Self-explanation is a powerful metacognitive strategy where you articulate your understanding of mathematical concepts, procedures, and problem-solving steps to yourself. This evidence-based technique enhances comprehension, retention, and transfer of mathematical knowledge.

Core Self-Explanation Methods for Mathematics

1. Explain Problem-Solving Steps

As you work through mathematical problems, verbalize or write out explanations for each step:

  • Why you chose a particular approach
  • How each step connects to mathematical principles
  • What the intermediate results mean in context

2. Connect New Concepts to Prior Knowledge

When learning new mathematical concepts:

  • Explain how new concepts relate to what you already know
  • Identify similarities and differences with familiar concepts
  • Create analogies that bridge new and existing knowledge

3. Explain Worked Examples

When studying worked examples:

  • Cover up the solution steps and try to predict what comes next
  • Explain why each step was taken in the solution
  • Identify the underlying principles being applied

4. Justify Mathematical Claims

Practice explaining:

  • Why mathematical properties or theorems are true
  • How you know a solution is correct
  • Why alternative approaches might or might not work

Example of Self-Explanation in Action

Problem: Solve 2x + 5 = 13

Standard work:

2x + 5 = 13
2x = 8
x = 4

With self-explanation:

"I need to isolate x to solve this equation. I'll start by subtracting 5 from both sides to get rid of the constant term on the left:
2x + 5 - 5 = 13 - 5
2x = 8
Now I need to divide both sides by 2 to isolate x:
2x ÷ 2 = 8 ÷ 2
x = 4
I can verify this is correct by substituting x = 4 back into the original equation:
2(4) + 5 = 8 + 5 = 13 ✓"

Implementation Strategies

  • Math Journal: Keep a dedicated notebook where you write out your self-explanations for new concepts and challenging problems.
  • Think-Aloud Practice: Verbalize your thought process as you solve problems, either alone or with a study partner.
  • Teach Concepts: Explain mathematical concepts to others (or to an imaginary audience) to reinforce your understanding.
  • Error Analysis: When you make mistakes, explain what went wrong and why the correct approach works.
  • Concept Maps: Create visual representations that connect related mathematical ideas, explaining the relationships between them.

Benefits of Self-Explanation in Mathematics

Deeper Conceptual Understanding

Self-explanation forces you to think about the "why" behind mathematical procedures, developing stronger conceptual knowledge rather than just procedural skills.

Identification of Knowledge Gaps

When you struggle to explain something, it immediately highlights areas where your understanding is incomplete.

Enhanced Problem-Solving Skills

By explaining your problem-solving process, you develop more strategic approaches and build a toolkit of strategies.

Improved Knowledge Transfer

Self-explanation helps you apply mathematical concepts to new contexts and problem types more effectively.

Tips for Effective Mathematical Self-Explanation

  • Be specific: Avoid vague explanations; use precise mathematical language.
  • Question assumptions: Regularly ask yourself "Why does this work?" or "How do I know this is true?"
  • Embrace confusion: When confused, use self-explanation to work through your misunderstandings rather than avoiding them.
  • Use multiple representations: Explain concepts using algebraic, graphical, numerical, and verbal representations.
  • Start simple: Begin with explaining basic concepts thoroughly before tackling more complex topics.

Application Across Mathematical Domains

  • Algebra: Explain why algebraic properties work and how to decide which technique to apply when solving equations.
  • Geometry: Articulate why geometric properties are true and how theorems connect to visual representations.
  • Calculus: Explain the conceptual foundations of limits, derivatives, and integrals beyond just applying formulas.
  • Statistics: Clarify why statistical methods work and what results mean in context.
  • Number Theory: Explain patterns and relationships between numbers and why certain properties hold.

By consistently incorporating self-explanation into your mathematics learning routine, you'll develop deeper understanding, stronger retention, and more flexible problem-solving abilities that can transform your mathematical performance.