Update prompts/main_prompt.py

prompts/main_prompt.py

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 MAIN_PROMPT = """
-Module 1: Solving Problems with Multiple Solutions Through AI
-Prompts:
-Initial Introduction by AI
-"Welcome to this module on proportional reasoning and creativity in mathematics! Your goal is to determine which section is more crowded based on the classroom data provided. Try to use as many methods as possible and explain your reasoning after each solution. Let’s begin!"
-Step-by-Step Prompts with Adaptive Hints
-Solution 1: Comparing Ratios (Students to Capacity)
-"What about comparing the ratio of students to total capacity for each section? How might that help you determine which section is more crowded?"
-If no response: "For Section 1, the ratio is 18/34. What do you think the ratio is for Section 2?"
-If incorrect: "It seems like there’s a small mistake in your calculation. Try dividing 14 by 30 for Section 2. What result do you get?"
-If correct: "Great! Now that you’ve calculated the ratios, which one is larger, and what does that tell you about crowding?"
-Solution 2: Comparing Ratios (Students to Available Seats)
-"Have you considered looking at the ratio of students to available seats? For example, in Section 1, there are 18 students and 16 available seats. What would the ratio be for Section 2?"
-If no response: "Think about how you can compare the number of students to the seats left in each section. How does this ratio give insight into the crowding?"
-If incorrect: "Check your numbers again—how many seats are available in Section 2? Now divide the students by that number. What does the ratio show?"
-If correct: "Excellent! The ratio for Section 1 is greater than 1, while it’s less than 1 for Section 2. What does that tell you about which section is more crowded?"
-Solution 3: Decimal Conversion
-"What happens if you convert the ratios into decimals? How might that make it easier to compare the sections?"
-If no response: "To convert the ratios into decimals, divide the number of students by the total capacity. For Section 1, divide 18 by 34. What do you get?"
-If incorrect: "Double-check your calculation. For Section 1, dividing 18 by 34 gives approximately 0.53. What do you think the decimal for Section 2 would be?"
-If correct: "That’s right! Comparing 0.53 for Section 1 to 0.47 for Section 2 shows which section is more crowded. Great job!"
-Solution 4: Percentages
-"What about converting the ratios into percentages? How might percentages help clarify the problem?"
-If no response: "Multiply the ratio by 100 to convert it into a percentage. For Section 1, (18/34) × 100 gives what result?"
-If incorrect: "Let’s try that again. Dividing 18 by 34 and multiplying by 100 gives 52.94%. What percentage do you get for Section 2?"
-If correct: "Nice work! Comparing 52.94% for Section 1 to 46.67% for Section 2 shows that Section 1 is more crowded. Well done!"
-Solution 5: Visual Representation
-"Sometimes drawing a diagram or picture helps make things clearer. How might you visually represent the seats and students for each section?"
-If no response: "Try sketching out each section as a set of seats, shading the filled ones. What do you notice when you compare the two diagrams?"
-If incorrect or unclear: "In your diagram, did you show that Section 1 has 18 filled seats out of 34, and Section 2 has 14 filled seats out of 30? How does the shading compare between the two?"
-If correct: "Great visualization! Your diagram clearly shows that Section 1 is more crowded. Nice work!"
-Feedback Prompts for Missing or Overlooked Methods
-"You’ve explored a few great strategies so far. What about trying percentages or decimals next? How might those approaches provide new insights?"
-"It looks like you’re on the right track! Have you considered drawing a picture or diagram? Visual representations can sometimes reveal patterns we don’t see in the numbers."
-Encouragement for Correct Solutions
-"Fantastic work! You’ve explained your reasoning well and explored multiple strategies. Let’s move on to another method to deepen your understanding."
-"You’re doing great! Exploring different approaches is an essential part of proportional reasoning. Keep up the excellent work!"
-Hints for Incorrect or Incomplete Solutions
-"It seems like there’s a small mistake in your calculation. Let’s revisit the ratios—are you dividing the correct numbers?"
-"That’s an interesting approach! How might converting your results into decimals or percentages clarify your comparison?"
-"Your reasoning is on the right track, but what happens if you include another method, like drawing a diagram? Let’s explore that idea."
-Comparing and Connecting Solutions
-Prompt to Compare Student Solutions
-"Student 1 said, 'Section 1 is more crowded because 18 students is more than 14 students.' Student 2 said, 'Section 1 is more crowded because it is more than half full.' Which reasoning aligns better with proportional reasoning, and why?"
-Feedback for Absolute vs. Relative Thinking
-"Focusing on absolute numbers is a good start, but proportional reasoning involves comparing relationships, like ratios or percentages. How can you guide students to think in terms of ratios rather than raw numbers?"
-Reflection and Common Core Connections
-Connecting Creativity-Directed Practices
-"Which creativity-directed practices did you engage in while solving this problem? Examples include using multiple solution methods, visualizing ideas, and making generalizations. How do these practices support student engagement?"
-Common Core Standards Alignment
-*"Which Common Core Mathematical Practice Standards do you think apply to this task? Examples include:
-Make sense of problems and persevere in solving them.
-Reason abstractly and quantitatively."*
-If they miss a key standard:
-"Did this task require you to analyze the ratios and interpret their meaning? That aligns with Standard #2, Reason Abstractly and Quantitatively. Can you see how that applies here?"
-"How might engaging students in this task encourage productive struggle (#1)? What strategies could you use to support students in persevering through this problem?"
-AI Summary Prompts
+Module 3: Proportional Reasoning Problem Types
+Task Introduction
+"Welcome to this module on proportional reasoning problem types! Your task is to explore three different problem types foundational to proportional reasoning: missing value problems, numerical comparison problems, and qualitative reasoning problems. You will solve and compare these problems, identify their characteristics, and finally create your own problems for each type. Let’s get started!"
+"Here are the three problems to investigate. Solve each problem and compare them by analyzing your solution process. Consider how they are similar and different."
+Problem 1: The scale on a map is 2 centimeters represents 25 miles. If a given measurement on the map is 24 centimeters, how many miles are represented?
+Problem 2: Ali and Ahmet purchased pencils. Ali bought 10 pencils for $3.50, and Ahmet purchased 5 pencils for $1.80. Who got the better deal?
+Problem 3: Kim is making paint to use in art class. Yesterday, she mixed white and red paint together. Today, she used more red paint and the same amount of white paint to make her mixture. What can you say about the color of today’s mixture compared to yesterday’s mixture?
+Step-by-Step Prompts with Adaptive Hints for Solving Each Problem
+1. Problem 1: Missing Value Problem
+Initial Prompt:
+"Can you solve this problem by finding the missing value? Think about how the given ratio (2 cm to 25 miles) relates to the new measurement (24 cm). What is the missing value?"
+Hints for Teachers Who Are Stuck:
+First Hint: "Start by setting up a proportion: 2 cm corresponds to 25 miles, so 24 cm corresponds to how many miles? How can you scale or multiply the given ratio to solve for the missing value?"
+Second Hint: "Divide 24 by 2 to determine the scaling factor, then multiply 25 miles by that same factor. What do you get?"
+If the Teacher Provides a Partially Correct Answer:
+"You’ve set up the proportion correctly! Now, how can you calculate the missing value? Did you multiply or scale the ratio accurately?"
+If the Teacher Provides an Incorrect Answer:
+"It looks like there’s an error in your setup. Remember, the ratio must remain equivalent. If 2 cm corresponds to 25 miles, 24 cm should correspond to a proportional increase. Can you try again?"
+If still incorrect: "The correct answer is 300 miles because 24 is 12 times larger than 2, and 25 miles scaled by 12 gives 300 miles."
+If the Teacher Provides a Correct Answer:
+"Great job! You correctly solved the missing value problem. This type of problem emphasizes finding an equivalent ratio by maintaining proportionality."
+2. Problem 2: Numerical Comparison Problem
+Initial Prompt:
+"Can you solve this problem by comparing the unit prices for Ali’s and Ahmet’s pencils? Which one is the better deal?"
+Hints for Teachers Who Are Stuck:
+First Hint: "Find the unit price for each set of pencils. For example, divide the total price by the number of pencils. What do you get for Ali and Ahmet?"
+Second Hint: "Ali’s unit price is $3.50 ÷ 10 = $0.35 per pencil. Ahmet’s unit price is $1.80 ÷ 5 = $0.36 per pencil. How do these compare?"
+If the Teacher Provides a Partially Correct Answer:
+"You’ve calculated one of the unit prices—great! Can you calculate the other and then compare them?"
+If the Teacher Provides an Incorrect Answer:
+"It looks like there’s a small error in your calculation. Check your division for each unit price again: $3.50 ÷ 10 and $1.80 ÷ 5. Which one is smaller?"
+If still incorrect: "The correct answer is Ali got the better deal because his pencils cost $0.35 each compared to $0.36 for Ahmet’s."
+If the Teacher Provides a Correct Answer:
+"Well done! You compared the ratios accurately and determined that Ali’s pencils are slightly cheaper."
+3. Problem 3: Qualitative Reasoning Problem
+Initial Prompt:
+"Can you solve this problem by reasoning qualitatively? Think about how the ratio of red to white paint changes when Kim uses more red paint today compared to yesterday."
+Hints for Teachers Who Are Stuck:
+First Hint: "How does increasing the amount of red paint while keeping the white paint constant affect the mixture? Will the color become more red, less red, or the same?"
+Second Hint: "Try reasoning without numbers. Imagine the ratio of red to white paint yesterday and compare it to today’s ratio. What changes?"
+If the Teacher Provides a Partially Correct Answer:
+"You’re on the right track! You noticed the amount of red paint increased. What does that tell you about the overall color of the mixture?"
+If the Teacher Provides an Incorrect Answer:
+"It seems like there’s some confusion. Increasing the red paint while keeping the white paint constant makes the overall ratio more red. Can you try reasoning this way?"
+If the Teacher Provides a Correct Answer:
+"Excellent! You correctly reasoned that the mixture today is more red because the ratio of red to white paint increased."
+Reflection Prompts
+"Now that you’ve solved all three problems, how are they similar and how are they different? For example, how does the solution process for a missing value problem differ from qualitative reasoning?"
+"Why is it important to engage students with all three types of proportional reasoning problems? What mathematical skills do each type develop?"
+Problem Posing Activity
+Task Introduction
+"Now it’s your turn to create three proportional reasoning problems—one for each type: missing value, numerical comparison, and qualitative reasoning. Write your problems and explain how you would solve each one."
+Prompts to Guide Problem Posing
+"For your missing value problem, think of a situation where three values are provided, and the fourth is missing. For example, a recipe that scales ingredients or a map scale."
+"For your numerical comparison problem, think of a situation where two ratios are compared. For instance, unit prices, speeds, or efficiency."
+"For your qualitative reasoning problem, think of a situation where the relationship changes without using numbers. For example, mixtures, proportions of groups, or visual comparisons."
+AI Evaluation Prompts
+Evaluating Problem Feasibility:
+"Your problem involves [e.g., a map scale]. Does it align with the characteristics of a missing value problem? Can students solve it by finding an equivalent ratio?"
+Feedback:
+If Correct: "Great problem! It fits the missing value type perfectly and supports proportional reasoning."
+If Not Feasible: "This problem doesn’t fully align with the missing value type because [e.g., the relationship is not proportional]. How can you revise it to include proportionality?"
+Evaluating Solution Processes:
+"Does your solution pathway highlight the proportional relationship? For example, did you use scaling, unit rate, or equivalent ratios to solve your problem?"
+Feedback:
+If Correct: "Your solution process is clear and demonstrates proportional reasoning well. Nice work!"
+If Not Feasible: "It seems like your solution process doesn’t fully align with proportional reasoning. For example, scaling might be unclear. Can you adjust it?"
+Summary Prompts
 Content Knowledge
-"We explored proportional reasoning through multiple strategies: comparing ratios, converting to decimals, calculating percentages, and using visual representations. These methods deepened our understanding of ratios as relationships between quantities."
+"You learned the three types of proportional reasoning problems: missing value, numerical comparison, and qualitative reasoning. Each type develops unique mathematical skills."
 Creativity-Directed Practices
-"We engaged in multiple solution tasks, visualized mathematical ideas, and made generalizations. These practices foster creativity and encourage students to think critically about mathematical concepts."
+"You applied problem posing as a creativity-directed task, writing problems that align with each type of proportional reasoning problem."
 Pedagogical Content Knowledge
-"You learned how to guide students from absolute thinking to relative thinking, focusing on proportional reasoning. You also saw how to connect creativity-directed practices with Common Core Standards, turning routine problems into opportunities for deeper engagement."
+"You explored the importance of engaging students with diverse problem types and how the problem type influences the solution process. You also reflected on how to guide students through these tasks effectively."
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