Once you’ve chosen a topic, crafting a precise and focused research question (RQ) is critical to the success of your Math IA. The RQ serves as the guiding statement for your exploration, ensuring clarity, direction, and alignment with the IA criteria.
Why Is the Research Question Important?
A well-crafted RQ:
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Establishes the purpose and scope of your IA.
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Ensures a clear mathematical focus.
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Guides the analysis and structure of your investigation.
Steps to Develop a Research Question
1. Understand Your Chosen Topic
Break your topic into its key components. Consider the real-world context and the mathematical concepts you aim to explore.
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Example Topic: Modeling ITC Ltd.'s Stock Prices with Regression Analysis
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Real-World Context: Stock price prediction is vital for investors and businesses.
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Mathematical Concepts: Linear regression, polynomial regression, residual analysis, RMSE, R².
2. Define the Focus of Your Exploration
Ask yourself:
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What am I trying to find out or prove?
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Which mathematical tools will I use?
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How will I measure the effectiveness of my analysis?
For the topic above:
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Objective: Compare the accuracy of polynomial and linear regression models.
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Focus: Assess model accuracy using RMSE and R² values.
3. Make It Specific and Measurable
A strong RQ avoids vagueness and defines measurable outcomes. Use terms that specify the scope and mathematical approach.
Weak Example:
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“How can regression analysis be used to study ITC’s stock prices?”
(Too broad and lacks specificity.)
Improved Example:
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“How accurately can polynomial regression model ITC Ltd.’s stock prices over a 10-year period, and how does it compare to linear regression?”
(Specific and highlights both the mathematical method and evaluation criteria.)
4. Ensure Mathematical Rigor
Choose an RQ that requires in-depth mathematical exploration rather than simple calculations.
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Good Example:
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“Can polynomial regression predict ITC’s stock prices more accurately than linear regression, as measured by RMSE and R² values?”
(Involves multiple steps: applying two regression models, calculating residuals, and interpreting statistical accuracy.)
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Poor Example:
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“What is the average trend of ITC’s stock prices over 10 years?”
(Descriptive, lacks analysis and mathematical complexity.)
5. Keep It Realistic
The RQ should match the time and resources available. Avoid overly ambitious questions that require advanced mathematics or inaccessible data.
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Example of Overambition:
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“How can machine learning algorithms predict ITC’s stock prices with 95% accuracy?”
(Unrealistic for an IA due to complexity and scope.)
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Refined Alternative:
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“How accurately can a quadratic regression model predict ITC’s stock prices compared to a linear regression model?”
6. Align with IB Criteria
The RQ should connect to the IB Math syllabus and demonstrate criteria such as personal engagement, mathematical communication, and reflection.
Template for Developing Research Questions
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Start with the mathematical method:
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“How effectively can [mathematical method] be used to model [real-world phenomenon]?”
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Add a comparative or evaluative element:
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“How does [Method A] compare to [Method B] in modeling [phenomenon]?”
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Specify evaluation criteria:
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“…as measured by [specific metrics].”
Example RQ Templates:
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“How accurately can polynomial regression predict/model [real-world phenomenon] compared to linear regression?”
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“What is the optimal degree of a polynomial function for modeling [phenomenon] as measured by [metric]?”
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“How does the predictive accuracy of [mathematical model] change when applied to [data subsets]?”
Examples for ITC Stock Prices Topic
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Basic:
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“How accurately can polynomial regression model ITC Ltd.’s stock prices over the past decade?”
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Comparative:
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“How does the accuracy of polynomial regression compare to linear regression in modeling ITC’s stock prices?”
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Optimization Focus:
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“What is the optimal degree of a polynomial function for predicting ITC’s stock prices, and how does this compare to a linear model?”
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Advanced:
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“How do varying data sample sizes impact the accuracy of polynomial regression in modeling ITC’s stock prices?”