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?"* """