Comparing Maths Solutions: Ask Why a Method Works, Not Only Which Is Faster

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When two students solve the same problem differently, the class has something valuable to examine. The useful question is not always which method is quickest. It is whether students understand why each method is valid and when it is helpful.

Choose a manageable comparison

Consider 18 multiplied by 5. One method splits 18 into 10 and 8: 50 plus 40 gives 90. Another treats 5 as half of 10: half of 180 is 90. Both answers agree, but the reasoning deserves attention.

Present complete, correct examples before asking students to compare them. If the calculation itself is unfamiliar, teach that prerequisite first. Otherwise, the comparison can overwhelm the concept it was meant to clarify.

Name what stays the same

Ask students to point to the original quantities in each solution. Where has the factor 18 gone? Why is halving justified in the second method? Which property supports splitting the number in the first?

Let students annotate the steps with words or a simple drawing. 'It just works' is a starting response, not the end of the discussion. Model one precise explanation without requiring unnecessary technical language.

Test the choice on a new problem

Offer 38 multiplied by 5, then 18 multiplied by 7. Ask whether the same method remains convenient and why. Students may decide that a different strategy is clearer. A method should be chosen for mathematical reasons, not because it belongs to the fastest student.

Finish with an independent calculation and a sentence explaining the chosen approach. Accept more than one valid strategy while correcting inaccurate transformations.

Avoid a race

Comparison should broaden understanding, not turn calculation into a public contest. Give thinking time and use invented or anonymised solutions when that helps students discuss mistakes safely.

Further reading: IES: Organizing Instruction and Study to Improve Student Learning. The numerical examples and discussion sequence are original teaching illustrations.

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