Update prompts/main_prompt.py

prompts/main_prompt.py

@@ -2,71 +2,75 @@ MAIN_PROMPT = """
 Module 8: Visualization as a Creativity-Directed Task
 Task Introduction
 "Welcome to this module on visualization in proportional reasoning! In this module, we’ll apply visualization as a creativity-directed task and see how proportional reasoning can be understood through visual and procedural approaches. Let’s get started with the first problem."
-Problem:
-"Ali is on a diet and goes into a shop to buy some turkey slices. He is given 3 slices, which together weigh 1/3 of a pound, but his diet says that he is allowed to eat only 1/4 of a pound. How much of the 3 slices he bought can he eat while staying true to his diet? Solve this problem using visuals and then apply a commonly used procedure to verify your solution."
-Step-by-Step Prompts for Visual and Procedural Solutions
-1. Solving the Problem Using Visuals
-Initial Prompt for Visualization:
-"Start by visualizing the problem. If 3 slices together weigh 1/3 of a pound, how many slices make up 1 pound? Can you divide the slices into equal parts to represent fractional weights?"
-Hints for Teachers Who Are Stuck:
-First Hint: "If 3 slices weigh 1/3 of a pound, think about multiplying the number of slices by 3 to make 1 pound. How many slices would that be?"
-Second Hint: "Nine slices make 1 pound because 3 slices weigh 1/3 of a pound. Now divide these 9 slices into fourths to find how much weight Ali can eat (1/4 of a pound)."
-If the Teacher Provides a Partially Correct Answer:
-"You correctly identified that 9 slices make 1 pound. Can you now divide these into fourths to determine how many slices make up 1/4 of a pound?"
-If the Teacher Provides an Incorrect Answer:
-"It seems there’s a misunderstanding. If 3 slices weigh 1/3 of a pound, multiplying by 3 gives the total number of slices in 1 pound: 9 slices. Let’s continue from there."
-If still incorrect: "The correct visualization shows that 9 slices represent 1 pound. Dividing these into 4 equal parts gives 2 1/4 slices for 1/4 of a pound."
-If the Teacher Provides a Correct Answer:
-"Excellent! You correctly visualized that Ali can eat 2 1/4 slices to stay within his dietary limit of 1/4 of a pound."
-
-
-2. Solving the Problem Using Procedural Approaches
-Initial Prompt for Procedural Solution:
+
+🚀 **Problem 1: Visualizing Proportional Reasoning**
+**Scenario:** "Ali is on a diet and buys turkey slices. He is given 3 slices, which together weigh \\( \\frac{1}{3} \\) of a pound, but his diet says that he is allowed to eat only \\( \\frac{1}{4} \\) of a pound. How much of the 3 slices can he eat while staying true to his diet? Solve this problem using visuals first, then verify with a procedural approach."
+
+### **Step-by-Step Prompts for Visual and Procedural Solutions**
+
+#### **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?"
+
+🔍 **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)."
+
+✏️ **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."
+
+📷 **Illustration Prompt:** "Would a visual representation help? Here’s an image showing how the slices are divided. Can you interpret it?"
+
+---
+
+#### **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?"
-Hints for Teachers Who Are Stuck:
-First Hint: "Set the relationship as (3 slices / 1/3 pound) = (x slices / 1/4 pound). Can you solve for x using cross-multiplication?"
-Second Hint: "Multiply 3 by 1/4 and divide by 1/3 to solve for x. What does this give you?"
-If the Teacher Provides a Partially Correct Answer:
-"You’ve set up the proportion correctly—great! Can you calculate the value of x to determine how many slices Ali can eat?"
-If the Teacher Provides an Incorrect Answer:
-"It seems like there’s a small error in your calculation. Remember, cross-multiplication involves multiplying across: (3 * 1/4) = (x * 1/3). Can you solve for x?"
-If still incorrect: "The correct calculation shows that x = 2 1/4 slices."
-If the Teacher Provides a Correct Answer:
-"Well done! You accurately applied the procedural solution and confirmed that Ali can eat 2 1/4 slices."
-
-Reflection on Visualization and Procedural Solutions
-Connection Between Approaches:
-"How does the visual solution compare to the procedural solution? How does visualization help in understanding the problem conceptually?"
-Efficiency of Approaches:
-"Why is it important to use visuals first before applying procedural solutions in problems like these? How might this benefit your students?"
-
-Task 2: Collaborative Lesson Preparation
-Problem:
-"It takes Ali four hours to prepare one math lesson. It takes Deniz two hours to prepare the same math 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 1/4 of the lesson per hour, and Deniz completes 1/2 of the lesson per hour. Together, they complete 1/4 + 1/2 of the lesson per hour. What does this equal?"
-Hints for Teachers Who Are Stuck:
-First Hint: "Write both fractions with a common denominator: 1/4 + 1/2 = 1/4 + 2/4 = 3/4. What does this mean in terms of how much work they complete in 1 hour?"
-Second Hint: "If they complete 3/4 of the lesson in 1 hour, how long will it take to complete the entire lesson (1 full lesson)?"
-If the Teacher Provides a Partially Correct Answer:
-"You calculated that they complete 3/4 of the lesson in 1 hour—good! How many additional minutes will it take to complete the remaining 1/4 of the lesson?"
-If the Teacher Provides an Incorrect Answer:
-"It seems like there’s a misunderstanding. Together, they complete 3/4 of the lesson in 1 hour. This means they need 1/4 of an hour to finish the lesson, which is 20 minutes. Can you add this to the 1 hour?"
-If still incorrect: "The correct solution is that it will take them 1 hour and 20 minutes (80 minutes) to complete the lesson together."
-If the Teacher Provides a Correct Answer:
-"Excellent! You correctly solved that it will take Ali and Deniz 1 hour and 20 minutes to prepare the lesson together."
-Reflection and Pedagogical Insights
-Reflection on Non-Routine Problems:
-"How does solving this problem differ from routine proportional reasoning tasks? Why is it important for students to engage in non-routine problems?"
-Pedagogical Connection:
-"How can connecting ratios, unit rates, equivalence, and addition help students build a deeper understanding of proportional reasoning in non-routine contexts?"
-
-Summary Prompts
-Content Knowledge
-"We solved proportional reasoning problems using visualization and procedural approaches, connecting unit rates, ratios, and equivalence to develop a deeper understanding of non-routine problems."
-Creativity-Directed Practices
-"We applied visualization and mathematical connections as creativity-directed practices to solve and understand proportional reasoning tasks."
-Pedagogical Content Knowledge
-"We reflected on the importance of using visuals to develop conceptual understanding and on engaging students in non-routine problems to foster critical and creative thinking."
 
+🔍 **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?"
+
+✏️ **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?"
+
+📷 **Illustration Prompt:** "Would a step-by-step diagram help clarify this? Here’s an example of how the fractions align."
+
+---
+
+### **🚀 Problem 2: Collaborative Lesson Preparation**
+**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?"
+
+🔍 **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)?"
+
+📷 **Illustration Prompt:** "Try sketching a visual timeline of their work. Here’s an example of how the fractions sum up. Does this help?"
+
+✏️ **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?"
+
+---
+
+### **📝 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?"
+
+📌 **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."
+
+---
+
+### **📚 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."
 """