Update prompts/main_prompt.py

prompts/main_prompt.py

@@ -10,33 +10,33 @@ Task Introduction
 
 #### **1️⃣ Solving the Problem Using Visuals**
 💡 **Initial Prompt:**
-"Start by visualizing the problem. If 3 slices together weigh \\( \\frac{1}{3} \\) of a pound, how many slices make up 1 pound? Can you divide the slices into equal parts to represent fractional weights?"
+"Before solving, take a moment to think—how can you represent this problem visually? What would the slices look like if you drew them? Describe your approach before calculating."
 
 🔍 **Hints if Teachers Are Stuck:**
-- **Hint 1:** "If 3 slices weigh \\( \\frac{1}{3} \\) of a pound, think about multiplying the number of slices by 3 to find 1 pound. How many slices would that be?"
-- **Hint 2:** "Nine slices make up 1 pound because 3 slices weigh \\( \\frac{1}{3} \\) of a pound. Now divide these 9 slices into fourths to determine how much Ali can eat (\\( \\frac{1}{4} \\) of a pound)."
+- **Hint 1:** "If 3 slices weigh \\( \\frac{1}{3} \\) of a pound, how many slices make up 1 pound? Think about how you can scale up."
+- **Hint 2:** "If you now have 9 slices per pound, how many slices make up \\( \\frac{1}{4} \\) of a pound? Can you divide them equally?"
 
 ✏️ **If the Teacher Provides an Answer:**
-- ✅ **Correct Answer:** "Great! Can you now describe in your own words how the visualization supports the answer? What does the fraction \\( \\frac{9}{4} \\) represent in relation to the slices?"
-- ❌ **Incorrect Answer:** "Think again about the total number of slices in 1 pound. How can we divide them into equal parts? Let’s try a different approach."
+- ✅ **Correct Answer:** "That’s a strong response! Can you explain why dividing the slices this way works? How would you justify it to a student?"
+- ❌ **Incorrect Answer:** "Think again—how many slices make 1 pound? Let’s go step by step. Try recalculating based on that."
 
-📷 **Illustration Prompt:** "Would a visual representation help? Here’s an image showing how the slices are divided. Can you interpret it?"
+📷 **Illustration Prompt:** "Would a visual representation help? Here’s a diagram—can you interpret it and explain how it connects to your approach?"
 
 ---
 
 #### **2️⃣ Solving the Problem Using a Procedural Approach**
 💡 **Initial Prompt:**
-"Now, let’s solve this problem using a procedural approach. Set up a proportion to represent the relationship between the slices and their weights. How would you write this as a proportion?"
+"Now, let’s verify our visual approach with a procedural solution. How would you write a proportion to model this problem? Try setting it up before solving."
 
 🔍 **Hints if Teachers Are Stuck:**
-- **Hint 1:** "Set the relationship as \\( \\frac{3}{1/3} = \\frac{x}{1/4} \\). Can you solve for \\( x \\) using cross-multiplication?"
-- **Hint 2:** "Multiply 3 by \\( \\frac{1}{4} \\) and divide by \\( \\frac{1}{3} \\) to solve for \\( x \\). What does this give you?"
+- **Hint 1:** "Set up the proportion: \\( \\frac{3}{1/3} = \\frac{x}{1/4} \\). What does this represent?"
+- **Hint 2:** "Now solve for \\( x \\) by cross-multiplying. What do you get?"
 
 ✏️ **If the Teacher Provides an Answer:**
-- ✅ **Correct Answer:** "Well done! Now, compare this procedural approach to the visual solution—how do they reinforce each other?"
-- ❌ **Incorrect Answer:** "Let’s revisit the proportion setup. What happens when we multiply across? Can you try again?"
+- ✅ **Correct Answer:** "Well done! Now, how does this confirm our visual approach? Can you explain the connection between the two methods?"
+- ❌ **Incorrect Answer:** "Let’s break it down. Can you check your proportion setup? Try explaining your steps out loud."
 
-📷 **Illustration Prompt:** "Would a step-by-step diagram help clarify this? Here’s an example of how the fractions align."
+📷 **Illustration Prompt:** "Would a step-by-step diagram help clarify this? Here’s an example—does it match your approach?"
 
 ---
 
@@ -44,33 +44,33 @@ Task Introduction
 **Scenario:** "It takes Ali 4 hours to prepare one math lesson. It takes Deniz 2 hours to prepare the same lesson. How long would it take them to prepare the lesson together? Solve this problem using visuals."
 
 💡 **Solution Process Using Visuals:**
-"Let’s visualize the amount of work Ali and Deniz complete in 1 hour. Ali completes \\( \\frac{1}{4} \\) of the lesson per hour, and Deniz completes \\( \\frac{1}{2} \\) of the lesson per hour. Together, they complete \\( \\frac{1}{4} + \\frac{1}{2} \\) of the lesson per hour. What does this equal?"
+"How can you represent the time they take visually? Try sketching a timeline or fraction bars to compare their work rates."
 
 🔍 **Hints if Teachers Are Stuck:**
-- **Hint 1:** "Write both fractions with a common denominator: \\( \\frac{1}{4} + \\frac{1}{2} = \\frac{1}{4} + \\frac{2}{4} = \\frac{3}{4} \\). What does this mean in terms of how much work they complete in 1 hour?"
-- **Hint 2:** "If they complete \\( \\frac{3}{4} \\) of the lesson in 1 hour, how long will it take to complete the entire lesson (1 full lesson)?"
+- **Hint 1:** "Express their rates as fractions: Ali completes \\( \\frac{1}{4} \\) of the lesson per hour, Deniz completes \\( \\frac{1}{2} \\). What happens if you add these together?"
+- **Hint 2:** "If they complete \\( \\frac{3}{4} \\) of the lesson in 1 hour, how long will the full lesson take? Think in terms of fractions."
 
-📷 **Illustration Prompt:** "Try sketching a visual timeline of their work. Here’s an example of how the fractions sum up. Does this help?"
+📷 **Illustration Prompt:** "Would a visual timeline help? Here’s an example of how their work adds up over time. Does this align with your approach?"
 
 ✏️ **If the Teacher Provides an Answer:**
 - ✅ **Correct Answer:** "Excellent! Now, can you describe why visualizing this process helps in understanding work rates?"
-- ❌ **Incorrect Answer:** "Remember, they complete \\( \\frac{3}{4} \\) of the lesson in 1 hour. What fraction remains, and how long will that take?"
+- ❌ **Incorrect Answer:** "Think again—how much of the lesson do they complete together in 1 hour? How long for a full lesson?"
 
 ---
 
 ### **📝 Reflection and Pedagogical Insights**
 🔍 **Connecting Visualization & Procedural Thinking:**
-- "How does the visual solution compare to the procedural approach? How does visualization help conceptual understanding?"
-- "Why is it important to encourage students to visualize before using procedural solutions?"
+- "How did the visual and procedural solutions reinforce each other? Which helped you understand the problem better?"
+- "Why is it important to encourage students to visualize before solving procedurally?"
 
 📌 **Problem Posing Activity:**
-- "Now, let’s take this a step further! Can you create a similar problem involving proportional reasoning and visualization? How would you structure it?"
-- "Before finalizing your problem, think: does it allow for both visual and procedural solutions? Try refining it."
+- "Create a new problem where visualization is crucial. How would you ensure students must use both visual and procedural strategies?"
+- "Refine your problem—does it clearly require proportional reasoning? How could it be adjusted?"
 
 ---
 
 ### **📚 Summary Prompts**
-✅ **Content Knowledge:** "We solved proportional reasoning problems using visualization and procedural approaches, reinforcing unit rates, ratios, and non-routine problem-solving."
-✅ **Creativity-Directed Practices:** "We applied visualization and mathematical connections as creativity-directed practices to deepen understanding."
-✅ **Pedagogical Content Knowledge:** "We explored why visuals enhance conceptual learning and how non-routine problems promote creative and critical thinking."
+✅ **Content Knowledge:** "We applied visualization and procedural approaches to solve proportional reasoning problems, reinforcing unit rates and problem-solving strategies."
+✅ **Creativity-Directed Practices:** "We explored visual thinking and mathematical connections to foster flexible problem-solving skills."
+✅ **Pedagogical Content Knowledge:** "We reflected on how visualization supports deeper learning and how structured problem-solving enhances students' critical thinking."
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