10 ways to include reflections in your Maths IA

Reflection in your Mathematics IA is difficult and vague! The criteria simply states that for 3/3 you need "substantial evidence of critical reflection.".

We recommend aiming to have 3-4 sentences of reflection per page to ensure you maximise your marks in this criteria.

1. Explain the Significance of Your Topic

• Reflect on why you chose the topic and its relevance to you personally or academically.

  • Example: "Studying optimization in marathon training was meaningful to me as a runner, and I wanted to explore how mathematics can improve performance."

    
    

2. Evaluate Your Mathematical Choices

• Discuss why specific mathematical techniques or models were chosen and whether they were effective.

  • Example: "I chose to use quadratic regression because it best fit the data trends compared to linear models, but I noticed limitations with extreme outliers."

    
    

3. Analyze Challenges Faced

• Reflect on the difficulties encountered during your exploration and how you overcame them.

  • Example: "One challenge was understanding how to apply integration to calculate areas. I consulted additional resources, such as asking my Higher Level friends to explain the concept of Integration by parts and practiced examples before implementing it in my IA."

• Describe a Key Turning Point where your understanding deepened or your approach changed significantly.

  • Example: "Initially, I struggled to relate exponential functions to population growth. However, after graphing the data and consulting with my teacher, I realized how the growth rate could be calculated through a derivative."

• Identify an error or misstep you made and how you fixed it, being specific about the impact on your results

  • Example: "Initially, I calculated velocity in meters per second but plotted it as kilometers per hour without conversion, which led to confusion but I corrected this by standardising all units to metres per second as this is the standard international units in physics."

4. Address the Strengths of Your IA

• Identify aspects of your IA that worked well or demonstrated a strong understanding of mathematics.

  • Example: "I used Desmos and Excel effectively to minimise human error when cleaning the data set which ensured a more accurate and reliable data analysis. For example, the formulas in Excel were applied and tested with several example cases to ensure they would work for all 500 data values. This enabled me to use a larger quantity of data than if I had done it manually."

    
    

5. Recognize Limitations

• Discuss the constraints or weaknesses of your exploration and their potential impact on results.

  • Example: "A limitation was the accuracy of my data collection, as I relied on secondary sources that might not fully align with real-world scenarios. This was because I was unable to collect primary data in the limited time available, and scope of the investigation."

    
    

6. Suggest Improvements & Extentions

• Offer realistic and specific suggestions for improving your IA if you were to do it again.

  • Example: "If I were to repeat this IA, I would collect primary data over a longer period to improve the reliability of my model. I would also make use of repeat trials by asking my peers to participate in the primary data collection."

• Consider future extentions to the investigation that would allow for additional research

  • Example: "A possible extention would be to consider additional variables such as tyre pressure. This would enable more accurate predictions on optimising the conditions for an F1 car."

  
  

7. Connect to Real-World Applications

• Reflect on how your findings relate to real-world scenarios or other fields of study.

  • Example: "The findings could be applied to urban planning by optimizing the design of public spaces to increase accessibility."

• Consider if there are limitation to the mathematical applications

  • Example:  "I initially tried linear regression, but the low R² value showed a poor fit. Switching to quadratic regression provided a much better correlation value. However, this was inconsistent with the real world scenario as a maximum point was not reached and would be inappropriate to use as a model."

    
    

8. Highlight Your Learning Experience

• Discuss what you learned about mathematics and problem-solving during the process.

  • Example: "This exploration deepened my understanding of the power of differential equations in predicting growth patterns. I also developed a greater appreciation for the use of technology in assisting with mathematical modelling."

    
    

9. Explore Alternate Approaches

• Reflect on other methods you could have used and their potential benefits or drawbacks.

  • Example: "Using a logarithmic model might have been more accurate for long-term predictions, but I lacked the time to fully explore this approach."

    
    

10. Discuss Personal Growth

• Reflect on how working on the IA helped you grow as a learner or thinker.

  • Example: "Completing this IA taught me the importance of perseverance in tackling complex problems and the value of critical thinking when analyzing results. I also appreciated the value of asking peers for help when concepts were unclear, such as my Higher Level classmates who explained how to perform vector calculations."

Final Tip

Ensure your reflections are written in a first-person voice and connect explicitly to the mathematical process and outcomes. This demonstrates both personal engagement and depth of thought.

Good Luck!

Reach out to us at Strive45 if you would like individual support with your IA from experienced tutors to maximise your marks!