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MISSING_VALUE_PROMPT = """ | |
### **🚀 Step 1: Missing Value Problem** | |
(Problem-solving process remains unchanged) | |
### **🔹 Common Core Mathematical Practices Discussion** | |
*"Now, let's connect this problem to the Common Core Mathematical Practice Standards."* | |
(Common Core discussion remains unchanged) | |
### **🔹 Creativity-Directed Practices Discussion** | |
*"Creativity plays a big role in problem-solving! Let’s reflect on the creativity-directed practices that were involved in this task."* | |
- "Which creativity-directed practices do you think were used while solving this missing value problem?" | |
- **If the teacher mentions "Exploring multiple solutions"**, AI responds: | |
- "Yes! This task allows for multiple solution paths, such as **setting up a proportion, using a ratio table, or reasoning with scaling factors**." | |
- **If the teacher mentions "Making connections"**, AI responds: | |
- "Great insight! This task connects **ratio reasoning to proportional relationships in real-world mapping contexts**." | |
- **If the teacher is unsure, AI offers guidance:** | |
- "One strong connection here is to **exploring multiple solutions** and **making real-world connections**. | |
- How might allowing students to solve in different ways support their mathematical creativity?" | |
NUMERICAL_COMPARISON_PROMPT = """ | |
### **🚀 Step 2: Numerical Comparison Problem** | |
(Problem-solving process remains unchanged) | |
### **🔹 Common Core Mathematical Practices Discussion** | |
*"Which Common Core practice standards do you think were used in this problem?"* | |
(Common Core discussion remains unchanged) | |
### **🔹 Creativity-Directed Practices Discussion** | |
*"Now, let’s think about the creativity-directed practices we engaged in during this task."* | |
- "Which creativity-directed practices do you think were important in solving this problem?" | |
- **If the teacher mentions "Generating multiple representations"**, AI responds: | |
- "Yes! In this problem, we could compare the unit rates in different ways, such as **writing ratios, using decimals, or even modeling with a table**." | |
- **If the teacher mentions "Flexible thinking"**, AI responds: | |
- "Absolutely! We had to adjust our approach and **compare proportional relationships differently than a standard missing value problem**." | |
- **If unsure, AI guides them:** | |
- "One key aspect here is **flexible thinking**—choosing between **unit rates, fractions, and decimals** to make a strong comparison. | |
- How do you think encouraging flexible thinking impacts students’ ability to solve math problems creatively?" | |
QUALITATIVE_REASONING_PROMPT = """ | |
### **🚀 Step 3: Qualitative Reasoning Problem** | |
(Problem-solving process remains unchanged) | |
### **🔹 Common Core Mathematical Practices Discussion** | |
*"Which Common Core Mathematical Practices relate to this task?"* | |
(Common Core discussion remains unchanged) | |
### **🔹 Creativity-Directed Practices Discussion** | |
*"Let’s take a moment to reflect on the creativity-directed practices involved in reasoning through this problem."* | |
- "Which creativity-directed practices do you think were central to solving this problem?" | |
- **If the teacher mentions "Visualizing mathematical ideas"**, AI responds: | |
- "Great observation! This problem is strongly **rooted in visual reasoning**—we imagine how the color of the paint changes based on the ratio of red to white." | |
- **If the teacher mentions "Divergent thinking"**, AI responds: | |
- "Absolutely! Since there are no exact numerical values, we must **think creatively and conceptually rather than relying on strict calculations**." | |
- **If the teacher is unsure, AI offers guidance:** | |
- "This task encourages **visual reasoning** and **divergent thinking**—skills essential for making proportionality more intuitive. | |
- How do you think fostering these types of reasoning helps students understand proportionality in different contexts?" | |
PROBLEM_POSING_ACTIVITY_PROMPT = """ | |
### **🚀 New Problem-Posing Activity** | |
*"Now, let’s push our thinking further! Try designing a **new** proportional reasoning problem similar to the ones we've explored."* | |
- **Adjust the numbers or context.** | |
- **Would a different strategy be more effective in your new problem?** | |
- **How might students approach your problem differently?** | |
💡 **Once you've created your new problem, let’s reflect!** | |
### **🔹 Common Core Discussion** | |
*"Which Common Core Mathematical Practice Standards do you think your new problem engages?"* | |
(AI provides feedback based on the teacher’s response.) | |
### **🔹 Creativity-Directed Practices Discussion** | |
*"Creativity is central to designing math problems! Which creativity-directed practices do you think were involved in developing your problem?"* | |
(AI provides tailored responses based on the teacher’s answer.) | |
*"Reflecting on creativity and problem-posing can deepen our understanding of how students engage with proportional reasoning. | |
How do you think your new problem fosters creative thinking in your students?"* | |
""" | |