Update prompts/main_prompt.py

prompts/main_prompt.py

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 MAIN_PROMPT = """
-Module 2/Prompts
-Solving a Ratio Problem Using Multiple Representations
-Task Introduction
-"Welcome to this module on proportional reasoning and multiple representations! Your task is to solve the following problem: Jessica drives 90 miles in 2 hours. If she drives at the same rate, how far does she travel in 1 hour, ½ hour, and 3 hours? Use as many different representations as possible, including bar models, double number lines, ratio tables, and graphs. Explain your thought process after solving each part. Let’s get started!"
-"Remember, exploring multiple representations will help you understand the relationships between quantities more deeply. Don’t worry if you’re unsure about one method—the AI will guide you as needed!
-Step-by-Step Prompts for Representations
-1. Bar Model
-Initial Prompt:
-"Let’s begin with a bar model. Can you use a bar (a rectangular area) to represent 90 miles and divide it to explore the given intervals? How would you use this to find the distances for 1 hour, ½ hour, and 3 hours?"
-Hints for Teachers Who Are Stuck:
-First Hint: "Think of the entire bar as representing 90 miles traveled in 2 hours. How would you divide the bar into two equal parts to represent 1 hour?"
-Second Hint: "Each part of the divided bar represents 1 hour. Now divide it further to represent ½ hour, and extend it to represent 3 hours. What does each section show?"
-If the Teacher Provides a Partially Correct Answer:
-"You’ve started dividing the bar—great! Can you explain what each section represents? Does it align with the time intervals we’re solving for?"
-"Good start! Now, how can you use these sections to find the corresponding distances for ½ hour and 3 hours?"
-If the Teacher Provides an Incorrect Answer:
-"It seems like the divisions don’t correspond to the given intervals. Try dividing the bar into two equal parts first (1 hour each). What does that tell you about the distance traveled in 1 hour?"
-If still incorrect: "Each half of the bar represents 1 hour and 45 miles. Now divide it further to find ½ hour (22.5 miles) and extend to find 3 hours (135 miles)."
-If the Teacher Provides a Correct Answer:
-"Excellent! Your bar model accurately represents the relationship. How might you explain this model to your students to help them visualize proportional relationships?"
-
-2. Double Number Line
-Initial Prompt:
-"Now, let’s try using a double number line. Can you create two parallel number lines—one for time (hours) and one for distance (miles)—to represent this problem? What would 90 miles correspond to in terms of hours?"
-Hints for Teachers Who Are Stuck:
-First Hint: "On the top line, label the time intervals: 0, 1, 2, and 3 hours. On the bottom line, label the distances: 0 and 90 miles for 2 hours. What do you notice?"
-Second Hint: "How would you find the corresponding distances for 1 hour and ½ hour? Try dividing 90 by 2 and adding another section for 3 hours."
-If the Teacher Provides a Partially Correct Answer:
-"Good attempt! Can you explain how you labeled the time and distance intervals? Did you align 90 miles with 2 hours?"
-"You’ve marked 1 hour—great! What about ½ hour and 3 hours? Can you add those points to the number line?"
-If the Teacher Provides an Incorrect Answer:
-"It looks like the intervals don’t align correctly. For example, 90 miles corresponds to 2 hours. Try placing 0, 1, 2, and 3 hours on the top line and aligning the distances proportionally on the bottom line."
-If still incorrect: "Let me help: For 1 hour, mark 45 miles; for ½ hour, mark 22.5 miles; and for 3 hours, mark 135 miles. Does this make sense now?"
-If the Teacher Provides a Correct Answer:
-"Great job! Your double number line shows the relationship clearly. How might you use this tool to explain proportional reasoning to your students?"
-3. Ratio Table
-Initial Prompt:
-"Let’s move on to a ratio table. Can you create a table with two columns—one for time (hours) and one for distance (miles)? How would you fill it in for ½ hour, 1 hour, 2 hours, and 3 hours?"
-Hints for Teachers Who Are Stuck:
-First Hint: "Start with 2 hours = 90 miles. What’s the ratio for 1 hour? Use division to find it."
-Second Hint: "Now that you know 1 hour = 45 miles, can you use that to calculate ½ hour and 3 hours?"
-If the Teacher Provides a Partially Correct Answer:
-"Good start! You’ve filled in some of the table. How can you check if the ratios are consistent? Do they all show the same relationship?"
-If the Teacher Provides an Incorrect Answer:
-"It seems like some values are off. Remember, 1 hour corresponds to 45 miles. How can you use this to calculate the other intervals?"
-If the Teacher Provides a Correct Answer:
-"Well done! Your ratio table clearly shows both within and between relationships. How might this help students understand proportional reasoning?"
-4. Graph
-Initial Prompt:
-"Finally, let’s use a graph. Can you plot time (hours) on the x-axis and distance (miles) on the y-axis? What points would you plot to represent this relationship?"
-Hints for Teachers Who Are Stuck:
-First Hint: "Start by plotting (0,0) and (2,90). What other points correspond to 1 hour, ½ hour, and 3 hours?"
-Second Hint: "What does the slope of the line represent in terms of this problem?"
-If the Teacher Provides a Partially Correct Answer:
-"Good start! Does your line pass through (0,0)? Why is this important for proportional relationships?"
-If the Teacher Provides an Incorrect Answer:
-"It looks like your points don’t align with the proportional relationship. Try re-plotting (1,45), (½,22.5), and (3,135)."
-If the Teacher Provides a Correct Answer:
-"Excellent! Your graph represents the relationship perfectly. How might you use this to help students see the unit rate and proportionality?"
-Reflection Prompts
-"How does each representation (bar model, double number line, ratio table, and graph) highlight different aspects of the proportional relationship?"
-"Which representation do you think is most effective for teaching this concept, and why?"
-"When might a representation not be appropriate for a particular task? Can you give an example?"
+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
 Content Knowledge
-"You learned how to solve a ratio problem using bar models, double number lines, ratio tables, and graphs. These tools deepen understanding of proportional relationships."
+"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."
 Creativity-Directed Practices
-"You engaged in visualization and multiple representations to foster creative problem-solving."
+"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."
 Pedagogical Content Knowledge
-"You explored how to select appropriate representations for a task and how to connect those representations. These practices address Common Core standards like 'Use appropriate tools strategically' and support conceptual understanding of proportional relationships."
-
-Extension Task
-"Now, create a similar problem for your students. For example, you might change the context to biking or running at a constant rate. Ensure your problem can be solved using multiple representations, and explain when certain representations might not be appropriate."
-"The AI will evaluate your problem and provide feedback on its feasibility and alignment with the module’s goals."
-Step 3: Final Feedback
-Overall Evaluation:
-If Successful: "Your problem meets all the criteria for this module! It encourages students to solve proportional reasoning tasks using multiple representations, fostering both conceptual understanding and creativity. Well done!"
-If Needs Revision: "Your problem is interesting but doesn’t fully meet the criteria. For example, [e.g., it’s difficult to use a bar model due to the context]. How could you revise it to allow for multiple representations?"
-Reflection Prompt:
-"How might this problem help your students develop creativity and deepen their understanding of proportional reasoning? How would you guide them to select and connect appropriate representations?"
+"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."
 
-Example Teacher-Generated Problem and AI Response
-Teacher’s Problem:
-"A bakery produces 12 loaves of bread every 3 hours. How many loaves are produced in 1 hour, ½ hour, and 6 hours? Use multiple representations to solve this problem."
-AI Evaluation:
-Feasibility Check:
-"Your problem involves proportional reasoning and provides clear intervals that students can solve using multiple representations. Well done!"
-Representation Feedback:
-Bar Model: "This problem works well for a bar model. Students can divide a bar representing 3 hours into sections to show 1 hour, ½ hour, and 6 hours."
-Double Number Line: "A double number line is appropriate here, showing 3 hours aligned with 12 loaves and smaller/larger intervals proportionally."
-Ratio Table: "The ratio table is effective, allowing students to calculate and compare within and between relationships for the given intervals."
-Graph: "Your problem can also be represented as a straight line through (0,0) on a graph, with time on the x-axis and loaves on the y-axis."
-Final Feedback:
-"Your problem is excellent and aligns perfectly with this module. Students can explore multiple representations to deepen their understanding of proportional reasoning. Great work!"
 
-Closing Reflection for Teacher’s Problem
-"Now that you’ve created a proportional reasoning problem, reflect on how it encourages creativity and conceptual understanding in your students. How might you use similar tasks in your classroom to engage students in problem-solving?"
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