Criterion D: Reflection

🪞 Criterion D: Reflection (3 marks total)

This criterion evaluates how well you review, analyze, and evaluate the math in your exploration. It’s not enough to just do the math—you must think about what it means, how it worked, and what it taught you.

✅ What Is “Reflection” in a Math IA?

Reflection is about stepping back and thinking critically about your process, results, and learning.

It includes:

• Evaluating the quality of your results

• Linking back to your aim

• Considering limitations and alternative methods

• Asking “what does this tell me?” and “what could I try next?”

🌟 Levels of Reflection

🔹 Basic (Limited Reflection):

• Just restates results without analysis

• No insight, no connections, no questions

❌ Example: “The model was a quadratic function. The R² value was 0.97.”
(Only describing; not evaluating or linking to the aim)

🔸 Meaningful Reflection:

• Comments on findings in light of the aim

• Mentions what was learned

• Identifies limitations or compares methods

✅ Example: “The model fits well for smaller data values, but breaks down as x increases. This shows that a quadratic model isn’t ideal for long-term predictions.”

🔶 Critical Reflection (for Top Marks):

• Goes deeper, explores implications

• Discusses mathematical significance

• Raises new questions or alternative approaches

• Reflection is found throughout, not just in the conclusion

🧠 Example: “Although the exponential model gave a high R², it underestimated the final values. This might be due to external factors like resource limitations, suggesting a logistic model might better represent the situation. If I were to extend this investigation, I would compare exponential and logistic models and analyze long-term behavior.”

✅ How to Show Reflection Throughout the IA

You can reflect at multiple points:

🔹 In the Introduction:

• Why did you choose this topic?

• What are you curious about?

“I’ve always wondered why traffic seems to build in waves. I want to see if a mathematical model can explain this.”

🔹 During the Exploration:

• Are the results what you expected?

• Did anything surprise you?

• Did you need to adjust your approach?

“Initially, I expected a linear relationship, but plotting the data revealed a curved pattern. This led me to test a power function instead.”

🔹 In the Conclusion:

• Did you meet your aim?

• What are the implications of your findings?

• What would you do differently next time?

“This model helps understand growth patterns in social media users, but it doesn’t account for sudden viral growth. Including a model with a variable rate of change could provide more accuracy.”

🧠 Key Phrases for Reflection

Here are some sentence starters you can use to naturally reflect in your writing:

• “This result suggests that…”

• “A limitation of this method is…”

• “An interesting pattern I noticed was…”

• “If I were to extend this exploration, I would…”

• “This made me realize that…”

• “Comparing both approaches showed that…”

✅ Summary Checklist for Criterion D

🔚 To Score Top Marks (Level 3):

• Show critical reflection (not just summary) in multiple parts of the IA

• Reflect on your mathematical results, your approach, and your learning

• Offer thoughtful next steps, alternative perspectives, or broader implications