Learning Science · Reading, representing and explaining
Explaining a step in your own words
Explain why a step follows, which principle licenses it and when it would fail.
Use the examples to connect this lesson with the earlier topics. No specialist equipment is needed.
Back to the chapterAfter reading, you can
- Distinguish a reasoned self-explanation from a paraphrase.
- Check a generated explanation against principles and examples.
Say more than what happened
A solution changes 3x + 6 = 18 into 3x = 12. Saying "they took away six" describes the visible operation. Explaining "subtracting six from both sides preserves equality and isolates the term containing x" connects the operation with a principle and a goal. That additional connection is the teaching value of self-explanation.
Self-explanation means generating an account to make sense of material for yourself. It may link a step to prior knowledge, identify a missing inference, or state a condition. It does not require elegant speech or a long essay. A short accurate explanation can reveal more than a fluent paragraph that repeats the example’s wording.
Use a precise prompt
Pause at a meaningful step and ask why it is allowed, what it accomplishes, or what would happen if it were omitted. An alternative prompt asks why a tempting move would be invalid. These questions direct attention to relationships that a learner might otherwise overlook while following a solution.
Research on students studying mechanics examples found that more successful learners generated explanations connecting solution actions with principles. That observed relationship does not mean that any amount of self-talk causes expertise. Generated explanations can be wrong, and learners may lack the knowledge needed to fill a gap. Provide a reliable explanation or a simpler case when the learner cannot check their account.
Explain, compare, repair
After writing an explanation, compare it with the relevant definition, rule or worked solution. Look for a missing condition or an invented reason. If the two accounts disagree, identify the exact claim in dispute. Merely replacing your sentence with the answer key loses an opportunity to understand why the first explanation failed.
Use prompts selectively. Interrupting every obvious arithmetic operation can fragment a coherent argument and burden a learner who already knows it. Focus on conceptually important transitions or steps the learner cannot justify. Later attempt a new problem without the explanation visible, then explain one critical choice. This checks whether the relationship can guide independent work.
Worked example
Explaining a fraction conversion
Why rewrite one half and one third as sixths before adding them?
- To add one half and one third, a learner rewrites them as three sixths and two sixths. An inadequate explanation says, "Make the bottoms the same because that is the rule." A more useful one says, "We need equal-sized units to count parts together. Multiplying numerator and denominator by the same nonzero number changes the name of the fraction while preserving its value."
- The learner draws equal-length strips divided into halves, thirds and sixths, and checks the correspondence. They then explain why adding denominators would not count equal units. The account links a procedure, a representation and a reason; its usefulness comes from those links, not from being expressed in informal words.
Use equal-sized parts: 1/2 = 3/6 and 1/3 = 2/6, hence the sum is 5/6 of the same whole. The explanation must preserve that whole and the fraction values.
Equal-sized sixths make addition meaningful
Try it yourself
Think through each question before opening the answer.
Improve "I divided by four because that was the next step."
Show the answer and reasoning
State the purpose and principle, for example: "Each of four equal shares is one quarter of the total, so dividing the total by four finds one share."
The reason identifies the equal-share relationship; “next step” does not justify division.
Your explanation sounds sensible but conflicts with the source. What next?
Show the answer and reasoning
Identify the conflicting claim and check the definition, assumptions and a concrete case.
Fluency or personal ownership does not establish correctness.
Should every line receive a lengthy explanation?
Show the answer and reasoning
No.
Select transitions whose reasons are new or uncertain. Excessive commentary can interrupt the larger reasoning chain.
What to carry forward
- Explain the reason, goal and conditions behind a step.
- Check generated explanations and practise using them in a new case.
References
Sources supporting the explanations and learning checks in this lesson.