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
-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."
-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."
-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."
+Module 9: Reflecting on Classroom Practices through Video Analysis
+Task Introduction
+"Welcome to this module on observing classroom practices! In this module, you’ll watch a video of a lesson on proportional relationships and reflect on the teacher’s practices, student reasoning, and the connections to Common Core standards. Let’s begin!"
+Video:
+"Watch the video provided at this link. Before observing the students, solve the task presented in the video. Then, watch the video to see how the teacher and students approach the problem."
+
+Pre-Video Task Prompt
+Initial Task:
+"Before watching the video, solve the problem presented. Focus on your solution process and how you reasoned about the proportional relationship."
+Hints if Teachers Are Stuck:
+"Think about how you can represent the task using visuals, such as bar models, circle diagrams, or equations."
+"Consider the proportional relationship in the problem. What fraction or percentage represents the key relationship in this task?"
+Reflection Before the Video:
+"How did solving the task help you think about proportional reasoning? What connections can you anticipate students might make as they solve this problem?"
+
+Post-Video Reflection Prompts
+1. Creativity-Directed Practices
+Initial Prompt:
+"What creativity-directed practices did you notice the teacher implementing during the lesson? Think about how the teacher encouraged students to approach the task creatively."
+Hints if Teachers Are Stuck:
+"Consider whether the teacher used visuals, multiple representations, or mathematical connections. Did the teacher encourage students to collaborate and freely share ideas?"
+Expected Answers:
+"Possible creativity-directed practices include using visuals, multiple representations, and making mathematical connections. The teacher also encouraged students to freely share ideas and collaborate."
+Follow-Up Prompt:
+"How might these practices support students’ conceptual understanding of proportional reasoning?"
+
+2. Small Group Interactions
+Initial Prompt:
+"What did you notice during the small group interactions? What types of questions did the teacher ask to guide students?"
+Hints if Teachers Are Stuck:
+"Did the teacher reference students’ visual models or ask questions that required students to interpret others’ representations?"
+"How did the teacher ensure that students connected their thinking to the content goal of the lesson?"
+Expected Answers:
+"The teacher referenced student-created visual models and asked questions that required students to make sense of others’ representations. These interactions fostered students’ mathematical understanding and encouraged them to connect their visual representations to the task’s content goals."
+Follow-Up Prompt:
+"How might asking pointed questions during small group interactions help students build a deeper understanding of proportional relationships?"
+
+3. Student Reasoning and Connections
+Initial Prompt:
+"How did the students reason with the task? How did they connect percent relationships to fractions?"
+Hints if Teachers Are Stuck:
+"Did students use visuals such as bar models or circles to represent the problem? How did they explain their reasoning?"
+"What connections did students make between their representations and the proportional relationships in the task?"
+Expected Answers:
+"Many students used circles or bar models to represent the entire class, splitting the whole into four parts and shading three of them to represent 3/4. Students explained how their representations connected to the task and used these visuals to reason about percent relationships."
+Follow-Up Prompt:
+"How might encouraging students to use visuals support their ability to connect proportional relationships to fractions and percentages?"
+4. Common Core Practice Standards
+Initial Prompt:
+"What Common Core practice standards do you think the teacher emphasized during the lesson? Choose four and explain how you observed these practices in action."
+Hints if Teachers Are Stuck:
+"Consider whether the teacher encouraged students to make sense of the problem, use visuals to model their thinking, construct arguments, or use tools strategically."
+"Did the teacher encourage students to reason abstractly and quantitatively or look for structures in the task?"
+Expected Standards and Justifications:
+"The teacher emphasized:
+Make sense of problems & persevere in solving them: Students interpreted the problem and continued reasoning through their visual models.
+Model with mathematics: Students used visual models such as bar models and circle diagrams to represent the proportional relationships.
+Use appropriate tools strategically: Students selected visual tools like bar models to help them make sense of the task.
+Construct viable arguments & critique the reasoning of others: Students explained their representations and reasoning, and the teacher facilitated peer discussions to critique and build on others’ ideas."
+Follow-Up Prompt:
+"How might these practices support students in developing a deeper understanding of proportional reasoning?"
+Objective Summary
+Content Knowledge:
+"Through this module, we explored how visuals and multiple representations support proportional reasoning and how these practices align with Common Core standards."
+Creativity-Directed Practices:
+"We observed creativity-directed practices such as visualization, multiple representations, and mathematical connections, as well as collaborative and student-centered approaches to reasoning."
+Pedagogical Content Knowledge:
+"We analyzed how teachers can use questioning techniques, small group interactions, and student-centered visuals to deepen students’ conceptual understanding of proportional reasoning. We also reflected on how these practices address Common Core standards such as modeling with mathematics, using tools strategically, and constructing viable arguments."
+
+Problem Posing Activity
+Task Introduction
+Initial Prompt:
+"Based on what you observed, pose a problem that encourages students to use visuals and proportional reasoning to solve a task. How might this problem help students connect their reasoning to Common Core practices?"
+Prompts to Guide Problem Posing:
+"What real-world context will you use for your problem? How will students use visuals like bar models or circle diagrams to represent proportional relationships?"
+AI Evaluation Prompts
+Evaluating Problem Feasibility:
+"Does your problem encourage students to use visuals and make sense of proportional relationships? How does it align with the Common Core standards we discussed?"
+Feedback:
+If Feasible: "Great problem! It aligns well with the objectives and encourages students to use visuals to reason about proportional relationships."
+If Not Feasible: "Your problem might need revision. For example, ensure students can represent the relationship using visuals and connect their reasoning to proportional thinking. How could you adjust it?"
+
+End of Module Reflection
+Final Prompt:
+"What are your key takeaways from this module? How might you apply the practices you observed in your own teaching to support students’ understanding of proportional relationships?"
+
+
 """