Why Critical Thinking Separates Good IAs from Great Ones
Critical thinking is the foundation of Criterion E (Reflection) — the skill that differentiates a technically correct IA from an intellectually impressive one.
It’s not just about doing the math; it’s about questioning, analyzing, and evaluating the mathematical decisions you make.
Examiners look for signs that you’ve thought about your math deeply: that you understand its assumptions, can evaluate its reliability, and can propose logical improvements.
With RevisionDojo’s IA/EE Guide, Reflection Prompts, and Evaluation Framework, you’ll learn how to show critical thinking naturally in every part of your IA.
Quick-Start Checklist
Before writing your IA, ask yourself:
- Do I explain why I chose this method, not just what I did?
- Have I discussed alternative approaches or limitations?
- Did I evaluate how well my model or method worked?
- Have I shown how my understanding evolved?
- Use RevisionDojo’s Reflection Prompts to embed critical thinking at every stage.
Step 1: Start by Asking Mathematical “Why” Questions
Critical thinking starts with curiosity.
Instead of only describing steps, ask why each one makes sense.
Example:
“Why does an exponential function describe this growth pattern better than a linear model?”
RevisionDojo’s Critical Question Bank helps you identify reflective prompts that encourage analytical reasoning.
Step 2: Justify Every Mathematical Decision
Each time you choose a formula, model, or method, explain why it fits your aim.
Example:
“Differentiation was used because it reveals the exact point where velocity changes direction — essential to determine maximum height.”
RevisionDojo’s Decision Justifier Tool helps you frame method selection as a rational, reflective process.
Step 3: Evaluate Strengths and Weaknesses of Your Approach
Critical thinkers don’t pretend their math is flawless.
They recognize both what worked and what didn’t.
Example:
“While the regression model fits the central data well, it fails to capture nonlinear fluctuations at the boundaries.”
RevisionDojo’s Evaluation Framework helps you phrase balanced analyses of method performance.
Step 4: Reflect on the Reliability of Your Data or Assumptions
Question whether your foundations are as solid as they seem.
Example:
“The assumption of constant air resistance simplified calculations but reduced physical accuracy.”
RevisionDojo’s Assumption Analyzer helps you identify weak spots and frame them constructively.
Step 5: Discuss Alternative Mathematical Methods
Show that you considered other ways to solve the problem — even if you didn’t use them.
Example:
“A logarithmic model was also tested but produced inconsistent residuals, confirming the exponential fit as more appropriate.”
RevisionDojo’s Alternative Method Builder helps you evaluate and compare different approaches succinctly.
Step 6: Reflect on the Meaning of Your Results
Don’t just present numbers — interpret them.
Ask what they tell you about the system or concept you’re studying.
Example:
“The decreasing derivative values suggest a slowing rate of change, consistent with energy loss over time.”
RevisionDojo’s Interpretation Prompts guide you toward deeper insight in analysis sections.
Step 7: Link Reflection to Mathematical Understanding
Critical thinking isn’t about vague commentary — it’s about showing how your mathematical understanding evolved.
Example:
“Initially, I expected a linear trend, but analyzing residuals revealed a clear curvature, prompting a deeper exploration into exponential behavior.”
RevisionDojo’s Learning Reflection Templates help you articulate intellectual growth clearly.
Step 8: Evaluate Your Model’s Limitations Objectively
Show that you can assess accuracy and scope critically.
Example:
“This model accurately predicts short-term motion but diverges for higher velocities due to unmodeled drag forces.”
RevisionDojo’s Limitations Evaluator helps phrase reflective commentary in a professional and objective tone.
Step 9: Propose Realistic Improvements
Critical thinkers don’t just point out flaws — they suggest ways to improve.
Example:
“Future exploration could incorporate variable resistance to improve alignment with experimental results.”
RevisionDojo’s Improvement Generator helps you write practical, forward-looking suggestions.
Step 10: Reflect on What You Learned About Mathematics Itself
End your IA by showing how the process changed your perspective.
Example:
“This investigation deepened my appreciation for how mathematical modeling transforms real-world complexity into understandable patterns.”
RevisionDojo’s Meta-Reflection Prompts guide you in connecting mathematical practice to personal insight.
Frequently Asked Questions
1. How is critical thinking graded in the IA?
It’s the core of Criterion E (Reflection) — showing awareness, insight, and evaluation earns top marks.
2. Is it possible to over-reflect?
No, as long as reflections are specific and mathematically relevant. Avoid repetition or vague commentary.
3. Where should I include critical thinking?
Throughout the IA — in your model choice, analysis, and evaluation sections. Don’t save it just for the end.
Final Thoughts
Critical thinking is what transforms your IA from procedural to powerful.
It proves that you don’t just apply mathematics — you analyze, question, and understand it.
With RevisionDojo’s IA/EE Guide, Reflection Prompts, and Evaluation Framework, you’ll learn to demonstrate analytical depth that impresses examiners and elevates your IA into the top scoring bands.
Call to Action
Think deeper, score higher.
Use RevisionDojo’s Reflection Prompts and IA/EE Guide to showcase critical thinking in every stage of your IB Math IA.
