## Question Generation Examples ### Overview The image presents instructions and examples for generating "Depth-2" questions that appropriately address a given "Depth-3" question. It outlines the criteria for these questions and provides four examples, each containing a Depth-3 question and a set of generated Depth-2 questions in JSON format. ### Components/Axes * **Instruction:** A set of guidelines for creating Depth-2 questions. * **Examples:** Four distinct examples, each consisting of: * **Depth-3 question:** The primary question to be addressed. * **Generated Depth-2 questions:** A list of questions designed to help answer the Depth-3 question. These are formatted as a JSON object with the key "Depth-2\_questions" and a list of question strings as the value. * **JSON Format:** The Depth-2 questions are structured in a JSON format: `{"Depth-2_questions": [list of Depth-2 question strings ]}`. ### Detailed Analysis or ### Content Details **Instruction:** * Create a maximum of 4 Depth-2 questions. * Depth-2 questions should focus on the application of procedural knowledge and skills, while Depth-3 questions focus on analysis and strategic knowledge. * Consider the cognitive complexity required to solve the Depth-3 question. * Ensure the Depth-2 questions adequately and comprehensively cover the necessary factual or conceptual knowledge. * Ensure the Depth-2 questions do not directly answer the Depth-3 question. * The number of generated Depth-2 questions should not exceed 4. **Example 1:** * **Depth-3 question:** "What is the intuition behind the Gram - Schmidt procedure?" * **Generated Depth-2 questions:** * "How do you project one vector onto another vector?" * "What does it mean for two vectors to be orthogonal, and how can you verify this property?" * "Describe the process of normalizing a vector." * "Explain how subtracting the projection of one vector from another results in orthogonality." * "Given a set of vectors, how can you determine if they are linearly independent?" * "How can the concept of linear independence be used to form a basis for a vector space?" **Example 2:** * **Depth-3 question:** "Why couldn't we test general relativity effects using the Eotvos experiment?" * **Generated Depth-2 questions:** * "How does the Eötvös experiment determine the equivalence between inertial mass and gravitational mass?" * "Describe the Equivalence Principle and its significance in the theory of General Relativity." * "Identify experiments or observations that could directly test the predictions of General Relativity, such as time dilation or the bending of light." * "How do experiments measuring time dilation differ in design and scope from those measuring mass equivalence?" **Example 3:** * **Depth-3 question:** "Why are aldehydes more readily oxidized to carboxylic acids compared to ketones, and how does this difference in reactivity influence their identification in the laboratory?" * **Generated Depth-2 questions:** * "How can you identify an aldehyde using Tollens' reagent?" * "Why does the carbonyl carbon in aldehydes have a significant partial positive charge?" * "How does the structure of ketones differ from that of aldehydes, and how does this affect their reactivity towards oxidation?" **Example 4:** * **Depth-3 question:** "In the context of computer programming, why is branching unstructured? And is it a bad design choice?" * **Generated Depth-2 questions:** * "What are the key differences between structured and unstructured branching in programming?" * "How does the 'goto' statement work in computer programming?" * "What are the potential risks involved with using unstructured branching in large software projects?" * "How does the structure of a program affect its maintainability?" * "How can the flow of execution in a program influence its debuggability?" ### Key Observations * The Depth-3 questions require a higher level of understanding and analysis. * The Depth-2 questions are designed to break down the Depth-3 question into smaller, more manageable parts. * The JSON format provides a structured way to represent the generated questions. * Each example provides a different subject area, showcasing the versatility of the question generation process. ### Interpretation The image illustrates a method for generating supporting questions (Depth-2) to aid in answering a more complex question (Depth-3). The instructions emphasize the importance of focusing on procedural knowledge for Depth-2 questions and analytical knowledge for Depth-3 questions. The examples demonstrate how to break down complex questions into smaller, more specific inquiries that, when answered, contribute to a comprehensive understanding of the original question. The use of JSON format suggests a potential application in automated question generation or knowledge representation systems. The examples cover diverse topics, indicating the broad applicability of this approach.

\n ## Text Document: User Prompt & Generated Questions ### Overview The image presents a text document containing a series of prompts and generated questions related to scientific and mathematical concepts. The document appears to be structured around a "Depth-3 question" followed by a set of "Depth-2 questions" designed to aid in answering the primary question. The document is formatted with hashtags indicating the type of question and example numbers. ### Components/Axes The document consists of text organized into sections delineated by hashtags. The sections are: * `#Instruction` * `#Example 1` * `#Depth-3 question` * `#Generated Depth-2 questions` * `#Example 2` * `#Depth-3 question` * `#Generated Depth-2 questions` * `#Example 3` * `#Depth-3 question` * `#Generated Depth-2 questions` * `#Example 4` * `#Depth-3 question` * `#Generated Depth-2 questions` * `#Additional Instruction` ### Detailed Analysis or Content Details **#Instruction:** "Create maximum of 4 Depth-2 questions that are necessary to answer the provided Depth-3 question correctly. - Remember that Depth-2 questions are centered on application of procedural knowledge and skills and Depth-3 questions are centered on analysis and strategic knowledge. - Take into consideration the level of cognitive complexity required to solve the Depth-3 question, so that your generated questions fall under the description of Depth-2 appropriately. - Ensure that your collection of generated Depth-2 questions adequately and comprehensively covers ALL the necessary factual or conceptual knowledge required to answer the given Depth-3 question. - Ensure that all of your generated Depth-2 questions do not directly answer to the given Depth-3 question. - The number of generated Depth-2 questions should not exceed 4. The generated Depth-2 questions should be in JSON format: {"Depth-2_questions": [list of Depth-2 question strings]}" **#Example 1:** `#Depth-3 question` What is the intuition behind the Gram - Schmidt procedure? `#Generated Depth-2 questions` ("Depth-2_questions": ["How do you project one vector onto another vector?", "What does it mean for two vectors to be orthogonal, and how can you verify this property?", "Describe the process of normalizing a vector.", "Explain how subtracting the projection of one vector from another results in orthogonality.", "Given a set of vectors, how can you determine if they are linearly independent?", "How can the concept of linear independence be used to form a basis for a vector space?"]) **#Example 2:** `#Depth-3 question` Why couldn’t we test general relativity effects using the Eötvös experiment? `#Generated Depth-2 questions` ("Depth-2_questions": ["How does the Eötvös experiment determine the equivalence between inertial mass and gravitational mass?", "Describe the Equivalence Principle and its significance in the theory of General Relativity.", "Identify experiments or observations that could directly test the predictions of General Relativity, such as time dilation or the bending of light.", "How do experiments measuring time dilation differ in design and scope from those measuring mass equivalence?"]) **#Example 3:** `#Depth-3 question` Why are aldehydes more readily oxidized to carboxylic acids compared to ketones, and how does this difference in reactivity influence their identification in the laboratory? `#Generated Depth-2 questions` ("Depth-2_questions": ["How can you identify an aldehyde using Tollens’ reagent?", "Why does the carbonyl carbon in aldehyde have a significant partial positive charge?", "Describe the mechanism of oxidation of aldehydes to carboxylic acids.", "What structural features of ketones hinder their oxidation to carboxylic acids?"]) **#Example 4:** `#Depth-3 question` Explain the role of the electron-hole pair in photoconductivity, and how does the wavelength of incident light affect the efficiency of this process? `#Generated Depth-2 questions` ("Depth-2_questions": ["What is the energy band gap in a semiconductor?", "Describe the process of electron-hole pair generation when a photon is absorbed by a semiconductor.", "How does the energy of a photon relate to its wavelength?", "Explain how the concentration of electron-hole pairs influences the conductivity of a semiconductor."]) **#Additional Instruction:** "Please confirm that you understand the instructions and the format of the expected output." ### Key Observations The document consistently follows a pattern of posing a complex "Depth-3" question and then breaking it down into more manageable "Depth-2" questions. The "Depth-2" questions are presented as a JSON formatted string. The questions cover a range of scientific disciplines, including linear algebra, physics (general relativity), organic chemistry, and semiconductor physics. ### Interpretation The document demonstrates a pedagogical approach to problem-solving, emphasizing the importance of decomposing complex questions into smaller, more focused inquiries. The use of "Depth-2" questions suggests a strategy for building foundational knowledge and procedural skills necessary to tackle more challenging analytical problems. The JSON format for the "Depth-2" questions indicates an intention for automated processing or integration with a question-answering system. The final instruction serves as a confirmation prompt, ensuring the user understands the task requirements. The document is a clear example of instructional design focused on fostering deeper understanding through structured questioning.

## Text Document: Instruction Set for Generating Depth-2 Questions ### Overview The image is a screenshot of a technical instruction document. It provides a detailed methodology and examples for creating "Depth-2" questions designed to support the answering of a more complex "Depth-3" question. The document is structured with a main instruction block followed by four illustrative examples and concludes with placeholders for a new question and answer. ### Components/Axes The document is organized into the following sequential sections: 1. **User prompt:** A header indicating the start of the instruction. 2. **## Instruction:** The core set of rules and guidelines. 3. **## Example 1 through ## Example 4:** Four complete examples demonstrating the application of the instructions. 4. **## Depth-3 question:** A placeholder for a new question to be processed. 5. **## Answer to the Depth-3 question:** A placeholder for the corresponding answer. 6. **## Generated Depth-2 questions:** A placeholder for the final output. ### Detailed Analysis / Content Details **1. Instruction Block (## Instruction):** The instructions specify the following rules for generating Depth-2 questions: * Create a maximum of 4 Depth-2 questions necessary to answer a provided Depth-3 question. * Depth-2 questions focus on **procedural knowledge and skills**. * Depth-3 questions focus on **analysis and strategic knowledge**. * The cognitive complexity of the generated Depth-2 questions must be appropriate for the Depth-3 question. * The collection of Depth-2 questions must comprehensively cover all necessary factual or conceptual knowledge to answer the Depth-3 question. * The Depth-2 questions must **not** directly answer the given Depth-3 question. * The number of generated Depth-2 questions should not exceed 4. * The output must be in JSON format: `{"Depth-2_questions": [list of Depth-2 question strings]}`. **2. Example 1:** * **Depth-3 question:** "What is the intuition behind the Gram - Schmidt procedure?" * **Generated Depth-2 questions (JSON):** ```json {"Depth-2_questions": ["How do you project one vector onto another vector?", "What does it mean for two vectors to be orthogonal, and how can you verify this property?", "Describe the process of normalizing a vector.", "Explain how subtracting the projection of one vector from another results in orthogonality.", "Given a set of vectors, how can you determine if they are linearly independent?", "How can the concept of linear independence be used to form a basis for a vector space?"]} ``` *Note: This example generates 6 questions, which exceeds the stated maximum of 4 in the instructions.* **3. Example 2:** * **Depth-3 question:** "Why couldn't we test general relativity effects using the Eotvos experiment?" * **Generated Depth-2 questions (JSON):** ```json {"Depth-2_questions": ["How does the Eötvös experiment determine the equivalence between inertial mass and gravitational mass?", "Describe the Equivalence Principle and its significance in the theory of General Relativity.", "Identify experiments or observations that could directly test the predictions of General Relativity, such as time dilation or the bending of light.", "How do experiments measuring time dilation differ in design and scope from those measuring mass equivalence?"]} ``` **4. Example 3:** * **Depth-3 question:** "Why are aldehydes more readily oxidized to carboxylic acids compared to ketones, and how does this difference in reactivity influence their identification in the laboratory?" * **Generated Depth-2 questions (JSON):** ```json {"Depth-2_questions": ["How can you identify an aldehyde using Tollens' reagent?", "Why does the carbonyl carbon in aldehydes have a significant partial positive charge?", "How does the structure of ketones differ from that of aldehydes, and how does this affect their reactivity towards oxidation?"]} ``` **5. Example 4:** * **Depth-3 question:** "In the context of computer programming, why is branching unstructured? And is it a bad design choice?" * **Generated Depth-2 questions (JSON):** ```json {"Depth-2_questions": ["What are the key differences between structured and unstructured branching in programming?", "How does the 'goto' statement work in computer programming?", "What are the potential risks involved with using unstructured branching in large software projects?", "How does the structure of a program affect its maintainability?", "How can the flow of execution in a program influence its debuggability?"]} ``` *Note: This example generates 5 questions, which exceeds the stated maximum of 4 in the instructions.* **6. Placeholders:** The document ends with three headers containing placeholders in curly braces, indicating where new content should be inserted: * `## Depth-3 question` `{question}` * `## Answer to the Depth-3 question` `{answer}` * `## Generated Depth-2 questions` ### Key Observations * **Inconsistency in Rule Adherence:** Examples 1 and 4 generate more than the maximum of 4 Depth-2 questions specified in the instructions (6 and 5, respectively). Examples 2 and 3 adhere to the limit (4 and 3, respectively). * **JSON Format:** All examples correctly use the specified JSON format for the output. * **Question Nature:** The generated Depth-2 questions successfully focus on procedural "how-to" or foundational concept questions (e.g., "How do you project...", "Describe the process...", "What are the key differences..."), avoiding direct answers to the overarching Depth-3 "why" or analytical questions. * **Content Coverage:** The sets of Depth-2 questions appear designed to build the prerequisite knowledge needed to tackle the more complex Depth-3 question. ### Interpretation This document serves as a **prompt engineering template or a few-shot learning guide** for an AI or a human tasked with decomposing complex analytical questions into a structured set of simpler, procedural sub-questions. The core pedagogical principle is that answering a high-level strategic question (Depth-3) requires mastery of several underlying procedural skills and factual knowledge (Depth-2). The examples demonstrate the desired transformation: * **From Analysis to Procedure:** Turning "Why..." or "What is the intuition behind..." questions into "How do you...", "Describe the process...", and "What does it mean..." questions. * **Knowledge Scaffolding:** The generated questions act as a learning scaffold. For instance, to understand the *intuition* behind Gram-Schmidt (Depth-3), one must first understand vector projection, orthogonality, and normalization (Depth-2). The inconsistencies in question count (violating the "max 4" rule) suggest the examples may be illustrative rather than strict, or that the rule is flexible. The final placeholders indicate this is a reusable template where a user can input any new Depth-3 question and its answer to receive a tailored set of supporting Depth-2 questions. The ultimate goal is to ensure comprehensive conceptual coverage before attempting synthesis or high-level analysis.

## Screenshot: Depth-2 Question Generation Framework ### Overview The image contains a structured technical prompt for generating Depth-2 questions to support answering a Depth-3 question. It includes formatting rules, examples, and a JSON output template. ### Components/Axes 1. **User Prompt Section** - **Labels**: - `## Instruction`: Defines requirements for generating Depth-2 questions. - `## Example 1`, `## Example 2`, etc.: Illustrate application of the framework. - **Content**: - Rules for Depth-2 questions (e.g., procedural knowledge, cognitive complexity). - JSON output format: `{"Depth-2_questions": ["list of strings"]}`. 2. **Example Structure** - **Depth-3 Question**: Complex, open-ended questions (e.g., "What is the intuition behind the Gram-Schmidt procedure?"). - **Generated Depth-2 Questions**: - Sub-questions addressing procedural steps, definitions, and conceptual relationships. - Example 1: - Depth-3: "What is the intuition behind the Gram-Schmidt procedure?" - Depth-2: - "How do you project one vector onto another?" - "What does it mean for two vectors to be orthogonal?" - "Explain how subtracting the projection of one vector from another results in orthogonality." - "How can the concept of linear independence be used to form a basis for a vector space?" 3. **JSON Output Template** - Key: `"Depth-2_questions"` - Value: Array of strings representing sub-questions. ### Detailed Analysis - **Formatting Consistency**: - All examples follow the same structure: `# Depth-3 question` followed by `# Generated Depth-2 questions` in JSON. - Depth-2 questions avoid directly answering the Depth-3 question but provide foundational knowledge. - **Content Patterns**: - Depth-2 questions focus on: 1. **Procedural Steps** (e.g., "How do you project one vector onto another?"). 2. **Definitions** (e.g., "What does it mean for two vectors to be orthogonal?"). 3. **Conceptual Relationships** (e.g., "How does the structure of ketones differ from aldehydes?"). 4. **Application of Principles** (e.g., "How can linear independence form a basis?"). - **Example Variations**: - **Example 1 (Math)**: Focuses on linear algebra concepts (orthogonality, projections). - **Example 2 (Physics)**: Relates to relativity and experimental design (Eötvös experiment). - **Example 3 (Chemistry)**: Compares reactivity of aldehydes vs. ketones. - **Example 4 (Programming)**: Explores unstructured branching in code. ### Key Observations 1. **Depth-2 Question Design**: - Questions are intentionally non-answerable in isolation but collectively enable solving the Depth-3 question. - Emphasis on foundational knowledge (e.g., definitions, procedural steps). 2. **Domain-Specific Adaptability**: - Framework applies across disciplines (math, physics, chemistry, programming). 3. **JSON Structure**: - Strict adherence to key-value pairing for programmatic parsing. ### Interpretation The framework demonstrates a systematic approach to decomposing complex problems into manageable sub-questions. By focusing on procedural, definitional, and conceptual layers, it ensures comprehensive coverage of prerequisite knowledge. The JSON format suggests automation potential, enabling scalable question generation for educational or AI training purposes. **Notable Insight**: The examples highlight the importance of aligning Depth-2 questions with the cognitive demands of the Depth-3 question, ensuring they address gaps in procedural or strategic understanding rather than factual recall.