Why Clear Reasoning Is the Core of Mathematical Communication
In the IB Math IA, examiners don’t just grade your calculations — they evaluate your reasoning.
It’s not enough to show that you used mathematics correctly; you must explain how and why each step leads logically to your conclusions.
Strong reasoning transforms your IA from a set of equations into a coherent mathematical argument.
With RevisionDojo’s IA/EE Guide, Writing Templates, and Exemplars, you’ll learn how to present reasoning that’s logical, elegant, and easy for examiners to follow.
Quick-Start Checklist
Before writing any reasoning section:
- Define what you’re solving and why it matters.
- Show logical progression between steps.
- Explain mathematical transitions, not just show them.
- Connect results back to your aim.
- Use RevisionDojo’s Writing Templates to structure explanations clearly.
Step 1: Understand What “Reasoning” Means in the IA
Reasoning is the bridge between your calculations and your conclusions.
It answers questions like:
- Why did you choose this method?
- Why does this result make sense?
- How does this support your aim?
RevisionDojo’s Reasoning Framework helps you turn mathematical processes into examiner-friendly explanations.
Step 2: Start Every Section With a Purpose Statement
Each mathematical section should begin by stating what you’re doing and why.
Example:
“To determine the time at which the projectile reaches maximum height, I used differentiation to find when the rate of change of height equals zero.”
This sets context before introducing any formulas.
RevisionDojo’s Purpose Builder provides phrasing templates for starting mathematical discussions clearly.
Step 3: Explain Key Steps Between Equations
Never assume the reader can infer your reasoning.
After every major step, include a short explanation of what changed and why.
Example:
“By integrating the velocity function, I obtained the displacement equation, which represents total distance traveled over time.”
RevisionDojo’s Step Annotation Prompts remind you to add interpretive sentences after each key calculation.
Step 4: Use Mathematical Connectives
Smooth transitions make reasoning flow naturally.
Use words like:
- “Therefore,”
- “Hence,”
- “It follows that,”
- “By substitution,”
- “As a result.”
RevisionDojo’s Writing Templates include pre-built connective lists for professional, examiner-approved phrasing.
Step 5: Support Every Step With Mathematical Logic
Reasoning must be consistent with mathematical principles — not guesses or assumptions.
If you approximate or simplify, explain why.
Example:
“The resistance term was neglected because its contribution was less than 1% of total force, based on experimental data.”
RevisionDojo’s Logic Checker ensures your explanations follow valid mathematical reasoning patterns.
Step 6: Combine Words and Math Naturally
Equations should flow within sentences, not stand alone.
Example:
“Using f(x) = 3x² + 2x – 1, the derivative f'(x) = 6x + 2 gives the instantaneous rate of change at any point.”
RevisionDojo’s Sentence Integration Tool helps you blend symbols and text for clean, readable presentation.
Step 7: Clarify Assumptions and Choices
Examiners reward awareness.
When you make choices — like selecting a function type or ignoring an outlier — explain your reasoning clearly.
Example:
“A quadratic model was chosen because the data exhibited a single turning point, consistent with parabolic motion.”
RevisionDojo’s Decision Justifier provides phrasing templates for defending mathematical choices.
Step 8: Link Reasoning Back to Your Aim
At the end of each section, tie results to your research question.
Example:
“This result supports the hypothesis that the range increases linearly with initial velocity, confirming the relationship proposed in the aim.”
RevisionDojo’s Aim Alignment Tool ensures your reasoning consistently reinforces your investigation goal.
Step 9: Use Diagrams or Graphs to Support Logic
Visuals often clarify relationships that equations alone can’t show.
Annotate graphs or sketches directly with reasoning cues like slopes, intercepts, and trends.
RevisionDojo’s Graph Annotation Tool helps integrate reasoning visually within your IA.
Step 10: End Each Major Section With a Mini-Reflection
Summarize what the reasoning achieved and how it advanced your understanding.
Example:
“This analysis demonstrated that mathematical reasoning can predict motion with high accuracy when ideal conditions are assumed.”
RevisionDojo’s Reflection Prompts make it easy to close sections with reflective insight.
Frequently Asked Questions
1. How much explanation is too much?
If a mathematically literate reader could follow your logic without extra words, you’re clear enough. Aim for precision, not repetition.
2. Should I explain simple algebraic steps?
Only when they introduce a new concept, pattern, or idea — not for routine manipulation.
3. What if I used technology for part of the reasoning?
Explain how the tool supported your logic, not just that it gave you an answer.
Final Thoughts
Clear reasoning is what separates “correct math” from “understood math.”
It transforms your IA into a coherent narrative that examiners can follow easily — and reward highly.
With RevisionDojo’s IA/EE Guide, Writing Templates, and Exemplars, you’ll learn to communicate mathematical reasoning that’s logical, structured, and deeply insightful.
Call to Action
Make your reasoning your strongest feature.
Use RevisionDojo’s Writing Templates and IA/EE Guide to craft clear, logical explanations that elevate every part of your IB Math IA.
