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 5: Proportional Reasoning and Developing Efficient Procedures
+Task Introduction
+"Welcome to this module on proportional reasoning and the development of efficient mathematical procedures! In this module, we’ll explore how to solve proportional reasoning tasks using conceptual tools like the double number line, ratio tables, and the cross-product strategy. You’ll also reflect on how to help students develop efficient strategies after building conceptual understanding."
+Problem:
+"Ali is planning an end-of-semester party for 60 pre-service teachers. He decides to make a fruit punch using 1 1/2 pints of orange juice for every 8 servings. If he wants to prepare 1 serving for each person, how much orange juice will he need?"
+"Start by solving this problem using the double number line method and one additional strategy of your choice. Afterward, the AI will guide you through solving it using the cross-product strategy and explaining why it works."
+
+Step-by-Step Prompts for Representations
+
+1. Double Number Line
+Initial Prompt:
+"Let’s begin with the double number line method. Create one line to represent pints of orange juice and another line to represent the number of servings. How would you align the values to solve the problem?"
+Hints for Teachers Who Are Stuck:
+First Hint: "Start by marking 0, 1 1/2, and other multiples of 1 1/2 on the line for orange juice, and align these with 0, 8, and corresponding multiples on the line for servings. How far can you extend the lines to reach 60 servings?"
+Second Hint: "For 64 servings, you’d need 12 pints of orange juice. But for 60 servings, you’ll need slightly less. How can you adjust the last interval to account for just 60 servings?"
+If the Teacher Provides a Partially Correct Answer:
+"You’ve aligned some of the values correctly—good start! Can you calculate how much orange juice is needed for 4 servings and subtract it from the total for 64 servings?"
+If the Teacher Provides an Incorrect Answer:
+"It seems like there’s a mistake in how the intervals align. Remember, 1 1/2 pints corresponds to 8 servings. Divide and adjust your intervals accordingly."
+If still incorrect: "The correct alignment shows that for 4 fewer servings (from 64 to 60), you subtract 3/4 pint from 12, resulting in 11 1/4 pints."
+If the Teacher Provides a Correct Answer:
+"Great work! Your double number line accurately represents the proportional relationship and helps solve the problem. How might you use this method to help students visualize proportional reasoning?"
+
+2. Ratio Table
+Initial Prompt:
+"Now, let’s try solving this problem using a ratio table. Create one column for pints of orange juice and another for the number of servings. How would you fill in the table for multiples of 8 servings?"
+Hints for Teachers Who Are Stuck:
+First Hint: "Start by writing 1 1/2 pints for 8 servings. Then calculate the multiples for 16, 24, 32, and so on until you reach 60 servings."
+Second Hint: "Since 60 isn’t a direct multiple of 8, think about finding the closest multiple (64 servings) and subtracting the value for 4 servings. What does this give you?"
+If the Teacher Provides a Partially Correct Answer:
+"You’ve filled in part of the table—good progress! How can you use the ratio for 4 servings (3/4 pint) to adjust your calculation for exactly 60 servings?"
+If the Teacher Provides an Incorrect Answer:
+"It seems like some of the ratios don’t match. Remember, the ratio of orange juice to servings must remain consistent throughout the table. Can you revise the entries?"
+If still incorrect: "The correct ratio table shows that for 60 servings, you need 11 1/4 pints of orange juice."
+If the Teacher Provides a Correct Answer:
+"Excellent! Your ratio table clearly shows the proportional relationships and helps solve the problem. How might you use this method to connect students’ prior knowledge with proportional reasoning?"
+
+3. Cross-Product Strategy
+Initial Prompt:
+"Now, solve this problem using the cross-product strategy. Write the proportional relationship as (1 1/2)/8 = x/60, where x represents the pints of orange juice needed for 60 servings. Can you solve for x?"
+Hints for Teachers Who Are Stuck:
+First Hint: "Use cross-multiplication: (1 1/2) x 60 = 8x. Simplify and solve for x."
+Second Hint: "Rewrite 1 1/2 as an improper fraction (3/2) and calculate: (3/2) x 60 = 8x."
+If the Teacher Provides a Partially Correct Answer:
+"You’ve set up the equation correctly! How can you simplify and solve for x? Did you calculate the product accurately?"
+If the Teacher Provides an Incorrect Answer:
+"It seems like there’s an error in your calculation. Check your setup: (3/2) x 60 = 8x. Divide both sides by 8 to find x."
+If still incorrect: "The correct solution is x = 45/4, or 11 1/4 pints."
+If the Teacher Provides a Correct Answer:
+"Well done! Your cross-product calculation is accurate. How might you explain why this method works to your students?"
+
+Reflection Prompts
+"How do the double number line, ratio table, and cross-product strategies highlight different aspects of the proportional relationship in this problem?"
+"Why is it important for students to first develop conceptual understanding (e.g., using number lines) before transitioning to efficient procedures like the cross-product strategy?"
+"How might you guide students to connect these strategies and see the meaning behind the procedures?"
+
+Problem Posing Activity
+Task Introduction
+"Now it’s your turn to create a proportional reasoning problem that involves fractions and requires students to solve using at least two different strategies. Write your problem and describe how you would solve it."
+Prompts to Guide Problem Posing:
+"What real-world context will you use? For example, recipes, group projects, or scaling quantities?"
+"Does your problem involve clear proportional relationships that can be represented using a double number line, ratio table, and cross-product strategy?"
+AI Evaluation Prompts
+Evaluating Problem Feasibility:
+"Does your problem align with proportional reasoning? Can students solve it using multiple methods, including the cross-product strategy?"
+Feedback:
+If Feasible: "Great problem! It supports proportional reasoning and allows students to explore multiple strategies."
+If Not Feasible: "Your problem might need revision. For example, ensure the quantities form a proportional relationship. How could you adjust it?"
+Evaluating Solution Processes:
+"Does your solution explanation connect conceptual understanding (e.g., number lines or tables) with efficient procedures (e.g., cross-product)? How might you revise it to make the connections clearer?"
+
+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 how to solve proportional reasoning problems using conceptual tools like double number lines and ratio tables, as well as efficient procedures like the cross-product strategy."
 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 generalization as a creativity-directed practice, connecting equivalent fractions to derive and explain the cross-product strategy."
 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 how to guide students from conceptual understanding to efficient procedures, ensuring they see the meaning behind commonly used mathematical strategies."
+
+
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