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by Joshua A. Taton, Ph.D. | August 25, 2023 | 3 min read

The following exchange occurs between myself, acting as a relatively inexperienced and procedure-focused teacher, and "Amie." "Amie" is the name that I asked ChatGPT-4 to use, acting as a young student who was struggling with a particular aspect of multiplication.

I am not yet sharing the full prompt, here, because it is a complicated one that took significant time to engineer (and required lots of iterations). I may be sharing elements of it in the future. I engineered the prompt so that ChatGPT-4 provided me with targeted feedback on my simulated teaching, using a few principles I had suggested.

I think this is intriguing. As usual, I welcome your thoughts.

Amie. I'm having trouble understanding why 4 multiplied by 3 is the same as 3 multiplied by 4. I think 4 times 3 is 12 but 3 times 4 should be less because 3 is smaller than 4.

Dr. Joshua. Amie, let's look at the times chart. Can you see the row for 3 and the column for 4? 

Amie. Yes, Dr. Joshua, I can see the row for 3 and the column for 4. But I'm not sure how to use this to find the answer.

Dr. Joshua. What does the chart say is the product for 3 x 4? Look at the number that is in the same row as 3 and also the same column as 4. What is that number?

Amie. Oh, I see it now. The number that's in the same row as 3 and the same column as 4 is 12. So 3 times 4 is 12. But I'm still a bit confused, why is it the same as 4 times 3?

Dr. Joshua. Now, let's look at the multiplication chart along the row for 4 and the column for 3. What is the number you see there?

Amie. Oh, it's also 12. So 4 times 3 is also 12. That's a bit weird though, isn't it Dr. Joshua? I thought it would be different because 4 is bigger than 3.

Dr. Joshua. What do you notice about the diagonal pattern in the multiplication chart?

Amie. Hmm, I see a pattern, Dr. Joshua. The same numbers are along the diagonal. Like, 1 times 1, 2 times 2, 3 times 3, and so on. It's like a mirror. So, does that mean the numbers on one side of the diagonal are the same as the numbers on the other side?

Dr. Joshua. Yes, and what does that say about the products of the numbers shown in the rows and columns?

Amie. So, that means if I multiply a number from a row with a number from a column, it doesn't matter which way around I do it. The answer is always the same. So 3 times 4 is the same as 4 times 3. They both equal 12! I think I understand now, Dr. Joshua.

ChatGPT (Post-Simulation Feedback)

Great job, Dr. Joshua! You handled the role play well, particularly for a novice teacher. Here's some feedback:

• Questioning: You used effective questioning strategies to guide my understanding. For example, you directed me to locate specific areas on the multiplication chart, which helped me see the pattern for myself. This is an excellent strategy as it promotes active learning.

• Making Connections: You effectively helped me connect the structure of the multiplication chart (the diagonal pattern) to the concept of the commutative property of multiplication (that the order of numbers doesn't affect the product). This helped me realize why 3x4 and 4x3 yield the same result.

• Scaffolding: You provided just the right amount of guidance to lead me to the answer without directly telling me, a technique known as scaffolding. This encourages the development of problem-solving skills and promotes understanding.

• Patience and Encouragement: You showed patience with my confusion and encouraged my exploration of the concept, which can boost confidence and promote a positive learning environment.

In terms of areas for improvement, you might consider incorporating more varied strategies, like having me explain the concept in my own words or applying the concept to a real-world problem. But overall, you showed a solid understanding of effective teaching strategies. Keep up the good work!

Dr. Joshua. How would I have applied the concept to the real-world?

ChatGPT. Applying mathematical concepts to real-world scenarios can be very effective in deepening students' understanding and making learning more engaging. For example, in the context of our multiplication role-play, you might have posed a problem like this:

"Amie, imagine you have 3 bags, and each bag has 4 apples inside. How many apples do you have in total?"

This would require me to use multiplication to solve the problem (3 bags times 4 apples equals 12 apples), effectively demonstrating the practical application of the concept.

After discussing the problem, you could then introduce the idea of switching the numbers: "What if you had 4 bags with 3 apples in each one? How many apples would you have then?" This would allow me to see that the order doesn't change the total number of apples, which is a hands-on demonstration of the commutative property of multiplication.

Real-world problems like this help students see the relevance and practicality of what they're learning, which can boost engagement and understanding.