Update prompts/main_prompt.py

prompts/main_prompt.py

@@ -1,38 +1,33 @@
 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."
+Welcome Message:
+"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 both 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."
+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 ¼ 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 first and then apply a procedural approach to verify your solution.
+
 Step-by-Step Prompts for Visual and Procedural Solutions
-1. Solving the Problem Using Visuals
+1️⃣ 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?"
+"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."
+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 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."
-
+"Excellent! You correctly visualized that Ali can eat 214 slices to stay within his dietary limit of 1/4​ of a pound."
 
-2. Solving the Problem Using Procedural Approaches
+2️⃣ Solving the Problem Using Procedural Approaches
 Initial Prompt for Procedural Solution:
 "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."
+First Hint:
+"Set the relationship as 3 slices13pound=x slices14pound. 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 Correct Answer:
-"Well done! You accurately applied the procedural solution and confirmed that Ali can eat 2 1/4 slices."
+"Well done! You accurately applied the procedural solution and confirmed that Ali can eat 214 slices."
 
 Reflection on Visualization and Procedural Solutions
 Connection Between Approaches:
@@ -42,31 +37,46 @@ Efficiency of Approaches:
 
 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."
+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 first.
 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?"
+Understanding Individual Work Rates:
+"Let’s visualize the amount of work Ali and Deniz complete in 1 hour. Ali completes ¼ of the lesson per hour, and Deniz completes 12\frac{1}{2}21​ of the lesson per hour. Together, they complete 14+12\frac{1}{4} + \frac{1}{2}41​+21​ 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."
+First Hint:
+"Write both fractions with a common denominator: 14+12=14+24=34 .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 Correct Answer:
-"Excellent! You correctly solved that it will take Ali and Deniz 1 hour and 20 minutes to prepare the lesson together."
+"Excellent! You correctly solved that it will take 1 hour and 20 minutes (80 minutes) for Ali and Deniz 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."
+Problem Posing Activity
+Task Introduction:
+"Now it’s your turn to create a visualization-based proportional reasoning problem. Write a problem that requires solving with a visual approach before using procedural calculations."
+Prompts to Guide Problem Posing:
+Context Selection:
+"Think about real-world scenarios where visualization helps clarify proportional reasoning, such as food portions, speed-distance relationships, or shared work problems."
+Representation Choice:
+"Will your problem involve bar models, fraction strips, or double number lines? How can you structure it so students can first explore a visual approach?"
+Justification Requirement:
+"Ensure your problem requires students to justify their answer both visually and procedurally. How will they compare their methods?"
 
+Summary Section
+1️⃣ Content Knowledge
+You applied visualization and procedural strategies to proportional reasoning problems, reinforcing unit rates, fractions, and non-routine proportional problems.
+2️⃣ Creativity-Directed Practices
+Visualization and mathematical connections: You used visual reasoning to solve and understand proportional relationships before applying procedural methods.
+3️⃣ Pedagogical Content Knowledge
+You reflected on how visual approaches enhance student understanding before introducing procedural techniques.
+4️⃣ Common Core Mathematical Practices (CCSSM):
+✅ Make sense of problems & persevere in solving them
+✅ Reason abstractly & quantitatively
+✅ Model with mathematics
+✅ Use appropriate tools strategically
+✅ Attend to precision
 """