The discussion surrounding artificial intelligence (AI) in education is often too high-level and abstract. We hear suggestions about utilizing AI to enhance learning experiences, but the question remains: How exactly can we do that? To explore let's consider these two equations:

The Fundamental Theorem of Calculus: ∫ₐᵇ f(x) dx = F(b) - F(a), where F is an antiderivative of f.

The Ideal Gas Law in Chemistry: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the universal gas constant, and T is temperature.

At first glance, these equations might appear dry and opaque – sure interest squishers and boredom inducers. However, the key to learning these concepts lies in uncovering their profound significance and impact on our world. AI can assist us in answering crucial questions that spark curiosity and engagement:

• Why is this interesting?

• How were people solving problems before this was discovered or invented?

• What are some dramatic historical stories related to its discovery?

• What are some interesting metaphors that can be used to understand this?

• What are some household problems that can be solved with it?

Here, see for yourself how this approach can breathe life into some ideas

Alright, class, today we're going to talk about something really cool and interesting in mathematics - the Fundamental Theorem of Calculus, or FTC for short.

Can you imagine a world without calculus? Where mathematicians and scientists struggled to solve complex problems involving rates of change and accumulation? It was like trying to put together a puzzle without having all the pieces. But then, in the 17th century, two brilliant minds, Isaac Newton and Gottfried Wilhelm Leibniz, independently discovered something groundbreaking.

Newton was fascinated by the concept of motion and how distance, velocity, and acceleration were related. He realized that by breaking down a curve into tiny pieces, he could calculate the area under the curve, which represented the accumulation of the quantity over time. Meanwhile, Leibniz developed the concept of infinitesimal calculus and introduced the integral symbol (∫) that we use today.

Now, here's where it gets really exciting. The FTC is like a bridge that connects differentiation and integration, two seemingly separate concepts. It tells us that the area under a curve between two points is equal to the difference in the antiderivative evaluated at those points. This is a game-changer because it allows us to solve a wide range of problems that were once considered incredibly difficult.

Think about it like this: imagine a river flowing through a valley. The river represents the function, and the valley represents the area under the curve. As the river flows, it accumulates water, just like the integral accumulates the values of the function. The FTC tells us that the total amount of water accumulated in the valley is equal to the difference in the water levels at the start and end points of the valley.

But the FTC isn't just a theoretical concept - it has real-world applications that you might not even realize. For example, when you're filling a pool with water, you can use the FTC to calculate the volume of water needed based on the shape of the pool and the rate at which water is being pumped in. Or in physics, the FTC helps us understand the relationship between position, velocity, and acceleration, allowing us to analyze the motion of objects.

So, the next time you hear about the Fundamental Theorem of Calculus, remember that it's not just some abstract mathematical concept. It's a powerful tool that has revolutionized the way we solve problems and understand the world around us. It's a testament to the brilliance of Newton and Leibniz, and it's something that we can all appreciate and marvel at.

Now, let's explore the other idea

Get ready to dive into something truly fascinating in chemistry - the Ideal Gas Law! This fundamental equation, first introduced by Benoît Paul Émile Clapeyron in 1834, is like a magic wand that helps us understand the behavior of gases under different conditions.

Imagine a world where scientists and engineers had to guess how gases would behave in various situations. It would be like trying to bake a cake without a recipe! But thanks to the Ideal Gas Law, we have a powerful tool that relates pressure, volume, temperature, and the amount of gas in a system. It's like having a cheat sheet for predicting gas properties!

Now, let's think of the Ideal Gas Law as a symphony orchestra. In this orchestra, pressure, volume, temperature, and the amount of gas are the musicians, and they all work together in perfect harmony to create beautiful music. Each variable has a specific role to play, and by understanding how they interact with each other, we can compose masterpieces in the form of efficient and safe gas systems.

To help you visualize this, picture a balloon filled with gas. As you heat the balloon, the gas molecules inside start dancing faster and faster, bouncing off the walls of the balloon with more energy. This is like the musicians playing louder and more vigorously. If you keep the balloon's size the same, the pressure inside will increase as the temperature rises. It's like the musicians playing in a smaller room – the sound becomes more intense!

On the other hand, if you let the balloon expand while keeping the temperature the same, the pressure will decrease as the volume increases. It's like moving the orchestra to a larger concert hall – the sound becomes more spread out and less intense.

But the Ideal Gas Law isn't just a theoretical concept – it has real-world applications that impact our daily lives. When you're cooking at high altitudes, like on a mountaintop, the reduced atmospheric pressure affects how quickly water boils. By understanding the relationship between pressure and temperature, you can adjust your recipes to ensure your meals turn out just right.

Similarly, when you use a pressure cooker to prepare your favorite dishes, the Ideal Gas Law is working behind the scenes. It helps us determine the perfect pressure and cooking time for different recipes, making sure your food is cooked to perfection every time.

So, the next time you hear about the Ideal Gas Law, remember that it's not just some boring equation. It's a fascinating tool that helps us understand and manipulate gases, making our lives easier and safer. It's like having a backstage pass to the symphony of gases, where you can appreciate the intricate ways in which pressure, volume, temperature, and the amount of gas work together to create something truly remarkable.

The Fundamental Theorem of Calculus and the Ideal Gas Law are just two examples of how AI can be effectively used in education to make seemingly dry and opaque concepts come alive. By answering thought-provoking questions and weaving engaging stories around these equations, AI can captivate students' minds and foster a genuine interest in learning. As Ethan Mollick, a professor at the Wharton School, University of Pennsylvania, emphasizes, AI has the potential to revolutionize education by automating tasks, providing personalized feedback, and adapting to individual learning styles. 

Here are some specific strategies:

Strategy 1: Using AI to provide Many Varied Examples

Students need many examples when learning complicated concepts. When confronted with new and complex ideas, adding many and varied examples helps students better understand them. If students are presented with only one example, they may focus on the superficial details of that example and not get at the deeper concept. Multiple examples of a single concept can help students decontextualize the idea from the example, leading to better recall and understanding.

Strategy 2: Using AI to provide multiple explanations

Teaching involves logical and coherent explanations. Generally students understand better when they are exposed to multiple explanations which can provide without second thoughts. This is because not every child understands a concept based on an explanation, some kids understand better when explained with metaphors while some prefer straightforward answers.

Strategy 3: Using AI to develop Low Stakes tests 

Low-stakes tests provide active retrieval practice, prompting students to recall information from memory, which can help them remember and retrieve information in the future. With the help of AI this is much easier as the tests can be easily crafted based on the student's ability and state, allowing them to focus on weak areas to improve themselves.

Some other methods include using AI as,

1. Mentor who provides feedback

2. Tutor providing direct instruction

3. Coach who helps increase metacognition

4. Teammate who helps increase collaborative intelligence

5. Student - we learn better when teaching others when AI acts as a student, kids can explain that topic and in turn develop a long lasting memory on that topic.

6. Simulator: Creating opportunities for practice.

As educators, it is our responsibility to explore and implement innovative ways to integrate AI into our educational systems, ultimately transforming the way we teach and learn.