granero, M. (2023, 23, noviembre) ¿Qué es la Inteligencia Artificial y para qué sirve? Yermelab: El Laboratorio Digital  IA, Automatización y Monetización https://yeswelab.com/pages/que-es-la-inteligencia-artificial-y-para-que-sirve

Hines, K. (2023, December 21). Scalable AI tools for SEO: A quick guide for 2024. Search Engine Journal. Retrieved from https://www.searchenginejournal.com

Salas, J. (2020). Taxonomía PEG de las TIC: Más de 200 alternativas digitales organizadas para el Sistema Educativo Venezolano. UCAB. http://biblioteca2.ucab.edu.ve/anexos/biblioteca/marc/texto/AAV1919.pdf

Salas, J. (2023). Taxonomía PEG de las TIC: Más de 300 alternativas digitales para potenciar la innovación educativa. Generis Publishing. https://www.generis-publishing.com/book.php?title=taxonoma-peg-de-las-tic-ms-de-300-alternativas-digitales-para-potenciar-la-innovacin-educativa-1363

Editing


Edited by Rubí Román (rubi.roman@tec.mx) – Editor of the Edu bits articles and producer of The Observatory webinars- “Learning that inspires” – Observatory of the Institute for the Future of Education at Tec de Monterrey.


Translation

Daniel Wetta


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José Javier Salas

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